The H.E.S.S. Galactic plane survey

# The H.E.S.S. Galactic plane survey

July 11, 2019
###### Key Words.:
H.E.S.S., Galactic plane survey, Cherenkov telescopes, gamma-ray sources
offprints: H.E.S.S. collaboration,
;
11footnotemark: 1 Corresponding authors

We present the results of the most comprehensive survey of the Galactic plane in very high-energy (VHE) -rays, including a public release of Galactic sky maps, a catalog of VHE sources, and the discovery of 16 new sources of VHE -rays. The High Energy Spectroscopic System (H.E.S.S.) Galactic plane survey (HGPS) was a decade-long observation program carried out by the H.E.S.S. I array of Cherenkov telescopes in Namibia from 2004 to 2013. The observations amount to nearly  of quality-selected data, covering the Galactic plane at longitudes from to and latitudes . In addition to the unprecedented spatial coverage, the HGPS also features a relatively high angular resolution ( arcmin mean point spread function 68% containment radius), sensitivity (% Crab flux for point-like sources), and energy range (0.2 to 100 TeV). We constructed a catalog of VHE -ray sources from the HGPS data set with a systematic procedure for both source detection and characterization of morphology and spectrum. We present this likelihood-based method in detail, including the introduction of a model component to account for unresolved, large-scale emission along the Galactic plane. In total, the resulting HGPS catalog contains 78 VHE sources, of which 14 are not reanalyzed here, for example, due to their complex morphology, namely shell-like sources and the Galactic center region. Where possible, we provide a firm identification of the VHE source or plausible associations with sources in other astronomical catalogs. We also studied the characteristics of the VHE sources with source parameter distributions. The 16 new sources were previously unknown or unpublished, and we individually discuss their identifications or possible associations. We firmly identified 31 sources as pulsar wind nebulae (PWNe), supernova remnants (SNRs), composite SNRs, or gamma-ray binaries. Among the 47 sources not yet identified, most of them (36) have possible associations with cataloged objects, notably PWNe and energetic pulsars that could power VHE PWNe.

## 1 Introduction

In this paper, we present the results from the High Energy Spectroscopic System (H.E.S.S.) Galactic plane survey (HGPS), the deepest and most comprehensive survey of the inner Milky Way Galaxy undertaken so far in very high-energy (VHE;  TeV) -rays. Results include numerous sky images (maps) and a new source catalog that is the successor of two previous HGPS releases. The first release (Aharonian et al. 2005b) was based on 140 h of observations with the imaging atmospheric Cherenkov telescope (IACT) array H.E.S.S. and contained eight previously unknown sources of VHE -rays. In the second release (Aharonian et al. 2006d), we used 230 h of data, covering to in Galactic longitude and in latitude. In total, we detected 22 sources of -rays in that data set. Since then, the HGPS data set enlarged by more than one order of magnitude in observation time, now comprising roughly  of high-quality data recorded in the years 2004 – 2013. The spatial coverage is also significantly larger, now encompassing the region from to in longitude. H.E.S.S. provided periodic updates on this progress by publishing new unidentified sources (Aharonian et al. 2008a) and through conference proceedings (Hoppe 2008b; Chaves et al. 2008a; Chaves 2009; Gast et al. 2011; Deil 2012; Carrigan et al. 2013a, b).

Compared to the first HGPS releases over a decade ago, the deeper exposure over a much larger sky area of the Galaxy, combined with improved -ray reconstruction, analysis, and modeling techniques, now results in a new catalog containing 78 VHE -ray sources. Figure 1 illustrates the HGPS region and compares this region to the structure of the Galaxy, represented by an all-sky Planck CO(1-0) map, and the smaller regions of previous surveys performed by the IACT arrays HEGRA (High-Energy-Gamma-Ray Astronomy, Aharonian et al. 2002) and VERITAS (Very Energetic Radiation Imaging Telescope Array System, Weinstein 2009). Even though the HGPS covers only a few percent of the entire sky, this region contains the vast majority of the known Galactic Fermi-LAT 2FHL -ray sources (Ackermann et al. 2016)111In this paper, we compare the HGPS with the Fermi-LAT 2FHL catalog, but not with 3FHL (The Fermi-LAT Collaboration 2017) or the HAWC 2HWC catalog (Abeysekara et al. 2017), which were not published at the time this paper was written and which already contain comparisons with Galactic H.E.S.S. sources.. The figure also shows the measured integral VHE -ray flux and the HGPS observation times. As can be seen from the map of observation times (Fig. 1, lower panel), the HGPS data set is not homogeneous. Nonetheless, the HGPS features on average a point-source sensitivity better than 1.5% Crab222Throughout this paper, and as is generally the case in VHE -ray astronomy, we use the Crab Nebula flux as a standard candle reference: 1 Crab unit is defined here as cm s (Aharonian et al. 2006b). in the core survey region within 60° in longitude of the Galactic center (see Fig. 4, lower panel).

In this paper, we aim to present the entire data set of the HGPS in a way that is accessible and useful for the whole astronomical community. We have made the maps of VHE -ray significance, flux, upper limits, and sensitivity available online for the first time in FITS format (Pence et al. 2010). We developed a semi-automatic analysis pipeline to construct a catalog by detecting and modeling discrete sources of VHE -ray emission present in these survey maps. We applied a standardized methodology to the characterization of the -ray sources to measure their morphological and spectral properties. The goal was to perform a robust analysis of sources in the survey region with as little manual intervention as possible. With such a generic approach, the catalog pipeline is not optimal for the few very bright and extended sources with complex (non-Gaussian) morphology. For these sources, dedicated analyses are more appropriate, and in all cases, they have already been performed and published elsewhere. We therefore exclude these sources, which are listed in Table 1 below, from the pipeline analysis but include the results from the dedicated analysis in the HGPS catalog for completeness.

We have structured the present paper as follows: we describe the H.E.S.S. telescope array, the data set, and the analysis techniques in Sect. 2. We provide the maps of the VHE -ray sky in various representations and details of their production in Sect. 3. Section 4 explains how the HGPS catalog of -ray sources was constructed, then Sect. 5 presents and discusses the results, including source associations and identifications with other astronomical objects. Section 6 concludes the main paper with a summary of the HGPS and its results. In Sect. 7, we describe the supplementary online material (maps and catalog in electronic form), including caveats concerning measurements derived from the maps and catalog.

## 2 Data set

### 2.1 The High Energy Stereoscopic System (H.E.S.S.)

H.E.S.S. is an array of five IACTs located at an altitude of 1800 m above sea level in the Khomas highland of Namibia. It detects Cherenkov light emitted by charged particles in an electromagnetic extensive air shower (EAS) initiated when a primary photon (-ray) of sufficient energy enters Earth’s atmosphere. This array consists of four smaller telescopes, built and operated in the first phase of the experiment (H.E.S.S. Phase I) and a fifth much larger telescope, which was added to the center of the array in 2012 to launch the second phase (H.E.S.S. Phase II) of the experiment.

H.E.S.S. accumulated the data presented here exclusively with the H.E.S.S. array during its first phase. These four H.E.S.S. Phase I telescopes have tessellated mirrors with a total area of 107 m and cameras consisting of 960 photomultipliers. The energy threshold of the four-telescope array is roughly 200 GeV at zenith and increases with increasing zenith angle. We can reconstruct the arrival direction and energy of the primary photon with accuracies of  and 15%, respectively. Because of its comparatively large field of view (FoV), 5° in diameter, the H.E.S.S. Phase I array is well suited for survey operations. The relative acceptance for -rays is roughly uniform for the innermost 2° of the FoV and gradually drops toward the edges to 40% of the peak value at 4° diameter (Aharonian et al. 2006b).

### 2.2 Observations, quality selection, and survey region

The HGPS data set covers the period from January 2004 to January 2013. H.E.S.S. acquired this data set by pointing the IACT array to a given position in the sky for a nominal duration of 28 min (referred to as an observation run hereafter). We considered all runs with zenith angles up to 65° and observation positions centered in the Galactic coordinate range to and . To reduce systematic effects arising from imperfect instrument or atmospheric conditions, we carefully selected good-quality runs as close as possible to the nominal description of the instrument used in the Monte Carlo (MC) simulations (see Aharonian et al. 2006b). For example, the IACT cameras suffer from occasional hardware problems affecting individual or groups of camera pixels, so we did not use observation runs with significant pixel problems. In addition, we only used those runs with at least three operational telescopes.

Furthermore, despite the very good weather conditions at the H.E.S.S. site, both nightly and seasonal variations of the atmospheric transparency occur and require monitoring. Layers of dust or haze in the atmosphere effectively act as a filter of the Cherenkov light created in an EAS, thereby raising the energy threshold for triggering the IACTs. Since we calculated the instrument response tables describing the performance of the instrument (e.g., the effective areas) with MC simulations, deviations from the atmospheric conditions assumed in the simulations lead to systematic uncertainties in the determination of energy thresholds, reconstructed energies, and -ray fluxes. To account for this, we applied a further quality cut using only observations where the Cherenkov transparency coefficient  (Hahn et al. 2014), which characterizes the atmospheric conditions, falls within the range (for clear skies, ).

After applying the aforementioned data quality selection cuts, 6239 observation runs remain, 77% of which are runs with four telescopes operational. The total observation time is 2864 h, corresponding to a total livetime of 2673 h (6.7% average dead time). The third panel of Fig. 1 is a map of the observation time over the survey region, clearly showing a non-uniform exposure. This is a result of the HGPS observation strategy, summarized as follows:

• Dedicated survey observations, taken with a typical spacing between pointings of in longitude and in different latitude bands located between and . In addition, for the longitude bands to and to , we extended the survey observations in latitude, adding observation pointings from to to explore the possibility of high-latitude emission.

• Deeper follow-up observations of source candidates (“hot spots”) seen in previous survey observations.

• Exploratory and follow-up observations of astrophysical objects located inside the survey region that were promising candidates for emitting VHE -rays.

• Observations to extend the HGPS spatial coverage and fill-up observations to achieve a more uniform sensitivity across the Galactic plane.

Combining all of these observations, we achieved a more uniform, minimum 2% Crab flux sensitivity in the region between to and (see the sensitivity map in Fig. 4).

### 2.3 Event reconstruction and selection

We first converted the camera pixel data to amplitudes measured in units of photoelectrons (p.e.), identifying the non-operational pixels for a given observation following the procedures described by Aharonian et al. (2004a). We then applied standard H.E.S.S. techniques for the analysis of the camera images: image cleaning, Hillas moment analysis, and the stereo reconstruction of the direction of the primary photon, described by Aharonian et al. (2006b). To suppress the hadronic background and select photon candidate events, we used a multivariate machine learning technique using boosted decision trees based on EAS and image shape parameters (Ohm et al. 2009). For the generation of the survey maps (Sect. 3), we applied the hard cuts configuration whereas for the extraction of source spectra (Sect. 5) we used the standard cuts. The most important distinguishing cut is a minimum of 160 p.e. for hard cuts and 60 p.e. for standard cuts, but there are other differences. See Ohm et al. (2009) for further information; specifically, we used the analysis cuts listed in Table 2(a) for the HGPS.

We cross-checked the results presented in this paper with an alternative calibration, reconstruction, and gamma-hadron separation method based on a semi-analytical description of the EAS development (de Naurois & Rolland 2009) with hard cuts of 120 p.e. for maps and standard cuts of 60 p.e. for spectra.

For the energy reconstruction of the primary photons, we compared the image amplitudes in the cameras to the mean amplitudes found in MC simulations of the array (Bernlöhr 2008). Those simulations, which were analyzed with the same chain as the real data for the sake of consistency, include the detailed optical and electronic response of the instrument. The range of optical efficiencies encountered in the HGPS data set is large; efficiencies start at 100% of the nominal value and drop to almost 50% for some telescopes prior to the mirror refurbishments conducted in 2009–2011. Therefore, we produced several sets of MC simulations, each with optical efficiencies of the four telescopes corresponding to their states at suitably chosen times: at the start of H.E.S.S. operations; at the point when efficiencies had dropped to 70%, before the first mirror refurbishment campaign; and after the mirror refurbishment of each telescope. We then chose the set of simulations most closely matching the state of the system at a given time. Finally, we corrected the remaining difference between simulated and actual optical efficiencies using a calibration technique based on the intensity of ring-shaped images from individual muons producing Cherenkov radiation above a telescope (Bolz 2004; Leroy 2004).

## 3 HGPS sky maps

In this section, we describe the methods used to produce the HGPS sky maps. We used the sky maps as the basis for subsequent construction of the HGPS source catalog; this catalog is also a data product that we release to the community along with this work.

We first computed sky maps for each individual observation run. We then summed these maps over all observations. We chose to use a Cartesian projection in Galactic coordinates, covering the region from to and , and we set the pixel size to  / pixel.

In Sect. 3.1, we describe the production of the map containing the detected events (events map). In Sect. 3.2, we describe the map of expected background events (acceptance map, Sect. 3.2.1), the estimation of a refined background map by introducing exclusion regions (Sect. 3.2.2), and the usage of the adaptive ring background method (Sect. 3.2.3). We then continue in Sect. 3.3 by describing the computation of the significance map, and, in Sect. 3.4, the exposure map (Sect. 3.4.1), which is used to derive quantities such as flux (Sect. 3.4.2), flux error and upper limits (Sect. 3.4.3), and sensitivities (Sect. 3.4.4).

### 3.1 Events map

The events map consists of the reconstructed positions of the primary -ray photons from all events in the sky. To avoid systematic effects near the edge of the FoV in each observation run, we only include events for which the direction of the primary photon is reconstructed within of the center of the FoV. This choice results in an effective analysis FoV of diameter.

At the lowest energies, the energy reconstruction is biased by EASs with upward fluctuations in the amount of detected Cherenkov light; downward fluctuations do not trigger the cameras. In order to derive reliable flux maps (see Sect. 3.4.2), we only kept events with an energy reconstructed above a defined safe energy threshold. We chose the level of this safe threshold such that, for each run, the energy bias as determined by MC simulations is below 10% across the entire FoV. This conservative approach (together with the use of hard analysis cuts defined in Sect. 2.3) leads to energy threshold values ranging from 400 GeV, where the array observed close to zenith, up to 2 TeV at 65 from zenith. Figure 2 plots the variation of the safe energy threshold with Galactic longitude, showing the energy threshold for each observation together with the minimum value for each longitude. The variations observed are mainly due to the zenith angle dependency, and regions of different Galactic longitude generally are observable at different zenith angles.

### 3.2 Background estimation

Events passing the event reconstruction and selection procedure are considered -ray candidate events. Since these events are still dominantly from EASs induced by -ray-like cosmic rays and electrons or positrons, we estimated the amount of remaining background events on a statistical basis using a ring model (Berge et al. 2007) as detailed further below. For each test position, we counted the photon candidates found in a suitable ring-shaped region around that position in the same FoV. This yields an estimate of the background level after proper normalization and after excluding regions with actual -ray emission from the background estimate.

#### 3.2.1 Acceptance map

The acceptance map represents the number of expected events from cosmic-ray backgrounds estimated from runs of sky regions at similar zenith angles but without VHE -ray sources. As for the events map (see Sect. 3.1), we computed the acceptance map for energies above the safe energy threshold. To account for the differences in optical efficiency and observation time between these runs and those under analysis, we normalized the acceptance map such that, outside the exclusion regions (see Sect. 3.2.2), the number of expected counts matches the number of measured counts. The acceptance maps are used to derive the normalization coefficient between the region of interest and the background region (see Sect. 3.3).

#### 3.2.2 Exclusion regions

The background estimation method described above only works if regions with VHE -ray emission are excluded from the background estimation region. We defined exclusion regions automatically using an iterative algorithm to avoid potential observer bias and to treat the entire data set in a uniform way. The procedure starts with the significance maps (see Sect. 3.3) produced for the two standard correlation radii and . These radii define the circular region over which a quantity (e.g., -ray excess) is integrated. The procedure identifies regions above and expands them by excluding an additional beyond the contour. This procedure is conservative; it minimizes the amount of surrounding signal that could potentially contaminate the background estimation. A first estimation of the exclusion regions is then included in the significance map production and a new set of exclusion regions is derived. We iterated this procedure until stable regions are obtained, which typically occurs after three iterations. The resulting regions are shown in Fig. 39 below.

In the HGPS, often exclusion regions cover a significant fraction of the FoV; therefore, we could not use the standard ring background method (Berge et al. 2007). For example, using a typical outer ring radius of 0.8° would lead to numerous holes in the sky maps at positions where the entire ring would be contained inside an exclusion region (i.e., where no background estimation was possible). A much larger outer radius (e.g., 1.5°) would be necessary to prevent these holes but would lead to unnecessarily large uncertainties in the background estimation in regions without, or with small, exclusion regions where smaller ring radii are feasible.

To address the limitations of the standard method, we do not use a static ring geometry but rather adaptively change the inner and outer ring radii, as illustrated in Fig. 3, depending on the exclusion regions present in a given FoV. For a given test position within a FoV, we begin with a minimum inner ring radius of and constant ring thickness and enlarge the inner radius if a large portion of the ring area overlaps with exclusion regions. We do this until the acceptance integrated in the ring (but outside exclusion regions) is more than four times the acceptance integrated at the test position. A maximum outer radius of avoids large uncertainties in the acceptance toward the edge of the FoV.

### 3.3 Significance maps

We produced significance maps to determine the exclusion regions (see Sect. 3.2.2). For each grid position in a significance map, we counted the number of photon candidates in the circular ON region, defined a priori by the correlation radius . We determined the background level by counting the number of photon candidates in the ring centered at . The background normalization factor is , where is the integral of the acceptance map within and is the integral of the acceptance map within the ring. The number of excess events within is then

 Nγ=NON−αNOFF. (1)

We computed the significance of this -ray excess according to Eq. 17 of Li & Ma (1983) without correcting further for trials.

### 3.4 High-level maps

We can derive additional high-level maps based on the measurement of within a given and the instrument response functions. In this work, we computed flux, flux error, sensitivity, and upper limit maps, starting from the formula

 F=NγNexp∫E2E1ϕref(E)dE, (2)

where is the integral flux computed between the energies and , is the measured excess, and is the total predicted number of excess events, also called exposure (see Sect. 3.4.1).

#### 3.4.1 Exposure maps

The exposure in Eq. 2 is given by

 Nexp≡E=∑R∈runsTR∫∞Eminϕref(Er)Aeff(Er,qR)dEr. (3)

Here, is the reconstructed energy, is the observation livetime, symbolizes the observation parameters for a specific run (zenith, off-axis, and azimuth angle; pattern of telescopes participating in the run; and optical efficiencies); is the effective area obtained from MC simulations, which is assumed constant during a 28 min run; and is the safe threshold energy appropriate for the observation (as described in Sect. 3.1). We computed the quantity for each position in the sky to create the expected -ray count map, also referred to as the exposure map in the following. The function is the reference differential photon number -ray source flux, assumed to be following a power law (PL) with a predefined spectral index, i.e.,

 ϕref(E)=ϕ0(E/E0)−Γ. (4)

#### 3.4.2 Flux maps

In Eq. 2, the flux value is completely determined by the scaling factor once the spectral shape is fixed. We chose to use and . We stress that is not the threshold energy used in the analysis, but the energy above which the integral flux is given. In Eq. 4, one can choose the flux normalization arbitrarily, since it cancels out in the computation of the flux. We also chose the spectral index in the released maps to be compatible with the average index of known Galactic VHE -ray sources. To test the impact of this latter assumption, we performed tests that show that, on average, flux variations are less than if the assumed spectral index is varied by (our systematic uncertainty of the spectral index).

The released flux maps contain values of integral flux above  TeV, calculated according to Eq. 2, in units of cm s. This should be interpreted as the flux of a potential source, assuming a spectrum , that is centered on a given pixel position in the map and fully enclosed within .

Figures 1 and 34 show two example flux maps computed with and , respectively. The maps contain nonzero values only in regions in which the sensitivity is better than 2.5% Crab to prevent very large (positive and negative) values due to statistical fluctuations in low-exposure regions.

#### 3.4.3 Flux error and upper limit maps

Statistical uncertainties on the flux were computed by replacing in Eq. 2 by , which are the upper and lower boundaries of the measured excess for a 68% confidence level. Those errors were computed with a Poisson likelihood method described in Rolke et al. (2005), using the same and integrated within the circle of radius used when computing the excess maps. The values reported in the flux-error maps are the average of the upper and lower error bars.

Similarly, an upper-limit map can be calculated by replacing in Eq. 2 by , that is, the upper limit on the excess found for a predefined confidence level of 95%; we used the same profile likelihood method as for the error bar.

#### 3.4.4 Sensitivity maps

The sensitivity is defined as the minimal flux needed for a source with the assumed spectrum and fully contained within the correlation circle to be detected above the background at statistical significance. Alternatively this can be thought of as a measure of , the number of photons needed to reach such a significance level above the background determined by and . To compute the sensitivity map, in Eq. 2 is replaced by , which is determined by numerically solving Eq. 17 of Li & Ma (1983) for (related to by Eq. 1 above). We note that possible background systematics are not taken into account in this computation.

The point-source sensitivity level reached by H.E.S.S. at all points in the HGPS data set is depicted in Fig. 4, where a projection of the sensitivity map along Galactic longitude at a Galactic latitude of is also shown. It is typically at the level of 1% to 2% Crab. The deepest observations were obtained around interesting objects for which additional pointed observations were performed. Examples include the Galactic center region (around , where the best sensitivity of % Crab is reached), the Vela region (), the regions around HESS J1825$-$137 and LS 5039 (), or around HESS J1303$-$631 and PSR B1259$-$63 ().

Similarly, the sensitivity values along Galactic latitude for two values of longitude are shown in Fig. 11. For most of the surveyed region, the sensitivity decreases rapidly above due to the finite FoV of the H.E.S.S. array and the observation pattern taken, except for a few regions, such as at where high latitude observations were performed (see Sect. 2). The best sensitivity is obtained around , reflecting the H.E.S.S. observation strategy; the latitude distribution of the sources peaks in this region.

We note that the sensitivity shown in Fig. 4 does not correspond to the completeness of the HGPS source catalog. One major effect is that the HGPS sensitivity is dependent on source size; it is less sensitive for larger sources, as shown in Fig. 13 and discussed at the end of Sect. 5.3. Other effects that reduce the effective sensitivity or completeness limit of HGPS are the detection threshold, which corresponds to ; the large-scale emission model; and source confusion, as discussed in the following Sect. 4

## 4 HGPS source catalog

### 4.1 Introduction and overview

The HGPS source catalog construction procedure intends to improve upon previous H.E.S.S. survey publications both in sensitivity and homogeneity of the analysis performed. The previous iteration, the second H.E.S.S. survey paper of 2006 (Aharonian et al. 2006d), used a 230 h data set with inhomogeneous exposure that was limited to the innermost region of the Galaxy. This survey detected a total of 14 sources by locating peaks in significance maps on three different spatial scales: , , and . It then modeled the sources by fitting two-dimensional symmetric Gaussian morphological models to determine the position, size and flux of each source, using a Poissonian maximum-likelihood method.

Since 2006, H.E.S.S. has increased its exposure tenfold and enlarged the survey region more than twofold, while also improving the homogeneity of the exposure. As illustrated in the upper panel of Fig. 5, the data now show many regions of complex emission, for example, overlapping emission of varying sizes and multiple sources with clearly non-Gaussian morphologies. Apart from discrete emission, the Galactic plane also exhibits significant emission on large spatial scales (Abramowski et al. 2014a). For these reasons, we needed to develop a more complex analysis procedure to construct a more realistic model of the -ray emission in the entire survey region. Based on this model, we compiled the HGPS source catalog.

We first introduce the maximum-likelihood method used for fitting the emission properties (Sect. 4.2). Next, we describe the H.E.S.S. point spread function (PSF; Sect. 4.3) and the TS maps (Sect. 4.4), which are two important elements in the analysis and catalog construction. The procedure is then as follows:

1. Cut out the Galactic center (GC) region and shell-type supernova remnants from the data set because of their complex morphologies (Sect. 4.5).

2. Model the large-scale emission in the Galactic plane globally (Sect. 4.6).

3. Split the HGPS region into manageable regions of interest (ROIs) (Sect. 4.7).

4. Model the emission in each ROI as a superposition of components with Gaussian morphologies (Sect. 4.8).

5. Merge Gaussian components into astrophysical VHE -ray sources (Sect. 4.9).

6. Determine the total flux, position, and size of each -ray source (Sect. 4.10).

7. Measure the spectrum of each source (Sect. 4.11).

8. Associate the HGPS sources with previously published H.E.S.S. sources and multiwavelength (MWL) catalogs of possible counterparts (Sect. 5.1).

### 4.2 Poisson maximum-likelihood morphology fitting

To detect and characterize sources and to model the large-scale emission in the Galactic plane, we used a spatially-binned likelihood analysis based on the following generic model:

 NPred=NBkg+PSF∗(E⋅S), (5)

where represents the predicted number of counts, the background model created with the adaptive ring method (described in Sect. 3.2.3), the exposure map (see Eq. 3 in Sect. 3.4.2), and a two-dimensional parametric morphology model that we fit to the data. Additionally, we took into account the angular resolution of H.E.S.S. by convolving the flux model with a model of the PSF of the instrument.

Assuming Poisson statistics per bin, the maximum-likelihood fit then minimizes the Cash statistic (Cash 1979),

 C=2∑i(Mi−DilogMi), (6)

where the sum is taken over all bins , and (model) represents the expected number of counts according to Eq. 5 and (data) the actual measured counts per bin.

To determine the statistical significance of a best-fit source model compared to the background-only model, we use a likelihood ratio test with test statistic TS. This is defined by the likelihood ratio or equivalently as the difference in between both hypotheses,

 TS=C0−CS, (7)

where corresponds to the value of the Cash statistic of the background-only hypothesis and the best-fit model that includes the source emission.

For a large number of counts, according to Wilks’ theorem (Wilks 1938), TS is asymptotically distributed as , where is the number of free parameters defining the flux model. In this limit, the statistical significance corresponds approximately to , where the sign of the best-fit flux is needed to allow for negative significance values in regions where the number of counts is smaller than the background estimate (e.g., due to a statistical downward fluctuation).

We performed the modeling and fitting described above in Eqs. 5, 6, and 7 in pixel coordinates using the HGPS maps in Cartesian projection. Spatial distortion of flux models are negligible as a result of the projection from the celestial sphere because the HGPS observations only cover a latitude range of . We implemented the analysis in Python using Astropy version 1.3 (Astropy Collaboration et al. 2013), Sherpa version 4.8 (Freeman et al. 2001), and Gammapy version 0.6 (Donath et al. 2015; Deil et al. 2017).

For HGPS, the PSF was computed for a given sky position assuming a power-law point source with a spectral index of 2.3 (average index of known VHE -ray sources) and assuming rotational symmetry of the PSF. Since the H.E.S.S. PSF varies with -ray energy and observing parameters such as the number of participating telescopes, zenith angle, and offset angle in the field of view, an effective PSF corresponding to the HGPS survey counts maps was computed by applying the same cuts (especially safe energy threshold) and exposure weighting the PSF of contributing runs (i.e., within the FoV of 2°). The per-run PSF was computed by interpolating PSFs with similar observation parameters, using precomputed lookups from MC EAS simulations. All computations were carried out using two-dimensional histograms with axes , where is the offset between the MC source position and the reconstructed event position, and , where is the reconstructed event energy; at the very end, the integration over energy was performed, resulting in a one-dimensional histogram with axis , which was fitted by a triple-exponential analytical function to obtain a smooth distribution,

 dPdθ2(θ2)=3∑i=1Aiexp(−θ22σ2i), (8)

where is the event probability, and and are the weights and widths of the corresponding components, respectively. This ad hoc model corresponds to a triple-Gaussian, two-dimensional, PSF model when projected onto a sky map.

For the HGPS catalog, the 68% containment radius of the PSF model adopted is typically  and varies by approximately at the locations of the HGPS sources. For observations with large FoV offsets, the 68% containment increases by almost a factor of two to 0.15°, which is mostly relevant for high Galactic latitude sources at the edge of the HGPS survey region. The HGPS PSF has a 95% containment radius of 0.2°and approximately varies by at the locations of the HGPS sources. The PSF at large FoV offsets (corresponding to high-GLAT regions in the survey map) is more tail heavy; there the 95% to 68% containment radius ratio increases from 2.5 up to 4. Section 4.10.2 discusses systematic uncertainties related to the PSF model in connection with upper limits on source sizes.

### 4.4 Test statistics maps

In addition to the standard Li & Ma significance maps described in Sect. 3.3, we also used TS maps in the analysis. The TS denotes the likelihood ratio of the assumed source hypothesis versus the null hypothesis (i.e., background only) for every position (pixel) in the map. We computed these maps assuming various spatial templates: a point-like source morphology (i.e., PSF only), and PSF-convolved Gaussian morphologies with widths , , and . During the computation of each map, at the center of each map pixel, we performed a single-parameter likelihood fit of the amplitude of the template, according to Eq. 5. We then filled the map with the TS value defined in Eq. 7.

We used the resulting TS maps primarily to compute residual maps and residual distributions. The main advantage over standard Li & Ma significance maps is that source morphology and PSF information can be taken into account. Additionally, this paper uses TS maps when presenting sky maps because they contain uniform statistical noise everywhere in the map. In contrast, flux or excess maps that are smoothed with the same spatial templates still show increased noise in regions of low exposure. We implemented the TS map algorithm available in Gammapy; see also Stewart (2009) for a more detailed description of TS maps.

### 4.5 Sources not reanalyzed

H.E.S.S. observations have revealed many sources with complex morphology, e.g., RX J0852.0$-$4622 (also known as Vela Junior), which has a very pronounced shell-like structure (H.E.S.S. Collaboration et al. 2016a), or the Galactic center region, which has multiple point-sources embedded in a very elongated ridge-like emission (H.E.S.S. Collaboration et al. 2017g). Dedicated studies model such regions of emission using complex parametric models, for example, model templates based on molecular data, shell-like models, asymmetric Gaussian models, and combinations thereof. It is challenging to systematically model the emission across the entire Galactic plane using these more complex models, which tend to yield unstable or non-converging fit results because of the large number of free and often poorly constrained parameters. This can be especially problematic in ROIs with multiple, complex overlapping sources.

Given the difficulties with modeling complex source morphologies, we decided to restrict the HGPS analyses to a symmetrical Gaussian model assumption and exclude all firmly identified shell-like sources and the very complex GC region from reanalysis. A complete list of the ten excluded (or cut-out) sources in the HGPS region is given in Table 1. The table also contains four sources that were not significant in the current HGPS analysis but were found to be significant in other dedicated, published analyses; these cases are discussed in detail in Sect. 5.4.3. We refer to these 14 sources in total listed in Table 1 as “EXTERN” HGPS sources and have included these sources in the HGPS source catalog because we wanted to give a complete list of sources in the HGPS region. We also have these sources included in the various distributions, histograms, and other plots exploring the global properties of the HGPS sources in Sect. 5.3. The morphological and spectral parameters for those sources were adapted from the most recent H.E.S.S. publication (listed in Table 1).444We note that the values in the HGPS catalog for EXTERN sources do not fully reflect the results of the original publication. Specifically, in some cases the information is incomplete (e.g., when certain measurements were not given in the paper) or not fully accurate (e.g., when the published measurements do not fully agree with the definition of measurements in this paper, or when parameter errors are different due to error inaccuracies in the error propagation when converting to HGPS measures.)

### 4.6 Large-scale emission model

We previously demonstrated that there exists VHE -ray emission that is large scale and diffuse along the Galactic plane (Abramowski et al. 2014a). In that paper, we constructed a mask to exclude the regions of the plane where significant emission was detected. The latitude profile of excess -rays outside this mask clearly showed the presence of significant large-scale -ray emission. We do not extend the analysis of this diffuse emission any further here. Whether the emission originates from interactions of diffuse cosmic rays in the interstellar medium or from faint, unresolved -ray sources (or a combination thereof) is not investigated. Instead, we take a pragmatic approach and model the large-scale emission present in the HGPS empirically as described in the following.

The presence of a large-scale component of -ray emission along the Galactic plane complicates the extraction of the Gaussian -ray source components. This large-scale emission can mimic the presence of spurious degree-scale sources in some regions of the plane and it also tends to broaden the Gaussian components that describe otherwise well-defined sources. It is therefore necessary to model the large-scale -ray emission to measure the flux and morphology of the HGPS sources more accurately.

To do so, we built an empirical surface brightness model of the large-scale emission (see Fig. 6), where the latitude profile is Gaussian and defined by three parameters: the peak position in latitude, the width, and amplitude of the Gaussian. We estimated the parameters using a maximum-likelihood fit in regions where no significant emission is measurable on small scales, i.e., outside the exclusion regions defined for the ring background model, taking exposure into account. Regardless of the physical origin of the large-scale emission, it is likely to be structured along the plane and not constant.

To estimate the variable parameters of the model, we fit the Gaussian parameters in rectangular regions of width in longitude and height in latitude. We excluded all pixels inside the standard exclusion regions used to produce the background maps (see Sect. 3.2). The Gaussian parameters were dependent on the size of both the exclusion regions and rectangular regions. We found that the typical variations were 25%. To obtain a smooth sampling of the variations, we followed a sliding-window approach, distributing the centers of the rectangular regions every in longitude and interpolating between these points.

The maximum-likelihood fit compares the description of the data between the cosmic-ray (CR) background only and the CR background plus the model. We used the likelihood ratio test to estimate the significance of adding the large-scale component in each 20-deg-wide window, finding it to be larger than (TS difference of 9) over most of the HGPS region. Figure 6 shows the resulting best-fit Gaussian parameters together with the associated uncertainty intervals estimated from the likelihood error function. After this fit, we froze the parameters of the model for use in the -ray source detection and morphology fitting procedure.

While the approach presented here provides an estimate of the large-scale emission present in the HGPS maps, it does not comprise a measurement of the total Galactic diffuse emission (see discussion in Sect. 5.2).

### 4.7 Regions of interest

To search for sources, we divided the whole HGPS region into smaller overlapping ROIs. This was necessary to limit both the number of simultaneously fit parameters and the number of pixels involved in the fit.

We manually applied the following criteria to define the ROIs:

1. All significant emission (above ) in the HGPS region should be contained in at least one ROI.

2. No significant emission should be present close to the edges of an ROI.

3. The width of each ROI should not exceed 10° in longitude to limit the number of sources involved in the fit.

4. ROIs should cover the full HGPS latitude range from to .

In cases in which criterion (b) could not be fulfilled, we excluded the corresponding emission from the ROI and assigned it to a different, overlapping ROI. Figure 39 illustrates the boundaries of the 18 ROIs defined with these criteria. Some of the ROIs show regions without any exposure; these regions were masked out and ignored in the subsequent likelihood fit.

### 4.8 Multi-Gaussian source emission model

After excluding shell-type supernova remnants (SNRs) and the GC region from reanalysis and adding a model for large-scale emission to the background, we modeled all remaining emission as a superposition of Gaussian components. We took the following model as a basis:

 NPred=NBkg+PSF∗(E⋅∑iSGauss,i)+E⋅SLS, (9)

where corresponds to the predicted number of counts, to the number of counts from the background model, the contribution of the large-scale emission model, the sum of the Gaussian components, and the exposure as defined in Eq. 3.

For a given set of model parameters, we integrated the surface brightness distribution over each spatial bin, multiplied it by the exposure , and convolved it with the PSF to obtain the predicted number of counts per pixel. For every ROI, we took the PSF at the position of the brightest emission and assumed it to be constant within the ROI.

For the Gaussian components, we chose the following parametrization:

 SGauss(r|ϕ,σ)=ϕ12πσ2exp(−r22σ2), (10)

where is the surface brightness, the total spatially integrated flux, and the width of the Gaussian component. The offset is defined with respect to the position of the component measured in Galactic coordinates.

We conducted the manual fitting process following a step-by-step procedure. Starting with one Gaussian component per ROI, we added Gaussian components successively and refit all of the parameters simultaneously until no significant residuals were left. In each step, we varied the starting parameters of the fit to avoid convergence toward a local minimum. The significance of the tested component was estimated from

 TS=C(with component)−C(best solution% without component). (11)

We considered the component to be statistically significant and kept it in the model when the TS value exceeded a threshold of . The probability of having one false detection in the HGPS survey from statistical background fluctuations is small (). This number was determined by simulating 100 HGPS survey counts maps as Poisson-fluctuated background model maps, followed by a multi-Gaussian peak finding method, resulting in three peaks with . However, we note that this assessment of expected false detections lies on the assumption that the hadronic background as well as the large-scale and source gamma-ray emission model are perfect. In HGPS, as in any other Galactic plane survey with complex emission features, this is not the case. Several components with are not confirmed by the cross-check analysis (see Sect. 4.9).

The definition of TS above differs slightly from the definition given in Eq. 7. For a single, isolated component, both values are identical. However, if a second, overlapping component exists, some of the emission of the first source is modeled by the second source, reducing the significance of the first. We therefore estimated the significance of a component from the TS difference in the total model of the ROI and not from the TS difference compared to the background-only model.

Applied to real data, we found a total of 98 significant Gaussian components using this procedure and TS threshold. Figure 7 depicts the residual distributions over the entire HGPS region. These distributions demonstrate that there is approximate agreement with a normal Gaussian distribution; in particular, we find no features above the detection threshold. Inherent imperfections in the background, large-scale emission models and source emission models lead to a slight broadening of the distributions with respect to a normal distribution, as expected.

For reference, the 98 Gaussian components have been assigned identifiers in the format HGPSC NNN, where NNN is a three-digit number (counting starts at 1), sorted by right ascension (which is right to left in the survey maps). The complete list of components is provided in the electronic catalog table (see Table 6).

### 4.9 Component selection, merging, and classification

We repeated the entire modeling procedure described in the previous section with a second set of maps produced with an independent analysis framework (see Sect. 2.3). Five of the 98 HGPS components were not significant in the cross-check analysis and were therefore discarded (see Fig. 5 and Table 6). Those components we labeled with Discarded Small in the column Component_Class of the FITS table.

We observed two other side effects of the modeling procedure. Firstly, very bright VHE sources, even some with center-filled morphologies such as Vela X, decomposed into several Gaussian components, modeling various morphological details of the source. Figure 5 illustrates this effect: there are two multicomponent sources shown. Therefore in cases where overlapping components were not clearly resolved into separate emission peaks, we merged them into a single source in the HGPS catalog. In total, we found 15 such multicomponent sources: ten consisting of two Gaussian components and five consisting of three Gaussian components. It would be intriguing to analyze the complex morphology of these multicomponent sources in greater detail, but this kind of analysis is beyond the scope of this survey paper. We labeled components that are part of a multicomponent source as Source Multi. We used the label Source Single, respectively, if there is only one component modeling the source.

The second side effect was that some of the Gaussian components appeared to have very large sizes coupled with very low surface brightness. We interpret these components as artifacts of the modeling procedure, which picks up additional diffuse -ray emission that is not covered by our simple large-scale emission model (Sect. 4.6). For example, as shown in Fig. 5, the emission around initially comprised three model components: two components that clearly converged on the two discrete emission peaks visible in the excess map and one very large and faint component that appeared to be modeling large-scale emission along the Galactic plane in between the two and not clearly related to either of the two peaks. In total, we found ten such large-scale components (see Table 6), which we discarded and did not include in the final HGPS source catalog as they are likely low-brightness diffuse emission. We labeled this class of components as Discarded Large in the component list.

### 4.10 Source characterization

#### 4.10.1 Position, size, and flux

For HGPS sources that consist of several components, we determined the final catalog parameters of the sources as follows:

##### Flux

The total flux is the sum of the fluxes of the individual components

 FSource=∑iFi. (12)
##### Position

We calculated the position by weighting the individual component positions with the respective fluxes. The final and coordinates of the source are written as{linenomath}

 ℓSource=1FSource∑iℓiFi and bSource=1FSource∑ibiFi. (13)
##### Size

We obtained the size in and directions from the second moment of the sum of the components as follows: {linenomath}

 σ2ℓ,Source= 1FSource∑iFi⋅(σ2i+ℓ2i)−ℓ2Source (14) σ2b,Source= 1FSource∑iFi⋅(σ2i+b2i)−b2Source, (15)

where additionally we defined the average circular size as

 σSource=√σℓ,Sourceσb,Source. (16)

We computed the uncertainties of the parameters using Gaussian error propagation, taking the full covariance matrix estimate from the fit into account.

#### 4.10.2 Size upper limits

In the morphology fit, we did not take into account uncertainties in the PSF model. However, studies using H.E.S.S. data (e.g., Stycz 2016) have revealed a systematic bias on the size of point-like extragalactic sources on the order of , so we have adopted this number as the systematic uncertainty of the PSF.

Given a measured source extension and corresponding uncertainty , we used the following criterion to claim a significant extension beyond the PSF:

 σSource−2ΔσSource>σsyst, (17)

i.e., if the extension of a source is beyond the systematic minimum . If this criterion is not met, we consider the source to be compatible with being point-like and define an upper limit on the source size as follows:

 σUL=max(σsyst,σSource+2ΔσSource). (18)

#### 4.10.3 Localization

The HGPS source location error is characterized by error circles with radius at confidence levels and , computed as

 Rα=fα×√Δℓ2stat+Δℓ2syst+Δb2stat+Δb2syst. (19)

The values and are the statistical errors on Galactic longitude and latitude , respectively, from the morphology fit. For the H.E.S.S. systematic position error, a value of per axis was assumed, following the method and value in (Acero et al. 2010b).

Assuming a Gaussian probability distribution, the factor is chosen as for a given confidence level (see Eq. 1 in Abdo et al. 2009b).

#### 4.10.4 Source naming

The 78  HGPS catalog sources have been assigned source names in the format HESS JHHMMDDd, where HHMM and DDd are the source coordinates in right ascension and declination, respectively. For new sources, the source name is based on the source location reported in this paper. For sources that had been assigned names in previous H.E.S.S. publications or conference presentations, the existing name was kept for the HGPS catalog, even if the position in the HGPS analysis would have led to a different name. Similarly, the source candidates (or hotspots, see Sect. 5.6.17) have been assigned names in the format HOTS JHHMMDDd.

### 4.11 Source spectra

After detection and subsequent morphological analysis of the sources, we measured a spectrum for each of the sources using an aperture photometry method. In this method we sum the ON counts within an aperture defined as a circular region centered on the best-fit position of each source. We fit a spectral model within that aperture using an ON-OFF likelihood method (Piron et al. 2001), where the OFF background is estimated using reflected regions defined on a run-by-run basis (Fomin et al. 1994; Berge et al. 2007). Based on the morphology model, we then corrected the measured flux for containment and contamination from other nearby sources. For the spectral analysis, we applied standard cuts, resulting in energy thresholds in the range 0.2–0.5 TeV, lower than the thresholds achieved using hard cuts in the detection and morphology steps. Figure 2 shows the variation of the threshold with longitude. In the following sections, we describe the spectral analysis process in more detail.

#### 4.11.1 Circular apertures and reflected region background estimate

The optimal choice for the size for the spectral extraction region is a balance between including a large percentage of flux from the source and limiting the contamination of the measurement by hadronic background events, large-scale emission, and other nearby sources. Following these requirements, we chose the aperture radius as follows:

• for 34 medium-size sources, where is the 70% containment radius measured on the PSF-convolved excess model image (R70 in the catalog),

• minimum for 21 small () sources,

• maximum for 9 very large () sources.

A minimal aperture radius of was imposed to make the measurement of the source spectrum more robust against systematic uncertainties of the PSF and the source morphology assumption.

The aperture radius was limited to a maximum radius of to limit the fraction of observations that cannot be used for the spectrum measurement because no background estimate could be obtained.

As illustrated in Fig. 8, the background is estimated using the reflected region method (Fomin et al. 1994; Berge et al. 2007). For every spectral extraction region (ON region), corresponding OFF regions with the same shape and offset to the pointing position are chosen outside exclusion regions.

The method works well for small, isolated -ray sources such as active galactic nuclei (AGNs) or the Crab nebula, where typically 10 OFF regions are found in every observation. This results in a well-constrained background, and all the exposure can be used for the spectral measurement. Because of the high density of sources in the Galactic plane, large areas of emission are excluded and only few reflected regions can be found. This effectively results in a loss of exposure for the spectrum measurement compared to the map measurement. For the HGPS analysis this is a large problem because of the very extensive exclusion regions used: 64% of the livetime is lost for spectral analysis compared to the total available livetime that is used in the map-based analysis. For each source, see the Livetime_Spec and Livetime information in the source catalog. In cases where the loss of exposure is very high, the background cannot be well constrained, which consequently results in spectral parameters that are not well constrained. The following sources are affected by this issue:

• Sources located in or near large exclusion regions (see Fig. 39). An area of width 2° is often excluded along the Galactic plane, and this covers a significant portion of the analysis FoV, which has a diameter of .

• Sources with large ON regions.

• Sources observed with too small or too large offsets because they are located close to other sources that were covered with dedicated observations.

#### 4.11.2 Flux containment and contamination correction

By construction and because of additional effects such as PSF leakage or source morphologies featuring tails, the spectral extraction region does not contain the full flux of the source. Additionally, the large-scale emission model and other nearby Gaussian components bias the flux measurement within the spectral region. Based on this emission model, we separate the contributions from the different components and derive a correction factor for the spectral flux measurement.

The total flux in the spectral measurement region is

 FONTotal=FONSource+FONLS+FONOther, (20)

where is the contribution from the source itself, is the contribution from the large-scale emission model, and is the contribution from nearby sources and other, discarded Gaussian emission components.

Assuming is the flux measurement from the morphology fit, we define the correction factor as

 CCorrection=FSource/FONTotal. (21)

To summarize the contributions from the large-scale emission model and other sources in close (angular) proximity, we define a quantity called contamination. This quantity measures the fraction of flux within the spectral region that does not originate from the source itself and is written as

 CContamination=FONLS+FONOtherFONTotal. (22)

Additionally, we define the containment of a source as the ratio between the flux of the source within the spectral measurement region (taking the morphology model into account) and the total flux obtained from the morphology fit as follows:

 CContainment=FONSource/FSource. (23)

The HGPS catalog provides all the quantities mentioned in this section, and all aperture-photometry based flux measurements in the HGPS catalog (see Table 5) are corrected by the factor given in Eq. 21 (see Sect. 4.11.3 and  4.11.4).

We note that this region-based spectral analysis method with a single integral flux correction factor assumes energy-independent source morphology. The spectra obtained for sources with energy-dependent morphology does not correspond to the correct total emission spectra of the sources. Currently energy-dependent morphology has been clearly established for two sources (HESS J1303631 and HESS J1825137), and there are hints of energy-dependent morphology for a few more. Furthermore, using an integral flux correction factor is not fully correct because the HGPS PSF is somewhat dependent on energy (smaller PSF at higher energies). The resulting inaccuracy on HGPS spectral results is small, because we have chosen a minimal spectral aperture radius of 0.15°, which contains most of the emission for point sources at all energies. Generally, spectra for sources with large correction factors are likely to be less accurate, because the morphology models used to compute the correction are only approximations.

#### 4.11.3 Spectral model fit

We performed the spectral fits on the stacked555Observation stacking was performed as described here: http://cxc.harvard.edu/ciao/download/doc/combine.pdf observations, using the ON-OFF Poisson likelihood function, referred to as the statistic (WSTAT) in XSPEC666See https://heasarc.gsfc.nasa.gov/xanadu/xspec/manual/XSappendixStatistics.html or Appendix A of Piron et al. (2001).. For each observation, we applied a safe energy threshold (see Sect. 3.1) cut at low energies, and the maximum energy was chosen at the highest event energy in the stacked counts spectrum for the on region (resulting in a maximum energy of 30 TeV to 90 TeV). Energy dispersion was not taken into account via a matrix, but in an approximate way in which the effective area is computed in such a way that it results in fully correct spectral results for power-law spectra with spectral index 2, and, given the good energy resolution of H.E.S.S., only small errors are made for other spectral shapes (Hoppe 2008a).

To describe the spectral shape of the VHE -ray emission, we fit a PL model to the data, i.e.,

 ϕ(E)=dNdE=ϕ0(EE0)−Γ, (24)

where is the differential flux at a reference (pivot) energy and is the spectral index. In addition, we also fit an exponential cutoff power-law (ECPL) model,

 ϕ(E)=ϕ0(EE0)−Γexp(−λE), (25)

which additionally contains the inverse cutoff energy as a third, free parameter. The reference (pivot) energy is not a free parameter in either model; we compute this parameter on a source-by-source basis to minimize the correlation between the other fit parameters.

We computed integral fluxes as

 F(E1,E2)=∫E2E1ϕ(E)dE, (26)

usually for the energy band above 1 TeV, with integral flux errors computed using Gaussian error propagation. We computed energy fluxes for a given energy band as

 G(E1,E2)=∫E2E1Eϕ(E)dE. (27)

The source catalog provides the PL fit results (see Table 5 for a description of columns) for every source and the ECPL parameters where the ECPL model is more likely (). All aperture-photometry based flux measurements are corrected by the factor given in Eq. 21.

#### 4.11.4 Flux points

Flux points are estimates of the differential flux at a given set of reference energies . To compute flux points for the HGPS catalog, we chose a method similar to that used for the Fermi-LAT catalogs (see, e.g., Sect. 5.3 in Acero et al. 2015a). For every source we selected a total number of six bins in reconstructed energy, logarithmically spaced between the safe energy threshold and a maximum energy of 50 TeV. The reference energy for the flux point estimation was set to the logarithmic bin center . The differential flux was computed via a one-parameter likelihood fit (same method as described in Sect. 4.11.3), under the assumption of the global best-fit PL and using only the data within the bin of reconstructed energy . An 1 asymmetric error on was computed from the likelihood profile, and for spectral points of small significance (), in addition an upper limit on was computed at 95% confidence level. All spectral point measurements in the HGPS catalog are corrected by the factor given in Eq. 21.

### 4.12 Method discussion

The sensitivity profile and map shown in Fig. 4 were computed assuming a point-like source morphology and using the Li & Ma significance estimation. The likelihood fit method including the large-scale emission model component used for the catalog production fundamentally differs from that. We qualitatively discuss below the most important differences and their influence on the effective sensitivity with which the catalog was produced.

In Sect. 3.4.4, the sensitivity was defined as the minimum required flux for a source to be detected with a certain level of confidence. Assuming the source is extended, which applies to most of the Galactic sources found by H.E.S.S., the total flux of the source is distributed over a larger area on the sky. Given a fixed background level, the signal-to-noise ratio is decreased and the sensitivity scales with the size of the source as

 Fmin(σsource)∝√σ2source+σ2PSF, (28)

where is the size of the source and the size of the PSF (Hinton & Hofmann 2009). It is constant for sources smaller than the PSF and increases linearly with source size for sources much larger than the PSF.

For low surface brightness sources close to the Galactic plane, high levels of contamination (defined as in Eq. 22) from the large-scale emission model were observed. This effectively reduces the sensitivity close to the Galactic plane and even caused a few previously detected H.E.S.S. sources to fall below the detection threshold (see also Sect. 5.4.3) chosen for the HGPS analysis. For sources far from the Galactic plane, however, the influence of the large-scale emission can be neglected.

Systematic and statistical background uncertainties, which are neglected in this analysis, bias the sensitivity for large, extended sources. Neglecting background fluctuations in the likelihood fit can lead to an overestimation of the significance of large sources, which can lead to unreliable detections of large emission components. In addition, the adaptive ring method (Sect. 3.2.3), which has a minimal inner ring radius of , does not provide a reliable background estimate for those large emission components.

Systematic uncertainties of various origins affect the spectral parameters of the sources. In addition to the transparency of the atmosphere, calibration, and event reconstruction (see Sect. 2), the analysis method itself can introduce uncertainties. In particular, the background and large-scale emission emission model, and the source extraction and measurement method (multi-Gaussian morphology and aperture photometry) influence the flux and spectral index measurement. We estimate the relative systematic uncertainties of the flux extracted from the maps (Sect. 3) and from the spectrum (Sect. 4.11) to be 30%; for the spectral index (Sect. 4.11) we estimate an absolute systematic uncertainty of 0.2. This estimate is based on the scatter seen in the cross-check analysis and other analyses (e.g., a source catalog extracted without a large-scale emission model component). For individual difficult sources (poor containment, large contamination, complex, and marginally significant morphology features), larger systematics may arise (see Sects. 5.4 and 5.5). We note that the systematic uncertainties quoted here are the same as in the previous HGPS publication (Aharonian et al. 2006d), and, as expected for a population of extended sources in the Galactic plane, these values are slightly larger than the systematic uncertainties previously estimated for isolated point-like sources such as the Crab nebula (Aharonian et al. 2006b).

A comparison of the two methods presented in this paper for calculating HGPS source integral flux ( TeV) was performed as a diagnostic test (see scatter plot in Fig. 9). The flux show on the x-axis is the total source flux estimated from the source morphology fit on the maps (given by Eqn. 12), assuming a power-law spectrum with index . The flux estimate on the y-axis was obtained from a spectral analysis (see Eqn. 26 in Sect. 4.11), using a PL or ECPL spectral model assuption (best-fit model) and an aperture photometry method that includes a containment and contamination correction according to the HGPS multi-Gaussian plus large-scale emission model. One can see that the two flux estimates agree very well for most sources within the statistical errors and the 30% flux systematic uncertainty that we quote above. There are exceptions however, which can to a large degree be attributed to differences in the underlying morphology and spectral model assumptions of the two flux estimators. We note that when comparing either of these HGPS source flux estimates against the cross-check, the level of agreement is similar, but not quite as good (see Sect. 5.5 for a discussion of individual cases). When comparing against previous publications, the scatter is even larger (flux differences up to a factor of 2 in a few cases), which can in many cases be understood to be the result of differences in morphology model (of the source itself, of nearby overlapping sources, or the large-scale emission model) or the spectral extraction region; most previous publications did not apply containment or contamination corrections.

## 5 Results and discussion

This section presents the results and a discussion of the HGPS based on the data set (Sect. 2), maps (Sect. 3), and catalog (Sect. 4).

### 5.1 Source associations and firm identifications

Determining the physical nature of a VHE -ray source often requires detailed spectral and morphological characterization of the VHE emission and availability of complementary MWL information. Finding a likely counterpart of a point-like VHE source is generally easy thanks to the limited region of the sky to investigate. For an extended source, such as the vast majority of the HGPS sources, the procedure is often much more involved because of multiple spatial associations, unless the VHE morphology is similar to that observed at other wavelengths (e.g., for a large shell-type SNR).

We therefore make a distinction between source associations and firm identifications of sources. The former is a list of astronomical objects, extracted from catalogs of plausible counterparts, which are are found to be spatially coincident with the HGPS source. When particularly solid evidence exists that connects one of these associated objects to the VHE emission, such as variability or shell-type morphology, we consider the HGPS source to be firmly identified.

In Sect. 5.1.1 we first describe the systematic association procedure, followed by the discussion of the results of this search for plausible counterparts in Sect. 5.1.2. Finally we present the list of firmly identified HGPS sources in Sect. 5.1.3.

#### 5.1.1 Source association procedure

Our objective is to associate each HGPS source with plausible counterparts found among nearby objects in the most relevant counterpart catalogs (that is catalogs of objects already identified as VHE emitters such as SNRs and pulsar wind nebulae and high energy -ray sources, see Table 2). We search for these counterparts in a region larger than the nominal HGPS source size (its 68% containment radius); we associate all the objects whose cataloged positions are at an angular distance smaller than the source spectral extraction radius, (Sect. 4.11.1; see also Fig. 35 ff.). This spatial criterion is motivated by the fact that often the origin of the relativistic particles is significantly offset from the VHE centroid, for example, when VHE pulsar wind nebulae (PWNe) are offset from energetic pulsars or extended well beyond their X-ray PWNe counterparts. We expect this procedure to be affected by source confusion (multiple associations that are difficult to disentangle), especially for larger VHE sources.

This criterion is a compromise between the number of spurious associations and the number of missed associations. A spurious association would be one with a counterpart that is physically unrelated to the HGPS source (e.g., a chance spatial coincidence in the same region of the sky). A missed association would be a real counterpart that is not selected by the procedure (e.g., a pulsar significantly offset from a VHE source could be missed even though it is known to generate a PWN). As a consequence of this spatial criterion, larger sources naturally has a larger number of associated objects. The criterion is intended to be loose (inclusive) to minimize missed associations at the expense of including potentially spurious associations. Nonetheless, this procedure has certain limitations, for example, difficulties in associating VHE emission with an SNR if the emission was produced in offset molecular clouds illuminated by cosmic rays that escaped from the SNR.

In the following paragraphs, we briefly describe the catalogs used for the automatic association procedure applied to search for counterparts. We also describe a list of additional objects that have been associated with HGPS sources in previous publications but are not present in the counterpart search catalogs. We note that some of these catalogs contain a single, specific type of object (e.g., supernova remnants), whereas other catalogs contain multiple types of physical objects because they are the result of broad surveys at energies relevant to the HGPS (e.g., the Fermi-LAT catalogs).

##### High-energy γ-ray sources

We searched for associated high-energy (HE) -ray sources in the Fermi-LAT 2FHL source catalog (Ackermann et al. 2016) and the full 3FGL catalog (Acero et al. 2015a). The 2FHL catalog covers the 50 GeV to 2 TeV energy range, and the 3FGL catalog covers the 0.1–300 GeV range. They contain 44 and 352 sources in the HGPS region, respectively. We expect the Fermi-LAT catalogs to contain a significant number of HGPS sources. In the case of 2FHL, this is due to its energy range, which partially overlaps that of the HGPS, and its sensitivity, which reaches 3-4% Crab in the HGPS region (Ackermann et al. 2016). But even without such overlaps, we expect to find many Fermi-LAT associations, since many objects emit -rays following a spectrum that extends from the HE to the VHE range. Even for noncontinuous spectra we expect to find numerous associations, for example, when a pulsar emits GeV emission detected by Fermi-LAT and its wind nebula emits TeV emission detected by H.E.S.S.

##### Supernova remnants and pulsar wind nebulae

Supernova remnants and PWNe are among the most common particle accelerators in the Galaxy and are well-known VHE -ray emitters. Nonetheless, it is often challenging to establish associations between SNRs and VHE sources. For example, only specific regions of an SNR shell could be emitting or neighboring molecular clouds could be illuminated by multi-TeV particles that escaped the shock front of the SNR. Pulsar wind nebulae evolve as their pulsar ages and the available rotational energy (spin-down power) decreases. Since the X-ray synchrotron radiation from PWNe arises from higher energy electrons than the IC radiation in the VHE gamma-ray band, and the cooling time of the electrons decreases with their energy (, for radiative losses ) we expect PWNe to shine longer in VHE gamma rays. Furthermore, a decreasing magnetic field with age can limit the emission time in radio and X-rays without affecting the VHE emission. As a result, some old PWNe should be undetectable outside the VHE -ray domain (see, e.g., Aharonian et al. (1997); de Jager & Djannati-Ataï (2009); H.E.S.S. Collaboration et al. (2017f)). For such old PWNe only the detection of a middle-aged energetic pulsar in the vicinity of a VHE source can provide evidence toward the true nature of the VHE emission.

To search for SNR and PWN associations, we take the most complete catalog of SNRs and PWNe to date into account, SNRcat777http://www.physics.umanitoba.ca/snr/SNRcat, accessed Oct 10, 2015 (Ferrand & Safi-Harb 2012). The SNRcat is a census of Galactic supernova remnants and their high-energy observations. It is based on the radio Catalogue of Galactic Supernova Remnants (Green 2014) but additionally includes other types of remnants in an effort to be as complete and up-to-date as possible. In particular, it contains plerionic objects, PWNe with no observed shell. The possible presence of a PWN is usually assessed based on the presence of diffuse, nonthermal emission in radio, X-rays, or even -rays. Several of these cataloged objects have been classified by SNRcat as candidate PWNe solely because of the presence of VHE emission in the vicinity of an energetic pulsar. We removed those objects from the catalog used in our association procedure to avoid cases in which we might misleadingly self-associate.

For the association procedure, we split the SNRcat objects into three subsets based on their apparent type. The first subset consists of objects that have no evidence of nebular emission and mostly belong to the shell or filled-center types in SNRcat; this subset contains 211 objects within the HGPS region. The second subset consists of objects that are listed in SNRcat as PWNe (or PWNe candidates) showing no evidence for shell-like emission; this subset contains 29 objects within the HGPS region. The third subset consists of objects showing evidence of both shell and nebular emission, which we refer to as composite objects; this subset contains 42 objects within the HGPS region. For a further discussion of a potential PWN nature of these objects see the population study presented in H.E.S.S. Collaboration et al. (2017f).

##### Energetic pulsars

We selected energetic pulsars from version 1.54 of the ATNF catalog of radio pulsars (Manchester et al. 2005). We excluded millisecond pulsars because they are not expected to power VHE PWNe and applied a cut on the spin-down energy flux  erg s kpc on the remaining pulsars. In addition, to take into account energetic pulsars of unknown distance, we included all objects with a spin-down luminosity  erg s, resulting in a total of 222 pulsars used in the association procedure. We did not take into account pulsars that do not have a measured . It is important to note that pulsars represent indirect associations: the associated pulsars are not directly emitting the unpulsed VHE -ray emission found in the HGPS, but rather indicate that they could be powering a PWN that directly emits such emission.

#### 5.1.2 Association results and discussion

##### He γ-ray sources

Of the 352 3FGL sources present in the HGPS region, we find 64 to be associated with an HGPS source. As expected, we also find a large portion of the 44 2FHL sources in the HGPS region to be associated with HGPS sources: only 13 of these have no HGPS counterpart. One of these sources is notably coincident with the VHE source candidate HOTS J1111$-$611 (Sect. 5.6.17). Many of the other 2FHL sources lacking an HGPS association tend to be located in low-sensitivity parts of the HGPS region. Only four 2FHL sources in parts of the HGPS with good sensitivity show no significant VHE emission in the HGPS: Puppis A (H.E.S.S. Collaboration et al. 2015c), 2FHL J0826.1$-$4500, $η$ Carinae, and the composite SNR G326.3$-$1.8 (Temim et al. 2013).

##### Supernova remnants

We find 24 of the 78 HGPS sources to be associated with shell-like SNRs. Given the large number of such objects in the HGPS region (211) and given their sizes, the number of chance coincidences is non-negligible. This is to be expected since we have not tried to specifically match SNR and HGPS source positions and sizes as in Acero et al. (2015b). Nonetheless, as discussed below, we find six known shells in the HGPS to be firmly identified and two more to be VHE shell candidates based on their specific morphologies (H.E.S.S. Collaboration et al. 2017a). We study the population of known SNRs in the HGPS further in a companion paper (H.E.S.S. Collaboration et al. 2017b).

##### Pulsar wind nebulae and composites

We find 37 of the SNRcat objects (in the HGPS region) containing a PWN or PWN candidate to be associated with an HGPS source. Conversely, we find more than 40% of HGPS sources to have at least one associated object in the PWN or composite classes. This supports the notion that systems containing PWNe are prolific VHE emitters. As discussed below, we are able to firmly identify about half of these associations using additional observational evidence such as similar MWL morphology or energy-dependent -ray morphology.

##### Pulsars

We find 47 of all the HGPS sources to be associated with an energetic pulsar. This suggests that the population of HGPS sources contains numerous PWNe. However, we selected a relatively low threshold in our association criteria to minimize missed associations. We quantitatively study such selection effects in a companion paper (H.E.S.S. Collaboration et al. 2017f) that provides a detailed look at the physical characteristics of firmly identified PWNe and a list of candidate PWN identifications based on various expected characteristics.

##### Extra associations

For completeness, in addition to the associations obtained through the catalog-based, automatic procedure, we add a list of 20 extra associated objects that are plausible counterparts for some HGPS sources and are not covered by the limited set of catalogs we use. Previous publications had proposed most of these associations, often thanks to dedicated MWL observations of VHE source regions (e.g., the X-ray source XMMU J183245$-$0921539 and HESS J1832$-$093). We propose other associations in this work for some of the new sources (Sect. 5.6). We also include the original identifiers of VHE sources discovered first by other instruments (e.g., VER J1930$+$188, which corresponds to HESS J1930$+$188). Table 12 includes all of these extra associations, labeled “EXTRA”.

##### Sources without physical associations

Eleven HGPS sources do not have any associations with known physical objects, although some are associated with HE -ray sources. We list and discuss these briefly here (the new VHE sources are discussed in Sect. 5.6):

1. HESS J1457$-$593 is one of the new sources detected in the HGPS analysis. Although the automatic association procedure does not find any counterparts, the VHE -ray emission may originate in a molecular cloud illuminated by CRs that escaped from the nearby but offset SNR G318.2$+$0.1. This scenario is briefly described in Sect. 5.6.2.

2. HESS J1503$-$582 is also a new HGPS source and does not have any compelling association except for the HE -ray sources 3FGL J1503.5$-$5801 and 2FHL J1505.1$-$5808, neither of which is of a firmly identified nature. We describe this enigmatic source in Sect. 5.6.4.

3. HESS J1626$-$490 has only one association, with the HE -ray source 3FGL J1626.2$-$4911. A dedicated XMM-Newton observation did not reveal any compelling X-ray counterpart either (Eger et al. 2011).

4. HESS J1702$-$420 is near the point-like source 2FHL J1703.4$-$4145. The elongation of the VHE -ray emission prevented the automated procedure from making the association, but a connection between the objects seems plausible. The small size SNR G344.7$-$0.1 (about in diameter) is also in the vicinity and in good positional coincidence with the (point-like) 2FHL source.

5. HESS J1708$-$410 has no compelling association, even though this source was the target of dedicated X-ray observations to look for associated emission (Van Etten et al. 2009). Given the brightness and relatively steep spectrum of this VHE source (), the absence of a counterpart at lower -ray energies in the Fermi-LAT catalogs is surprising and suggests the emission peaks in the hundreds of GeV range.

6. HESS J1729$-$345 is north of the nearby SNR HESS J1731347 (H.E.S.S. Collaboration et al. 2011a). An investigation into a potential connection between the two suggests the VHE emission from the former could be from a molecular cloud illuminated by hadronic particles that escaped from the SNR (Cui et al. 2016).

7. HESS J1741302 is the subject of a dedicated companion paper (H.E.S.S. Collaboration et al. 2017c) discussing potential PWNe and SNR-related association scenarios, among others. These aspects are therefore not discussed here.

8. HESS J1745$-$303 is close to, but offset from, SNR G359.1$-$0.5. Suzaku observations have revealed neutral iron line emission in the region, suggesting the presence of molecular matter and making this object another possible case of a CR-illuminated cloud (Bamba et al. 2009). We find this object also to be associated with the HE -ray sources 2FHL J1745.1$-$3035 and 3FGL J1745.1$-$3011.

9. HESS J1828$-$099 is a new HGPS source described in Sect. 5.6.8.

10. HESS J1832$-$085 is also a new HGPS source, described in Sect. 5.6.9.

11. HESS J1858$+$020 has an association with the HE -ray source 3FGL J1857.9$+$0210 and is close to, but offset from, SNR G35.6$-$0.4. A dedicated study (Paredes et al. 2014) did not find any compelling X-ray counterpart, although multiple possible scenarios were investigated, including CR-illuminated molecular clouds.

#### 5.1.3 Firmly identified HGPS sources

In this section, we go one step further and treat those HGPS sources for which the physical origin of the VHE -ray emission has been firmly identified. Whereas the association criteria were principally based on positional evidence (angular offset), we also perform a census of the additional evidence that is available to reinforce spatial associations and arrive at firm identifications. The supplementary observables we consider are correlated MWL variability, matching MWL morphology, and energy-dependent -ray morphology (Hinton & Hofmann 2009). Table 3 summarizes the results, along with the respective references for the additional evidence. Among the 78 sources in the HGPS region, we determine 31 to be firmly identified.

Firm identifications rely on different forms of evidence that vary depending on the source class. The VHE -ray emission from compact binary systems is always point-like and should exhibit variability that is also seen at lower energies. In contrast, the VHE emission from shell-type SNRs is extended (provided the SNR is sufficiently large and close) and nonvariable, but can be identified based on the specific shell morphology and correlated morphology at lower energies.

Composite SNRs have both a shell and an interior PWN detected at lower energies and can be more complex to identify correctly. If the angular size of the shell emission is larger than the size of the VHE emission, we can identify the VHE emission as coming from the PWN filling the SNR. This is the case, for example, for HESS J1747281 (PWN in SNR G0.9$+$0.1) and HESS J1554550 (PWN in SNR G327.1$-$1.1). In other cases, we are only able to identify the HGPS source with the composite SNR as a whole, i.e., we are confident that the VHE emission originates in the composite object but cannot disentangle whether it comes predominantly from the PWN or the shell (usually due to PSF limitations).

More evolved stellar remnant systems are difficult to identify firmly. We can make a firm PWN identification when there is a PWN of comparable size and compatible position detected at lower energies. This is the case, for example, for HESS J1420607 (PWN G313.54$+$0.23) and HESS J1356645 (PWN G309.92$-$2.51). In the absence of any clear PWN, or when its size at lower energies is much smaller than the VHE source, we have to rely on other evidence. The clearest such evidence is the detection of energy-dependent morphology, expected in PWNe because of the cooling of energetic electrons as they are transported away from the pulsar. At higher energies, the extent of the emission shrinks and its barycenter moves closer to the pulsar. This is the case for two sources thus far, HESS J1303631 (PWN G304.10$-$0.24) and HESS J1825137 (PWN G18.00$-$0.69). In the absence of such evidence, the identification of a VHE source as a PWN remains tentative when the only evidence is an energetic pulsar in the vicinity. Candidate PWN identifications are evaluated in detail in a companion paper (H.E.S.S. Collaboration et al. 2017f).

A large percentage (39%) of the 31 firmly identified sources are PWNe. The next largest source classes identified are SNR shells (26%) and composite SNRs (26%). Finally, -ray binary systems are also identified in the HGPS. It is not yet possible to identify firmly more than half of the total 78 HGPS sources with the conservative criteria we adopted, although the vast majority have one or more promising spatial associations that could prove to be real identifications following more in-depth studies beyond the scope of this work. We do not find any physical associations for 11 of the VHE sources in the HGPS, although for some of these, potentially related emission is seen in HE -rays, and for others, offset counterparts are present but simply not found by the automated association procedure adopted (see previous section). Figure 10 summarizes these identifications.

We note that one source in HGPS, HESS J1943$+$213, is likely an extragalactic object. It has no measured extension and a radio counterpart that many recent studies tend to classify as a BL-Lac object (Peter et al. 2014; Straal et al. 2016; Akiyama et al. 2016). However, its VHE flux has not revealed any variability so far, which is unusual for such an object (Shahinyan & the VERITAS Collaboration 2016).

### 5.2 Large-scale emission

In Sect. 4.6, we introduced an empirical spatial model to account for the large-scale VHE -ray emission we observed along the Galactic plane to detect and characterize accurately the discrete VHE -ray sources. This model provides an estimate of the spatial distribution of the large-scale VHE emission discovered by Abramowski et al. (2014a). We find that the fit amplitude, latitudinal width, and position of this model, shown on Fig. 6, are consistent with the latitude profile of that previous work. The width is also comparable to the HGPS source latitude distribution (Fig. 11, ff.) but smaller than that of molecular gas traced by CO emission (Dame et al. 2001).

Owing to the observational constraints and analysis used, the large-scale emission model cannot be considered a measurement of the total Galactic diffuse emission. The large-scale emission model provides an estimate of the diffuse emission present in the HGPS maps. Its parameter values depend on the map construction technique, in particular the exclusion region mask used in the analysis (Sect. 3.2.2), i.e., changes in the mask can alter the parameters of the model. For instance, the peak observed at in Fig. 6 is due to the presence of low-level emission that is just below the threshold to be covered by the exclusion mask we use for the HGPS. While a significant percentage of the large-scale emission is expected to be truly interstellar diffuse emission, it is very likely that emission from discrete but unresolved sources contributes as well. Finally, some features in the HGPS large-scale emission model are likely artifacts of errors in the estimation of the background model of gamma-like cosmic ray EAS events (see Sect. 3.2); these events are the dominating model component in the HGPS counts maps, thus small relative errors in that background model can lead to significant changes in the excess model of the HGPS sources, but even more so the HGPS large-scale emission model.

### 5.3 Source parameter distributions

In the following section we study the global properties of the VHE -ray sources in the HGPS catalog. We compare certain key source parameters against each other and briefly discuss the implications in the context of the Galactic VHE source population, survey sensitivity, and firmly identified MWL source classes.

The latitude distribution of the 78 HGPS sources is shown in Fig. 11. The distribution has a mean of and a width of . For visual comparison, the latitude distributions of the main classes of associated counterparts (Sect. 5.1) — SNRs, energetic pulsars, 3FGL sources, and 2FHL sources — are shown in this figure. Also shown for reference is an estimate of the matter density profile as traced by Planck measurements of CO(1-0) line emission (Planck Collaboration et al. 2016). It should be kept in mind throughout this section that the HGPS sensitivity is not uniform as a function of longitude or latitude (Sect. 3.4.4).

The HGPS latitude distribution of sources correlates well with both potential counterparts and tracers of matter density. The distribution is somewhat skewed toward negative latitudes even though the HGPS sensitivity has a relatively wide and flat coverage in latitude. In Fig. 11, the sensitivity is illustrated by two curves showing regions of relatively good sensitivity (e.g., at ) and relatively poor sensitivity (e.g., at ). These curves demonstrate that the HGPS sensitivity coverage in latitude is, in general, much wider than the HGPS source distribution. Although there are local exceptions at some longitudes, the latitude coverage is generally flat in the range , at various locations even in . However, the counterpart catalogs are known to suffer from various selection biases and the Galactic disk itself is known to not be perfectly symmetric as observed across the spectrum.

In addition, one might still argue that, given the narrow range of latitudes observed with respect to surveys at other wavelengths, the HGPS sources may not be representative of the underlying distribution of VHE -ray sources. However, in light of the counterpart distributions, in particular the 2FHL sources, it can be reasonably assumed that the limited latitude coverage only has a weak effect on the observed source population distribution.

The longitude distribution of the 78 HGPS sources is shown in Fig. 12, together with the molecular interstellar matter column density profile as traced by CO(1-0) line emission (same as in the previous figure). The latter, measured by Planck (Planck Collaboration et al. 2016), has a uniform exposure (sensitivity) over the sky, unlike the HGPS, adding caveats to potential detailed correlations seen in this figure. We can nevertheless robustly conclude that there is a very general correlation in longitude between the number of HGPS sources and the molecular matter column density and that the HGPS sources are mostly found in the inner 60° of the Galaxy. Additionally, the spiral arm tangents as traced by CO (Vallée 2014) are shown in Fig. 12. An increased number of sources could be expected in the directions of the near spiral arm tangents (see Fig. 16). In the longitude distribution, a slight excess of sources in the direction of Scutum and between Norma and Crux-Centaurus can be observed. However, because of the limited sample size of 1–6 sources per bin, no significant increased source density in the direction of spiral arm tangents can be observed.

For comparison, we also added distributions for the Fermi-LAT catalogs 3FGL and 2FHL to Fig. 12. While Fermi-LAT has a roughly uniform exposure, their sensitivity in the HGPS region is reduced in the inner Galaxy where diffuse emission is brighter, and also the source extraction is very different from the HGPS approach, so that a direct comparison is not possible. Finally we have chosen not to show the SNR and pulsar distributions in the Galactic longitude distribution at all because the coverage of those catalogs is not uniform.

We compare the HGPS source integral fluxes ( TeV) to source sizes in panel A of Fig. 13 and show the distributions of fluxes and sizes separately in panels B and C, respectively. In the flux–size figure, we plot the approximate flux sensitivity limit of the HGPS as a function of source size. One can see that the sensitivity worsens as the source size increases, as expressed by Eq. 28. The HGPS sources indeed generally follow this trend. From Fig. 13, we therefore conclude that the HGPS can be considered complete down to 10% Crab for sources . For smaller sources (), the HGPS achieves completeness at a few % Crab (see also Fig. 4).

We show the distribution of HGPS source integral fluxes ( TeV), which are calculated assuming a spectral index of , in panel B of Fig. 13. At higher fluxes, we naturally expect the number of sources to decrease. At the lowest fluxes, we also expect the number to be small, because we reached the sensitivity limit of the HGPS.

As can be seen in panel C of Fig. 13 and despite the modest H.E.S.S. PSF (), the majority of sources are not compatible with being point-like but rather found to be significantly extended and as large as . Owing to the methods used for background subtraction (see Sect. 3.2.3), the HGPS is not sensitive to sources with larger sizes.

The firmly identified HGPS sources (Sect. 5.1) are highlighted in Fig. 13. It can be seen that all identified binary systems appear as point-like sources in the HGPS, as expected. The PWNe appear to have various angular sizes, in agreement with the diversity observed in the VHE PWN population (H.E.S.S. Collaboration et al. 2017f). Most identified SNRs are extended, likely owing to selection bias (smaller SNRs are difficult to identify, e.g., through shell-like morphology) and the H.E.S.S. PSF. The identified composite SNRs, on the other hand, are typically smaller, owing to the difficulty in disentagling VHE emission from the SNR shell and interior PWN, similarly related to the H.E.S.S. PSF. In any case, it does not seem possible to identify the nature of the many unidentified sources solely on the basis of their sizes or a flux–size comparison.

Figure 14 shows the distribution of the HGPS source power-law (PL) spectral indices . For consistency, the PL model spectral index is used for all sources, even those for which an exponential cutoff power law (ECPL) fits better. The index distribution has a mean . This is compatible with the index () adopted in the production of the HGPS flux maps (Sect. 3.4.2) and the HGPS PSF computation (Sect. 4.3). We note that individual source indices have typical statistical uncertainties of order and a similar systematic uncertainty; HGPS data are often not sufficient to precisely constrain the index because the energy range covered with good statistical precision is typically only about one decade ( TeV). Finally, the figure also shows how the firmly identified HGPS sources are distributed in index, showing no strong tendency with respect to source class.

We show the cumulative distribution of HGPS source integral fluxes ( TeV, obtained from the maps) in Fig. 15. The 78 HGPS sources span a range in flux from 0.6% Crab to 103% Crab; 32 sources are above 10% Crab. We performed an unbinned likelihood fit of a PL model to the distribution (also shown in Fig. 15), using only the range % Crab where we consider the HGPS survey mostly complete. The best-fit value of the PL slope is (for the cumulative distribution), and the amplitude corresponds to sources above 10% Crab. This slope is consistent with Galactic models in which equal-luminosity sources are homogeneously distributed in a thin disk, which predict a slope of .888The flux of a source scales with the distance like , where is the intrinsic luminosity of the source. For a thin disk, we have , which corresponds to a slope of in the cumulative distribution.

The only robust statement that can be inferred from the distribution of HGPS sources is that it provides a lower limit on the true distribution; that is, there are at least, for example, 70 sources above 1% Crab. If one assumes that distributions are always concave (which most “reasonable” spatial distributions and source luminosity functions encountered in the literature are), then the extrapolation of the PL fit shown in Fig. 15 sets an upper limit of sources above 1% Crab, with a statistical error of a factor of 2.

More detailed analyses of the distribution or of the flux-size distribution are possible in principle but in practice do not yield robust results because of the limited number of sources and the large uncertainties concerning the effective sensitivity achieved. We emphasize that the catalog creation procedure is complex (special treatment of known shell-type sources, large-scale emission model component, 15 discarded and several merged components; see Sect. 4.9), with the net effect that the sensitivities shown in Fig. 4 and panel A of Fig. 13 are not reliably achieved, because those sensitivity estimates assume isolated sources, there is no underlying large-scale emission or source confusion, and there is a detection threshold of , whereas the component detection threshold of corresponds to  .

A representation of the Galaxy seen face-on is depicted in Fig. 16 to visualize how much of the Galaxy the HGPS has been able to probe at different sensitivity levels. Two limits are shown, illustrating the sensitivity detection limit (horizon) of the HGPS for potential point-like sources with presumed luminosity of and  erg/s. Given the achieved sensitivity in the Galactic plane, it is clear that H.E.S.S. has only probed a small fraction of the Galaxy – just up to a median distance of  kpc for bright ( erg/s) point-like sources (and less for extended sources). Furthermore, this illustrative look at survey completeness strengthens the hypothesis that the large-scale emission described in Sect. 4.6 could be partly explained by a population of unresolved sources, presumed to be distant.

### 5.4 Comparison with previous VHE publications

In total, we reanalyzed 48 VHE -ray sources that have been the subject of past H.E.S.S. publications. In this section we present a systematic comparison of the present HGPS results, with the latest published results, as summarized in gamma-cat999https://github.com/gammapy/gamma-cat, accessed July 24, 2017, the open TeV source catalog.

We associated HGPS sources with previous analyses simply by the name of the source, which was unique except for three cases: HESS J1800$-$240, HESS J1746$-$308, and HESS J1930188, which we discuss in detail in Sect. 5.4.2. We excluded these sources from the systematic comparison in the first place.

To further identify the cases for which we obtained significantly different results from previously published analyses, we compared the position, size, spectral index, and flux of the remaining uniquely associated sources, taking statistical and systematic errors of the measurements into account. For each of these parameters, we estimated the total uncertainty as the 1 statistical and systematic uncertainties added in quadrature. We estimated this quantity for both the HGPS-derived source parameters and previously published H.E.S.S. values.

The systematic uncertainties on position and size are given in Sect. 4.10.3 and Sect. 4.10.2, respectively. Additionally, we assumed a systematic uncertainty on the spectral index and 30% on the flux of the source, in agreement with previous estimates (Aharonian et al. 2006b). We then defined the criterion for significant outliers as

 ΔHGPS−H.E.S.S.>2√σ2tot,HGPS+σ2tot,H.E.S.S., (29)

where is the difference between the corresponding parameter values. When comparing the position we chose the angular separation as comparison parameter. We note that for many sources, the data sample used here is significantly different from that used in the publication, hence the correlation of statistical errors is usually not too large.

We first discuss the general level of agreement between the current and previous analyses (excluding the outliers) in Sect. 5.4.1 and later discuss the outliers of the comparison individually in Sect. 5.4.2.

#### 5.4.1 Agreement with previous publications

For the vast majority of sources, we find that there is good agreement between the HGPS-derived position, morphology, and spectrum within the statistical and systematic uncertainties.

##### Position

We found the position of 43 (out of 45) sources to be compatible with the previously published value, according to Eq. 29. For point-like sources we found an average shift of  deg, while for extended sources the value was  deg. Both values agree well with the expected scatter considering the statistical and systematic uncertainties on the measurements. As an additional check, we also verified that the positions of the identified -ray binaries (known point sources) HESS J1826148 and HESS J1302638 are in good agreement (within 40) with the reference positions of the corresponding objects LS 5039 and PSR B125963 as listed in SIMBAD.

##### Size

Comparing the sizes of the extended sources we found 30 (out of 35) sources to be compatible with the previously published value. The average size difference for the extended sources was on the order of  %, the distribution of values having a width of  %. This indicates that with the current analysis we measured slightly larger sizes of the sources on average, but the distribution is dominated by a large scatter. We expect the scatter to result mainly from differences in the analysis procedure. Previous analyses mainly fitted single Gaussian morphologies, while in this analysis we allowed for multiple Gaussian components. Further differences are the addition of the large-scale emission model and the systematic modeling of emission from neighboring sources.

Previous publications found seven sources to be compatible with a point-like source. In the current analysis we found all these sources to be compatible with a point-like source again. Additionally, we identified the following three cases that are compatible with a point-like source according to Eq. 18, which were previously found to be extended:

1. For HESS J1427$-$608 we measured a size of °, compared to ° in Aharonian et al. (2008a). This source is a borderline case that just meets our criterion for a point-like source.

2. For HESS J1714385 we found a size of ° compared to ° in Aharonian et al. (2008c). With the current analysis, a smaller size was found because underlying emission was modeled by separate emission components (see Fig. 5).

3. We now measure the size of HESS J1808$-$204 to be ° (consistent with point-like, in the definition of Eq. 18), compared to the previously measured size ° (extended) (Abdalla et al. 2016). This discrepancy is due to the HGPS’s inclusion of a large-scale emission component that now models -ray excess previously accounted for in the source component itself.

##### Flux

We found the flux of 42 (out of 45) sources to be compatible with the previous published value, according to Eq. 29.

The average difference in flux for extended sources was  % with a width of  % for the distribution of values. While the average value is compatible with previous analyses, we still found a large scatter (albeit compatible to the systematic and statistical errors) of the distribution.

A fair comparison between flux values obtained with the current method and earlier analyses proved to be difficult again because of fundamental differences between the methods used. In previous publications, aperture photometry was mostly used, while in this analysis the main flux measurement was based on a model fit, taking the PSF and morphology of the source and large-scale emission into account. Flux estimate differences with these two methods are shown in Fig. 9 (both measures from the HGPS analysis, not with respect to previous publications). Many of the differences in spectra and fluxes measured in the HGPS analysis and previous publications are the result of changes in the spectral extraction region (position and size).

##### Spectral index

For all sources we found the spectral power-law indices to be compatible with the previously published values. The mean difference in spectral index was with a width of for the distribution. This is well compatible with the expected scatter taking statistical and systematic uncertainties of the measured spectral indices into account.

#### 5.4.2 Differences with previous publications

In the following paragraphs, we list and discuss the outliers as identified by Eq.29.

##### Hess J0835−455

This source (Vela X) exhibits complex morphology, and the HGPS analysis best models the VHE emission as a superposition of three Gaussian components with an average size . This value is somewhat larger than the value published first in Aharonian et al. (2006c), where it was modeled as a single asymmetric Gaussian of size . However, a more recent H.E.S.S. publication (Abramowski et al. 2012a) studied the complex emission more thoroughly. It fit profiles of the emission along two perpendicular axes, the main one aligned with the primary orientation of the emission. Along the major axis, the study measured a Gaussian size , and along the minor axis, two Gaussians (sizes and ) were required to best fit the emission. The HGPS model of the emission from HESS J0835455 is thus largely compatible with the most recent dedicated study of the VHE emission, and the apparent discrepancy is simply a result of comparing two different multi-component models with our general outlier criterion (Eq. 29).

##### Hess J1646−458

HESS J1646$-$458 is a complex emission region located in the vicinity of the stellar cluster Westerlund 1. Its morphology suggests it consists of multiple sources. Abramowski et al. (2012b) separated the emission into at least two distinct features (with radii and , respectively) as well as some structured extended emission, distributed over the signal region of 2.2° diameter, and even extending beyond. A flux above 1 TeV in the signal region of  cm s was derived, and a spectral index of . An ON-OFF background estimation technique was used to cope with the large source size.

In the HGPS analysis, this complex emission is modeled by a single Gaussian component of 0.5° size shifted by 0.47° from the center of the region used in Abramowski et al. (2012b), with a lower flux above 1 TeV of  cm s, and steeper index of . Given the complex morpology and the large scale of the spectral extraction region used in Abramowski et al. (2012b), significant differences in source parameters are to be expected; in the HGPS analysis part of the flux is absorbed in the large-scale diffuse background.

##### Hess J1708−410

The flux above 1 TeV of HESS J1708410 is found to be smaller in the HGPS analysis than in Aharonian et al. (2008a). While the size of the source is similar in both cases, the different approaches used in the HGPS analysis lead to different integration radii used to derive the source spectrum. The HGPS analysis uses an integration radius about two times smaller than in the dedicated analysis, which explains the apparent discrepancy.

##### Hess J1729−345

For HESS J1729345, the HGPS analysis finds a flux above 1 TeV larger than in H.E.S.S. Collaboration et al. (2011a). Because of the HGPS morphology modeling of the source and its procedure to define the integration radius, the spectrum of this source is derived in a region with a radius about two times larger than in the dedicated publication, accounting for the observed difference.

##### Hess J1745−303

HESS J1745303 was studied in Aharonian et al. (2008b) with 80 h of data. Its morphology is complex and three subregions, called A, B, and C, were discussed. In the HGPS analysis, with more than 160 h on the region, two distinct sources are detected: HESS J1745303 and HESS J1746308. The former encloses the hotspots A and C and a fraction of region B. A second source is now detected at latitude. This source contains part of hotspot B and emission at large latitudes that was not significant before, likely due to the additional livetime obtained since 2008. It is fainter and its spectrum is very steep but poorly constrained. There is also a third extended () Gaussian component in the region. It is currently considered to be a diffuse component. The association of the two sources and the extended component is unclear and the exact morphology of the VHE emission in the region will require dedicated studies.

##### Hess J1800−240

In Aharonian et al. (2008d) the emission in the region of W 28 was found to be split into two components: HESS J1801233 (addressed below), which is not significant in the HGPS analysis and is coincident with the W 28 SNR itself, and a complex region HESS J1800240 offset by to the south. The latter was previously found to be resolved into three hotspots dubbed HESS J1800240 A, B, and C (Aharonian et al. 2008d). Since sources HESS J1800240 A and B are spatially coincident with molecular clouds, Aharonian et al. (2008d) suggested that they were produced by CRs that had escaped the SNR and had illuminated ambient gas clouds, making this system an archetype of CR escape from evolved SNRs (see, e.g., Aharonian & Atoyan 1996; Slane et al. 2015; Gabici & Montmerle 2015).

In the HGPS analysis, however, only one source is redetected, HESS J1800240, as one large Gaussian component centered on the hotspot B. The separation into several components does not result in a high enough TS to separate it into several significant sources in the analysis shown here.

##### Hess J1825−137

HESS J1825137 is a large PWN with a bright core surrounded by extended, asymmetric emission. The HGPS analysis finds it has a size of , using three Gaussian components to model the VHE entire -ray emission. This is significantly larger than the obtained with a single symmetric Gaussian model or the with a single asymmetric Gaussian in Aharonian et al. (2006g). These models were stated to have rather poor goodness-of-fit values. The more complex approach taken for the morphology modeling in the HGPS improves the description of the -ray emission from this PWN and accounts for the differences with respect to previous, simpler modeling.

##### Hess J1837−069

The HGPS analysis finds HESS J1837069 to have a size of based on modeling the VHE -ray emission as three Gaussian components. This is larger than the size previously derived using a single asymmetric Gaussian (Aharonian et al. 2006d), i.e., by ; and using a single Gaussian (Marandon et al. 2008), i.e., . The more complex modeling of the HGPS, which also takes into account more of the extended nebular emission from this identified PWN, explains the apparent discrepancy. Consequently, we used a larger region (twice the radius compared to Aharonian et al. (2006d)) to derive the spectrum, leading to an integral flux above 1 TeV that is larger by a factor of 3 than in the dedicated publication.

##### Hess J1857+026

The size of the source HESS J1857$+$026 is significantly larger in this analysis than previously published in Aharonian et al. (2008a). In the latter, the source is fit with an asymmetric Gaussian (), whereas the HGPS analysis best models the source with two Gaussian components for an approximate size of . The difference in size is explained by the multicomponent approach of the HGPS that better takes into account the larger scale emission underneath the central bright core.

##### Hess J1908$+$063

The position and size published in Aharonian et al. (2009) are significantly different from those obtained in the HGPS analysis. The position is offset by and the size is found to be , which is larger. We note that the size we find is consistent with that measured by the VERITAS Collaboration (Aliu et al. 2014b), even though the positions differ by . A plausible cause for these discrepancies is that this is a large source likely composed of multiple components, where results are expected to be sensitive to the morphology assumptions and to details in background modeling techniques, in particular, if those tend to absorb large-scale features.

##### Hess J1923+141

The VHE -ray source HESS J1923$+$141 (preliminary H.E.S.S. results published in Fiasson et al. 2009) is spatially coincident with the W 51 region, studied in detail with the MAGIC IACT (Aleksić et al. 2012). The HGPS results are generally compatible with those from MAGIC. However, the latter shows evidence for a -ray source composed of two components above 1 TeV, which cannot yet be confirmed by H.E.S.S. One component is coincident with the interaction region between W 51C and W 51B, while the other is coincident with the potential PWN CXOU J192318.5$+$140305 (Koo et al. 2005), suggesting that HESS J1923141 may be a composite of VHE emission of different astrophysical origins.

##### Hess J1930+188

The VHE -ray source, discovered with VERITAS (with the identifier VER J1930188, Acciari et al. 2010), is coincident with the composite SNR G54.1$+$0.3 and the pulsar PSR J1930$+$1852. We report on the H.E.S.S. observations of this source for the first time here. The HGPS source is found to have a slightly displaced position from the pulsar and the VERITAS best fit (by ). Despite the agreement with the VERITAS spectral index, the integral flux above 1 TeV found in our analysis is 40% lower than their published flux. We note, however, that the apparent discrepancy with VERITAS is not confirmed by our cross-check analysis, which yields a flux for this source that is larger by more than the nominal 30% systematic flux uncertainty, and is in agreement with the VERITAS measurement.

#### 5.4.3 Sources not redetected

In total, there are four previously published VHE -ray sources that are not redetected with the current HGPS analysis. All of these are rather faint sources which, for the HGPS analysis, yield significances close to the HGPS detection threshold of . We consider these as real sources of -rays; the nondetection in the HGPS is primarily a result of differences between the HGPS analysis and specific analysis methods. We found that some of the most relevant differences are

1. event reconstruction and -ray-hadron separation cuts that are less sensitive compared to more specialized methods that have been used in individual source analyses;

2. higher energy threshold in the HGPS analysis, in conjunction with a soft spectrum of the tested source;

3. use of the FoV offset cut (see Sect. 3.1), which is tighter than the value used in many previous H.E.S.S. publications ( or even