The Palermo Swift-BAT Hard X-ray Catalogue

The BatImager integrates each single DPH in a selected energy range, producing the corresponding DPI. A preliminary cleaning of the disabled and noisy pixels is performed, and the DPI is cross correlated with the mask pattern, in order to identify and subtract bright sources (with S/N $>8$). Then the background, modelled on a large scale from the analysis of the shadowgram residuals by performing a Principal Component Analysis (Kendall, 1980), is subtracted. A further search for bad pixels is performed, obtaining the final map of all pixels to be excluded in the following steps. A further correction is applied to take into account differences in the detection efficiency of single detector pixels, through a time/energy dependent efficiency map, built stacking all the processed DPI and equalizing the average residual contribution for each pixel. The original DPI, corrected for the efficiency map and cleaned for the bad pixels, is processed again, with all the contributions from the background and the bright sources identified in the previous steps computed simultaneously, in order to correct for cross-contamination effects. These contributions are subtracted from the DPI, that is then converted into a sky image, using the Healpix projection (Górski et al., 2005). This projection provides an equal-area pixelization on a sphere and allows the generation of an all-sky map, avoiding the distortion introduced by other types of sky projections far from the projection center. This sky map is then corrected for the occultation of Sun, Earth and Moon. The sky maps produced from each DPI are added together, with the intensity in a given sky direction computed from the contribution from all the sky images, each inversely weighted for its variance in that direction. As described above, the bright sources and background were already subtracted from each single DPI; therefore this all-sky mosaic contains only the residual sky contribution. In order to correct for residual systematic effects (e.g. imperfect modelling of the source illumination pattern or of the background distribution), the all-sky S/N map is sampled on a scale significantly larger than the PSF: the local average S/N is subtracted and its measured variance used to normalize the local S/N distribution. Finally, we obtain a S/N map with zero average and unitary variance that can be used for a blind source detection.

We have created all-sky maps in three energy bands: 14–150 keV, 14–70 keV, 14–30 keV. The source detection in the all-sky map is performed by searching for local excesses in the significance map. The source position and its peak significance are then refined with a fit restricted within a region of a few pixels where the excess dominates over the noise distribution. Only detections with peak significance greater than 4.8 sigma are included in our list of detected sources. We found that this threshold represents the optimal value that maximizes the number of detectable sources, maintaining at the same time an acceptable number of spurious detections: taking into account the total number of pixels in the all sky map, the PSF and the Gaussian distribution of the noise, we expect 23 spurious detections above our threshold in each energy band, due to statistical fluctuations. Therefore, the total number of spurious detections will be between 23 and 69 (2.4% to 7.2% of the total number of our detections, see below), the best case occurring if each noise fluctuation above the threshold appears simultaneously in all three bands, the worst case occurring if each fluctuation appears only in one energy band. A few sources ($\sim 5\%$) detected with a significance slightly lower than our threshold were included in the detection list because their S/N is significantly larger than the negative excess (in modulus) of the local noise distribution.

The resulting detection catalogues (one for each of the three energy bands) have been cross-correlated and merged in a single catalogue: when source candidates closer than 10 arcmin are present in the sky maps of different energy bands, they were reported in the merged catalogue as a single source candidate. We obtain a final number of 962 source candidates (detected in at least one of the three energy bands). We adopt as best source position the one corresponding to the energy range with the highest detection significance.

We have evaluated the hardness ratio of the detected sources as Rate(30–150 keV)/Rate(14–30 keV) (the hard rate is evaluated as the difference between the count rates in the 14–150 and in the 14–30 energy bands). In Figure 1 we plot the hardness ratio as a function of the significance for each detected source, showing the energy range where the detection has the highest significance. Repeating the detection process in three energy bands optimizes the S/N for each source, and this yields better values for the source position, whose uncertainty scales inversely with the significance. Moreover, a significant subsample of sources was detected in only one of the three energy bands ( 56 in the 14–150 keV energy band, 38 in the 14–30 keV energy band, 78 in the 14–70 keV energy band) demonstrating that searching in different energy bands maximizes the number of detectable sources.

Figure 2 shows that the distribution of the detected sources (orange squares) vs. Galactic latitude flattens for $|b|>5$, which we shall hereon consider our operational definition of the Galactic plane.

The identification of the counterpart of the BAT detections was performed following three different strategies.

A. The position of each of the 962 detected excesses was cross-checked with the coordinates of the sources included in the INTEGRAL General Reference Catalogue³³3http://isdc.unige.ch/?Data+catalogs (v. 27), that contains 1652 X-ray emitters, and with the coordinates of the counterpart of the 48 new identifications of BAT sources already published (Markwardt et al., 2005; Tueller et al., 2008; Ajello et al., 2008a, b) and not included in the above catalogue. We adopted as counterpart a source within a radius $R=8.4$ arcmin from the BAT position (4 standard deviations error circle for a source detection at 4.8 standard deviations, Segreto et al., 2009). With this method we obtain 458 identifications, 295 with $|b|>5^{\circ }$. The choice of the error radius is strategic to maximize the associations and keep the number of spurious associations to a negligible level. The number of spurious identifications due to chance spatial coincidence has been evaluated using the following expression:

where, A${}_R$ is the selected error circle area, A is the total sky area under investigation, $N$ and $N_{cat}$ are the number of BAT detections and of candidate counterparts in A. The above formula assumes both source distributions to be uniform over the sky. In order to take into account the higher density of sources on the Galactic plane we have divided the sky into two regions: $|b|\le 5^{\circ }$ (the Galactic plane, with $N=190$, $N_{cat}=651$) and $|b|>5^{\circ }$ ($N=772$, $N_{cat}=1049$). The number of expected spurious identifications is 2.1 within $|b|<5^{\circ }$ and 1.3 elsewhere. As the assumption of uniform distribution could be only a crude approximation, we have verified the evaluation of expected spurious associations with an alternative method: we produced a set of 962 coordinate pairs by inverting the position of the detected excesses with respect to the Galactic reference system and cross-correlated these positions with the INTEGRAL General Reference Catalogue extended with the published BAT identifications. We obtained 3 spurious associations, in full agreement with the value obtained in Eq.1.

B. We have searched for observations from Swift/XRT containing the remaining (504) unidentified excesses in their field. We found Swift/XRT observations for 186 BAT source candidates. Source detection inside these X-ray images was performed using XIMAGE (v4.4). When a source was detected inside a $6.3$ arcmin error circle (99.7% confidence level for a source detection at 4.8 standard deviations, Segreto et al., 2009) we first checked for its hardness ratio in the 0.3–10 keV range (with 3 keV as a common boundary of the two ratio bands) and for its count rate above 3 keV. We identified a source as the counterpart of a BAT detection if at least one of the above conditions was satisfied: hardness ratio $>0.5$, count rate above 3 keV $>5\times {10}^{-3}$ c s${}^{-1}$. In seven cases where two candidates, satisfying at least one of the threshold conditions, were found inside the BAT error circle, we chose as counterpart the closest source to the BAT position. With this method we identified 170 source counterparts. In order to evaluate the number of expected spurious identifications we collected a large sample of XRT observations of GRB fields, using only late follow-ups (where the GRB afterglow has faded) with the same exposure time distribution as the XRT pointings of the BAT sources. We searched for sources within a 6.3 arcmin error circle centered at the nominal pointing position in each of these fields, excluding any GRB residual afterglow, and satisfying at least one of the above threshold conditions. We detected 7 sources, therefore, the number of expected spurious identifications is consistent with the number of multiple XRT detections inside the BAT error circle. We also searched for field observations with other X-ray instruments (XMM-Newton, Chandra, BeppoSAX), finding 25 identifications, out of 30 pointings. Given the low number of available fields, the number of expected spurious identifications within this sample is irrelevant.

C. For the remaining unidentified sky map excesses (309) we searched for spatial coincidence inside an error circle of 4.2 arcmin radius ($90\%$ confidence level for a source detection at 4.8 standard deviations, Segreto et al., 2009) with sources included in the SIMBAD catalogues. The size of the search radius was fixed to 4.2 arcmin in order to have a negligible number of spurious identifications (see below). We restricted our search to the following SIMBAD object classes: Cataclysmic variable (CV), High mass X-ray binaries (HXB), Low mass X-ray binaries (LXB), Seyfert 1 (Sy1), Seyfert 2 (Sy2), Blazar and BL Lac (Bla, BLL), LINERs (LIN), for a total of 22425 objects in the SIMBAD database. This strategy allowed us to identify 92 detections, with only one source at low Galactic latitude ($|b|<5^{\circ }$). The number of expected spurious identifications was evaluated with the two methods described for the strategy A. According to Eq.1 we expect 0.03 spurious identifications within $|b|<5^{\circ }$ (20 BAT detections and 391 Simbad sources in the classes of interest) and 2.7 elsewhere (289 BAT detections and 22034 Simbad sources); using the set of 309 coordinate pairs obtained inverting with respect to the Galactic center the positions of the sources in our sample we find 3 spurious associations, consistent with the first method. The cross correlation between unidentified sky excess and the SIMBAD catalogue of QSOs was treated separately because the coincidence error circle of 4.2 arcmin radius results in a high number of spurious associations (9 out of 17 associations). A radius of 2 arcmin allowed us to identify 9 sources as QSOs, and to optimize the ratio between the total number of associations and the expected number of spurious associations ($\sim 2$).

In Fig. 3 we report the offsets of each BAT source with respect to its identified counterpart as a function of the detection significance (S/N). The offset vs. the detection significance can be modeled with a power-law plus a constant. The best fit equation we obtained is the following:

The constant in Eq. 2 represents the sistematic due to a residual boresight misalignment. At the detection threshold of 4.8 standard deviations the average offset is $\sim 2.6$ arcmin.

Fig. 4 shows the distribution of the identified sources for each identification strategy as a function of the offset between the BAT position and the counterpart position. The peak of the distribution is at lower offset for strategy A because the sample of the sources identified with this strategy contains the brightest objects. The peak of the distribution relevant to strategy B is at a lower offset with respect to the distribution of strategy C because the XRT follow-up observations were performed on the more significant still unidentified source candidates.

All the identifications obtained with the three strategies (754) were merged in the final catalogue reported in Table 2 (see Section 6) where a flag indicates the identification method for each source. Figure 2 shows the distribution of all identified sources (black diamonds) as a function of the Galactic latitude.

A set of 208 detections could not be associated with a counterpart. These source candidates have detection significance between 4.8 and 14 standard deviations and flux in the 14–150 keV band between $6.7\times {10}^{-12}$ and $2.7\times {10}^{-11}$ erg cm${}^{-2}$ s${}^{-1}$. 33 sources out of 208 are detected in all the three enegy bands and 63 in two energy bands. The unidentified detections are distributed quite uniformly in the sky (Figure 2, green circles), with 190 sources out of 208 located above the Galactic plane ($|b|>5^{\circ }$).

Table 1 details the distribution of the 754 sources in our catalogue among different object classes: $\sim 69$% of the catalogue is composed of extragalactic objects, $\sim 27$% are Galactic objects, $\sim 4$% are already known X-ray or gamma ray emitters whose nature is still to be determined. Figure 7 shows the distribution of all the sources in our catalogue, colour-coded according to the object class, with the size of the symbol proportional to the 14–150 keV flux (for those sources not detected in the 14–150 keV band the flux in the widest band of detection has been extrapolated to the 14–150 keV range using the BAT Crab spectrum).

We have compared this distribution with the third ISGRI catalogue (Bird et al., 2007). The results are plotted in Figure 8. We find a dramatic improvement in the detection of extragalactic objects, both in the nearby Universe (normal galaxies, LINERs) and at higher distances (Seyfert galaxies, QSO, clusters of galaxies). As expected from the sky coverage achieved by the BAT survey data (Figure 5), most of our identified sources have a flux below $1\times {10}^{-10}$ erg s${}^{-1}$ cm${}^{-2}$ and are located outside the Galactic plane. We also detect many Galactic sources that are not included in the ISGRI catalogue, most of which are cataclysmic variables and X-ray binaries. This can be explained in part with the different pointing strategy of the two instruments. Hovewer, Figure 2 shows that, although most of our newly identified sources (red triangles) are above the Galactic plane, where the ISGRI exposure is low, we also detect a few sources on the Galactic plane most of which we identify as X-ray binaries (1E 1743.1–2852, GRO 1750–27, SAX J1810.8–2609 and XTE J1856+053). We have verified that their detections are due to a transient intense emission observed in the large FoV of BAT.

We detect emission from 18 clusters of galaxies. We verified that for 17 of them the spectral distribution in the 14–150 keV band is consistent with the tail of a thermal emission with kT $\sim 10$ keV without evidence for the presence of a hard non-thermal emission. Only for Abell 2142 we find evidence for a power law component that could be ascribed to the AGN content of the cluster.

The catalogue contains 519 extragalactic objects. Figure 9 shows the distribution of the redshift within our sample for the main classes of extragalactic objects. Most of the emission-line AGNs are located at $z<0.1$, but we also detected a few Seyfert 1 galaxies at larger redshift (up to $\sim 0.29$). Seyfert 2 galaxies are detected up to $z\sim 0.4$. Blazars are detected up to $z\sim 3.7$, and QSOs are detected up to $z\sim 2.4$.

We verified the completeness of our sample of 366 emission line galaxies (i.e. the significance limit down to which we are including in the sample all objects above a given flux limit) using the $V/V_{Max}$ test (Schmidt, 1968; Huchra & Sargent, 1973). This method was developed to test the evolution of complete samples of objects, but can be also used to test the completeness of non-evolving samples. For each source, $V$ is the volume enclosed by the object distance, while $V_{Max}$ is the volume corresponding to the maximum distance where the object could be still revealed in the survey (and thus depends on the limiting flux in the direction of the object). In case of no evolution the expected value of $<V/V_{Max}>$, averaged over the entire sample, is 0.5. We assume the hypothesis of no evolution and uniform distribution in the local Universe. For each source in the sample, and for each significance level tested for completeness (${\sigma }_T$), we compute the quantity $V/V_{Max}$ as $\left[F/{\sigma }_T\Delta F\right){]}^{-3/2}$, where $F$ is the flux of the source and $\Delta F$ its 1 standard deviation uncertainty. $<V/V_{Max}>$ is obtained averaging $V/V_{Max}$ over the number N of all sources in the sample detected with a significance higher than ${\sigma }_T$, and its error is $1/12N$. Figure 10 shows the results of this test: the distribution becomes constant at $S/N\gtrsim 4.5\sigma$, with a mean value of $0.497\pm 0.007$, consistent with the expected value of 0.5. Thus we can confidently assume that our sample is complete down to our adopted significance threshold of $4.8\sigma$.

The $\log \left(N\right)-\log \left(S\right)$ distribution was evaluated by summing the contribution of all the detected sources firmly identified with extragalactic objects (Table 2) and all the unidentified detections. We selected only sources with $|b|>5^{\circ }$: Figure 2 (orange squares) shows that the detection distribution is uniform above this Galactic latitude limit. The cumulative distribution is weighted by the area in which these sources could have been detected. The following formula has been applied:

In order to avoid the presence of systematic errors in the determination of the $\log \left(N\right)-\log \left(S\right)$ arising because of spurious source detections and to the large relative uncertainty on the sky coverage at the lower end of the flux scale, we limited the construction of the $\log \left(N\right)-\log \left(S\right)$ to fluxes greater than $\sim 1.5\times {10}^{-11}$ erg cm${}^{-2}$ s${}^{-1}$. The resulting $\log \left(N\right)-\log \left(S\right)$ distribution contains 330 sources ( 14 unidentified) and covers a flux range up to $3\times {10}^{-10}$ erg s${}^{-1}$ cm${}^{-2}$.

We applied a linear least-square fit to derive the slope of the $\log \left(N\right)-\log \left(S\right)$ distribution assuming a power law in the form $N(>S)=K\times (S/S_0{)}^{-\alpha }$, where $S_0$ is set to $1\times {10}^{-11}$ erg cm${}^{-2}$ s${}^{-1}$. The fit gives a value of $\alpha =1.56\pm 0.06$ and a normalization of $570\pm 24$ sources with flux greater than ${10}^{-11}$ erg cm${}^{-2}$ s${}^{-1}$, corresponding to a density of $(1.38\pm 0.06)\times {10}^{-2}$ deg ${}^{-2}$. The single power-law model is found to give an acceptable description of the data (${\chi }^2=0.65$; 31 dof) with a slope consistent with an Euclidean distribution.

The presence of spurious detections in the sample of unidentified sources could introduce a systematic effect both in the slope and in the normalization of the $\log \left(N\right)-\log \left(S\right)$. We expect between 23 and 69 spurious detections due to statistical fluctuations (see Sect.4.2), that correspond to a percentage between $\sim 11$ and $\sim 33$ % in the sample of the $\sim 208$ unidentified sources. This means that 2-5 unidentified sources among those used in the fit of the $\log \left(N\right)-\log \left(S\right)$ could be spurious.We have checked that their contribution does not introduce any significant systematics in the best fit values.

The integrated flux is $\sim 4.5\times {10}^{-13}$ erg cm${}^{-2}$ s${}^{-1}$ deg${}^{-2}$ corresponding to $\sim$1.4% of the intensity of the X-ray background in the 14–170 keV energy band as measured by HEAO-1 (Gruber et al., 1999).

We have compared this $\log \left(N\right)-\log \left(S\right)$ law with the one derived from the INTEGRAL data (Krivonos et al., 2007) in the $17-60$ keV band. To convert our $\log \left(N\right)-\log \left(S\right)$ into the $17-60$ keV band we use the Crab spectral parameters derived by the INTEGRAL analysis (Laurent et al., 2003). We find a slope of $\alpha =1.62\pm 0.08$ and a normalization of $240\pm 12$ sources with flux higher than 1 mCrab, corresponding to a density of $(5.8\pm 0.3)\times {10}^{-3}$ deg${}^{-2}$. These parameters are in full agreement with those reported by Krivonos et al. (2007).