# Deep Fabry-Perot Halpha Observations of NGC 7793: a Very Extended Halpha Disk and a Truly Declining Rotation Curve

I. Dicaire, C. Carignan, P. Amram, M. Marcelin, J. Hlavacek-Larrondo, M.

-M. de Denus-Baillargeon, O. Daigle, O. Hernandez

► To cite this version:

I. Dicaire, C. Carignan, P. Amram, M. Marcelin, J. Hlavacek-Larrondo, et al., Deep Fabry-Perot Halpha Observations of NGC 7793: a Very Extended Halpha Disk and a Truly Declining Rotation Curve. The Astrophysical Journal, 2008, 135 (6), pp.2038. 10.1088/0004-6256/135/6/2038. hal-00325346

HAL Id: hal-00325346

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# DEEP FABRY-PEROT Hα OBSERVATIONS OF NGC 7793: A VERY EXTENDED Hα DISK AND A TRULY DECLINING ROTATION CURVE

I. DICAIRE<fnref n="1" />, C. CARIGNAN<fnref n="1" />, P. AMRAM<fnref n="2" />, M. MARCELIN<fnref n="2" />, J. HLAVACEK-LARRONDO<fnref n="1" />, M.-M. DE DENUS-BAILLARGEON<fnref n="1" />, O. DAIGLE<fnref n="1" />,<fnref n="2" />, AND O. HERNANDEZ<fnref n="1" />

Received 2007 October 7; accepted 2008 February 13; published 2008 May 1

## ABSTRACT

Deep Hα observations of the Sculptor Group galaxy NGC 7793 were obtained on the ESO 3.60 m and the Marseille 36 cm telescopes at La Silla, Chile. Hα emission is detected all the way to the edge of the H1 disk, making the H2 disk of NGC 7793 one of the largest ever observed in a quiet non-active galactic nucleus (AGN) late-type system. Even in the very outer parts, the H2 ionizing sources are probably mainly internal (massive stars in the disk) with an unlikely contribution from the extragalactic ionizing background. The Hα kinematics confirms what had already been seen with the H1 observations: NGC 7793 has a truly declining rotation curve. However, the decline is not Keplerian and a dark halo is still needed to explain the rotation velocities in the outer parts.

**Key words:** galaxies: individual (NGC 7793) – galaxies: ISM – galaxies: kinematics and dynamics – instrumentation: interferometers – techniques: radial velocities

## 1. INTRODUCTION

NGC 7793 is one of the five bright members of the classical Sculptor Group along with NGC 55, NGC 247, NGC 253, and NGC 300. Sculptor is the closest group of galaxies outside the Local Group. It covers an area of ~20° in diameter centered on the constellation Sculptor at $α = 0^h30^m$ and $δ = -30°$ (de Vaucouleurs 1959). However, it is still debated whether Sculptor is really a group. Karachentsev et al. (2003) suggest instead that it may be a part of a filament that extends along the line of sight from the Local Group out to ~5 Mpc.

The optical parameters of NGC 7793 are summarized in Table 1. It is a typical Sd galaxy with a very tiny bulge and a filamentary spiral structure (see Figures 1 and 2). It is an intrinsically small system with an exponential scale length $α^{-1} \simeq 1$ kpc. For this study, a distance of 3.38 Mpc (Puche & Carignan 1988) is adopted, based on numerous distance indicators. However, somewhat larger distances of e.g. 3.82 (Karachentsev et al. 2003) and 3.91 Mpc (Karachentsev 2005) have also been suggested. For our adopted distance, NGC 7793 has an absolute B magnitude of -18.3 for a total blue luminosity of ~3.1 × 10⁹ L⊙.

Previous kinematical studies of NGC 7793 were done in the optical, using Fabry-Perot (FB) interferometry by Davoust & de Vaucouleurs (1980). Their Hα rotation curve (RC) extends to ~4', which barely reaches the maximum velocity. Ten years later, deep Very Large Array (VLA) H1 observations (13.5 h in C/D configuration) allowed one to derive the RC twice as far, out to ~8' (Carignan & Puche 1990). A remarkable result of those H1 observations was that, contrary to most spirals, the RC is not flat in the outer parts but appears to be declining ($ΔV_{rot} \simeq 30$ km s⁻<fnref n="1" /> or 25% of $V_{max}$ between the maximum velocity and the last point of the RC), even after a careful modeling (tilted-ring model) of the warp ($ΔPA \simeq 20°$) in the outer H1 disk. While the RC is declining in the outer parts, it is less steep than a pure Keplerian decline and a dark halo is still needed to properly model the mass distribution.

<table><caption>**Table 1**
Optical Parameters of NGC 7793</caption><thead><tr><th>Parameter</th><th>Value</th><th>Reference</th></tr></thead><tbody><tr><td>Morphological type</td><td>SA(s)d</td><td>a</td></tr><tr><td>R.A. (2000)</td><td>23<sup>h</sup> 57<sup>m</sup> 49.5</td><td>a</td></tr><tr><td>Decl. (2000)</td><td>-32° 35' 24"</td><td>a</td></tr><tr><td>Isophotal major diameter D<sub>25</sub></td><td>10.1'</td><td>b</td></tr><tr><td>Holmberg radius R<sub>HO</sub></td><td>6.1'</td><td>b</td></tr><tr><td>Exponential scale length α<sup>-1</sup>, kpc</td><td>1.1</td><td>b</td></tr><tr><td>Axis ratio q = b/a</td><td>0.60</td><td>b</td></tr><tr><td>Inclination (q<sub>0</sub> = 0.12), i</td><td>53.7°</td><td>b</td></tr><tr><td>Position angle, PA</td><td>279.3°</td><td>b</td></tr><tr><td>Corrected total B magnitude, B<sup>0,i</sup><sub>T</sub> (A<sub>g</sub> = 0.02)</td><td>9.33</td><td>a,b</td></tr><tr><td>Adopted distance (Mpc)</td><td>3.38<br>(1' = 0.98 kpc)</td><td>c</td></tr><tr><td>Absolute B magnitude, M<sup>0,i</sup><sub>B</sub></td><td>-18.31</td><td>b</td></tr><tr><td>Total blue luminosity (M<sub>☉</sub> = 5.43), L<sub>☉</sub></td><td>3.1 × 10<sup>9</sup></td><td>b</td></tr><tr><td>(B-V)</td><td>0.54</td><td>a</td></tr></tbody></table>

**Notes.**

It would be interesting to be able to check the uniqueness of this RC with independent observations using a tracer other than H1. As we have seen, previous Hα observations (Davoust & de Vaucouleurs 1980) only extend to ~4' or 80% of the optical radius $R_{25}$. However, deep Hα imaging with a 68 Å (FWHM) filter (Ferguson et al. 1996) showed that the diffuse ionized gas (DIG, also referred to as warm ionized medium (WIM)) component in NGC 7793 easily extended out to $R_{25}$. Thus, one of the main motivations of the observations presented in this paper was the hope to extend the Hα kinematics, at least out to that point, in order to confirm (or not) the decline of the H1 RC.

The other motivation was to try to detect the DIG component out to very low levels, if possible at radii larger than $R_{25}$. Large DIG components have been seen in nearby starburst and active galaxies (Veilleux et al. 2003) and can sometimes have sizes comparable to the H1 component (see, e.g., NGC 1068), but

<footnote n="1">¹ Laboratoire d'Astrophysique Expérimentale, Département de physique, Université de Montréal, C. P. 6128, Succ. centre-ville, Montréal, Québec H3C 3J7, Canada</footnote>

<footnote n="2">² Laboratoire d'Astrophysique de Marseille, Observatoire Astronomique Marseille Provence, Université de Provence & CNRS, 2 place Le Verrier, F-13248 Marseille CEDEX 04, France</footnote>

<footnote>a de Vaucouleurs et al. (1991).</footnote>

<footnote>b Cariguan (1985a).</footnote>

<footnote>c Puche & Carignan (1988).</footnote>
<figure><img src="image_2.png" /><figcaption>**Figure 1.** FB observations of NGC 7793 on the 3.60 m. Top left: DSS Blue Band image. Top right: Spitzer infrared array camera (IRAC) 3.6 µm image. Middle left: Hα monochromatic image. Middle right: Hα velocity field. Bottom: position-velocity (PV) diagram.</figcaption></figure>

not much is known on the extent of the DIG component of quiet late-type systems. Comprehensive studies of the large-scale structure of DIG components have been done on edge-on systems (Rand et al. 1990; Dettmar & Schulz 1992; Veilleux et al. 1995), on selected small regions of M31 (Walterbos & Braun 1994), and on large samples (Kennicutt et al. 1995; Zurita et al. 2000; Thilker et al. 2002; Meurer et al. 2006; Oey et al. 2007).

Massive stars clearly provide the largest source of Lyman continuum (Lyc) photons in spiral galaxies; an issue concerns whether the bulk of these photons is deposited over localized regions, such as the Strömgren spheres which define HII regions, or whether a significant fraction can escape from the regions of recent star formation where they were created and thus ionize the interstellar medium over much larger scales (Ferguson

et al. 1996). The large-scale radial distribution of the DIG across galactic disks can provide stringent constraints on the source of its ionization. For example, if the number of Lyc photons produced in star-forming regions were the only factor responsible for producing the DIG, then the ionized gas distribution should follow very closely, both on small and large scales, the distribution of discrete HII regions. This addresses the possible internal sources of ionization.

However, if ionized gas is detected past the HI truncation edge (Corbelli et al. 1989; van Gorkom 1993), one possible explanation for that truncation could be that, at large radii, the thin HI disks get fully ionized by the metagalactic UV background, as discussed by Bland-Hawthorn et al. (1997). This is another incentive to try to push the detection of the diffuse Hα as far out as possible. If Hα could be detected
<figure><img src="image_3.png" /><figcaption>**Figure 2.** FB observations of NGC 7793 on the 36 cm. Top left: DSS Blue Band image. Top right: Spitzer IRAC 3.6 µm image. Middle left: Hα monochromatic image. Middle right: Hα velocity field. Bottom: PV diagram.</figcaption></figure>

that far, it could even be used to put a limit on that UV background.

Section 2 will present the new FB Hα observations and discuss data reduction while Section 3 will derive the kinematical parameters and the RCs. This will be followed in Section 4 by a study of the mass distribution and Section 5 will discuss the extent of the DIG. Finally, the principal results will be discussed in Section 6 and a summary and the main conclusions will be given in Section 7.

## 2. OBSERVATIONS AND DATA REDUCTION

The FP observations were obtained on the Marseille 36 cm (from 2005 October 27 to 2005 November 2) and on the ESO 3.6 m (2005 November 3) telescopes at La Silla, Chile,

using the photon-counting camera FaNT0mM (Gach et al. 2002; Hernandez et al. 2003). The same focal reducer, interference filter, FB etalon, and camera were used on both telescopes. The interference filter, with a peak transmission $T_{max} \sim 80\%$, was centered at $\lambda_c = 6563$ Å and had a FWHM of 30.4 Å. The interference order of the FB interferometer was $p = 765$ at Hα for a free spectral range (FSR) of 8.6 Å or $\sim 390$ km s$^{-1}$. The mean finesse of the etalon was $\sim 18.5$ (resolution $\simeq 14,000$). The finesse is a dimensionless value expressing the spectral resolution of the etalon ($\Delta\lambda = \text{FSR}(\text{Å})$/finesse). The FSR was scanned in 60 channels in steps of 0.14 Å. The photon-counting camera FaNT0mM is based on a Hamamatsu photocathode coupled with a Dalsa commercial CCD. The photocathode has a quantum efficiency of $\sim 23\%$ at Hα and the CCD has 1024 × 1024 12.5 µm
square pixels. The CCD was operated in its low spatial resolution where pixels are binned 2 × 2 at 40 frames s⁻¹.

A photon-counting camera, such as FaNT0mM, is an essential tool for this kind of work. Its ability to rapidly scan the FP interferometer allows the photometric variations to be averaged out. For comparison, in CCD observations, each FP channel must be observed for at least five continuous minutes to prevent the read-out noise of the CCD from masking the weak galaxy's signal. This means that photometric conditions must not significantly change for ~5 h with CCD observations. In photon counting, channels are observed for 5–15 s and a complete cycle is obtained every 5–15 min. Many cycles are made during an observation and since the data are analyzed on-line, signal-to-noise ratio (S/N) estimations can be made throughout the observations and the observer can decide when to stop the integration. The wavelength calibration is done using a Ne lamp at 6598.95 Å. Since the calibration lamp is strong compared to the galaxies' fluxes, calibrations are done in analog mode (non-photon counting). Typically, calibration channels are integrated 1 s each, such that a whole calibration only takes 1 min.

The galaxy was observed for a total of 100 min on the 3.60 m (1.67 min per channel) and for 1200 min (20 min per channel) over four nights on the 36 cm telescope. Raw observational data consist of many data files that contain the photons' positions for every cycle per channel duo. With a cycling of 10 s integration time per channel, one file was created every 10 s. The different steps of the data reduction are as follows.

1. integration of raw data files into an interferogram data cube (3D data cube sliced for every FB channel);

2. phase correction of interferograms to create wavelength-sorted data cubes (3D data cube sliced for every wavelength interval);

3. Hanning spectral smoothing;

4. sky emission removal;

5. spatial binning/smoothing (e.g. adaptive binning);

6. radial velocity map extraction from emission line positions;

7. addition of astrometry information;

8. kinematical information extraction.

All the reduction was performed with IDL routines inspired by the ADHOCW reduction package (http://www.oamp.fr/adhoc/adhocw.htm). Details on the data reduction can be found in Hernandez et al. (2005), Chemin et al. (2006), and Daigle et al. (2006a) and the routines are available at http://www.astro.umontreal.ca/~odaigle/reduction. In particular, the way the profiles are found, the way the sky emission is subtracted, which is a crucial step when trying to detect very weak emission, and the way the data are smoothed using an adaptive smoothing technique are all described in detail in Daigle et al. (2006c).

A first attempt at detecting the DIG in the outer disk of NGC 7793 was done in 1993 October, during 13 observing nights, for a cumulative total exposure time of 64 h. The same instrumentation was used (36 cm telescope, focal reducer, interference filter, and interferometer), but the detector was different. This first data set was obtained with our old image photon-counting system (IPCS), a Thompson camera based on a Silicium Nocticon TV tube technology (Boulesteix et al. 1984). However, the camera used to obtain the data set presented in this paper used a new GaAs tube technology (Gach et al. 2002) and has a detective quantum efficiency ~25%, at least four times larger than the old Thompson IPCS. Thus, this second run was

less time consuming (20 h instead of 64 h) for reaching a higher S/N. Moreover, the shortening of the individual elementary exposure time together with the diminution of the total observing time and better reduction software (Daigle et al. 2006c) allowed a better removal of the night sky lines which is critical at such a low signal level.

### 3. KINEMATICAL PARAMETERS AND ROTATION CURVES

In order to derive the RCs, one must find the set of orientation parameters (rotation center ($x_0, y_0$), systemic velocity $V_{sys}$, inclination $i$, position angle PA of the major axis) that best represents the observed velocity fields, shown in Figures 1 and 2, at all radii. The data in an opening angle of 40° about the minor axis are excluded from the analysis to minimize errors due to deprojection effects. A cosine-weighting function (using the angle $\theta$ from the major axis) is used for the rest of the data, which gives maximum weighting on the major axis. The task ROTCUR in the reduction package GIPSY (Vogelaar & Terlouw 2001) is used to find those parameters.

Since they are correlated, the dynamical center and the systemic velocity are sought first, by keeping $i$ and PA fixed (using the photometric values given in Table 1). We find that ($x_0, y_0$) corresponds to the optical center and that $V_{sys} = 238 \pm 3$ km s⁻¹ for the 3.6 m and $230 \pm 4$ km s⁻¹ for the 36 cm data. This can be compared to the Carignan & Puche (1990) H1 global profile midpoint velocity of $230 \pm 2$ km s⁻¹ and intensity-weighted mean velocity of $235 \pm 4$ km s⁻¹ or to their systemic velocity derived in the same way from the H1 velocity field of $227 \pm 3$ km s⁻¹. The agreement is very good considering that a slight zero-point shift can be expected since the calibration is done at the Ne wavelength and not at the observed wavelength.

The next step is to obtain a least-squares solution for $i$, PA, and $V_{rot}$ in concentric annuli in the plane of the galaxy, by keeping ($x_0, y_0$) and $V_{sys}$ fixed. This is shown in Figure 3. For both data sets, inclinations $i = 47° \pm 9°$ for the 3.6 m and $\pm 6°$ for the 36 cm are adopted. For the PA we found $277° \pm 3°$ for the 3.6 m and $286° \pm 4°$ for the 36 cm. This is consistent with the H1 data (Carignan & Puche 1990) which show that the PA is smaller in the inner parts than in the outer parts. In order to see if the solution found is a good representation of the whole galaxy, separate solutions are also obtained for the approaching and the receding sides. The three solutions (both sides, approaching, receding) and the adopted RCs are given in Figure 4 for the 3.6 m and in Figure 5 for the 36 cm data. The adopted errors are the biggest difference between the kinematical solution for both sides and the separate solutions for either the approaching or the receding sides or the intrinsic error from the tilted-ring model, if larger. The values of the RCs are tabulated in Tables 2 and 3, respectively.

For the 3.60 m data of Figure 4, only the velocity points up to 132" will be used because further out there are not enough points on the receding side and the errors become too large. Similarly, for the 36 cm data in Figure 5, even if the Hα emission is detected out to ~8.5' (~$R_{H1}$), only the data up to 7' will be used because there is no emission after that radius on the receding side.

### 4. MASS MODELING

As can be seen in Figure 6, the Hα RC is very similar to the H1 RC (errors on the 3.6 m data were not plotted to facilitate
<figure><img src="image_4.png" /><figcaption>**Figure 3.** Kinematical parameters of NGC 7793 derived from the 3.6 m (left) and the 36 cm (right) FB observations.</figcaption></figure>

the comparison; see Figure 4) so that the mass models are expected to be very similar. However, since the H1 velocities are slightly lower in the very inner parts and slightly higher in the intermediate parts, one could expect slight differences.

In order to compare our results with those obtained using the H1 RC (Carignan & Puche 1990), the same approach for the study of the mass distribution will be used. The dark halo is represented by an isothermal sphere which can be described by two free parameters: the one-dimensional velocity dispersion $\sigma$ and the core radius $r_c$. The central density is then given by $\rho_0 = 9\sigma^2/4\pi Gr_c^2$. The other free parameter is the mass-to-light ratio $(M/L)_*$ of the stellar disk. Details on the method used can be found in Carignan (1985b) and Carignan & Freeman (1985).

The parameters of the models and the main results are given in Table 4 and illustrated in Figure 7. As expected, the slightly higher $H\alpha$ velocity ~1 kpc gives a higher $(M/L_B)_*$ for the stellar disk; thus reducing the dark component and the slightly lower $H\alpha$ velocities ~5 kpc also gives a lower-density dark component. Those two factors, combined with the fact that the H1 RC extends slightly further out, explain the fact that the $M_{dark}/M_{lum}$ goes down from 0.97 to 0.75 at the last point. Nevertheless, within the uncertainties, one can say that the $H\alpha$ data confirm the results obtained with the H1 data with $M_{dark}/M_{lum} \simeq 0.75 - 1.0$ at the last velocity point for a total mass for NGC 7793 of ~1.3 - 1.5 $\times 10^{10} M_{\odot}$. Again, one can

see that even if the RC is declining over the second half of the radius range, a dark halo is still needed to reproduce the observed kinematics.

### 5. $H\alpha$ EXTENT

The first observation that NGC 7793 had an extended ionized component was by Monnet (1971) from quite shallow photographic data. A deeper and more detailed study was done more recently by Ferguson et al. (1996). They showed that the observed $H\alpha$ luminosity of the DIG component of NGC 7793 was large, accounting for ~40% of the total $H\alpha$ emission, similar to what is seen in M31 (Walterbos & Braun 1994) or the SMC (Kennicutt et al. 1995). Ferguson et al. (1996) argue that the integrated minimum Lyc power required to sustain the DIG is enormous and can only easily be met by the ionizing output from massive star formation; the mechanical energy from supernovae and stellar winds falls short of that required by at least a factor of 2. Their results support the hypothesis that the DIG is photoionized by Lyc photons leaking out of discrete HII regions.

A comparison between our deep FB $H\alpha$ map and the deep $H\alpha$ continuum subtracted image from Ferguson et al. shows a very good general agreement. Nevertheless, we reach fainter diffuse $H\alpha$ emission in the outskirts of the galaxy located between HII regions. In addition, spurs are visible on our image
<figure><img src="image_5.png" /><figcaption>**Figure 4.** Left: rotation curve derived from the 3.6 m data for the whole galaxy (black) and separately for the receding (red) and the approaching (blue) sides with $V_{\text{sys}} = 238$ km s$^{-1}$, PA= 277° and $i = 47°$. Right: 3.6 m adopted Hα RC for NGC 7793. The data are also tabulated in Table 2.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 5.** Left: rotation curve derived from the 36 cm data for the whole galaxy (black) and separately for the receding (red) and the approaching (blue) sides with $V_{\text{sys}} = 230$ km s$^{-1}$, PA = 286° and $i = 47°$. The H1 data are plotted as crosses (green). Right: 36 cm adopted Hα RC for NGC 7793. The data are also tabulated in Table 3.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Figure 6.** H1 (green), 3.60 m Hα (blue), and 36 cm Hα (red) rotations curves of NGC 7793.</figcaption></figure>

that were not detected by Ferguson et al. (1996). Figure 8 shows the Hα radial profile of NGC 7793, derived using the GIPSY task ELLINT (Vogelaar & Terlouw 2001). Since our data were not photometrically calibrated, our profile was adjusted in order to be in rough agreement with the profile of Ferguson et al. (1996) in the outer parts. This should be regarded as just an order of magnitude representation since the Ferguson et al. (1996) data were obtained in imagery with a 68 Å filter which included not only Hα but also the [NII] lines. While they corrected for the [NII] contamination using [NII]/Hα = 0.22, Bland-Hawthorn et al. (1997) found a ratio close to unity in the outer parts of the other Sculptor Group galaxy NGC 253. So, even if the intensity scale could be off by a factor of a few, this is

sufficient to show that our long FB observations (20 h total or 20 min per channel) on a 36 cm telescope nearly reach the limit of the H1 disk ($D_{H1} = 1.7D_{25}$; Carignan & Puche 1990). To be able to reach so large radii is interesting since it was estimated that if the truncation edge (Corbelli et al. 1989; van Gorkom 1993) of the H1 disks is due to the ionization of the hydrogen by the cosmic background radiation, the expected flux (Bland-Hawthorn et al. 1994, 1997) should be an Hα emission measure $E_m(Hα) \sim 0.2-2.0$ pc cm$^{-6}$, which is the level reached by our deep observations.

Contrary to what was found by Bland-Hawthorn et al. (1997) (hereafter referred to as BFQ1997) for NGC 253, the Hα disk of NGC 7793 does not extend past the H1 emission even if it gets close to it. Indeed, BFQ1997 have detected ionized gas out to $1.4 R_{25}$, while the H1 extends only out to $1.2 R_{25}$. We should nevertheless notice that these authors did not give an Hα map of NGC 253 but only presented some discrete Hα emission located at a single position. Using FB techniques as well, they computed a radial velocity for this emission region and since they used a fixed etalon, instead of a scanning one as we did, they do not have full spatial coverage of the galaxy. Moreover, they have only observed one side of the galaxy. Further observations of NGC 253 are needed to verify if the outer H2 region detected by BFQ1997 is isolated or if it is a fragment of a more extended region. In addition, it is necessary to search for a counterpart of this region on the other side of the galaxy to strengthen their conclusions.

## 6. DISCUSSION

The outer regions of galaxies are expected to deliver important clues on the way galaxies are assembled. It is into these regions that the material was accreted during violent interactions
<table><caption>**Table 2**
Hα RC from the 3.6 m Data</caption><thead><tr><th>Radius<br>(arcsec)</th><th>V<sub>rot</sub><br>(km s<sup>-1</sup>)</th><th>ΔV<sub>rot</sub><br>(km s<sup>-1</sup>)</th><th>Radius<br>(arcsec)</th><th>V<sub>rot</sub><br>(km s<sup>-1</sup>)</th><th>ΔV<sub>rot</sub><br>(km s<sup>-1</sup>)</th></tr></thead><tbody><tr><td>6.0</td><td>9.1</td><td>8.5</td><td>70.0</td><td>67.3</td><td>10.1</td></tr><tr><td>8.0</td><td>17.6</td><td>7.4</td><td>72.0</td><td>70.3</td><td>9.7</td></tr><tr><td>10.0</td><td>19.3</td><td>7.4</td><td>74.0</td><td>69.6</td><td>9.8</td></tr><tr><td>12.0</td><td>24.8</td><td>6.4</td><td>76.0</td><td>70.5</td><td>9.3</td></tr><tr><td>14.0</td><td>30.0</td><td>7.2</td><td>78.0</td><td>69.4</td><td>8.8</td></tr><tr><td>16.0</td><td>35.0</td><td>7.3</td><td>80.0</td><td>71.3</td><td>11.2</td></tr><tr><td>18.0</td><td>38.3</td><td>7.6</td><td>82.0</td><td>73.2</td><td>11.2</td></tr><tr><td>20.0</td><td>42.7</td><td>8.8</td><td>84.0</td><td>75.4</td><td>8.8</td></tr><tr><td>22.0</td><td>47.0</td><td>5.3</td><td>86.0</td><td>76.1</td><td>7.2</td></tr><tr><td>24.0</td><td>49.8</td><td>5.6</td><td>88.0</td><td>75.3</td><td>11.4</td></tr><tr><td>26.0</td><td>52.2</td><td>6.2</td><td>90.0</td><td>79.0</td><td>11.9</td></tr><tr><td>28.0</td><td>53.4</td><td>6.3</td><td>92.0</td><td>80.6</td><td>11.1</td></tr><tr><td>30.0</td><td>54.6</td><td>5.9</td><td>94.0</td><td>80.3</td><td>13.6</td></tr><tr><td>32.0</td><td>55.5</td><td>6.9</td><td>96.0</td><td>80.9</td><td>14.1</td></tr><tr><td>34.0</td><td>55.9</td><td>7.5</td><td>98.0</td><td>84.6</td><td>13.7</td></tr><tr><td>36.0</td><td>58.3</td><td>7.4</td><td>100.0</td><td>85.5</td><td>13.5</td></tr><tr><td>38.0</td><td>59.3</td><td>6.3</td><td>102.0</td><td>88.1</td><td>10.2</td></tr><tr><td>40.0</td><td>59.5</td><td>6.7</td><td>104.0</td><td>87.3</td><td>10.5</td></tr><tr><td>42.0</td><td>61.1</td><td>6.1</td><td>106.0</td><td>85.3</td><td>9.3</td></tr><tr><td>44.0</td><td>61.8</td><td>6.6</td><td>108.0</td><td>86.7</td><td>8.1</td></tr><tr><td>46.0</td><td>61.7</td><td>8.0</td><td>110.0</td><td>84.4</td><td>10.0</td></tr><tr><td>48.0</td><td>62.7</td><td>8.5</td><td>112.0</td><td>83.7</td><td>14.4</td></tr><tr><td>50.0</td><td>63.2</td><td>8.1</td><td>114.0</td><td>89.9</td><td>12.7</td></tr><tr><td>52.0</td><td>62.4</td><td>9.2</td><td>116.0</td><td>90.8</td><td>10.5</td></tr><tr><td>54.0</td><td>63.9</td><td>7.4</td><td>118.0</td><td>89.9</td><td>10.9</td></tr><tr><td>56.0</td><td>61.8</td><td>9.3</td><td>120.0</td><td>92.0</td><td>13.6</td></tr><tr><td>58.0</td><td>61.1</td><td>11.4</td><td>122.0</td><td>91.8</td><td>22.1</td></tr><tr><td>60.0</td><td>62.4</td><td>10.2</td><td>124.0</td><td>94.2</td><td>23.9</td></tr><tr><td>62.0</td><td>66.4</td><td>9.2</td><td>126.0</td><td>93.0</td><td>22.3</td></tr><tr><td>64.0</td><td>66.7</td><td>10.7</td><td>128.0</td><td>95.4</td><td>22.3</td></tr><tr><td>66.0</td><td>66.8</td><td>10.2</td><td>130.0</td><td>94.7</td><td>21.7</td></tr><tr><td>68.0</td><td>65.7</td><td>10.6</td><td>132.0</td><td>87.9</td><td>13.1</td></tr></tbody></table>

<table><caption>**Table 3**
Hα RC from the 36 cm Data</caption><thead><tr><th>Radius<br>(arcsec)</th><th>V<sub>rot</sub><br>(km s<sup>-1</sup>)</th><th>ΔV<sub>rot</sub><br>(km s<sup>-1</sup>)</th><th>Radius<br>(arcsec)</th><th>V<sub>rot</sub><br>(km s<sup>-1</sup>)</th><th>ΔV<sub>rot</sub><br>(km s<sup>-1</sup>)</th></tr></thead><tbody><tr><td>10.0</td><td>27.8</td><td>6.6</td><td>220.0</td><td>112.3</td><td>8.1</td></tr><tr><td>20.0</td><td>36.7</td><td>5.6</td><td>230.0</td><td>113.9</td><td>7.6</td></tr><tr><td>30.0</td><td>49.4</td><td>3.7</td><td>240.0</td><td>116.5</td><td>7.2</td></tr><tr><td>40.0</td><td>53.9</td><td>4.3</td><td>250.0</td><td>114.5</td><td>7.8</td></tr><tr><td>50.0</td><td>59.1</td><td>5.1</td><td>260.0</td><td>109.2</td><td>8.2</td></tr><tr><td>60.0</td><td>62.6</td><td>5.5</td><td>270.0</td><td>105.3</td><td>6.4</td></tr><tr><td>70.0</td><td>65.6</td><td>4.8</td><td>280.0</td><td>105.3</td><td>5.5</td></tr><tr><td>80.0</td><td>70.7</td><td>4.6</td><td>290.0</td><td>107.3</td><td>6.4</td></tr><tr><td>90.0</td><td>73.9</td><td>4.0</td><td>300.0</td><td>106.1</td><td>7.8</td></tr><tr><td>100.0</td><td>78.5</td><td>4.2</td><td>310.0</td><td>100.3</td><td>5.4</td></tr><tr><td>110.0</td><td>82.4</td><td>4.6</td><td>320.0</td><td>100.2</td><td>4.6</td></tr><tr><td>120.0</td><td>87.1</td><td>4.9</td><td>330.0</td><td>98.2</td><td>4.8</td></tr><tr><td>130.0</td><td>89.6</td><td>5.4</td><td>340.0</td><td>92.9</td><td>7.7</td></tr><tr><td>140.0</td><td>94.9</td><td>5.7</td><td>350.0</td><td>92.0</td><td>12.6</td></tr><tr><td>150.0</td><td>98.1</td><td>5.0</td><td>360.0</td><td>96.2</td><td>11.6</td></tr><tr><td>160.0</td><td>99.3</td><td>5.7</td><td>370.0</td><td>102.4</td><td>18.9</td></tr><tr><td>170.0</td><td>98.6</td><td>7.2</td><td>380.0</td><td>103.5</td><td>21.9</td></tr><tr><td>180.0</td><td>101.1</td><td>8.7</td><td>390.0</td><td>101.0</td><td>19.5</td></tr><tr><td>190.0</td><td>103.2</td><td>9.4</td><td>400.0</td><td>97.7</td><td>16.0</td></tr><tr><td>200.0</td><td>107.0</td><td>9.1</td><td>410.0</td><td>94.9</td><td>13.6</td></tr><tr><td>210.0</td><td>114.0</td><td>7.4</td><td>420.0</td><td>85.5</td><td>14.7</td></tr></tbody></table>

in the past and where new material continues to fall today. Cosmological simulations of disk galaxy formation predict a wealth of baryonic structures and substructures up to ultra-

faint surface brightness levels, possibly due for instance to tidal debris from accretion and disruption of an expected rich population of luminous satellites (Bullock & Johnston 2005).
<table><caption>**Table 4**
Parameters and Results for the Mass Models</caption><thead><tr><th></th><th>H I RC<sup>a</sup></th><th>36 cm Hα RC<sup>b</sup></th></tr></thead><tbody><tr><td>Luminous component</td><td>(M/L<sub>B</sub>)<sub>*</sub> = 2.2 M<sub>☉</sub>/L<sub>☉</sub></td><td>(M/L<sub>B</sub>)<sub>*</sub> = 2.6 ± 0.3 M<sub>☉</sub>/L<sub>☉</sub></td></tr><tr><td>Dark halo component</td><td>r<sub>c</sub> = 2.7 kpc<br>σ = 40.8 km s<sup>-1</sup><br>ρ<sub>0</sub> = 0.038 M<sub>☉</sub> pc<sup>-3</sup></td><td>r<sub>c</sub> = 2.9 ± 0.8 kpc<br>σ = 37.0 ± 6.0 km s<sup>-1</sup><br>ρ<sub>0</sub> = 0.027 ± 0.009 M<sub>☉</sub> pc<sup>-3</sup></td></tr><tr><td>At R<sub>HO</sub> (6.0 kpc)</td><td>ρ<sub>halo</sub> = 0.0025 M<sub>☉</sub> pc<sup>-3</sup><br>M<sub>dark</sub>/M<sub>lum</sub> = 0.80<br>M<sub>(dark+lum)</sub> = 1.3 × 10<sup>10</sup> M<sub>☉</sub></td><td>ρ<sub>halo</sub> = 0.0020 M<sub>☉</sub> pc<sup>-3</sup><br>M<sub>dark</sub>/M<sub>lum</sub> = 0.67<br>M<sub>(dark+lum)</sub> = 1.2 × 10<sup>10</sup> M<sub>☉</sub></td></tr><tr><td>At the last point</td><td>r<sub>outer</sub> = 7.35 kpc<br>ρ<sub>halo</sub> = 0.0015 M<sub>☉</sub> pc<sup>-3</sup><br>M<sub>dark</sub>/M<sub>lum</sub> = 0.97<br>M<sub>(dark+lum)</sub> = 1.5 × 10<sup>10</sup> M<sub>☉</sub></td><td>r<sub>outer</sub> = 6.84 kpc<br>ρ<sub>halo</sub> = 0.0015 M<sub>☉</sub> pc<sup>-3</sup><br>M<sub>dark</sub>/M<sub>lum</sub> = 0.75<br>M<sub>(dark+lum)</sub> = 1.3 × 10<sup>10</sup> M<sub>☉</sub></td></tr></tbody></table>

**Notes.**

<sup>a</sup> Carignan & Puche (1990).

<sup>b</sup> This work.

<figure><img src="image_8.png" /><figcaption>**Figure 7.** Mass model (isothermal sphere halo) for the 36 cm Hα RC (filled circles) of NGC 7793. The H I curve (open circles) is also shown.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Figure 8.** Radial Hα profile of NGC 7793. Superposed on it is the radial profile (filled circles) of Ferguson et al. (1996).</figcaption></figure>

The faintest features visible in M31 reach effective V-band surface brightnesses greater than $\mu_V \sim 30$ mag arcsec$^{-2}$. The currently most powerful technique to probe the very low surface brightness regions is resolved star counts, but it is only applicable to our nearest large neighbors, such as M31 and M33. Both galaxies appear to show evidence for metal-poor, pressure-

supported stellar halos but only M31 shows evidence for recent accretion (Ibata et al. 2005). The combination of diffuse light surface photometry with resolved star counts allowed Irwin et al. (2005) to reach an effective V-band surface brightness of $\mu_V \sim 32$ mag arcsec$^{-2}$ for M31. Globular cluster and planetary nebula populations also offer additional clues to the formation and evolution at large radii.

The presence of the neutral gas component, detected through its H I emission, at radii several times larger than the optical disk (measured from its surface brightness at $\mu_B = 25$ mag arcsec$^{-2}$) has now been well known for more than 30 years. Many of the extended H I RCs are rising or flat at their outermost points, while others are slightly decreasing. Nevertheless, none of them shows a Keplerian decline, meaning that the edge of the mass distribution has not yet been found (Puche & Carignan 1991). The only suggestion that such an edge could have been reached is for the dwarf galaxy DDO 154 (Carignan & Purton 1998). Deep H I observations have shown that H I disks are abruptly truncated at column densities near $10^{18} - 10^{19}$ atoms cm$^{-2}$, where the RCs still do not have a Keplerian behavior (e.g. van Gorkom 1993). If the metagalactic UV background is sufficiently strong, beyond a certain galactic radius the cold gas may become ionized (Bochkarev & Siuniaev 1977).

The total Hα emission from star-forming galaxies is divided roughly in half, between discrete H II regions and the DIG. Pioneering work by Reynolds (1984) established that only the massive OB stars are able to ionize the DIG. On the other hand, all the observers agree on the fact that the DIG fraction seems to be independent of galaxy parameters such as star-formation rate and Hubble type. This appears somewhat controversial. More recently, Reynolds et al. (1999) and Collins & Rand (2001) suspected that OB stars cannot exclusively explain the ionization state of the DIG. Dopita et al. (2006) suggested that part of the DIG may consist of extremely evolved filamentary H II regions which may be difficult to detect.

On the other hand, if ionizing radiation escapes from H II regions to ionize the DIG, it does escape from the galaxies and affects the ionization state of the intergalactic medium (IGM) and the galactic medium of external galaxies which may be partially at the origin of this UV radiation. Indeed, a key question is the origin of the UV photons responsible for ionizing the hydrogen in the intergalactic medium (the Lyα forest). The most
likely sources of ionizing photons are young hot stars in galaxies and quasi-stellar objects (QSOs) (Barkana & Loeb 2001) but their exact origin remains one of the unsolved questions of modern cosmology. Observations of high-redshift quasars imply that the re-ionization of cosmic hydrogen was completed by $z \sim 6$ (e.g. Fan et al. 2006, and references therein). Lack of observational evidence and theoretical uncertainties makes it difficult to estimate the contribution made by both sources and leads to inconsistent results. To complicate the scheme, the relative contribution of QSOs and star-forming galaxies depends on the lookback time (and references therein Fan et al. 2006).

Recently, based on the first data release of the SINGG survey of H1-selected galaxies (Meurer et al. 2006), Oey et al. (2007) have undertaken a quantification of the ionization in neutral galaxies and the diffuse and warm ionized medium (NGC 7793 is unfortunately not included in the first SINGG data release of 109 galaxies). They concluded that the mean fraction of diffuse ionized gas in their sample is ~0.59, slightly higher but consistent with the value ~0.40 found in previous samples (e.g. Thilker et al. 2002; Zurita et al. 2000; Wang et al. 1999; Hoopes et al. 1996) and also consistent with the value ~0.50 found by Ferguson et al. (1996) for NGC 7793. The difference between Oey et al. (2007) and previous studies may be due to selection effects favoring large, optically bright and nearby galaxies with high star-formation rates. NGC 7793 is closer than any (except one) of the first SINGG data release. We have computed, for NGC 7793, its Hα effective (half light) radius $\sim 1.97 \pm 0.05$ kpc (~120 arcsec). Referring to Equation (1) from Oey et al. (2007), and using the Hα total luminosity of $4.1 \times 10^{40}$ erg s$^{-1}$ computed by Ferguson et al. (1996), we found that the logarithm of effective surface brightness $log(\Sigma_{H\alpha}) = 38.65$ erg s$^{-1}$ kpc$^{-2}$. Following Oey et al. (2007), this allows NGC 7793 to be classified as a normal galaxy with respect to its star-formation rate.

## 6.1. Possible Origins of the Ionization: Internal and/or External

Several mechanisms for the ionization of the neutral hydrogen and for heating the electron population belonging to the DIG may be found in the literature. BFQ1997 review them in the specific context of NGG 253. The main source of ionization and heating may be (see references in BFQ1997) the metagalactic ionizing background; compact halo sources; compact disk sources (white dwarf populations or horizontal-branch stars, young enough to produce significant UV emission); ram pressure heating (NGC 253 and NGC 7793 lie both in the Sculptor group having little intracluster medium); turbulence-driven MHD-wave heating; mixing layers driven by bulk flows; galactic fountain material driven by the inner starburst through shocks; dilute photoionization; gas phase depletion (induced by the formation of grains); low-energy cosmic-ray electrons and young stellar disk.

BFQ1997 ruled out most of these mechanisms, except ionization by the hot young stars of the disk. Even if those young stars are in the disk and most of them further in, the warp of the H1 disk (which is the case for both NGC 253 and NGC 7793) makes it possible to expose it to their radiation. In particular, they ruled out ionization by the cosmic UV background which is suspected to be ~ five times below the ionizing flux necessary to explain the emission seen in NGC 253. As the Hα disk does not reach the outskirts of the H1 disk of NGC 7793, it is very unlikely that the source of ionization of the DIG is the metagalactic UV background. Indeed, if the metagalactic UV background were at the origin of the ionization it should have

principally affected the outer H1 regions, which is not the case. An alternative could be that the Hα detection level is not yet low enough to be able to detect the ionization by the cosmic UV background radiation; thus, this should mean that the expected flux should have an Hα emission measure $E_m(H\alpha)$ lower than what was measured for NGC 7793, namely ~0.2–2.0 pc cm$^{-6}$.

## 6.2. A Truly Declining Rotation Curve

The existence of falling RCs was first claimed in the context of the effect of cluster environments on the member galaxies. Following the work of Dressler (1980), the increase of intergalactic gas and of gravitational interactions expected toward the centers of clusters should not only affect the morphological types of the systems but also their kinematics and mass distribution. Whitmore et al. (1988), from long-slit emission-line observations, presented evidence for a correlation in the sense that the inner-cluster spirals tend to have falling RCs, while those of the outer cluster and the vast majority of field spirals seem to have flat or even rising RCs. However, Amram et al. (1993) using full 3D FB data did not confirm these correlations and moreover found that many galaxies for which Whitmore et al. (1988) claimed a falling RC had in fact a flat or even rising RC after a careful analysis of the FB 2D velocity fields (Amram et al. 1996).

Declining RCs have been seen before in other systems (Casertano & van Gorkom 1991; Honma & Sofue 1997; Ryder et al. 1998; Sofue & Rubin 2001; Noordermeer 2007). However, those galaxies are most of the time earlier-type systems (S0–Sbc) with highly concentrated stellar light distribution and the maximum rotation velocity is reached at small radii (few hundreds kpc and $<\alpha^{-1}$). This is certainly not the case for NGC 7793 which has a very small bulge and a relatively diffuse (exponential) light distribution and where $V_{max}$ is reached at ~$4\alpha^{-1}$. Keplerian declines have also been observed in a few edge-on systems (e.g. NGC 891: Sancisi & Allen 1979; Oosterloo et al. 2007, NGC 3079: Veilleux et al. 1995 and NGC 4244: Olling 1996), but the interpretation in the case of those galaxies is much more difficult. Finally, a truncation of the halo at ~10 kpc was advocated to explain the decline of the last two points of the RCs of NGC 5204 (Sicotte & Carignan 1997) and NGC 253 (Bland-Hawthorn et al. 1997), but here the decrease of $V_{max}$ and the last velocity point is only ~10% of $V_{max}$ and ~10% of $r_{max}$, while, for NGC 7793, the decrease is ~25% of $V_{max}$ and over about half the radius range.

For late-type nearly bulgeless galaxies, such as NGC 7793, a declining RC is extremely rare. As can be seen in Figure 6, the decline of the RC seen with the H1 data is confirmed by the Hα 36 cm data and the kinematical analysis of the three sets of data (H1 & Hα) gives very similar results. Since a bulge component cannot be invoked to explain the falling gradient of the RC, NGC 7793 really seems to have a genuine declining RC. The new data also confirm that the decline is slower than Keplerian and that a dark component is still necessary to explain the observed kinematics.

## 7. SUMMARY AND CONCLUSIONS

Deep Hα observations of NGC 7793 have been presented. The main results are as follows.

1. A total of 20 h of observations was obtained on the Marseille 36 cm telescope which allowed us to reach sensitivities of the order of $E_m(H\alpha) \sim 0.2–2.0$ pc cm$^{-6}$;
2. this allowed the detection of diffuse Hα emission out to the edge of the H I disk;

3. a warp of the disk plane already seen in the H I data is also seen in the H II disk;

4. an RC is derived out to 2.2' from the 3.6 m data and out to 7' from the 36 cm data;

5. the two Hα RCs superposed exactly with the H I RC;

6. the Hα results confirm the H I findings that NGC 7793 has a truly declining RC;

7. a model of the mass distribution gives a total mass for NGC 7793 of $M_{\text{(dark+lum)}} = 1.3-1.5 \times 10^{10} M_{\odot}$ for $M_{\text{dark}}/M_{\text{lum}} = 0.75-1.0$ at the last velocity point.

This was our first experiment of doing such long integrations using a 36 cm telescope coupled with our FANTOMM scanning FB system. This yielded very interesting results for NGC 7793 by detecting diffuse Hα emission all the way to the edge of the H I disk and confirming its peculiar kinematics. In the near future, we intend to carry out the same kind of observations for all the Sculptor Group galaxies, hoping to reach even fainter levels. This should be possible with an even more sensitive camera soon to be available (Daigle et al. 2004, 2006b), based on an EMCCD, which should allow us to increase the detective quantum efficiency by a factor ~3–4.

We would like to thank the staff of the ESO La Silla Observatory for their support. We acknowledge support from the Natural Sciences and Engineering Research Council of Canada and the Fonds Québécois de la recherche sur la nature et les technologies. The Digitized Sky Surveys (DSS images) 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. The IR images were obtained by the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA.

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