The VIRUS-P Exploration of Nearby Galaxies (VENGA)

# The VIRUS-P Exploration of Nearby Galaxies (VENGA): Survey Design, Data Processing, and Spectral Analysis Methods

Guillermo A. Blanc1 , Tim Weinzirl2 , Mimi Song2 , Amanda Heiderman2 , Karl Gebhardt2 , Shardha Jogee2 , Neal J. Evans II2 , Remco C. E. van den Bosch3 , Rongxin Luo4 , Niv Drory5 , Maximilian Fabricius6 , David Fisher7 , Lei Hao4 , Kyle Kaplan2 , Irina Marinova2 , Nalin Vutisalchavakul2 , Peter Yoachim8
1affiliation: Observatories of the Carnegie Institution for Science, Pasadena, CA
2affiliation: Department of Astronomy, The University of Texas at Austin, Austin, TX
3affiliation: Max Planck Institute for Astronomy, Heidelberg, Germany
7affiliation: Shanghai Astronomical Observatory, Shanghai, China
4affiliation: Instituto de Astronomía, Universidad Nacional Autónoma de México, México DF, México
5affiliation: Max Planck Institute for Extraterrestrial Physics, Garching, Germany
6affiliation: Department of Astronomy, University of Maryland, College Park, MD
8affiliation: Astronomy Department, University of Washington, Seattle, WA
###### Abstract

We present the survey design, data reduction, and spectral fitting pipeline for the VIRUS-P Exploration of Nearby Galaxies (VENGA). VENGA is an integral field spectroscopic survey, which maps the disks of 30 nearby spiral galaxies. Targets span a wide range in Hubble type, star formation activity, morphology, and inclination. The VENGA data-cubes have FWHM spatial resolution, Å FWHM spectral resolution, sample the 3600Å-6800Å range, and cover large areas typically sampling galaxies out to . These data-cubes can be used to produce 2D maps of the star formation rate, dust extinction, electron density, stellar population parameters, the kinematics and chemical abundances of both stars and ionized gas, and other physical quantities derived from the fitting of the stellar spectrum and the measurement of nebular emission lines. To exemplify our methods and the quality of the data, we present the VENGA data-cube on the face-on Sc galaxy NGC 628 (a.k.a. M 74). The VENGA observations of NGC 628 are described, as well as the construction of the data-cube, our spectral fitting method, and the fitting of the stellar and ionized gas velocity fields. We also propose a new method to measure the inclination of nearly face-on systems based on the matching of the stellar and gas rotation curves using asymmetric drift corrections. VENGA will measure relevant physical parameters across different environments within these galaxies, allowing a series of studies on star formation, structure assembly, stellar populations, chemical evolution, galactic feedback, nuclear activity, and the properties of the interstellar medium in massive disk galaxies.

galaxies: spiral, kinematics and dynamics, techniques: spectroscopic, methods: data analysis
slugcomment: Draft

## 1. Introduction

In the context of CDM cosmology, the formation and evolution of galaxies takes place in the bottom of the deepest gravitational potential wells in the dark matter distribution (dark matter halos). Gas accretion into these halos and merging processes ultimately trigger star formation giving rise to galaxies (Blumenthal et al., 1984; White et al., 1988; Somerville & Primack, 1999). Although consensus has been reached concerning this picture, the details of the baryonic physics behind galaxy formation in the centers of dark matter halos are still aggressively debated. The triggering of star formation and the variables that set the star formation rate (, Kennicutt, 1998; Kennicutt & Evans, 2012; McKee & Ostriker, 2007; Leroy et al., 2008; Krumholz et al., 2009), the contribution from different types of feedback processes (AGN, supernovae, stellar radiation, e.g. Kauffmann et al., 1999; Croton et al., 2006; Thompson, 2009), as well as the impact of gas accretion from the inter-galactic medium (IGM, e.g. Dekel et al., 2009; Fumagalli et al., 2011; Davé et al., 2011; van de Voort et al., 2011), at regulating the gaseous budget, structure, chemical composition, and kinematics of the ISM, and the role that major and minor mergers as well as secular evolution processes play at shaping galaxies (Toomre & Toomre, 1972; Kormendy & Kennicutt, 2004), are currently the subjects of active research. All these processes play a major role in determining how galaxies evolve throughout cosmic time, building up their stellar mass and shaping their present day structure.

The detailed manner in which the above physical phenomena (star formation, gas accretion, feedback, interactions, and secular evolution) proceed, ultimately determines the morphology, kinematics, and chemical structure of both the ISM and stellar components of a galaxy. We can therefore study these processes by obtaining spatially resolved measurements of quantities like the , the metallicity, the stellar and ionized gas velocity and velocity dispersion, the age of the observed stellar populations, the atomic and molecular gas surface density, etc., and analyzing how they relate to each other and to the global properties of the galaxies under study. In this way, we can test current theoretical models describing the above phenomena and their impact on galaxy evolution.

Wide field optical integral field unit (IFU) spectroscopy allows the measurement of many of these quantities in nearby galaxies. Optical IFU data-cubes, in combination with multi-wavelength broad band photometry, and sub-mm and radio maps of the same galaxies, are powerful datasets to study galaxy evolution.

Integral field spectroscopy of nearby galaxies has been somewhat limited in the past, mostly due to the small field-of-view of available IFUs. During the last decade, a new generation of wide field integral field spectrographs like SAURON on the 4.2m William Herschel Telescope (Bacon et al., 2001), PPAK on the 3.5m at Calar Alto Observatory (Kelz et al., 2006), SparsePak on the WIYN 3.5m telescope (Bershady et al., 2004), and the Mitchell Spectrograph (formerly known and hereafter referred to as VIRUS-P) on the 2.7m Harlan J. Smith telescope at McDonald Observatory (Hill et al., 2008), have opened the path to study nearby systems subtending large angular diameters on the sky.

Early surveys of nearby galaxies using IFUs mostly focused on studying the kinematics and stellar populations of early type systems. These include the SAURON Survey (Bacon et al., 2001; de Zeeuw et al., 2002), and its extension, the Atlas3D Survey (Cappellari et al., 2011) which by now have mapped hundreds of elliptical and lenticular galaxies. Wide field IFU studies of later type disk galaxies include the work of Ganda et al. (2006) who used SAURON to observe the central regions of 18 nearby late-type spirals, the Disk Mass Project (Bershady et al., 2010) which used SparsePak and PPAK to measure H velocity fields for 146 face-on spirals, and stellar kinematics for a subset of 46 objects, with the aim of constraining the distribution of stellar mass and dark matter in disk galaxies, and the PPAK IFS Nearby Galaxies Survey (PINGS, Rosales-Ortega et al., 2010), which maps the disks of 17 nearby disk galaxies. The PPAK IFU is currently being used to conduct the Calar Alto Legacy Integral Field Area survey (CALIFA, Sanchez et al., 2011b), a massive project mapping galaxies of all Hubble types, selected based on their angular size and distance (in order for them to fill the PPAK field-of-view). In the future the MANGA SDSS IV project will produce optical datacubes for tens of thousands of galaxies. A number of IFU studies of galaxies have been conducted at high redshift (), where target sizes are well suited to the small fields of view of IFUs in 10m class telescopes (e.g. Genzel et al., 2006; Förster Schreiber et al., 2006; Law et al., 2007; Wright et al., 2007; Lemoine-Busserolle et al., 2010).

In this work, we present the VIRUS-P Exploration of Nearby Galaxies (VENGA), an IFU survey of 30 nearby spirals which uses VIRUS-P (currently the IFU with the largest field-of-view in the world) to spectroscopically map large portions of the disks of these objects. The sample spans a wide range in Hubble types, s, and morphologies, including galaxies with classical and pseudo-bulges as well as barred and unbarred objects. Ancillary multi-wavelength data exist for many of the targets. This includes HST optical and near-IR imaging with ACS and NICMOS, Spitzer mid-IR and far-IR imaging with IRAC and MIPS, near-UV and far-UV imaging from GALEX, and far-IR HERSCHEL data. Also CO and HI 21cm maps are available for most of the sample. VENGA’s potential lies in a combination of wide spatial and spectral coverage, good spatial resolution, and depth. The large field-of-view of the IFU allows us to typically sample each system out to by tiling only a few VIRUS-P pointings. The size of the VIRUS-P optical fibers ( in diameter) samples physical scales of 300 pc at the median distance of our targets and makes our observations very sensitive to low-surface brightness emission. We obtain spectra with a median per fiber per spectral resolution element which allows good measurements of stellar absorption and nebular emission line spectral features at the native spatial resolution of the instrument over most of the data-cube for every galaxy.

In comparison to other IFU surveys of spiral galaxies VENGA is factors of a few deeper than surveys like PINGS and CALIFA while having a similar wavelength coverage and a factor fo two larger spatial resolution. As mentioned above a key advantage of the VENGA sample is the existance of extensive multi-wavelength ancillary data for most of these very nearby galaxies. In particular the far-IR, mm, and radio data is essential for studying the relation between stars and the ISM and the process of star formation. While CALIFA and in the future MANGA will produce datacubes for hundreds and tens of thousands of spiral galaxies, only few of those targets will have such extensive ancillary datasets. In that sense the VENGA data can provide a good base to interpret results from larger but shallower surveys of more distant galaxies.

In the near future, VENGA will also include a high spectral resolution component consisting of IFU mapping at of the central regions of a subset of the sample using the VIRUS-W spectrograph (Fabricius et al., 2008). The high resolution VIRUS-W observations will complement the broad wavelength range VIRUS-P observations and will provide a more detailed view of the kinematics of gas and stars in the central regions of spiral galaxies. This component of the survey will be presented in a future publication. In this work we limit ourselves to discussing the VIRUS-P data.

The VENGA data are being used to conduct an extensive set of studies on star-formation, structure assembly, stellar populations, gas and stellar dynamics, chemical evolution, ISM structure, and galactic feedback. The data will also provide an excellent local universe control sample for IFU studies of high-z galaxies. The survey is designed with the following science goals:

• Study the process of star-formation on galactic scales (Kennicutt & Evans, 2012, and references therein), including the correlations between the and the star formation efficiency () with other parameters like gas and stellar surface density, metallicity, galaxy dynamics, and stellar populations. The ultimate goal is to understand what are the relevant parameters setting the across different environments within galaxies (see Blanc et al., 2009, 2012).

• Investigate the assembly of central spheroidal stellar components in disk galaxies (Kormendy & Kennicutt, 2004, and references therein). This includes characterizing the dynamics, stellar populations, and chemical abundances of classical and pseudo-bulges in spiral galaxies, in order to constrain their star-formation history and understand their origin. The goal is to distinguish between different evolutionary paths that might give rise to these structures (secular evolution, galaxy-galaxy interactions, etc.).

• Provide detailed observations of radial gas inflow in the central parts of disk galaxies, induced by barred and oval potentials (Kormendy & Kennicutt, 2004, and references therein). This includes studying the velocity field of ionized gas and stars in the regions influenced by the presence of bars and ovals, and also the effects of induced gas condensation and shocks in the local star formation efficiency.

• Construct two-dimensional maps of the stellar and gas phase metallicity of spiral galaxies (e.g. Moustakas et al., 2010; Rosales-Ortega et al., 2011). These maps will allow the study of radial abundance gradients measured with exquisite detail, the dispersion in abundances as a function of galactocentric radius, and deviations from axisymmetry in the two dimensional metallicity distribution. Comparing these measurements to chemical evolution models will help constrain the chemical enrichment, gas accretion, and star-formation history of disk galaxies in the local universe.

• Use nebular emission line diagnostics to study the nature of the ionizing sources influencing different parts of the disks of spirals (e.g. Kewley et al., 2001; Ho, 2008; Haffner et al., 2009, and references therein). This includes the study of low luminosity active galactic nuclei (LLAGN), and their impact on the physical conditions of gas in the central parts of galaxies, and the study of the structure, metallicity, and kinematics of the diffuse ionized gas (DIG) in the ISM. In particular, for the two edge-on systems in the sample, we will also be able to constrain the properties of the DIG as a function of distance above the mid-plane. All these studies will provide insight about different feedback processes at play in star-forming disk galaxies, and the transport of UV photons in the multi-phase ISM.

• Study the distribution of stellar mass and dark matter in spiral galaxies, by using a combination of the VENGA gas and stellar velocity fields and constraints on the ratio from stellar populations (e.g. Bershady et al., 2010; Adams et al., 2012). The data should allow us, in principle, to set constraints on the shape of the dark matter halo density profile on these systems, which we can use to test the predictions of CDM models. Of particular importance for these measurements is the high spectral resolution VIRUS-W component of the survey.

Throughout this paper we use the VENGA data on the face-on SA(s)c galaxy NGC 628 to exemplify our methodology. This nearby grand-design spiral galaxy has been extensively studied in the past and IFU spectroscopy has been obtained in its central region by Ganda et al. (2006) and over a larger area than presented here, although to a shallower depth, by the PINGS survey (Rosales-Ortega et al., 2011; Sanchez et al., 2011b). In this work we limit ourselves to presenting the methods used to observe, reduce, and analyze the VENGA IFU data, and we postpone the presentation of scientific results on NGC 628 to separate publications, including an accompanying paper studying the radial profile of the CO to H conversion factor () and its relation to the physical conditions across the disk of the galaxy (Blanc et al., 2012). We also expect to present and make public the full VENGA dataset in a future publication once the processing and analysis of the whole survey is complete.

In §2 we describe the survey design, including a description of the VENGA sample and the observing strategy adopted to conduct the survey. We present the VIRUS-P observations of NGC 628 in §3. The data processing pipeline and construction of the final VENGA data products (i.e. reduced and calibrated spectral data-cubes) is presented in §4, followed by a description of the techniques used to fit the spectra, measure stellar and gas kinematics, and extract emission line fluxes (§5). In §6 we fit the stellar and ionized gas velocity fields of NGC 628 using a harmonic decomposition technique and introduce a new method to measure the inclination of nearly face-on systems based on the matching of the stellar and gas rotation curves using asymmetric drift corrections. Finally, we present our conclusions in §7. Throughout the paper we adopt a standard set of CDM cosmological parameters, km sMpc, , and (Dunkley et al., 2009).

## 2. Survey Design

In this section we present and characterize the VENGA sample and we discuss the physical properties of the target galaxies. We also describe the observing strategy and the instrumental configurations used to execute the survey.

### 2.1. The VENGA Sample

Table 1 presents the galaxies observed in VENGA and lists their main properties. Targets are chosen to span a wide range in Hubble types, from S0 to Sd, a wide range in inclinations from face-on to edge-on systems, and they include both barred and unbarred objects. The sample also spans a wide range in right ascension in order to allow observations to be carried out throughout the whole year, and all objects have declinations to make them accessible from McDonald Observatory. Figure 1 presents Digitized Sky Survey (DSS222The Digitized Sky Surveys were produced at the Space Telescope Science Institute under U.S. Government grant NAG W-2166. The images of these surveys are based on photographic data obtained using the Oschin Schmidt Telescope on Palomar Mountain and the UK Schmidt Telescope. The plates were processed into the present compressed digital form with the permission of these institutions. ) cutouts for all the galaxies in VENGA. Overlaid are the VIRUS-P pointings obtained on each galaxy. While VENGA is designed to map galaxies out to , for NGC 3198, NGC 4569, NGC 4826, NGC 5055, and NGC 7731, only a central pointing was observed due to observing time constraints.

Since one of the goals of VENGA is to study the origin and properties of stellar spheroids in the inner parts of disk galaxies, we included objects showing both classical bulges and pseudo-bulges (Kormendy & Kennicutt, 2004, and references therein). To distinguish between these two types of stellar structures we adopt a criterion based on the Sérsic index of the spheroidal component (). Following the results of Fisher & Drory (2008) we adopt a limit of . We consider classical bulges those with and pseudo-bulges those with with . Table 2 presents the bulge-to-total light fractions (B/T) and values for 18 of the 30 VENGA galaxies taken from Dong & De Robertis (2006), Fisher & Drory (2008), and Weinzirl et al. (2009). Of the galaxies for which we found bulge Sérsic index measurements in the literature, 50% are classified as classical bulges and 50% as pseudo-bulges using the criterion.

In order to understand how well the galaxies in our sample represent the overall population of galaxies in the local universe, we compare their stellar mass () and distributions to that of galaxies at from the Sloan Digital Sky Survey (SDSS, York et al., 2000) MPA/JHU DR7 catalog of star formation rates (Brinchmann et al., 2004). For the VENGA galaxies, we estimate from their -band luminosity by assuming a mass-to-light ratio of (de Jong, 1996). The -band luminosities are computed using the distances reported in Table 1 and the total -band apparent magnitudes from the 2MASS Large Galaxy Atlas (LGA, Jarrett et al., 2003) except for NGC 1042, NGC 3147, NGC 3949, NGC 5981, NGC 7479, and NGC 7331 which are not included in the LGA so their magnitudes are taken from the 2MASS Extended Source Catalog (Jarrett et al., 2000). We do not correct the luminosity for dust extinction but we expect this effect to be small (10% in the -band).

We were able to find integrated measurements in the literature for 24 of the 30 galaxies in the VENGA sample. These are taken from Lee et al. (2009), Kennicutt et al. (2003), and Thilker et al. (2007) in that order of preference when multiple measurements are found. The stellar masses and s of the VENGA galaxies are reported in Table 3. Figure 2 shows the VENGA and SDSS galaxies on the versus plane. Our sample spans a range in from 0.2 to 39 M yr, and is distributed in this parameter similarly to the star forming SDSS galaxies. In term of stellar mass, the VENGA galaxies span a range between M and M, but with 93% (28/30) of the sample having M. By comparing the stellar mass distribution to that of the SDSS star forming galaxies it is evident that our sample is biased towards the high-mass end of the local star forming population. Figure 2 shows that our targets fall both on and below the main sequence of star forming galaxies, so starburst systems are not present in the sample. The VIRUS-P Investigation of the Extreme Environments of Starbursts (VIXENS) project is conducting a similar study to VENGA but on a sample of 15 interacting/starburst galaxies in the local universe (Heiderman, 2012). VENGA is primarily a survey of massive spiral galaxies. Dwarf galaxies, early type galaxies, and starburst are not well represented in the sample.

Finally, it is important to characterize the spatial resolution we can achieve with VIRUS-P at the distances of our targets. Table 1 reports the physical scale in pc corresponding to one arcsecond at the distance of each galaxy. The IFU fibers subtend a diameter on sky which corresponds to a spatial resolution between 80 pc for the closest galaxy (NGC 6503) and 1020 pc for the farthest (NGC 5981). As will be described in §4.7 the PSF of the final data-cubes is given by the convolution of the native instrumental resolution (set by the fiber size) with the seeing and a gaussian weighting filter used to combine different frames at different dither positions. This translates into an effective PSF FWHM of in the final VENGA data-cubes which corresponds to a range in spatial resolution of 109 pc - 1.35 kpc, and a median resolution of 383 pc. Figure 3 presents a histogram of the physical scale in pc of the VIRUS-P native fiber size (black) and the final data-cube PSF FWHM (red) for our targets.

### 2.2. Observing Strategy

The VIRUS-P IFU is a square array of 246 optical fibers (each in diameter) which samples a field-of-view (FOV) with a 1/3 filling factor. Three dithers provide full coverage of the FOV. The instrument images the spectra of the 246 fibers on a 2k2k Fairchild Instruments charged-coupled device (CCD) with 15 m pixels. The CCD electronics deliver 3.6-4.3 e read-noise depending on the read-out mode used. Fiber spectra have an approximately gaussian spatial profile of 5 pixels FWHM, and are stacked vertically on the CCD at approximately 8 pixels apart from each other, minimizing cross-talk between fibers.

For each VIRUS-P pointing we observe 3 dithers at relative positions , , and from the origin to ensure full coverage of the FOV. Therefore in each pointing we obtain spectra for 738 independent regions. Depending on the angular size of the targets we observe up to three pointings on each galaxy providing full coverage of the central part of the galaxies and a sampling of the disk of most targets out to (see Figure 1 and last column of Table 1). Overall the VENGA survey consists of 60 individual pointings composed of 3 dithers each, amounting for spectra of independent regions (typically a few 100 pc in diameter) across the disks of the 30 galaxies in the sample.

The spectral range of VIRUS-P can be adjusted within the 3600-6800 Å window. The instrument has a set of volume phase holographic gratings which provide different spectral resolutions and wavelength coverages. For VENGA we use the lowest resolution grating (VP1) which provides a spectral resolution of Å FWHM and coverage over a 2200 Å wide spectral window . We observe each galaxy in a blue setup (3600-5800 Å) and a red setup (4600-6800 Å), obtaining full spectral coverage in the 3600-6800 Å range and doubling the effective exposure time in the overlap region (4600-5800 Å). All the data are taken with binning, which translates into a spectral dispersion of Å pixel, except for some early observations of the central pointing of NGC 5194 which were taken using binning in the spectral direction (Blanc et al., 2009).

In terms of depth, the goal of VENGA is to obtain spectra that reaches a median in continuum per spectral resolution element (FWHM) per fiber across each galaxy. For most scientific applications this high S/N per fiber requirement prevents us from having to bin our data over many spatial resolution elements therefore ensuring good spatial resolution throughout most of the maps. Exposure times for different galaxies were scaled using their effective -band surface brightness taken from the RC3 catalog (de Vaucouleurs et al., 1991, Table 1) and typically range from 45 min to 3 hr per dither. The three dither positions and two wavelength setups used imply effective exposure times ranging from 4.5 hr to 18 hr per pointing.

## 3. Observations

The VENGA survey is still in the phase of data acquisition. Observations of all targets in the red spectral setup started in April 2008 and were completed in July 2010. Blue setup observations started in September 2010 and we expect them to be completed during 2013. Table 4 lists all the observing runs we have conducted as part of VENGA, the instrumental setup used, the number of nights observed, and the galaxies for which data were obtained.

As mentioned above the typical exposure times for each dither range from 45 min to 3 hr, typically divided in shorter 15 to 25 min exposures. When conditions are not photometric we increase the exposure times to ensure reaching the desired depth. Because of the large angular diameter of our targets, during most observations the VIRUS-P IFU never samples regions of blank sky. Therefore, off source sky exposures are necessary to measure and subtract the sky spectrum from the science data. We obtain 5 min sky frames bracketing each science exposure. The off-source frames are taken 30’ north of each galaxy in fields that have been confirmed not to contain extended sources.

Bias frames, arc lamps, and twilight flats are obtained at the beginning and end of each night. For the red setup we use a combination of Ne+Cd comparison lamps and for the blue setup we use Hg+Cd. These combinations of lamps provide a good set of strong lines over the full spectral range of each setup allowing a good wavelength calibration with minimal extrapolation towards the CCD edges.

During most nights we obtain data for one or two spectro-photometric standard stars using the six-position fine dithering pattern presented in Blanc et al. (2009). As described in §4.5 and §4.6 standard stars are used to perform the relative flux calibration while the absolute flux level is calibrated against broad-band images. During some observing runs the spectra of 1 to 3 out of the 246 fibers fell off the CCD due to camera and grating alignment problems. This translates in a lack of spectra for a few fibers in the corner of the field-of-view which does not affect the data significantly.

### 3.1. NGC 628 Data

In this paper we present the VENGA data over 3 VIRUS-P pointings on the face-on Sc galaxy NGC 628. A summary of the data are provided in Table 5. Observing conditions were variable between different runs and within different nights during the same observing run, ranging from photometric to partly cloudy conditions with average atmospheric transparency down to 60%. The seeing (as measured from the guide star in the co-focal guider camera of the instrument) ranged between and (FWHM) with a median of .

Table 5 presents a summary of the NGC 628 VENGA data after rejecting 12 out of 207 frames (6%) which are affected by pointing errors or catastrophic sky subtraction problems (see §4.4 and §4.6). For each dither in each pointing on the galaxy we list the total on-source exposure time, the number of frames, the average seeing of the frames, and the mean atmospheric transparency (as measured in §4.6). Overall we obtained 84.2 hours of exposure on NGC 628 which translates into an extremely deep spectral data-cube for this galaxy. The VENGA data on NGC 628 is roughly a factor of two deeper than for the typical target in VENGA.

## 4. Data Reduction and Calibration

Data reduction is performed using the VACCINE pipeline (Adams et al., 2011) in combination with a series of custom built IDL routines. In this section we describe the data processing including the flat-fielding, wavelength calibration, and sky subtraction of individual science frames, and their flux calibration (both in the relative, i.e. across wavelength, and absolute sense). We also discuss astrometric corrections applied to the data. Both the astrometry and absolute flux calibration are based on the comparison of reconstructed broad-band images from the VIRUS-P IFU spectra and archival broad-band images of the galaxies. Finally we describe the method used to combine individual frames taken in different wavelength setups and at different positions in order to create the final data-cubes and row-stacked-spectra (RSS) files for the VENGA galaxies. At each step in the data reduction VACCINE and our set of external IDL routines propagate a properly calculated error frame which is associated with each science frame and used to compute the uncertainty in the final spectra.

Throughout this section we use the NGC 628 VENGA data to exemplify the results of different procedures. We describe processing steps in the order in which they are applied to the data.

### 4.1. Basic CCD Processing, Cosmic Ray Rejection, and Fiber Tracing

All individual frames (bias, flats, arcs, sky, and science) are overscan subtracted. We combine all the overscan subtracted bias files for each observing run (usually ) to create an image of any residual bias structure which is subtracted from all the flat, arc, sky, and science frames.

We use the LA-Cosmic laplacian cosmic ray identification algorithm of van Dokkum (2001) to identify and mask cosmic rays in the science images. We tune the algorithm to be robust enough to identify most cosmic rays in the science frames while ensuring that real emission lines are not masked. Any residual cosmic rays not identified in this pass are removed from the data during the combination of multiple frames (§4.6).

Twilight flats are used to trace the spectrum of each fiber on the CCD. VIRUS-P is mounted on a gimbal attached to the broken Cassegrain focus of the 2.7m telescope. The gimbal keeps the spectrograph at a constant gravity vector, making flexure effects on the optical path of the instrument negligible. Thanks to this, with VIRUS-P there is no need to obtain calibrations at the same time and telescope position of the science data. We have observed shifts in the positions of fibers on the CCD (at the 0.1 pixel level) when large changes in temperature occur. VACCINE corrects for these small offsets during the flat-fielding stage to properly remove the spatial PSF of each fiber from the 2D spectra (§4.3). To minimize the magnitude of these temperature induce offsets we use the set of twilight-flats which is closest in temperature to the average temperature at which the science data are taken for both tracing and flat-fielding. Most of the time this means the twilight-flats taken at dawn are used.

We extract the 2D spectrum of each fiber in the science, sky, arc, and flat frames using a 5 pixel aperture centered around the pixel containing the centroid of the fiber’s spatial profile. Using a discrete pixel instead of a fractional pixel aperture centered on the trace centroid itself avoids having to re-sample the data and conserves the noise properties of individual pixels. Using a fixed aperture that matches the FWHM of the fiber spatial profile implies that we recover 76% of the total flux passing through the fiber and makes the effects of neighboring fiber cross-talk negligible. We prefer to adopt this approach instead of a more sophisticated method to recover the flux in the wings of the fiber spatial profile (e.g. Gaussian Suppression, Sánchez, 2006) as the potential % improvement in S/N that could be gained in the case of perfect deblending and extraction is hampered by the systematic flat-fielding uncertainty introduced by the correction of temperature induced offsets in the edges of the fiber profile.

At this stage in the reduction VACCINE constructs a formal error map which accounts for both read-noise and Poisson uncertainty for each pixel in the 2D spectrum of each fiber. These maps are properly propagated throughout the rest of the reduction (assuming gaussian uncertainties) and end up providing the weights used when combining and collapsing spectra from different frames, as well as the flux error in the final data-cube.

### 4.2. Wavelength Calibration and Characterization of the Instrumental Spectral Resolution

Arc lamp frames are combined to produce a master arc for each night. VACCINE is typically able to match and fit emission lines in the blue setup lamps (Hg+Cd) and lines in the red setup lamps (Ne+Cd). We fit the wavelength solution for each fiber independently using a 4th order polynomial. Residuals in the wavelength solution show an r.m.s. dispersion of Å, or a tenth of a pixel ( km s at 5000Å).

We also use the emission lines in the master arc frame to characterize the spectral resolution as a function of wavelength for each fiber. We measure the FWHM of non-blended arc lines by performing single gaussian fits. By fitting a second order polynomial to the measured FWHM values across the spectral direction for each fiber we create a robust map of the instrumental spectral resolution (FWHM) of each fiber as a function of wavelength. Good knowledge of the resolution is essential at the time of fitting galaxy spectra with linear combinations of empirical or synthetic templates which must be convolved to the same resolution of the data in order to extract meaningful line-of-sight velocity distributions (LOSVDs) from the fits.

The VIRUS-P instrumental resolution is observed to change smoothly as a function of position on the detector, with values ranging from 4.6Å to 6.1Å FWHM. No variation in the instrumental spectral resolution is observed between observing runs. In the final data-cube of NGC 628 the median instrumental resolution in velocity units is km s.

### 4.3. Flat Fielding

The flat-fielding process in VACCINE is used to divide out three different effects from the data: (1) the relative fiber-to-fiber throughput, (2) the profile of the fiber PSF on the detector across the spatial direction, and (3) the CCD pixel-to-pixel variations in quantum efficiency. A master twilight flat is created for each night by combining the set of flat frames closer in temperature to the average throughout the night. First, VACCINE removes the signal from the solar spectrum from the master twilight flat. For each fiber, this is achieved by fitting a bspline to the twilight spectra of a set of 60 neighboring fibers on the chip (which share a similar spectral resolution) to create a template solar spectrum (which also includes the spectral response of the instrument), and then normalizing the spectrum of the fiber of interest by this combined high S/N template (see Adams et al., 2011). Since each fiber provides an independent wavelength sampling of the twilight spectrum, combining data from a large set of neighboring fibers effectively yields a sub-pixel sampled spectrum which after being fit by the bspline can be evaluated at the exact wavelength scale of the fiber of interest.

From the resulting normalized flat, VACCINE creates a “fiber profile” flat by running a median smoothing kernel across the spectral direction. This new frame contains only the relative fiber-to-fiber throughput and the fiber PSF spatial profile. Dividing the normalized flat by this smoothed version yields a pixel-to-pixel flat that is applied to the data.

As mentioned in §4.1, small (sub-pixel) temperature induced offsets in the fiber positions on the CCD are sometimes present in the data. This can translate into undesired residuals when removing the spatial profile of the fibers if the data are divided by a flat-field that is offset in the spatial direction. Residuals can be particularly large at the edges of fibers, where the data values are divided by smaller numbers than at the fiber core. These offsets must be corrected for, in order to remove the fiber PSF across the spatial direction. To do so, VACCINE traces each fiber in the science frame (after running a 30 pixel boxcar filter across the spectral direction to ensure a high S/N measurement of the fiber centroid), and computes an offset with respect to the same fiber centroid in the “fiber profile” flat. These offsets are used to resample the smoothed “fiber profile” flat using an optimal sinc-interpolation method in order to align it with the data. We divide the science and sky frames by this resampled smoothed flat frame, therefore removing the fiber spatial profile from the data.

### 4.4. Sky Subtraction

Sky spectra are measured by combining information from the two off-source sky exposures taken before and after each science frame. In Blanc et al. (2009) we simply averaged the before and after off-source frames to create the sky frame used for background subtraction. While this method worked well on the NGC 5194 data presented there, those observations were taken far from twilight and under very stable and dark conditions. We find that when conditions are not optimal (e.g. close to twilight, when clouds are present, or near moon-rise or moon-set) the sky brightness can change non-linearly with time, making the simple averaging of bracketing sky frames insufficient to produce an adequate sky subtraction. We adopt a more sophisticated method to estimate and subtract the sky spectrum from our data, which makes use of the temporal information we can extract regarding the variability of the sky brightness as a function of wavelength, from all the sky frames obtained throughout a single night.

As an example, Figure 4 shows the raw (i.e. not flux calibrated) sky spectrum measured from 13 off source sky frames taken during the night of November 7th 2008 using the red VIRUS-P setup. The spectra are color coded by UT time, with purple at the beginning of the night and red at the end of the night. We adopt the UT time corresponding to the middle of each exposure. The elevated brightness and blue color of the spectrum at the beginning of the night is due to the first quarter moon. Moonset at McDonald Observatory on that date occurred at 8.47 hr UT and can be clearly seen as a sharp drop in the sky brightness, particularly at blue wavelengths. For this night, the darkest skies occurred between 9 hr and 10 hr UT. These are followed by a monotonous increase in sky brightness which is steeper at redder wavelengths. This brightening and reddening is due to both the approachment of twilight and the fact that the observations were being done at increasing airmass. Our sky subtraction method uses all this information regarding the wavelength and time dependance of the sky brightness throughout each night to correct the two bracketing off-source sky exposures so they match the sky spectrum at the time the science frame is taken.

To trace these changes we average the spectra of all fibers in each individual sky frame and then divide this average sky spectrum into 500 wavelength bins (each corresponding roughly to a spectral resolution element). On a night-by-night basis, we use the time stamps of all sky frames to construct a nightly “light curve” of the night sky surface brightness at the central wavelength of each of these 500 bins. Figure 5 shows the relative change in sky brightness across the same night presented in Figure 4, for three different wavelength bins near the blue end, middle, and red end of the spectrum (blue, green, and red respectively). Measurements for individual sky frames are shown as filled circles. For reference, the black open diamonds show the change in bolometric brightness (i.e. in the total flux integrated across the whole spectrum). The trends described in the last paragraph are clearly seen. At the beginning of the night the sky brightness falls more steeply in the blue than in the red as the moon sets, and rises faster in the red than in the blue as we approach twilight at the end of the night. Vertical dashed lines mark the beginning and end of observations of the same galaxy. The discontinuity in the sky brightness at these times is expected since the telescope is pointed in a different direction. We refer to each of these sections of the night as “observing blocks”.

Within each individual observing block, we fit the temporal evolution of the sky brightness in each wavelength bin using a cubic spline (color solid curves in Figure 5). The best-fit splines allow us to evaluate the overall spectral shape of the sky emission at any arbitrary UT time within an observing block. This allows us to calculate a wavelength dependent normalization curve by which the two bracketing sky frames must be multiplied in order to reconstruct the sky spectrum at the exact UT time of the science exposure. Since the normalization factors computed in the 500 wavelength bins are inherently noisy, we fit them as a function of wavelength using a fifth order polynomial. This allows us to multiply the sky frames by a smooth function of wavelength containing the correction without introducing further noise into the observed sky spectrum. We apply this procedure to correct the before and after sky frames to the UT time of each science frame, and then average the two corrected frames to create a single sky background file associated with each science exposure. Sky subtraction is performed by VACCINE using this composite corrected sky frame.

Once this final sky frame is available, the method used by VACCINE to subtract the sky spectrum is analog to the bspline algorithm used to remove the solar spectrum from the twilight flats (see §4.3). Briefly, for each fiber in the science exposure the sky spectra of a set of neighboring fibers in the background frame is simultaneously fit using a bspline and is then subtracted from the science fiber spectrum after scaling for the difference in exposure time between science and sky frames. As mentioned above, this procedure greatly benefits from the sub-pixel sampling of the sky obtained by combining information from different fibers having slightly different wavelength solutions.

The quality of the sky subtraction in VENGA is excellent. We typically see sky subtraction residuals that are fully consistent with Poisson plus read-noise uncertainties. Larger systematic residuals usually appear at the wavelengths of the 4 brightest sky emission lines in our wavelength range. These resiudals are caused by the fast time variability of these spectral features, which is independent of the variability of the sky continuum and broad emission bands which dominate our corrections. These bright sky lines are masked during the analysis of the science data. Rarely (less than 4% of the frames in the case of NGC 628), when observations are taken under extremely bad observing conditions (usually combinations of clouds and moon, or clouds and proximity to twilight), obvious residuals in the sky subtraction can be observed in the sky-subtracted science exposures. We reject these frames from the dataset.

### 4.5. Spectrophotometric Flux Calibration

We use observations of spectrophotometric standard stars from Massey et al. (1988) and Oke (1990) to calibrate the VENGA spectra. The method used to construct sensitivity curves from the IFU observations of standard stars is described in Blanc et al. (2009). The only difference with the approach taken in that previous work is that here standard stars are only used to perform the relative flux calibration as a function of wavelength. The absolute scale of the calibration comes from a comparison to broad-band optical images of the VENGA galaxies. The absolute calibration is described in the next section.

We calculate sensitivity curves for all standard stars taken during each observing run. These curves are normalized to a common scale and averaged to create a master sensitivity curve for each run. All science frames obtained during each observing run are multiplied by these curves to convert them to units of erg s cm Å. Since the atmospheric transparency at the time of the science and standard star observations is unknown we need the absolute scaling described in the following section. The error maps for each frame are scaled accordingly to the data. By looking at the dispersion between different sensitivity curves within each month, we estimate a typical uncertainty in the relative flux calibration of %.

### 4.6. Astrometry and Absolute Flux Calibration

The pointing of VIRUS-P is done using an offset guider camera which images a field north of the IFU science field. An astrometric calibration between the two fields allows the observer to point the IFU by putting a guide star at specific pixel coordinates on the guider detector. Adams et al. (2011) found systematic offsets of the order of between the same pointings made over different observing runs. These offsets are also present in our data and must be taken into account before combining multiple frames. In order to accurately recover the astrometry of the VENGA science observations we register reconstructed broad-band images of the galaxies made from the IFU data to archival broad-band images. These comparisons are also used to calibrate the spectra in terms of absolute flux. For the NGC 628 blue and red IFU data we use the SDSS-III444SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, University of Cambridge, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University. DR8 -band and -band mosaics.

For every science exposure we integrate the spectrum of each fiber over the corresponding SDSS transmission curve ( or for blue and red setup data respectively) in order to measure the monochromatic flux at the effective wavelength of the broad-band filter. Simultaneously we convolve the SDSS image of the galaxy with a gaussian kernel to match the PSF to the seeing under which the VIRUS-P data was taken and we perform aperture photometry at the fiducial position of each fiber. We use circular apertures that match the fiber size. After correcting the VIRUS-P fluxes for atmospheric extinction at the airmass of the observations we compare them to the SDSS fluxes and fit them using the following expression:

 fSDSS=A×fVP+B (1)

where is a normalization factor recovering the absolute flux scale and recovers any residual background left from the sky subtraction process. A perfect background subtraction in both the SDSS image and the VIRUS-P spectra should translate in .

We perturb the fiducial astrometry of the VIRUS-P pointing by applying offsets in both right ascension and declination in order to minimize the of the fit. This registering process provides corrected astrometry for each science frame. Given the wealth of spatial information encoded in the relative brightness of hundreds of VIRUS-P fibers, the registering is very accurate and has a typical uncertainty of . The value of at the registered position provides the absolute scale for the flux calibration and the science frame is multiplied by this value. This ties our flux calibration to that of SDSS which has a zero-point uncertainty of 2% in the bands used here. For the 195 individual frames used to construct the NGC 628 data-cube, we measure a mean erg s cm Å with a standard deviation of erg s cm Å. This level of sky subtraction residuals correspond to less than 2% of the median continuum level in the data and this is only an upper limit since the residuals have some contribution from the error in the SDSS sky subtraction.

Figure 6 shows the astrometric offsets we measure for the three pointings on NGC 628 with respect to the fiducial dithering pattern. For each pointing the fiducial positions of a fiber on dithers 1, 2, and 3 are marked by black stars and solid red, green, and blue circles respectively. Color crosses mark the actual positions at which independent science exposures were obtained. These positions are measured using the registration method described above. The black squares and dashed color circles show the average position for all exposures in each dither.

Overall the VIRUS-P acquisition accuracy is good compared to the fiber size. We observe systematic offsets from the fiducial dithering pattern in the range -, with a mean of . This is in good agreement with the accuracy found by Adams et al. (2011). As mentioned above, once the VENGA frames are registered to the broad-band images and these offsets are corrected we estimate an astrometric uncertainty of .

When registering the data and building the final VENGA data-cubes (next section) we ignore the effects of atmospheric differential refraction (ADR). At a typical observation airmass of we expect less than of ADR from the blue to the red end of our data. Given the fiber size of VIRUS-P and the FWHM PSF of the final data-cubes (§4.7), we decide not to apply an ADR correction.

To evaluate the quality of our spectrophotometric calibration we compare the VENGA spectrum of NGC 628 to the long-slit driftscan spectrum obtained by Moustakas & Kennicutt (2006) as part of the ancillary data for the Spitzer Infrared Nearby Galaxies Survey (SINGS, Kennicutt et al., 2003). To do so, we use the final combined VENGA data-cube described in the following section. We integrate the IFU spectra over the same region sampled by the SINGS long-slit driftscan.

The comparison is shown in top panel Figure 7. We observe an 18% offset between the two spectra. This offset is produced by contamination from the wings of a bright foreground star which falls slightly outside the SINGS driftscan box, but which significantly contributes to the flux inside the box at the resolution of the VENGA data-cube. Masking the contaminated spaxels (see §6.1) brings the VENGA and SINGS spectra to agreement. Except for regions on top of strong emission and absorption lines, where residuals arising from differences in spectral resolution dominate, both spectra show less than 5% deviations from each other over 80% of the overlap spectral range, rising towards the 10% level at the blue end of the spectrum. This is well within the 10%-30% uncertainty in the absolute calibration and the 3%-4% uncertainty in relative flux calibration of the SINGS spectrum as estimated in Moustakas & Kennicutt (2006), and the 8% relative flux error in the VENGA data (derived from the dispersion between different sensitivity curves in §4.5).

To further test the quality of the VENGA flux calibration we compute broad-band monochromatic fluxes from the integrated spectrum over the full VENGA datacube and compare them to the flux measured over the same area in both the SDSS and -band images, and the SINGS and -band optical ancillary images. The SINGS images are independent from our flux calibration. As shown in the bottom panel of Figure 7 the VENGA data agrees with the flux measured in all four images within the quoted uncertainties. From these tests we conclude that the accuracy of the VENGA absolute and relative flux calibrations is good.

### 4.7. Final Combined Data-cubes and RSS Files

At this stage in the data reduction process we have a reduced, sky subtracted, wavelength and flux calibrated 2D spectrum of each fiber (and its associated 2D error spectrum) in every individual science exposure. By 2D spectrum we mean a non-collapsed spectrum of the fiber PSF on the detector, which contains no spatial information about the source, given the fact that optical fibers scramble the input light. Also, the position of each fiber on the sky is known to accuracy thanks to the registering process described in the last section.

Here we describe the methods used to extract and combine data from different exposures into a final data-cube containing a 1D spectrum at each position on the sky. We also describe the construction of our final row-stacked spectra (RSS777RSS files, in which every row contains the spectrum of a spaxel, should be distinguished from data-cubes, as they are two dimensional instead of three dimensional representations of IFU data. They must be accompanied by a position table for all spaxels in order to allow for a geometrical reconstruction of the data.) files. These multi-extension FITS888Flexible Image Transport System files are described below and contain the spectrum and error spectrum, as well as the J2000 equatorial coordinates for each spaxel in the data-cube. Also contained in the RSS file is information regarding the central wavelength and spectral instrumental resolution for every pixel in the spectra.

Data from different nights and observing runs have independent wavelength solutions. Therefore, before combining we need to re-sample all the spectra to a common wavelength grid. In VENGA we produce two versions of the same data-cube, one with a regularly spaced linear sampling of wavelength and another with a regular logarithmic sampling (i.e. spaced regularly in velocity space). The linear version has pixels spaced by 1.1Å (similar to the average dispersion in the original data), while the logarithmic data-cubes have pixels that are spaced by km s. We work with spectra in flux density units so total flux is properly conserved when re-sampling.

The reason behind producing two versions of the data is that while most users will be interested in using the linear version for many applications, the spectral fitting software used in the following section to extract stellar and gas kinematics, as well as emission line fluxes, requires input spectra that is regularly sampled in velocity space. Instead of interpolating the spectra to a linear grid for the effects of combining, and later re-interpolating the combined spectra to a logarithmic scale, we do both re-samplings directly from the original data. In this way we avoid the effects of S/N degradation associated with extra interpolations.

For each fiber in each science frame, after re-sampling the 2D spectra we have 5 pixels at any given wavelength which provide a measurement (with its associated error) of the flux density at a certain position on the sky. We then define a regularly spaced spatial grid of spaxels. The grid has a spaxel scale of chosen to roughly Nyquist sample the final data-cube PSF. For every spaxel in the grid we compute the final spectrum by combining the spectra of surrounding fibers using a Gaussian spatial filter and adopting an inverse variance weighting scheme. Therefore, the spectrum of each spaxel in the data-cube is given by

 fλ(λ)=∑i,j,kwi,j,k(λ)fi,j,kλ(λ)∑i,j,kwi,j,k(λ) (2)

where is the flux density of pixel () at wavelength of fiber in frame , and the weights are given by

 wi,j,k(λ)=1(σi,j,k(λ))2×e−d2i,j2σ2g (3)

where is the error in the flux, is the distance in arcseconds between the fiber center and the spaxel in question, and is the width of the spatial Gaussian filter used to combine the data. We use a value of which matches the fiber size to the FWHM of the Gaussian filter. The sum in Equation 2 is performed over all fibers within a maximum distance of the spaxel of interest. This distance cut is given by a 99% drop in the Gaussian filter weight. During the combination process we apply 3 clipping rejection to remove any cosmic rays that were not masked by LA-Cosmic in §4.1. The final spatial PSF of the data-cube is given by the convolution of the top-hat diameter fiber profile with the seeing ( FWHM for the NGC 628 data) and the FWHM Gaussian spatial filter used to combine the data. Figure 8 presents these three components and the product of their convolution (red solid line). The final PSF is well described by a FWHM Gaussian and is largely independent of the seeing. Direct measurement of the FWHM of bright foreground stars in the NGC 628 data-cube empirically confirms the value of .

As mentioned in §4.2, the instrumental spectral resolution at different wavelengths, for each fiber, is extracted from the arc lamps. To create a spectral resolution map for the data-cube, we combine the master arc lamp frames associated with each individual science frame in the same way as the science data (i.e. using the same weights). We then use the method described in §4.2 to create a map of the instrumental spectral resolution from this combined arc.

The final VENGA data products for each galaxy are a data-cube (used mostly for visualization purposes) and a RSS file (used for spectral fitting and analysis). The data-cube consists of a multi-extension fits file, in which each extension corresponds to an image of the galaxy at a given wavelength (sampled at either linear or logarithmic steps as described above). The data-cubes are in units of flux density (erg s cm Å).

The corresponding linear and logarithmically sampled VENGA RSS files are stored as multi-extension FITS files, and contain the following information in their different extensions:

1. Flux density spectrum for each spaxel in units of erg s cm Å

2. Error spectrum for each spaxel in units of erg s cm Å

3. Central wavelength of all pixels in the spectrum of each spaxel in units of Å.

4. Right ascension and declination of each spaxel in units of decimal degrees.

5. Instrumental spectral resolution (FWHM) as a function of wavelength for each spaxel in units of Å.

The final VENGA data-cube of NGC 628 covers an area of and samples the disk of this galaxy out to 8 kpc (). Figure 9 shows an -band image of NGC 628 reconstructed from the final VENGA data-cube. All maps presented in this paper have north pointing up and east pointing left. Black dots mark the position of each spaxel in the data-cube and the white circle on the top right corner shows the PSF FWHM. The final combined spectra was integrated over the SDSS -band transmission curve to create this map. For comparison, isophotal contours from the SDSS -band image (with the PSF degraded to ) are overlaid in black. The similarity between the two surface brightness distributions confirms that the flux calibration and astrometric correction of the individual science frames has been done properly. The spectra in the final data-cube of NGC 628 has a median in the continuum per spectral resolution element (FWHM). In the central parts of the galaxy we typically have , while the spectra in the faintest regions has . In terms of surface brightness depth, the NGC 628 data reaches a 5 detection limit for continuum at a -band surface brightness of 25.0 mag arcsec (AB). We remind the reader that the data on NGC 628 is about a factor of two deeper than for the average VENGA target.

## 5. Spectral Analysis Pipeline

In order to extract emission line fluxes, gas and stellar kinematics, and information about the stellar populations present in different parts of the galaxies, we fit the VENGA spectra using a linear combination of templates convolved with a LOSVD plus a set of Gaussian emission line profiles. To do the fitting we use the pPXF (Cappellari & Emsellem, 2004) and GANDALF (Sarzi et al., 2006) IDL routines developed for this purpose by the SAURON team. In this section we describe the fitting process and present an example fit in the NGC 628 data-cube. We also discuss how the uncertainty in the fitted parameters is calculated. In this paper we fit the stellar continuum using empirical stellar templates (§5.1). The same type of fitting can be performed using stellar population synthesis (SPS) templates to extract information about the stellar populations present in different regions within the galaxies. The SPS fitting of the VENGA galaxies will be presented in a future publication. Before fitting the spectra, the data is corrected for Galactic extinction adopting a Milky Way (MW) extinction law as parametrized by Pei (1992), and extinction values from the maps of Schlegel et al. (1998) ( mag or mag for NGC 628).

### 5.1. Stellar Kinematics

We mask the spectrum of each spaxel around regions affected by sky subtraction residuals due to bright sky lines, regions potentially affected by the nebular emission lines listed in Table 6, and the edges of each of the individual instrumental setups (red and blue). We then fit for the stellar line-of-sight velocity () and velocity dispersion () with the pPXF software, which uses the “penalized pixel” fitting technique (Cappellari & Emsellem, 2004) to fit the spectrum as a linear combination of templates convolved with an LOSVD. Although the software uses a Gauss-Hermite polynomial LOSVD, and allows for the fitting of high order terms (,), for the data presented here we only fit for the first two moments and .

The logarithmically sampled RSS files are used as input for pPXF, which requires the spectra to be regularly sampled in velocity space. We use the MILES stellar library version 9.1 (Sánchez-Blázquez et al., 2006; Falcón-Barroso et al., 2011) as a source of empirical templates. A subset of 48 stars spanning a wide range in spectral types (O through M), luminosity classes (I through V), and metallicities ([Fe/H]) is used. Also included in the subset are horizontal branch and asymptotic giant branch (AGB) stars.

Before fitting, the templates are re-sampled to the wavelength scale of the data. We match the spectral resolution of all spaxels in the VENGA data and the templates to the worst instrumental resolution at any given wavelength in the data-cube by convolving the spectra with a running Gaussian kernel with a wavelength dependent width. This translates in a spectral resolution of km s in the red edge and km s in the blue end of the spectrum. The median instrumental resolution across the convolved data-cube is km s. To convolve the templates we assume the corrected MILES library intrinsic resolution of 2.54Å (Beifiori et al., 2011).

Close inspection of fits to very high signal-to-noise spaxels in the data-cube () shows systematic residuals caused by template mismatch at the 1% level in the 5000Å-6800Å region, and rising up to 2% towards the blue end of the wavelength range. It is important to include this systematic uncertainty floor during the fitting process. Particularly for high spectra where it becomes the dominant source of discrepancy between the best fit models and the data. We assume a systematic uncertainty of 2% at 3600 Å, linearly decreasing towards 1% at 5000 Åand staying flat at this level redwards. We add this uncertainty in quadrature to the photometric errors before fitting the spectra.

In order to account for the effect of dust extinction on the shape of the continuum as well as systematic differences in the flux calibration of the data and the templates, during the minimization we fit both additive and multiplicative low order Legendre polynomials. The low order of the polynomials prevents them from introducing features on small scales of the order of the instrumental resolution. The polynomials only match the large-scale (Å) shape of the continuum in the linear combination of stellar templates and the data and they do not affect the fitting of individual spectral features.

We fit the spectrum of each spaxel individually and store the kinematic parameters (, ). We limit the wavelength range to the Mg I absorption feature (5100-5300 Å) for the purpose of extracting the stellar velocity dispersion. We do this to avoid a systematic overestimation of caused by the broad wings of Balmer absorption lines which are subject to rotation and pressure broadening. As discussed below, this effect is particularly significant in the spectra of star-forming regions which have a large contribution from A type stars. We also experimented with using other strong absorption features like Ca H+K and the G-band, finding that Mg I provides a better agreement with the published high precision measurement of the velocity dispersion profile of NGC 628 by Herrmann et al. (2008) (see §6.4) while the other features always produced systematically higher values of . Issues regarding the overestimation of when using Balmer lines, Ca H+K and the G-band have been extensively discussed in the literature (e.g. Kormendy & Illingworth, 1982; Bernardi et al., 2003; Greene & Ho, 2006). The instrumental resolution in the convolved spectra at the Mg I feature is km s.

We also perform a second fit using the full wavelength range to estimate . Our simulations show that while the best fit is biased when using the full spectrum, the best fit is not and the uncertainty in its value is reduced significantly by using the full wavelength range. After fitting, we keep the LOSVD parameters fixed over the next fitting iteration (§5.3), in which we also fit for the emission lines in the spectrum. Kinematic maps of NGC 628 are presented in §6.

### 5.2. Error Estimation for LOSVD Parameters

To estimate the uncertainty in the best-fit LOSVD parameters ( and ) we fit a series of Monte Carlo realizations of simulated spectra with different stellar velocity dispersion, signal-to-noise ratio, and combination of stellar templates. To construct the simulated synthetic spectra we start with the best-fit linear combination of stellar templates for three different regions in NGC 628 chosen to sample an old stellar population with a spectrum dominated by K giants (taken from the central part of the galaxy), a bright star forming HII region on a spiral arm, and a region showing a post-starburst spectrum dominated by A type stars. The three simulated spectra are convolved with Gaussian LOSVDs having 10, 25, 50, 100, 200, 300, and 500 km s. Gaussian noise is artificially added to the spectra creating 40 Monte Carlo realizations of each at levels per resolution element (FWHM) of 25, 50, 100, and 200.

We fit the synthetic spectra using the same methods used for the data and described in the previous section. Even though the simulated spectra do not contain emission lines we mask the same regions which we censored when fitting the science data in order to match the available spectral information. In an attempt to account for the effects of template mismatch we remove the templates used to create the synthetic spectra from the list of templates used to fit them. The large number of templates used () allows us to do this without the worry of a particular stellar type not being represented in the remaining template subset. We present results for two fits, one using the full available spectral range, and one limited to the 5100-5300 Å region around the Mg I feature.

The results of the simulation are presented in Figures 10 and 11. In Figure 10 we compare the input and recovered values for the velocity dispersion at different ratios. In Figure 11 we present the error in the recovered radial velocity as a function of for all the simulated spectra with km s (typical of spiral galaxies). Results for fits using both the full spectral range and the limited 5100Å-5300Å window are reported.

When using the full spectral range the recovered stellar velocity dispersions are overestimated by % at km s, become underestimated by % below that value, and then become largely overestimated for values of which are about a factor of 10 smaller than the instrumental resolution. In the case of the full spectral range fit this trends are almost independent of the ratio. As can be seen in the right panel of Figure 10, limiting the spectral window to the Mg I region removes most of these systematic deviations at the cost of larger random error-bars on the recovered values. Systematic deviations are still seen at low and low . Balmer lines play a significant role in introducing the systematic deviations seen in the full spectral range case as is confirmed by the fact that the effect is stronger for the “star-forming” and “post-starburst” spectrum, than it is for the “old stellar population” spectrum. No significant difference is seen on the recovered velocity dispersions for the three different types of spectra once the wavelength range is limited to the Mg I feature.

An effect of limiting the spectral window is an increase in the random error in the recovered value of . This increase is expected because of the high EW of the rejected Balmer absorption lines. The error in for each spaxel in the data-cube is computed by linear interpolation of the measured errors in the simulation to the spaxel’s and .

The radial velocity is recovered with no systematic deviations. Considering all simulated spectra with km s (typical of the disks of spiral galaxies) and at all the ratios probed, we measure mean offsets of and km s for the fits using the full spectral range and the 5100Å-5300Å window respectively. The error in the recovered radial velocity depends on as shown in Figure 11 and it is reduced by about a factor of two at the typical ratio of the data by using the full spectral range including the strong Balmer lines. The improvement is even more dramatic at low signal-to-noise (), where the Mg triplet starts to get lost in the noise while the Balmer lines can still be easily seen in the spectra. Errors in for each spaxel are computed from the by linear interpolation of the simulation results (black line in Figure 11), and adding in quadrature the wavelength solution r.m.s of 6 km s(§4.2).

### 5.3. Emission Line Fluxes and Ionized Gas Kinematics

After measuring the LOSVD of each spaxel we use GANDALF to fit the spectrum including the emission lines. GANDALF recomputes the weights given to the different stellar templates at the same time of adding Gaussian profiles to model the contribution from emission lines. We attempt to fit all the transitions listed in Table 6.

During this fit the stellar LOSVD computed in the previous section is held fixed but the emission lines velocity, velocity dispersion, and amplitude, as well as the weights given to the stellar templates are free parameters. While in principle we could fit the kinematics of different lines independently, this becomes very hard for faint transitions detected at low . Therefore we tie the kinematics of all emission lines to a common set of parameters (, ) during the fit. This ensures that the kinematic parameters are dominantly constrained by the brightest emission lines in the spectrum (typically H, [OIII]5007, and [OII]3727). In this second iteration we also use additive and multiplicative Legendre polynomials to match the continuum shape.

Figure 12 presents the observed and best-fit spectrum of a randomly selected spaxel in the data-cube. This spectrum provides a good representation of the quality of our fits. The observed spectrum is shown in blue, with photometric errors marked by the cyan envelope, and total errors (photometric plus systematic) shown as a green envelope. The solid red line is the best-fit stellar plus emission line spectrum and the dotted red line shows the best-fit stellar spectrum alone. The vertical cyan bands represent regions masked around sky line residuals and the ends of the blue and red setup spectra. Also shown are zoomed in windows around relevant spectral features. Overall GANDALF produces fits to the VENGA spectra of excellent quality.

### 5.4. Errors in Emission Line Parameters and Kinematics

GANDALF returns emission line parameter errors based on the covariance matrix computed during the non-linear Levenberg-Marquardt fitting. Therefore, the quality of this error estimates depends critically on the uncertainty in the observed spectrum being properly estimated. In particular for low EW emission lines detected in very high spectra, for which the formal photometric errors are small, the inclusion of the systematic uncertainties associated with template mismatch (described in §5.1) is crucial in order to obtain adequate emission line flux errors. If this floor of systematic uncertainty is not included, errors in the measured emission line parameters can be significantly underestimated.

Figure 13 shows maps of the flux of the H, H, [OII]3727, [OIII]5007, [NII]6584, and [SII]6716 lines across NGC 628. We only show spaxels in which the line is detected with a significance higher than 3. The H line is detected at 5 over the full data-cube. The nebular emission clearly traces the two main spiral arms of the galaxy where ongoing star formation gives rise to prominent HII regions. In the inter-arm regions we still detect significant amounts of H emission although with a surface brightness that is one to two orders of magnitude fainter than in the arms. A large fraction of this emission arises from the diffuse ionized gas component of the galaxy’s ISM and is enhanced in low ionization ratios like [SII]/H and [NII]/H (Mathis, 2000; Haffner et al., 2009; Blanc et al., 2009). Also clearly seen in Figure 13 is a circum-nuclear star forming ring with a diameter of kpc and a H hole in the center of the galaxy. These features and their physical origin will be discussed in a future paper.

For each transition in Table 6 we report the median over all spaxels in the data-cube and the fraction of the observed area in which the emission line is detected at 5 and 3. Our data on NGC 628 reaches a 5 line flux limit per spaxel (4 arcsec) of erg s cm.

As mentioned above, we detect H at 5 over the full data-cube with a median . Other transitions are usually detected at lower significance than H. Individual members of the [NII]6548,6583 and [SII]6717,6731 doublets, as well as H, H, [OIII]5007, and the blended [OII]3726,3729 doublet are detected at 3 over more than 90% of the observed area, and the [OIII]4959 line is detected at 3 over 58% of the area.

### 5.5. Nebular Extinction from Balmer Decrement

For the typical extinction regimes found in spiral galaxies the H to H flux ratio (a.k.a Balmer decrement) provides a good estimate of the amount of dust extinction in the regions giving rise to the nebular emission (see discussion in Blanc et al., 2009). Assuming an intrinsic H/H ratio of 2.87 for Case B recombination in cm, K gas (Osterbrock & Ferland, 2006), the observed ratio provides the amount of dust reddening by means of the following relation

 E(B−V)=−2.5log([Hα/Hβ]obs2.87)k(λHα)−k(λHβ) (4)

where is the observed line ratio and is the extinction law. We assume a foreground MW extinction law as parameterized by Pei (1992). SMC and LMC laws were tested (also using the Pei, 1992, parametrization), and no significant change was observed in the derived extinction values (these 3 extinction laws are practically identical at optical wavelengths).

Figure 14 presents a map of across the disk of NGC 628. Errors in the measured values of are computed by propagating the uncertainty in the H and H line fluxes. In Figure 14 we have masked regions in which the error in is larger than 0.2 mag, which roughly amounts to an uncertainty of % in the extinction correction factor at the wavelength of H. Regions of high extinction follow the inner rims of the spiral structure (as traced by H), and a visual comparison to CO maps of NGC 628 (Leroy et al., 2008) shows almost perfect coincidence between high dust extinction and high molecular gas surface density regions. Also presented in Figure 14 is a map of H after correcting for dust extinction. The Balmer decrement method implies a median extinction across all regions with good measurements of mag (assuming ).

In Figure 15 we compare the VENGA Balmer decrement dust extinction measurements to a compilation of HII region measurements in the literature. The VENGA datacube of NGC 628 covers 20 HII regions from the catalog of Rosales-Ortega et al. (2011) (built from the PINGS IFU datacube of the galaxy), 4 HII regions from the multi-slit study of Gusev et al. (2012), and two HII regions from the McCall et al. (1985) sample, one of which was also studied by Ferguson et al. (1998). The two regions from the McCall et al. (1985) sample were also detected by PINGS so the total number of unique comparison HII regions in 24. In our literature search we only considered regions with statistically significant extinction measurements in the respective studies.

Beacuse of the large spatial resolution of our data the comparison to seeing limited slit spectroscopy measurements is challenging. Even the PINGS data has a spatial resolution which is a factor two smaller than ours. For the VENGA measurements we use the average extinction in a diameter aperture centered in each region, expecting the nebular emission in that spatial resolution element to be dominated by the HII region. Considering the differences in methodology the comparison shows a reasonable agreement between the values measured in VENGA and those measured by previous authors. The observed scatter is consistent with the scatter seen in extinction among different studies. For the one HII region which is common to the Rosales-Ortega et al. (2011), McCall et al. (1985), and Ferguson et al. (1998) studies the authors measure values of 0.38, 0.56, and 1.66 mag respectively while the VENGA data yields an intermediate value of 1.27.

## 6. Fitting the Stellar and Ionized Gas Velocity Fields

In this section we present the methods used to fit the stellar and ionized gas velocity fields of NGC 628. We are interested in measuring the galaxy’s rotation curve using both the stellar and gaseous component with the goal of understanding any differences observed between both velocity fields. We propose a new method to measure the inclination of face-on disk galaxies which is based on matching the gas and stellar rotation curves by means of the asymmetric drift correction.

### 6.1. Removal of Foreground Stars

In Figure 16 we present the stellar and ionized gas velocity field of NGC 628 resulting from the fits described in §5. Foreground Milky Way stars can be clearly seen in the stellar velocity field as sources of low velocity along the line of sight. This is evident by looking at the SDSS -band isophotes overploted on the top panel of Figure 16. Guided by the SDSS broad-band image, we flag these low velocity spaxels in the data-cube as spectra which are significantly contaminated by foreground stars. We mask all regions within of these flagged pixels. The resulting stellar and ionized gas velocity fields after the masking of foreground stars are shown in the second and bottom panels of Figure 16. Even at the low inclination of NGC 628 (see below for a discussion on the actual value) the VENGA data allows us to clearly detect the rotation of both the stellar and gaseous components of the galaxy.

### 6.2. Kinematic Position Angle and Systemic Velocity

We use the symmetrization method described in Appendix C of Krajnović et al. (2006) and implemented by Michele Cappellari in the IDL routine FIT_KINEMATIC_PA999http://www-astro.physics.ox.ac.uk/mxc/idl/ to measure the kinematic position angle (PA) and systemic velocity () from both maps. In brief, for a given set of values (PA, ), the method assumes mirror symmetry in the velocity field and a symmetrized velocity field is constructed by averaging the absolute values of the velocity at mirroring points on opposite sides of the perpendicular to the line of nodes. The best-fit PA and are those which minimize the residuals between the observed and symmetrized velocity fields.

For the kinematic PA we obtain consistent values of and for the stellar and ionized gas velocity fields respectively. This value is in agreement with the RC3 -band photometric PA of (de Vaucouleurs et al., 1991), but is inconsistent with the 2MASS -band reported value of (Jarrett et al., 2003). The kinematic PA of the ionized gas velocity field in the inner parts of the disk of NGC 628 has been measured independently in the past by Daigle et al. (2006) and Fathi et al. (2007) using Fabry-Perot H spectroscopy. These two studies measured inconsistent values of and . The value derived from the VENGA data sits right in between these two measurements and we consider it to be more reliable as it is based on deeper data, using the kinematics of multiple emission lines, and shows good agreement with the kinematic PA of the stellar component.

Kamphuis & Briggs (1992) used VLA HI 21 cm observations to reveal the presence of an extended HI disk in NGC 628 reaching out to a galactocentric radius of 30 kpc and showing complex morphology and kinematic structure. The HI velocity field shows a sharp transition in both PA and inclination around a galactocentric radius of ( kpc) believed to be caused by the presence of a warp in the outer HI disk. The VENGA IFU data does not sample the disk out to such large galactocentric radii but the stellar and ionized gas kinematics are consistent with the HI kinematics within the inner disk of the galaxy. The HI velocity field has a kinematic PA of within the central (Figure 6 in Kamphuis & Briggs (1992)), consistent with our measured value.

The symmetrization procedure also yields the systemic velocity of the galaxy. For the gaseous component we obtain a value of km s, in agreement with the HI 21cm derived values of km s (Kamphuis & Briggs, 1992) and km s (Walter et al., 2008), but in stark disagreement with the value of km s derived by Fathi et al. (2007) from the H velocity field. This inconsistency probably reflects a systematic error in the parameters of the kinematic model in Fathi et al. (2007) who also report a decreasing rotation curve within the central kiloparsec of the galaxy, feature which is not observed neither by Daigle et al. (2006) nor in this study. The VENGA stellar velocity field yields a consistent systemic velocity of km s also agreement with the HI 21cm derived values mentioned above.

### 6.3. Harmonic Decomposition Modeling

In order to measure the rotation curve of the galaxy we model the observed stellar and ionized gas velocity fields using the harmonic decomposition method (Franx et al., 1994; Wong et al., 2004; Krajnović et al., 2006). In particular we use the IDL KINEMETRY101010http://www.eso.org/ dkrajnov/idl/#kinemetry package to perform the fitting (Krajnović et al., 2006). We fit the azimuthal dependance of the LOS velocity along a set of elliptical annuli at different radii along the semi-major axis of NGC 628. The annuli semi-major axes are spaced following the combination of linear and logarithmic increase factors described in Krajnović et al. (2006) with a minimum radius of . For each ellipse the LOS velocity is fit as

 v(R,ψ)=vsys+3∑n=1[An(R)sin(nψ)+Bn(R)cos(nψ)] (5)

where is the systemic velocity measured independently for each component in the previous section, is the ellipse semi-major axis, and is the eccentric anomaly angle. The outermost radius at which the fit is performed is set by the requirement that data is available for 70% of the points along the ellipse. For NGC 628, this translates in an outermost radius of ( kpc).

During the fitting, the geometric parameters of the ellipses (center, PA, and inclination) are held fixed. We use the average of the two globally derived kinematic PAs for stars and gas of (§6.2), and the central coordinates from NED111111The NASA/IPAC Extragalactic Database (NED) is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.. As discussed below, the choice of an inclination value for NGC 628 is far from trivial.

Using photometric axis ratios () to compute the inclination of NGC 628 by adopting the Tully (1988) method we derive () for the RC3 -band measurements (de Vaucouleurs et al., 1991) and () for the 2MASS -band photometry (Jarrett et al., 2003). The detailed photometric decomposition of Fisher & Drory (2008) implies an inclination of () for the disk component. Given the projected circular velocities measured at large radii in both the 21cm HI and H velocity fields (Kamphuis & Briggs, 1992; Daigle et al., 2006; Fathi et al., 2007), such inclinations would imply a deprojected velocity of km s for the flat part of the rotation curve. Such a small circular velocity is wildly inconsistent with expectations from the Tully-Fisher (TF) relation (Tully & Fisher, 1977) for NGC 628.

Using the -band TF relation from Verheijen (2001)121212We use the parameters from the fit to their “RC/FD Sample, Excluding NGC 3992” in Table 4 of Verheijen (2001) and the 2MASS -band absolute magnitude from Table 1 we obtain km s, where the random error comes from the uncertainty in the distance and apparent magnitude of the galaxy and the systematic uncertainty comes from the 0.26 mag scatter in the adopted TF relation. The inconsistency between this value and that derived from the photometrically measured inclination is not surprising given that the uncertainty in explodes as one approaches a nearly face-on configuration. This is also the case for kinematically derived inclinations. In fact, letting the inclination be a free parameter for the ellipses in our harmonic decomposition fits yields an unrealistic median value of . Daigle et al. (2006) derives a kinematic inclination of from their tilted ring analysis of the H velocity field. For an excellent discussion on the uncertainties associated with measuring the inclination of disk galaxies see Bershady et al. (2010b).

Given the unreliability of both photometric and kinematic inclinations for face-on galaxies, most studies of NGC 628 have assumed a value of (e.g. Kamphuis & Briggs, 1992; Daigle et al., 2006; Fathi et al., 2007; Herbert-Fort et al., 2010). This value was adopted by Kamphuis & Briggs (1992) so the flat part of the HI rotation curve would reach an arbitrary chosen value of km s. A notable exception is the work of Herrmann et al. (2008) who fit an exponential model to the THINGS 21 cm HI velocity field of NGC 628 to obtain an inclination of .

Under the assumption that NGC 628 exactly follows the TF relation, a better value for the inclination would be (assuming an error of 10 km s for the value of measured at large radii by Kamphuis & Briggs (1992) and propagating the errors in the apparent magnitude and distance of NGC 628 as well as the scatter in the TF relation). This so called “Tully-Fisher inclination” method is discussed in Bershady et al. (2010b) and provides more reliable estimates of the inclination for face-on systems than photometric or kinematic techniques do.

In the following section we propose a new alternative method to derive the inclination of face-on disk galaxies by demanding agreement between the ionized gas and stellar rotation curves after applying the asymmetric drift correction to the stellar component.

### 6.4. Rotation Curve and Asymmetric Drift Correction: A New Method to Measure Inclinations

Because of the collisional nature of gas, as opposed to the collisionless nature of stars, the cold ISM of disk galaxies is expected to be confined to a relatively thin disk supported mainly by rotation. Although pressure support in the ISM can become important under certain circumstances (e.g. high turbulence, strong pressure gradients, etc.), the small and relatively constant H velocity dispersion of km s measured by Fathi et al. (2007) across the disk of NGC 628 implies that the gaseous disk of this galaxy is almost fully supported by circular motions, with random motions only having a minor effect. The importance of pressure support against gravity in gaseous galactic disks is extensively discussed in Dalcanton & Stilp (2010). Using the flat dispersion profile of Fathi et al. (2007) and applying equation 11 from Dalcanton & Stilp (2010) we compute a correction to the ionized gas rotation curve of NGC 628 of km s. This is many times smaller than the 1 uncertainty in the rotation curve itself. Given the small magnitude of this effect we decide not to apply these corrections and neglect the effect of pressure support in the gaseous disk of NGC 628. Therefore we consider the ionized gas rotation curve to roughly follow the dynamics of a test particle under the gravitational potential in the mid-plane of the galaxy.

Stellar disks can also experience support against gravity provided by random motions. As in the case of pressure support in gaseous disks, stellar random motion support translates in a measured circular velocity which is smaller than the actual circular velocity at which a test particle would orbit in the gravitational potential of the galaxy. This effect, first noted as a difference in orbital velocity for stellar populations of different ages (and therefore different velocity dispersions) in the solar neighborhood is known as “asymmetric drift” (Stromberg, 1922). As noted by Dalcanton & Stilp (2010) the equations describing it are similar to those describing pressure support in gaseous disks but the physical phenomena are fundamentally different.

Starting from the Jeans equations (Jeans, 1915) and following Binney & Tremaine (1987), for a stellar axisymmetric disk in steady state, under the assumption that the “epicyclic approximation” holds and that the stellar velocity ellipsoid (SVE) is aligned with the disk in cylindrical coordinates and its shape is independent of the vertical distance to the plane, the quadratic difference between the true and the observed circular velocities is given by

 v2c−v2ϕ=σ2R2(∂ln(vϕ)∂ln(R)−1−2∂ln(νσ2R)∂ln(R)) (6)

where is the circular velocity of a test particle in the potential, is the observed circular velocity, is the velocity dispersion in the radial direction, and is the number density of stars. While and its logarithmic derivative with radius can be directly measured from the harmonic decomposition fits described in §6.3, calculating the last term in the perenthesis in Equation 6 requires making a series of assumptions which we describe below.

In order to apply the asymmetric drift correction we assume a constant scale height and -band mass-to-light ratio for the disk of NGC 628. These assumptions imply that is proportional to the stellar mass surface density and that the latter is well traced by the surface brightness profile of the galaxy. In particular we use the best-fit disk plus pseudo-bulge -band decomposition of Fisher & Drory (2008) to trace the radial dependance of when calculating the last term in Equation 6. Note that knowledge of the -band mass-to-light ratio is not necessary as it cancels out in the logarithmic derivative.

Using a measurement of the stellar velocity dispersion along the line of sight () we can estimate , provided our assumptions regarding the shape and orientation of the SVE. The third panel in Figure 16 presents the map of the stellar velocity dispersion () measured from the VENGA data in §5.1. In the central regions of NGC 628 we see falling from a central value of km s. Figure 17 presents the radial profile of . To measure the radial profile we only considered spaxels with high enough as to provide a reliable fit of the LOSVD (i.e. those which are not masked in Figure 16). Red circles mark the median in 0.5 kpc wide radial bins. Error bars show both the standard deviation in each radial bin (red) and the median error in for each spaxel (black).

Also plotted in Figure 17 is the central stellar velocity dispersion value of km s from HyperLeda (blue circle). The HYPERLEDA value is an average over six literature measurements and is driven by an outlier at 116 km s (di Nella et al., 1995). Rejecting this outlier the HYPERLEDA average comes down to km s, in even better agreement with our measurements (blue triangle in Figure 17). The velocity dispersions we measure in the central regions of the galaxy are also consistent with the nuclear value of km s measured by Ho et al. (2009) (green circle). Our measurements also agree with the central dispersion of km s measured by Ganda et al. (2006) using SAURON IFU spectroscopy. The radial profile measured in this last study is shown as a dashed black line in Figure 17. While our measured values in the center of the galaxy are consistent with the ones in Ganda et al. (2006) we find no evidence to support their claim of an increasing velocity dispersion with radius in NGC 628. At larger radii Figure 17 shows the dispersion profile measured by Herrmann et al. (2008) using the kinematics of a large sample of planetary nebulae (PN). The dashed line shows the best fit dispersion profile from Herrmann et al. (2008) which follows an exponential with a scalength aproximately equal to two times the photometric scalelength of the galaxy. The latter agrees with theoretical expectations for constant scaleheight disks in which , with the proportionality constant depending on the detailed vertical profile of the disk (exponential, sech or sech, van der Kruit, 1988; Bershady et al., 2010; van der Kruit & Freeman, 2011, and references therein).

The 145 km s spectral resolution at Mg I in the VENGA VIRUS-P data makes the measurement such low values of the velocity dispersions very challenging. The large error bars in Figure 17 indicate that for single spectra individual measurements of low dispersion values ( km s) are extremely noisy even at the high of our data. Nevertheless, by averaging over many spaxels in the data-cube we seem to recover the velocity dispersion profile of the galaxy at least out to kpc where the VENGA measurements flatten around a value of km s. Comparison to the dispersion profile derived from PN kinematics shows that this flattening is not real and most likely corresponds to a systematic floor caused by uncertainties associated with template missmatch and deviations from the assumed Gaussianity in the instrumental line spread function most likely set this limit. This is not surprising given that it happens at about a fourth of the instrumental resolution and that a similar behavior is seen in the simulations presented in §5.2.

We fit an exponential dispersion profile to the VENGA data in the kpc region in order to avoid regions in which the stellar dynamics are contaminated by the central spheroidal component (see discussion in Bershady et al., 2010b). We fix the scale length of the profile to two times the scale length of the disk component in the Fisher & Drory (2008) decomposition. The best fit profile is shown as a solid line in Figure 17, implies a central velocity dispersion of km s (consistent with the HYPERLEDA, Ho et al. (2009) and Ganda et al. (2006) values) and is in excellent agreement with the Herrmann et al. (2008) best fit profile and with theoretical expectations for the dynamics of stellar disks. This profile is used to derive in order to calculate the assymetric drift correction using Equation 6.

Following the method outlined in Bershady et al. (2010b) we assume the following shape for the SVE in order to deproject the LOS velocity dispersion profile and compute :

 α=σzσR=0.6 (7)
 β=σϕσR=√12(∂ln(vϕ)∂ln(R)+1) (8)

where the first equation comes from expectations from the solar neighborhood (Binney & Merrifield, 1998) and observations of nearby galaxies (Bershady et al., 2010b) and the second comes from adopting the epicyclic approximation. This allows us to compute all the terms in Equation 6 and apply the asymmetric drift correction to the stellar velocity field of the galaxy. We use Monte Carlo simulations to calculate the error in the asymetric drift correction. In the error calculation we include the uncertainty in the observed rotation curve which is propagated to compute the uncertainty in the logarithmic radial derivative of the rotation curve and the value of , an error of (Bershady et al., 2010b), and an error in of 10 km s.

In the upper panel of Figure 18 we present the VENGA rotation curve of NGC 628 for both stars (black circles) and ionized gas (red circles), as measured from the first order cosine term of the harmonic decomposition model . We show measurements of the rotation curve for two different assumed inclination values of (derived from the RC3 axis ratios, open circles) and (Kamphuis & Briggs, 1992, , filled circles). The horizontal dashed line marks the expectation from the TF relation km s (§6.3). The high inclination implied by the photometric axis ratio dramatically underestimates the amount of rotation expected in NGC 628. This highlights the lack of reliability of geometrically measured inclinations in face-on systems.

Independent of the assumed inclination, the observed stellar circular velocity (before applying the asymmetric drift correction) is systematically lower than the observed circular velocity of the gaseous component. This implies the presence of significant kinematic support arising from random motions in the stellar disk of NGC 628. For the case the corrected stellar rotation curve after accounting for asymmetric drift using equation 6 is shown by the black open squares in the top panel of Figure 18. Errorbars in the corrected stellar rotation curve are calculated using Monte Carlo simulations and including the uncertainty in all the quantities entering the correction. For an assumed value of the magnitude of the asymmetric drift correction is not sufficient to account for the discrepancy between the observed stellar and gaseous rotation curves.

The above problem can be solved by changing the assumed value for the the inclination. We remind the reader that the value typically used in the literature for NGC 628 was arbitrarily adopted by (Kamphuis & Briggs, 1992) to make the flat part of the rotation curve reach a velocity of 200 km s. From the TF relation we have seen in §6.3 that the expected asymptotic velocity in the flat part of the rotation curve of NGC 628 is smaller than what was assumed by Kamphuis & Briggs (1992) with a value closer to km s. This asymptotic velocity implies an inclination of .

The lower panel in Figure 18, shows the result of matching the gas and asymmetric drift corrected stellar rotation curves to obtain the inclination of the galaxy. The method consists of sampling a range of inclination values in order to find the inclination which minimizes the residuals between both rotation curves. For each inclination value we measure the rotation curves by performing harmonic decomposition fits to the velocity fields, we deproject the LOS velocity dispersion profile to compute the asymmetric drift correction, and we compute a statistic in order to quantify deviations between the gas and corrected stellar rotation curves.

The inset in the lower panel of Figure 18 shows the distribution as a function of inclination. The minimum corresponds to a best-fit value for the asymetric drift inclination of in perfect agreement with the value derived from the TF relation. The exact agreement in both the value and the error-bars implies that both methods produce consistent results with similar precisions, at least in the case of NGC 628. The TF and asymmetric drift methoda are highly complementary. The TF method requires knowledge of the observed rotation velocity in the flat part of the rotation curve at large radii, while the asymmetric drift method can be used even when only kinematic measurements are only available in the central regions of galaxies. Furthermore, the measurement of an independent asymetric dirft inclinations can allow for highly inclined systems to be included when measuring the TF relation.

We propose the matching of the gaseous and asymmetric drift corrected stellar rotation curves as a new method to estimate the inclination of nearly face-on disk galaxies. The fact that a very small difference of 2.2 in the adopted inclination can produce a catastrophic inconsistency between the observed gas and stellar kinematics as in the case highlights the sensitivity of this method as tool to measure inclinations.

## 7. Summary and Conclusions

In this work we have presented the survey design, sample, observing strategy, data reduction, and spectral analysis methods for VENGA. Wide field integral field spectroscopy proves to be a powerful tool to study a large set of physical phenomena occurring in nearby galaxies. We characterized our sample of 30 nearby disk galaxies in terms of their stellar masses and s, and showed that VENGA is a representative sample of massive ( M) spiral galaxies in the local universe. A large range of morphological parameters (bulge-to-disk ratio, bar presence, bulge Sérsic index, inclination) is represented in the sample. The distance distribution of our targets implies a median spatial resolution in physical units of 383 pc. Our targets typically span a few arcminutes in angular size, and we tile the VIRUS-P IFU in order to provide a coverage out to 0.7 for most galaxies. This implies that the VENGA data-cubes are among the largest optical IFU data-cubes ever constructed. In particular, the NGC 628 data-cube presented in this paper spans .

The wealth of information produced by integral field spectrographs stresses the need for optimized and pipelined software tools to process and analyze the data. This becomes essential when this observational technique is used to conduct large surveys like the one presented here. We have presented the reduction and calibration pipeline used for the VENGA data. We have also described our spectral analysis pipeline which we use to extract stellar and gas kinematics as well as emission line fluxes, and we have discussed the methods used to estimate the uncertainties in all these parameters. When possible, we have adapted existing publicly available software to be used on the VIRUS-P data. We assessed the quality of the VENGA data obtained on NGC 628 and we find it to be excellent. VIRUS-P provides high S/N spectra for single fibers out to large galactocentric radii. Thanks to the ability of reconstructing broad-band images from the IFU data and cross-correlating them with archival broad-band images of the galaxies in our sample we can achieve good astrometric precision () and better than 10% flux calibration accuracy across the full wavelength range.

Finally we have used an harmonic decomposition technique to fit the stellar and ionized gas velocity fields in NGC 628. The observed kinematics imply that the gaseous disk of the galaxy (as traced by nebular emission from ionized gas) is almost fully supported by rotation while the stellar disk shows significant levels of dynamic support arising from random motions. This is evident by a km s offset between the ionized gas and stellar rotation curves.

We have shown that the above discrepancy in the rotation curves can be explained if one takes into account the effect of stellar random motions by applying an asymmetric drift correction. The agreement between the ionized gas rotation curve and the asymmetric drift corrected stellar rotation curve depends strongly on the assumed value for the inclination. We take advantage of this dependance and propose this as a method to estimate the actual inclination of nearly face-on disk galaxies for which classically used geometrically derived inclinations are extremely unreliable. Applying this method we find a revised asymmetric drift inclination for NGC 628 of , in excellent agreement with the expected value of , which comes from assuming that NGC 628 satisfies the local TF relation.

The main purpose of this work is to present the VENGA survey and some preliminary scientific results have been discussed only briefly. We expect to use the VENGA sample to conduct a series of studies on star formation, galactic structure assembly, stellar populations, chemical evolution, galactic feedback, nuclear activity, and the properties of the interstellar medium in massive disk galaxies, and to present these results in a series of future publications. As an example of the practical uses of this data, in a recent paper we have presented a study of the radial profile in the CO to H conversion factor and its relation to other parameters like the metallicity, the gas surface density and the ionization parameter across the disk of NGC 628 (Blanc et al., 2012).

Once all the VENGA data is processed we expect to make it publicly available to the community. The richness of large IFU datasets like the one we are compiling goes beyond the scientific goals of our team. We expect VENGA to be a useful resource that will complement the wealth of multi-wavelength datasets that the community has acquired on nearby spiral galaxies over the last few decades.

The VENGA collaboration acknowledges the generous support from the Norman Hackerman Advanced Research Program (NHARP) ARP-03658-0234-2009, GAB. acknowledges the support of Sigma Xi, The Scientific Research Society, Grant in Aid of Research. NJE and ALH were supported by NSF Grant AST-1109116. RXL and LH acknowledge the supports by the National Natural Science Foundation of China under grant No. 11073040, by 973 Program of China under grant No. 2009CB824800, and by Shanghai Pujiang Talents Program under grant No. 10pj1411800. The construction of the Mitchell Spectrograph (formerly VIRUS-P) was possible thanks to the generous support of the Cynthia & George Mitchell Foundation. We thank Phillip McQueen and Gary Hill for designing and constructing VIRUS-P, and for their advice on the use of the instrument. We also acknowledge David Doss and the staff at McDonald Observatory for their invaluable help during the observations. This research has made use of NASA’s Astrophysics Data System, and of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

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