UNVEILING THE NATURE OF M94's (NGC4736) OUTER REGION: A PANCHROMATIC PERSPECTIVE

In order to explore in detail the structural characteristics of the outer region of M94 in the optical regime, we decided to take a very deep exposure of this galaxy (see Figure 1) using the Ritchey–Chrétien 0.5 m telescope of the BlackBird Remote Observatory (BBRO) situated in the Sacramento Mountains (New Mexico, USA). The camera used was a Santa Barbara Instrument Group (SBIG) STL-11100 CCD camera, which has a field of view (FOV) of 277 × 182 and a pixel size of 045. The angular resolution of this image is ∼34.

To maximize the photon collection, our imaging consists on multiple deep exposures through a very broad non-infrared clear luminance filter (3500 Å < λ < 8500 Å), and a set of red, green, and blue filters from the SGBI custom scientific filters set.⁷ The total luminance exposure time allocated to this image was 555 minutes. In addition, to decrease the effect of noise, and consequently increase the detection and enhancing of the faint structures we have applied a Gaussian blur filter (Davies 1990, p. 42; Haralick & Shapiro 1992, Chapter 7). The sigma of the Gaussian kernel used on convolving the images is 1 pixel. This kernel was applied only to the outer regions to reveal more clearly this structure. As shown in a previous work (Martínez-Delgado et al. 2008), the faintest structures reachable with the BBRO telescope using the luminance filter with similar exposure times is ≳27.5 mag arcsec⁻² in the R band.

Since we lack a calibration of the optical luminance filter, our image is used only to show the faint structure of the outer disk at these wavelengths.

The UV observations are obtained from the GALEX mission (Martin et al. 2005). In particular, these data were retrieved from the Nearby Galaxy Survey mission (Bianchi et al. 2003a, 2003b; Gil de Paz et al. 2004, 2007). GALEX imaging benefits from a large FOV (125 diameter), a very low sky background and high sensitivity. We have used its two UV filters: a far-ultraviolet (FUV) filter centered at 1528 Å (FWHM 269 Å) and a near-ultraviolet (NUV) filter centered at 2271 Å (FWHM 616 Å). The angular resolution of these imaging is ∼46, and pixel size is 15. Absolute calibration uncertainties are ∼15% in both the FUV and NUV (Dale et al. 2007). An image of M94 (NGC4736) in the UV filters can be seen in the left panel of Figure 2.

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Optical data in five bands (u', g', r', i', and z') were obtained from the SDSS (York et al. 2000) archive. SDSS images have a pixel size of 0396 and typical angular resolution of ∼1''. Due to the large apparent size of the galaxy, we had to create a mosaic of eight individual SDSS frames (135 × 98 each) to cover the total galaxy angular extension. An image of the galaxy in the SDSS optical bands can be seen in the central panel of Figure 2.

J_s, H, and K_s images were extracted from the 2MASS NASA/IPAC Infrared Science Archive (IRSA). This galaxy is included in the 2MASS Large Galaxy Atlas (Jarrett et al. 2003). This atlas already provides a single image (20' × 233) covering this galaxy composed of the individual 2MASS fields. The angular resolution is ∼3'' and the pixel size is 1''.

IRAC (3.6 μm, 4.5 μm, 5.8 μm, and 8 μm) bands and MIPS (24 μm, 70 μm, and 160 μm) bands were obtained from the Spitzer Legacy program SINGS (Kennicutt et al. 2003). The pixel size is 075 for the IRAC (246 × 179) mosaics, and 15, 45, and 9'' for MIPS 24 μm, 70 μm, and 160 μm mosaics, respectively. Calibration uncertainties are ∼10% for IRAC data, and 4% (24 μm), 7% (70 μm), 12% (160 μm) for MIPS data (Dale et al. 2007). An image of M94 (NGC4736) in the Spitzer infrared filters can be seen in the right panel of Figure 2. The angular resolution of these images is summarized in Table 1.

The observed profiles coupled with the galaxy morphology suggest classifying this galaxy as a Type III (Erwin et al. 2005). In fact, one of the most interesting features of the surface brightness profiles of M94 is the unchanging nature of the global structure of the galaxy from the UV to the far-infrared. This implies that stars of all ages as well as dust are similarly distributed throughout the galaxy structure. The similarity between the UV and FIR profiles is more or less expected as both wavelength ranges are tracing the most active star formation regions of the galaxies. In relation to the optical and NIR data (although we warn that for these last data we lack the information in the outer region) which trace the intermediate-old stellar component, we think that the fact that they also share the shape of the young stellar component implies that the galaxy, globally, is actively forming new stars through all the disk and that this activity has been maintained similarly in the last gigayears. As we will show later in the paper, this scenario is supported by the specific star formation rate (sSFR) distribution of the galaxy which is relatively constant within a factor of 3 through the whole galaxy and by the fact that the gas exponential infall timescales are similar along the galaxy.

An exception is seen for the 70 and 160 μm MIPS bands, where we see the inner star-forming ring is almost invisible. However, that is clearly the effect of the larger point-spread function (PSF) at these wavelengths (cf. Table 1).

One of the most interesting features of the surface brightness profile of M94 is the brightness (∼23.5 mag arcsec⁻² in r' band) at which the outer disk appears. Normally, for Type III galaxies, the break occurs at faintest surface brightness. For example, Pohlen & Trujillo (2006) find a typical surface brightness of ∼24.7 ± 0.8 mag arcsec⁻² in the r' band, whereas Erwin et al. (2008a) find ∼24.2 ± 0.5 mag arcsec⁻² in the R band. This makes M94, in comparison, a Type III galaxy having an outer disk on the very bright side. However, M94 is not an unique example within the family of Type III objects, in fact, it is possible to find other galaxies with similar characteristics. For example, M77 (NGC1068) is strikingly similar to M94 (see its profile on Pohlen & Trujillo 2006). In the case of M77, the outer disk starts at ∼23 mag arcsec⁻², and morphologically also, both have similar features. For this reason, we think that both of these two galaxies could be considered as examples of Type III galaxies having the brightest (<23.5 mag arcsec⁻² in r' band) anti-truncated outer disks. However, a note of caution should be stated about the type of the galaxy M94. The Type III classification is based on the assumption (following the traditional picture of this galaxy) that the inner region (75''–200'') is a true disk. If this region is, however, considered as an oval distortion (i.e., a structure with a bar-like nature and not a real disk), then the genuine disk of the galaxy is the outer region (>200'') and the galaxy should be better considered as a Type I.

At any given wavelength, it can be shown that the surface brightness profiles μ_λ can be converted into stellar mass surface density profiles as follows:

$$\begin{equation} \log (M/(M_{\odot }\,{\rm pc}^2)) = \log (M/L)_{\lambda }-0.4(\mu _\lambda -m_{\rm abs,\odot,\lambda })+8.629 \end{equation} \tag{ 1 }$$

with (M/L)_λ the stellar mass-to-light ratio in solar units and m_abs,☉,λ the absolute magnitude of the Sun at a given wavelength λ. Lacking a deep near-infrared image, we have chosen the SDSS r band to estimate the M/L ratio. This band is selected because it is the reddest of the deepest SDSS bands. To estimate the (M/L)_r ratio, we have used the (g − r) color following the prescription given by Bell et al. (2003). We add 0.15 dex to the M/L obtained in Bell et al. (2003) to normalize the predicted M/L to a Salpeter (1955) initial mass function (IMF). The (g − r) color profile, the (M/L)_r, and the stellar mass density profile are shown in Figure 4. The minimum observed both in color and (M/L)_r is associated with the nuclear stellar ring. The shape of the stellar mass density profile is very similar to the shape of the reddest (stellar origin) surface brightness profiles we have. The stellar mass density at which the outer disk starts is ∼60 M_☉ pc⁻². As expected due to M94's bright outer disk, this value is higher than the mean value measured for late-type Type III galaxies (∼10 M_☉ pc⁻²; Bakos et al. 2008).

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Using the stellar mass density profile based on colors, one can calculate a rough estimate of the total stellar mass of the galaxy: ∼6.5 × 10¹⁰ M_☉. In each of the galaxy regions,⁹ the amount of stellar mass we measure is bulge region (3.2 × 10¹⁰ M_☉), inner disk region (1.7 × 10¹⁰ M_☉), and outer disk region (1.5 × 10¹⁰ M_☉). Due to the significant brightness of the outer disk, its contribution to the total stellar mass budget of the galaxy is quite significant (∼23%). This is a factor of ∼2 larger than the average late-type Type III outer disk (Bakos et al. 2008).

To assess the origin of the outer disk structure, a key element is to measure its star formation rate (SFR). This value can give us clues on whether this region of the galaxy is still forming (i.e., creating new stars) or whether it is an old structure. Following Muñoz-Mateos et al. (2007), the SFR can be computed from the apparent magnitude (corrected for internal extinction) in the FUV (AB system) using the calibration given by Kennicutt (1998)

$$\begin{equation} \log ({\rm SFR})(M_{\odot }\,{\rm yr}^{-1}) = 2\log d({\rm pc})-0.4\ {\rm FUV}\ -9.216. \end{equation} \tag{ 2 }$$

This can be transformed to a SFR per surface area as follows:

$$\begin{equation} \log ({\rm SFR}_\mu)(M_{\odot }\,{\rm yr}^{-1}\,{\rm pc}^{-2}) = -0.4\mu _{\rm FUV}+1.413. \end{equation} \tag{ 3 }$$

To estimate the internal extinction A_FUV,in in the FUV, we follow the empirical relation between the TIR-to-FUV ratio (i.e., the total luminosity in the infrared over the luminosity in the FUV), log(F_TIR/F_FUV) and the observed (FUV–NUV) color derived by Boissier et al. (2007). Once log(F_TIR/F_FUV) is obtained, the attenuation profiles are computed using the fit of Buat et al. (2005)

$$\begin{equation} A_{{\rm FUV,in}} = -0.0333X^3+0.3522X^2+1.1960X+0.4967 \end{equation} \tag{ 4 }$$

with X = log(F_TIR/F_FUV). The median value of A_FUV,in within the inner 430'' is 1.7 mag. This translates (using A_K = 0.0465A_FUV; Muñoz-Mateos et al. 2007) to an inner median extinction in the K-band profile of 0.079 mag.

Using Equation (2), we can estimate the total SFR of the galaxies as well as the SFR at the different components. We find that the total SFR for M94 is 1.04 M_☉ yr⁻¹ which is distributed across the different regions of the galaxy as follows: bulge (0.75 M_☉ yr⁻¹), inner disk (0.14 M_☉ yr⁻¹), and outer disk (0.15 M_☉ yr⁻¹). The amount of stars the outer disk is forming is comparable to the inner disk and it is a significant (∼10%–15%) fraction of the total SFR of the galaxy. This clearly shows, that at least for M94, the outer disk is a very active region of the galaxy. This activity is directly visible when looking at the UV and IR images shown in Figure 2, where the unobscured young stars as well as the hot dust are clearly seen in form of spiral arms in the outer region of the galaxy.

Another important parameter to measure is the sSFR, i.e., the amount of star formation per unit stellar mass. This value informs about the efficiency of the star formation in the different regions of the galaxies. The sSFR can be derived from the combination of Equations (1) and (3) to give

$$\begin{eqnarray} \log ({\rm sSFR})(\,{\rm yr}^{-1}) &=& -0.4(\rm FUV-{\it m}_{\lambda })-\log ({\it M/L}_{\lambda }) \nonumber \\ &&-0.4{\it m}_{\rm abs,\odot,\lambda }-{\rm 7.216}. \end{eqnarray} \tag{ 5 }$$

Both SFR and sSFR radial distributions are plotted in Figure 5. Our estimates agree very well by those produced by Boissier et al. (2007) for the SFR density (their Figure 9.39) of this galaxy: ∼10⁻⁸ M_☉ pc⁻² yr⁻¹ at 50'' (bulge), ∼5 × 10⁻⁹ M_☉ pc⁻² yr⁻¹ at 150'' (inner disk), and ∼4 × 10⁻¹⁰ M_☉ pc⁻² yr⁻¹ at 300'' (outer disk). Muñoz-Mateos et al. (2007) have noted that nearby spirals show a slightly positive increase of the sSFR from inside-out. This result also applies in the particular case of M94, where we find that the outer disk has a larger sSFR (∼0.012 Gyr⁻¹) than the inner disk (∼0.006 Gyr⁻¹). In other words, per unit stellar mass, the outer disk is more active (efficient) forming stars.

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Using the fluxes obtained in the 17 filter bands, we have created the spectral energy distributions (SEDs) ranging from 0.15 to 160 μm in the different regions of the galaxy (see Table 2). The SEDs across the galaxy are shown in Figure 6.

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To extract some relevant physical parameters from the SEDs, we have used synthetic templates computed with the code GRASIL (Silva et al. 1998). This code couples the spectral (and chemical) evolution of stellar populations with the radiative transfer through a dusty interstellar medium. Consequently, the models consistently account for the emission from stars as well as absorption and emission from dust in galaxies. GRASIL allows the variation of a large set of free parameters but here we concentrate only in the small subset that mostly affect the shape of the SED (Panuzzo et al. 2007). We describe briefly which parameters were left to change during the fitting of the SEDs (see Silva et al. 1998 for a detailed description of the code) as follows.

• 1.  
  Total infall mass, M_inf. This is the amount of primordial gas that has infalled to form the galaxy. We have allowed the following range of variation depending on the region of the galaxy which is fitted: bulge ((0.8–5) × 10¹⁰ M_☉), inner disk ((0.6–3) × 10¹⁰ M_☉), outer disk ((0.6–3) × 10¹⁰ M_☉), and the full galaxy ((1–7) × 10¹⁰ M_☉).
• 2.  
  Exponential infall timescale, τ_b. Gas is assumed to be continuously infalling at a rate proportional to exp(−t/τ_b). τ_b was allowed to change from 0.1 to 10 Gyr.
• 3.  
  Efficiency of Schmidt-type law, ν. The SFR is assumed in GRASIL to follow a Schmidt-type law of the form SFR(t) = νM_g(t)^k, where M_g is the gas mass at any time, k is the exponent of the Schmidt law which we fixed to 1, and ν is the free efficiency parameter varying from 10⁻³ to 4.
• 4.  
  Fraction of molecular mass to total gas mass (M_mol/M_gas). We allow this parameter to range from 0.1 to 0.99.
• 5.  
  The escape timescale of newly born stars from their parent molecular clouds, t_esc. We let this vary from 10⁻³ to 10⁻¹ Gyr.
• 6.  
  The mass of the molecular clouds, M_MC. The mass of the molecular clouds together with the radii of the molecular clouds is related to the optical depth of the molecular clouds, τ_MC ∝ M_MC/r²_MC. We fixed r_MC = 14 pc and let M_MC vary from 10³ to 10⁷ M_☉.

To allow a comparison with other works the adopted IMF is a Salpeter IMF in the mass range from 0.1 to 100 M_☉. Due to the low inclination of our galaxy, we use the output of the code with zero inclination. We assume that the galaxy has a present age of 13 Gyr.

For the SED of each region, we have computed the minimum χ². Due to the large number of free parameters (six in our case), we have avoided a brute force approach that implies to compute a large set of templates. For example, assuming that 10 values per parameter are desired, 10$^{N_{\rm par}}$ templates should be created. In current powerful desktops every GRASIL template takes ∼30 s to be computed. Consequently, the amount of time required in a brute force approach is prohibitive. To overcome this difficulty, we have applied a Markov chain Monte Carlo technique based on the Metropolis algorithm (Metropolis et al. 1953; Neal 1993). The details of the code that we have used are in Asensio Ramos et al. (2007).

The best-fit parameters together with the 1σ error are shown in Table 3. Together with these values, GRASIL also provides the present SFR and the optical depth of molecular cloud at 1 μm τ_MC and the amount of mass in gas and stars.

We can conduct now a comparison between the stellar mass obtained using the (g − r) color and the ones obtained using the GRASIL code. Comparing the stellar mass determined with GRASIL with the ones derived in Section 6.2, following Bell et al. (2003), we find them systematically (∼0.7) lower. However, it is worth stressing that within the error bars both estimations agree. From the above comparison, we think it is safe saying that the amount of stellar mass contained within the different regions of the galaxy is as follows: (2.8 < M_⋆ < 3.2) × 10¹⁰ M_☉ (bulge), (1.3 < M_⋆ < 1.7) × 10¹⁰ M_☉ (inner disk), (0.9 < M_⋆ < 1.5) × 10¹⁰ M_☉ (outer disk), and (4.2 < M_⋆ < 6.5) × 10¹⁰ M_☉ (total). In relation to the SFR, we find that GRASIL and the prescription presented in Muñoz-Mateos et al. (2007) agree very well within the error bars.

The GRASIL prediction in relation to the amount of present gas (i.e., not transformed into stars) in the different regions of the galaxy can be also compared with the recent measurements of H i (Walter et al. 2008). These authors find a total amount of gas of 4 × 10⁸ M_☉ for M94. This number is in excellent agreement with the GRASIL prediction (4.5 ± 1.0) × 10⁸ M_☉.

From the GRASIL results one can extract the following information. (1) The efficiency of the star formation, as characterized by the ν parameter is very similar through the whole structure of the galaxy, with no significant changes from the bulge to the outer disk. (2) The mass of the typical molecular clouds where the star formation is taking place seems, however, to be much smaller in the inner region of the galaxy than in the outer region. This could be related to the much more violent conditions (influence of the active nucleus) close to the center of the galaxy preventing the formation of massive molecular clouds. (3) The exponential infall timescale of the gas seems to vary also across the galaxy. The gas appears to take more time to be deposited in the bulge than what requires to be placed in the outer disk. This could be understood if the gas requires, as expected, a large loss of angular momentum to feed the bulge than the inner disk.

It has been proposed (Peñarrubia et al. 2006) that extended galactic disks can be form by a tidally disrupted dwarf galaxy in prograde orbit that is coplanar with the host galaxy disk. As a result of this merging, the stellar debris ends up resettling into an extended exponential disk in dynamical equilibrium. Depending on the mass of the satellite, orbit eccentricity and inclination, the stellar debris exhibit a rotation that could range from 30–50 km s⁻¹ lower than the host circular velocity up to a factor of ∼2 smaller.

Favoring a merger origin for the outer disk of M94 is the fact that its rotation curve is declining from the inner region (∼3 kpc) to the outer region (∼9 kpc) by ∼30% (Mulder 1995; de Blok et al. 2008). However, a common concern with the merging scenario (particularly if the merger has a large mass ratio) is the possibility that the accretion destroys the inner disk (Hopkins et al. 2009). In our case, the outer disk of M94 contains a large fraction (∼23%) of the total mass of the galaxy. If all the outer disk were entirely the result of a disrupted dwarf the implied merger ratio would be as high as 1:4.

Another problem with the merger scenario, if we want to explain entirely the outer region of M94 as a tidally disrupted satellite, is the very different ellipticity the inner disk and the outer region has. In the merging hypothesis, the ellipticities of both components can be interpreted as a reflect of the different inclination they have. In fact, transforming the observed ellipticities to inclinations, we find that the inner region will have an inclination of ∼35° whether the outer disk will have only ∼8°. Merging simulations of massive satellites with disk galaxies whereas the disk survived the encounter only found a maximum tilt of ∼7° for the outer regions (Velázquez & White 1999). This is much smaller than what is observed for this galaxy.

Even in the case that the origin of the outer region of M94 could not be explained by a major merger it could be well the case that an interaction of M94 with another galaxy could be the responsible of triggering both the star formation we see in this part of the galaxy as well as the many morphological structures this galaxy has inner ring, inner disk/oval distortion, gap, outer spiral arms, etc. The interaction possibility is, however, disfavored by the observations. Although M94 is the main member of the Canes Venatici I Group, it seems unlikely that it has suffered any interaction with another member of that group recently. In fact, such group has been found to be only weakly gravitationally bound. Moreover, most of the galaxies in this group appear to be moving with the expansion of the universe, which will prevent nearby (repeated) encounters affecting M94 (Karachentsev et al. 2003).

We also explore whether the plethora of structures we see in M94 as well as the enhanced star formation in its periphery could be created assuming a perturbation of internal (secular) origin. It is well known that bars can be produced via dynamical instabilities in galactic disks. A particular form of bars is what is known as oval distortion which are weak bars also called "fat bars" that often resemble normal slightly inclined disk having even spiral arms (see, e.g., Jogee et al. 2002). As mentioned in Section 2, the inner disk of M94 has been sometimes considered as an oval distortion more than a truly inclined disk (Kormendy & Norman 1979). This seems to be a reasonable hypothesis since the inclination of the galaxy, as derived in the UV and IR imaging for the outer disk, is lower than what it would be derived from the shape of the inner disk. It is worth stressing that this conclusion suggesting that the inner region of M94 is an oval distortion more than an truly inclined disk cannot firmly established on the basis of the optical images alone (which were the main source of information used in previous works), but, both the UV and IR images presented in this paper clearly show that there is a continuation in the spiral arms from the inner (oval) region to the outer disk. If both structures were decoupled, as suggested by the apparent different inclination and explained in the merger scenario, this prolongation of the spiral arms would be extremely unlikely. Under the hypothesis that the inner region is an oval distortion the problem with the different inclinations among the inner and the outer disk of M94 is solved since the oval distortion is not inclined but has a different ellipticity than the outer disk because is intrinsically oval and not circular.

If the inner region is an oval distortion, this structure could be a serious candidate to explain the spiral arm structure we see in the outer disk (Binney & Tremaine 1987, and references therein), and consequently to be the ultimate responsible of the enhanced star formation we measure in this part of the galaxy. Oval distortions are known to create spiral arms that can be sustained for long time in isolated galaxies (e.g., Lindblad 1960; Toomre 1969; Sanders & Huntley 1976; Athanassoula 1980). In fact, oval distortions have been considered as important as bars when considering the secular evolution of a disk galaxy (Kormendy & Kennicutt 2004).

We have created a toy model to explore whether the observed oval distortion can produce spiral arms similar to what we see in the outer disk. Our simple model is composed of a bulge, an oval distortion, an outer disk, and a dark matter halo. To characterize the different components of the galaxy, we use different analytical formulae that we fit to the stellar mass density profile in order to have realistic parameters (see Figure 7). Considering the oval distortion as a very mild bar, we use the analytical formula by Ferrers (1877) to describe it

$$\begin{equation} \begin{centering} \rho = \left\lbrace \begin{array}{@{}ll@{}} \frac{15}{8}\frac{M_{\rm od}}{\pi abc}(1-m^2)^1, & m\le 1\\ 0, & m\ge 1, \end{array}\right. \end{centering} \end{equation} \tag{ 6 }$$

where $m^2 = \frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}$, and a is the major axis, b is the minor, and c is the vertical axis, taken here as 500 pc, with a > b > c. This bar model is very popular in the literature (see, e.g., Sanders & Tubbs 1980; Papayannopoulos & Petrou 1983; Schwarz 1985; Athanassoula 1992; Patsis 2005, etc.). From the fit to the stellar surface mass density we obtain a = 4.9 kpc, b = 4.1 kpc, and a total mass for the oval distortion equal to M_od = 1.3 × 10¹⁰M_☉.

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The remaining components of the galaxy (the bulge, the outer disk, and the dark matter halo) have been modeled using the Miyamoto & Nagai (1975) analytical models. The Miyamoto–Nagai potential is described by the equation

$$\begin{equation} \begin{centering} \Phi _{M}(R,z) = -\frac{GM}{\sqrt{R^2+(a+\sqrt{z^2+b^2})^2}}. \end{centering} \end{equation} \tag{ 7 }$$

The parameters retrieved from the fit to the stellar mass surface density are bulge (M = 2.0 × 10¹⁰ M_☉, a = 0.05 kpc, and b = 0.6 kpc), outer disk (M = 2.8 × 10¹⁰ M_☉, a = 6.5 kpc, and b = 0.5 kpc), and halo (M = 20.0 × 10¹⁰ M_☉, a = 0.0 kpc, and b = 30 kpc). Note that the outer disk in this model has a factor of ∼2 more stellar mass than what we have measured before using the outer region (200''–430'') of the stellar mass profile. This is explained because in the model the stellar mass density profile is extrapolated in- and outward, to zero and infinity, respectively. Once the galactic potential is set, we can start running a simulation and see how a gaseous disk responds to the potential. Before doing this, we can use the linear approximation to calculate the angular frequency, and therefore estimate the radii of the main resonances (Figure 8) associated with the gravitational potential we have created. This is important for this galaxy since several resonant structures like the inner ring are observed.

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One of the key issues when considering bars, or oval distortions, and their corresponding resonances is the pattern speed, i.e., how fast the bar rotates as a solid body. The pattern speed determines many different structures, such as the radii of the different resonant rings, or their actual existence. In the case of our study, the variation of the pattern speed also determines the appearance of the spiral arms and their shape. A precise study of the spiral arms and their origin (Romero-Gómez et al. 2007) establishes that when increasing the pattern speed in a given barred model, the spiral arms become more tightly wounded.

Several pattern speeds have been proposed to explain different features in M94. We started with Ω_p = 56 km s⁻¹ kpc⁻¹ proposed by Mulder & Combes (1996) and decreased this value down to Ω_p = 30 km s⁻¹ kpc⁻¹. We found that a model that is able to reproduce the shape of the outer spiral arms as well as the inner ring of the galaxy has Ω_p = 38 km s⁻¹ kpc⁻¹. This number agrees nicely with previous studies, such as Waller et al. (2001), where they studied the central part of the galaxy and obtained Ω_p = 35 km s⁻¹ kpc⁻¹. With the pattern speed that we are using, R_CR = 5.2 kpc, and consequently R_CR/R_bar = 1.04. In that sense, the oval distortion that we have created would be considered as a fast bar (Aguerri et al. 2003). In addition, our pattern speed produces an inner ring at a radius of ∼1 kpc, at the same distance than the one observed.

Once the gravitational potential and the pattern speed are fixed, we run our simulation to explore the response on a pure gas disk. We use the code FTM 4.4 (updated version) from Heller & Shlosman (1994), which allow us to study the dynamical response of the gas based on smoothed particle hydrodynamics (SPH). We use 150,000 collisional particles to simulate the gas, isothermal and non self-gravitating. Initially, the gaseous particles are distributed following a Miyamoto–Nagai density distribution. In Figure 9, left panel, we show a snapshot of our simulation showing clearly the spiral arms, as a result of the oval distortion. In addition, the inner ring that is observed in the real galaxy can be seen. To make a more quantitative comparison of our toy model with the observations, in Figure 9, right panel, we compare the density profile of the gas in our simulation with the FUV surface brightness profile. The peaks on the FUV profile represent the places where the star formation is enhanced. We can see that there is a reasonable agreement between the peaks in the FUV and the position of the peaks where the density of the gas in the model is higher.

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According to our simulation, if the oval distortion survives for long time (Athanassoula & Misiriotis 2002; Martinez-Valpuesta et al. 2006), the spiral arm and the ring will also survive. However, a slow secular evolution is expected in the radius of the oval structure and the pattern speed. In addition, we should take into account the slowly consumption of the gas by the star formation (which could be somehow counterbalance by the new gas infall) that will also decrease the amount of gas in the spiral arms and oval distortion.

In a forthcoming paper (I. Martínez-Valpuesta et al. 2010, in preparation), we plan to increase the resolution of our hydrodynamical simulation to explore in more detail the inner region of the galaxy. In particular, we will explore the velocity shear field of the galaxy to probe whether the dynamics linked to the oval distortion can help to explain the GRASIL findings in relation to the efficiency, molecular cloud mass, and infall timescale found from the stellar population analysis. Our aim is to find a consistent model able to reproduce at the same time the new H i kinematic data (de Blok et al. 2008) in the outer region.