Dynamical model of the grand-design spiral galaxy NGC 157

Transcription

1 Astron. Astrophys. 317, (1997) ASTRONOMY AND ASTROPHYSICS Dynamical model of the grand-design spiral galaxy NGC 157 M.J. Sempere 1,2, and M. Rozas 2 1 University of Chicago, Yerkes Observatory, Williams Bay, WI , USA 2 IAC, Instituto de Astrofísica de Canarias, E La Laguna, Tenerife, Spain Received 20 November 1995 / Accepted 7 June 1996 Abstract. Numerical simulations of the interstellar medium under the action of a density wave provide an accurate method for determining the positions of the main resonances in grand design spiral galaxies. Barred spiral galaxies are among the best candidates for a single and well defined wave mode, because bars are standing waves which may share the same pattern speed as the spiral structure. In line with our previous work on determination of the pattern speed in barred spiral galaxies (M 51, NGC 4321 and NGC 7479) by the method employed in this article, we have applied it to the grand design spiral NGC 157 and compared the results with previous determinations of the position of the resonances in this galaxy. NGC 157 is an interesting case to test the theoretical predictions on star formation and nuclear activity and their relation with the existence and position of the main resonances induced by a spiral density wave: it is an isolated grand design galaxy and possesses a weak bar, an inner and an outer pseudo ring and a nuclear starburst. A pattern speed of Ω p =40 km s 1 kpc 1 is derived from our numerical model and this places the corotation resonance at a radius of R CR 5 kpc ( 50 ), in the middle of the disc and close to the point where the two inner arms suffer a bifurcation and broadening. This result differs slightly from the optical determination by Elmegreen et al. (1992) and Elmegreen & Elmegreen (1995), who identified the location of the corotation radius at the endpoint of the ridges of star formation, at a radius R CR =0.44 R 25 ( 56 ). With this pattern speed two inner Lindblad resonances are predicted at radii R ILR1 = 0.25 kpc and R ILR2 = 0.75 kpc respectively. The bar ends well inside the corotation limited by the disc scale length ( 35 ) and a stellar nuclear oval misaligned with the major axis of the bar could be confined within the ILR 2. The Hα image features and the starburst nucleus of NGC 157 are related to the global dynamics of the galaxy and therefore to the positions of the resonances. The Hα image shows a ringlike region of star formation located between the corotation and the outer Lindblad resonance (OLR). An inner pseudo ring appears surrounding the main bar which is almost Send offprint requests to: M.J. Sempere Present address: Observatorio Astronómico Nacional. Campus Universitario. E Alcalá de Henares (Madrid), Spain void of HII regions with the exception of three hot spots that appear near the centre of the galaxy, one at the nucleus, and the two others at a radius of 0.4 kpc, between the ILR 1 and the ILR 2. These circumnuclear Hα features could be the signature of a patchy ring. NGC 157 has been classified as a late type galaxy (SAB(rs)bc); its kinematical behaviour as well as the distribution of HII regions along the bar and its nuclear starburst are in agreement with recent surveys of star formation in bars (Arsenault, 1989) and classification of bar types in early and late type galaxies (Combes & Elmegreen 1993). Key words: galaxies: kinematics and dynamics galaxies: spiral galaxies: individual: NGC 157 galaxies: SM radio lines: galaxies 1. Introduction Interest in barred systems has increased recently since infrared images of galaxies are revealing the existence of ovals and barred potentials in at least a 60% of disc galaxies (Sellwood & Wilkinson 1993; Ho et al. 1995). Bars have been postulated as one of the possible mechanisms responsible for the origin of density waves. Numerical simulations (Sanders & Huntley 1976; Combes & Gerin 1985) have shown how even a weak barred potential can trigger a spiral perturbation in the gaseous component and exert strong tidal torques which transfer angular momentum outwards. In particular, the patterns in isolated grand design galaxies can be satisfactorily explained on the basis of a predominant and well defined wave mode driven by a bar. A bar itself, is a standing m = 2 wave mode which in many models shares the same pattern speed as the spiral structure. However, several numerical simulations show that if the central mass concentration is very high (producing a very peaked rotation curve in the centre), two wave modes with different pattern speeds can coexist for some time in a galaxy disc (Sellwood & Sparke 1988; Friedli & Martinet 1992). In this case, the spiral could be the driven response to the large amplitude

2 406 M.J. Sempere & M. Rozas: Dynamical model of the grand-design spiral galaxy NGC 157 bar, through three mode coupling (Tagger et al 1987). Nevertheless, this behaviour would be transient and more appropiate to describe the kinematics of early type galaxies. The possibility of different pattern speeds in the central region of a galaxy ( 1 kpc), where bars within bars can coexist, has been shown in numerical simulations by Friedli & Martinet (1993) and could not be rouled out in the case of misaligned bars. These systems of nested bars have been invoked as a mechanism of gas fueling in active galactic nuclei (AGNs) and starburst galaxies (STBs) (Shlosman et al. 1989, 1990). The problem of how bars form and evolve and its influence on the global evolution of a galaxy disc is directly associated with the determination of the bar pattern speed and the location of the main resonances in the disc. Since the evolution of a bar is essentially a function of accreted mass (Friedli & Benz 1993) the pattern speed will vary with time. The Hubble sequence could under these circunstances be a dynamical classification where galaxies evolve from late to early types. Bars in early and late type galaxies would have different dynamical characteristics. Many observational and numerical studies have been recently developed to shed light on this matter. Combes & Elmegreen (1993), using of self consistent N body numerical simulations show how the pattern speed of the bar depends critically on the bulge to disc mass ratio and the disc scale length. Bars in late type galaxies would be limited by the scale length of the disc rather than by resonances, and early type galaxies would possess bars limited by the corotation resonance. Friedli & Benz (1993; 1995) have carried out 3 D self consistent numerical simulations of the secular evolution of isolated barred galaxies, including stars, gas, star formation and radiative cooling. They find that bars can modify the dynamical evolution of galaxies. The gravitational coupling between stellar bars and interstellar medium can provide gas fueling to the nucleus that ultimately leads to the destruction of the bar because of the appearance of a strong and extended inner Lindblad resonance. The influence of bars in star formation is extensively analysed and it is predicted that bars do not affect the global SFR in the disc but they can modify severely circumnuclear star formation. Compared to unbarred spirals of the same type, barred galaxies have a higher probability of exhibiting star formation round the nucleus and a higher formation rate of massive stars in the inner regions, more evident in early type galaxies (Kennicutt 1994; Martin 1995; Ho et al. 1995). In the bar region, energy release leads to a significant alteration of the power law relation between SFR and gas surface density, and a non linear behaviour can take place here: an increase in the gas mass does not result in a corresponding increase in SF (Friedli & Benz 1995). Recent surveys of barred galaxies show a general trend: young bars in late type galaxies present intense star formation along their major axis (Martin 1995). On the contrary, for early type barred spirals a very small number of HII regions are observed in their bars, distributed as nuclear hotspots or circumnuclear rings. The nuclear activity in spiral galaxies has been long suspected to be related to the bar and ring features. In a survey of different morphological types of spiral galaxies carried out by Arsenault (1989) it is clearly found an excess of barred and ringed galaxies in STBs and AGNs. Moreover, AGNs are found to belong typically to early types and STBs to late types. The central mass distribution is the main property that differences early and late type galaxies and therefore the shape of their rotation curves. Star formation activity is linked to the perturbation of orbits at the ILRs. An effective star formation at the ILRs would stop the feeding of a central engine, and is more likely to happen in molecular gas rich late type spirals. That leads to the suggestion that an effective nuclear starburst phase is an inhibition mechanism to a more powerful type of activity like in AGNs. NGC 157 is a good candidate to make observation comparisons with the theoretical predictions for barred galaxies. It joins all the previous discussed features: it is an isolated grand design spiral galaxy with a weak bar, a circumnuclear ring and a starburst nucleus. Likewise, it possesses a spectacular burst of star formation in its disc and inner and outer pseudo rings. We have tried to find the connection between the global dynamics and the star formation morphology, through the determination of the position of the main resonances in its disc. In Sect. 2 we present a detailed description of NGC 157. Sect. 3 is devoted to the description of the numerical model. Finally, in Sect. 4, we discuss the main results of comparing the observed galaxy disc with the simulated one and we interpret the location of the resonances derived from the numerical simulations when compared to the features of the red and Hα images. 2. Global properties NGC 157 is a grand design spiral galaxy that has been classified as SAB(rs)bc by de Vaucouleurs et al. (1991) and as arm class 12 by Elmegreen & Elmegreen (1984). Its appearance changes notably if we analyse optical pictures taken at different wavelengths. In the near infrared atlas of spiral galaxies by Elmegreen (1981), the bar of NGC 157 is clearly contrasted. On the contrary, the blue band image of NGC 157 (see Elmegreen et al. 1992) shows a symmetric spiral structure in the inner disc which is broken in the outer disc with the bifurcation and broadening of the two inner symmetric arms, but no bar is discernible. In a deprojected red (R band) image of the galaxy (Fig. 1a, 1b) a weak bar with a PA b =93 and whose semi major axis extends 3.5 kpc, can be seen. An intense dust lane crosses it at the east side. The isophotes at this place are affected by dust extinction and the bar seems to be divided in two parts. An inner oval structure is guessed in the inner kpc but the presence of dust in this region does not allow us to affirm it conclusively. The spiral structure seems to be three armed in the inner region and multiarmed in the outer disc. In a previous study of the optical tracers of spiral wave resonances in galaxies using blue band images, Elmegreen et

3 M.J. Sempere & M. Rozas: Dynamical model of the grand-design spiral galaxy NGC Fig.1.aR band image of NGC 157 deprojected onto the galaxy plane to show the mass distribution used in numerical simulations to infer the stellar potential and the rotation curve. The three arm inner spiral structure can be appreciate. In the outer disc the arms bifurcate and became flocculent. b An enlargement of the 3 inner kpc showing the bar. The minor and major axis of the galaxy are oriented along the x and y axis respectively. al. (1992) found that NGC 157 presents three symmetric arms within the region limited by the 3:1 resonance. The m = 3 spiral is interpreted as due to the asymmetry in the two predominant spiral arms, that produce an m = 1 component driven by the two arm spiral and with the same pattern speed. The formation of the three arm component would require several revolutions after the formation of the asymmetric two arm system and it would be much weaker than the two arm component. The Hα CCD image recently obtained by Rozas et al. (1996a) (Fig. 2) shows a nicely delineated pattern of the arms extending to the edge of the optical disc. The main HII regions are concentrated along the inner spiral arms and in an inner pseudo ring enclosing the main bar. There is also a quasi ringlike structure at the outer disc, that Elmegreen & Elmegreen (1992) identify with the corotation circle. On the contrary, the bar is almost devoid of HII regions with the exception of a central hot spot at the nucleus and a very patchy circumnuclear ring. An estimate of the star formation rate (SFR) at the starburst nucleus of NGC 157 gives a value of 1 M yr 1 The distribution of the HII regions and their luminosities and other physical properties have been analysed in Rozas et al. (1996a,b). There are no significant differences in the luminosity functions of the HII regions in the arms and the interarm disc, and there is evidence of a population of highly luminous density limited regions in the arms. We have also measured the symmetry in the Hα images of the distribution of star formation of the two principal arms (Rozas et al. 1995), via cross correlation, and find that there is a strong degree of symmmetry only at the ends of the bar, but not in the arms where intense peaks of star formation in one arm are not reproduced spatially in the other. In an analysis of the radial distribution of the HII regions in external galaxies, Athanassoula et al. (1993) found no general correlation between the position of the corotation and the outer Lindblad resonance (OLR) determined by Elmegreen et al. (1992), and the radial density peaks of star formation. In the particular case of NGC 157 they found that the corotation is situated just at the radius of a surface brightness maximum. This study could be not conclusive, because the determination of the resonances by optical tracers involves a high degree of uncertainty. On the other hand, the resonances need not be confined to narrow regions, but may show considerable radial extent due, for example, to the distortion of the orbits produced by a bar (García Burillo et al. 1994). The CO(1 0) emission observed by Tinney et al. (1990) displays a pronounced non axisymmetry. The total H 2 mass calculated is M H2 = M and the ratio of the far infrared continuum luminosity to the CO luminosity, L FIR /L CO =38. In the survey carried out by Young et al. (1995) the measured global CO flux of this galaxy is 500±90 Jy km s 1 and they fit the CO distribution by a model with smooth radial fall off that peaking at the centre of the galaxy disc. Braine & Combes (1992) calculate a log M H2 =8.78 for the nucleus (inner kpc). They note the fact that this galaxy does not present strong Hα emission in the centre although it has a high optical surface brightness and strong CO. In the IRAS survey NGC 157 is found to be an intermediate IRAS luminosity galaxy with L FIR = L. The integrated H i flux (corrected beam dilution) obtained by Staveley Smith & Davies (1987) is FI=62.6± 5.5 Jy km s 1 and M HI M. These authors note the asymmetry of the

4 408 M.J. Sempere & M. Rozas: Dynamical model of the grand-design spiral galaxy NGC 157 Fig. 2. Hα deprojected image of NGC 157. Strong star formation is located along two symmetric inner arms, an inner ring surrounding the bar and distributed in a quasi ringlike structure in the outer disc The bar is devoid of HII regions with the exception of three nuclear spots and two brilliant concentrations at the edges of the bar and the beginning of the spiral arms. The circles are the predicted positions of ILR 1, ILR 2 and corotation obtained for the best fit of the numerical model. H i disribution and point out the presence of MCG at a distance 8. 9 SE. The first attempt to determine a rotation curve was carried out by Burbidge et al. (1961), who found an extended internal region of rigid body rotation. However, more recently Afanasiev et al. (1988) derived a new rotation curve from high resolution Hα data, which shows a two humped feature with a rapidly rotating nucleus ( 110 km s 1 ) in the inner 0.5 kpc. We will use in this paper the Hα and R band images taken by M. Rozas et al. with the 4.2m William Herschel telescope at the Roque de los Muchachos Observatory (Spain) to compare with the results of our numerical simulations. A detailed description of the observations can be found in Rozas et al. (1996a). We have used a distance to the galaxy of 22.5 Mpc (corresponding to an H o =75 km s 1 Mpc 1 ). At this distance 1 109pc. The adopted deprojection angles are i= 45 and PA=35 (Grosbøl 1985). As conventional, our diagrammes are oriented with the kinematical minor and major axes parallel to the x and y axes, respectively. 3. Numerical models The numerical models applied to NGC 157 have been used for the determination of the pattern speed in several grand design galaxies: M 51, García Burillo et al. (1993); NGC 4321, García Burillo et al. (1993) and Sempere et al. (1994); NGC 7479, Sempere et al. (1995). For the present study we performed two different runs of numerical simulations of the dynamical behaviour of the molecular interstellar medium following: The model of cloud inelastic collisions proposed by Combes & Gerin (1985). A modification of the previous model including the gas self gravitation and partially inelastic collisions. The models are designed to find the best global morphological fit between the molecular gas and the stellar disc potential, since the observations indicate that the distribution of molecular gas in isolated spiral galaxies follows the perturbation of the potential due to the bar and the spiral component as shown in a significant number of observations. Nevertheless, the existence of ILRs in the inner region of a spiral galaxy can produce a shift between a gas bar and a stellar bar (Sanders & Tubbs 1980; Combes & Gerin 1985; Shaw et al. 1993). A detailed analysis of the gas behaviour in the centre of the galaxy would require a more sofisticated numerical model based in a polar grid which provides more spatial resolution at these radii and a better tracer of the potential than a R band image. Our method is only a first step that can help us in later observations and in applying a more accurate numerical model to study new features. The two main input parameters of the numerical simulations are the pattern speed of the bar+spiral perturbation, Ω p, and the adopted mass distribution (or rotation curve). The accuracy of our method is based on the sensitivity of the model to the value of the pattern speed: very small variations of this parameter can change apreciably the final global morphologies. We have performed in the following steps, in our comparison of theory with observations: We need to derive the stellar potential for both runs of numerical simulations. The best tracer for this purpose would be an infrared image (unfortunately not available), but red images are fairly good tracers of the mass distribution in normal spiral galaxies where dust absorption does not affect dramatically the red wavelengths. However, we have to point out that NGC 157 has a lot of dust uniformly distributed all over its disc, with the exception of the central region ( 1 kpc). This fact could be expected since this galaxy presents a strong maximum of molecular gas emission at this place and neutral gas is associated to dust. In the V-R diagramme no peculiar features as rings can be appreciate. The only remarkable feature is an intense dust lane that crosses the east side of the bar (del Río, private communication). We can assume that the M/L ratio does not varies abruptly with radius. An R band image of the galaxy with a spatial resolution of /pixel and a seeing of 0. 8 was used to derive the mass distribution via the simplest hypotheses for the radial variation of the M/L ratio. In a first step, the foreground stars are removed and the image is deprojected onto the plane of the galaxy. Finally, the stellar surface density is computed from the brigthness distribution. The corresponding gravitational potential and rotation curve are calculated using a Fast Fourier Transform. The FFT method uses a two

5 M.J. Sempere & M. Rozas: Dynamical model of the grand-design spiral galaxy NGC Fig. 3. We show the comparison of the rotation curves in NGC 157 as derived from Hα data by Afanasiev et al. (1989) (stars) and from our model (solid line). dimensional cartesian grid of pixels of angular size which is equivalent to a spatial resolution of 59 pc. The numerical simulations begin adopting a constant M/L ratio and then the rotation curve derived from the model is compared with the best curve obtained from interstellar Hα emission observations (Afanasiev et al. 1988). In this first step, they are slightly different and we need to modify softly the M/L relation in the inner region (0.5 kpc) to obtain the final adopted rotation curve that fits the observed curve (Fig. 3). It was not necessary to add any dark matter component. The modelled rotation curve and the observed one present minor differences at some radius possibly due to the dust absorption, but the general shape is well reproduced. Fig. 4 shows the circular angular velocity Ω and the Lindblad precession frequencies, Ω κ/2, andω+κ/2, versus radius. The potential is extended in the z direction, perpendicular to the plane, under the assumption of cylindrical symmetry (i.e., x and y forces independent of z), since we are concerned only with the molecular gas of thickness 0.5 kpc. For the vertical forces, we assume that each stellar plane obeys the equilibrium of an infinite layer with a density law ρ = ρ 0 sech 2 (z/h), where we have adopted H = 2 kpc as the characteristic height. Finally, the total stellar potential is divided in its axisymmetric and non axisymmetric parts. The symmetric part is the azimuthal average of the total potential for each radius. The non axisymmetric component is obtained by subtraction of the axisymmetric part from the total potential and represents the contribution of the spiral arms and stellar bar to the potential. In both runs of numerical simulations we begin by launching molecular clouds in the axisymmetric potential with its rotational velocity and giving the clouds a small velocity dispersion of 10 km s 1. The non-axisymetric potential is Fig. 4. The angular frequencies Ω, Ω κ/2 and Ω+κ/2inkms 1 kpc 1 versus radius in kpc. The positions of the main resonances are shown for an Ω p =40kms 1 kpc 1 of the bar+spiral perturbation. There are two ILRs located at 0.25 and 0.75 kpc from the centre respectively and the co rotation resonance lies at a radius of 5 kpc. introduced gradually with a delay of a 25% the total time of the run ( years) and with a constant pattern speed Ω p. In the first model a total number of clouds are distributed according to a mass spectrum ranging from 10 3 to 10 6 M (Casoli & Combes 1982). The initial radial distribution is an exponential disc of scale length a d =3.5kpc and the distribution perpendicular to the plane is gaussian, as expected from the equilibrium of a multi component system. The clouds move as test particles in the stellar potential computed from the R band image, and interact via inelastic collisions which can produce coalescence, mass exchange or fragmentation, the total mass being conserved during the run. The energy lost by collisions is re injected via simulated star formation events: when a cloud reaches a mass M (giant molecular cloud), it is automatically fragmented into small clouds with a velocity dispersion of 10 km s 1 after a GMC life time of years. The total simulation time of a run is years ( 2 galaxy rotations). After this time molecular gas has been trapped into the potential well created by the non axisymmetric structure and has reached a quasi stationary state. In the second model we introduced the self gravity of the gas in order to better analyse the behaviour of the gas in the centre of the galaxy. NGC 157 has a total molecular gas mass M g = M and the total stellar mass inferred from our red image is M = M. The influence due to gas self gravitation in the global disc could not be very important because M g /M =0.08 < 0.1 (Wada & Habe 1992; Friedli & Benz 1993). Nevertheless, as we have previously noted in Sect. 2, Braine & Combes (1992) find a big amount of molecular gas in the central kpc, where

6 410 M.J. Sempere & M. Rozas: Dynamical model of the grand-design spiral galaxy NGC 157 Fig. 5a and b. Molecular cloud distribution obtained from the numerical simulations for two extreme values of Ω p: a 15 km s 1 kpc 1 and b 60 km s 1 kpc 1. The bar + spiral morphology is very different from the real galaxy and it is not quasi stationary. The physical size of the frame is the same than for Fig. 1a. gas self gravitation could be significant and would produce gravitational instability (Wada & Habe 1992). To obtain a clear picture of the simulation plots we have suppressed the star formation events to follow better the particle orbits. We have chosen arbitrarily all clouds with the same mass: 10 3 M. Clouds interact via partially inelastic collisions. The value of the inelasticity parameter in the direction parallel to the relative velocity between two colliding clouds is 0.65 and 1 in the perpendicular direction to assure the conservation of the angular moment. The gravitational forces due to the gas have been computed by an FFT method and added to the imposed stellar potential (Combes et al 1990). The total mass of the molecular gas in the optical disc is M H2 = (Tinney et al. 1990) within the R 25 radius. 4. Comparison between the model and the observations To compare the results of our models with the red and Hα images we produced simulated maps of the molecular gas under the assumption that the interstellar medium is optically thin in clouds (i.e. molecular cloud crowding factor is low for all the velocity clouds). We have computed and projected in the sky plane the position and radial velocity of each particle after a total run time. A data cube is built by convolving the expected emission of the clouds using a telescope beam halfwidth of 12. The cell size of the cube is 6 6 in the spatial dimensions and 3 km s 1 in velocity. Figures 5 and 6 show the final configurations of the molecular gas for several runs of the first model of inelastic collisions with different Ω p values ranging from 15 to 60 km s 1 kpc 1. Fig. 5 displays the results for the two extreme cases: Ω p =15 and Ω p =60kms 1 kpc 1 respectively. It can be seen that the final gas distribution obtained for these values of Ω p does not fit the global morphology of the galaxy. In particular, the bar plus spiral arms structure is very different from the real structure, and it is not quasi stationary, disappearing rapidly after one rotation period. A spiral structure similar to that observed is obtained only for a restricted values of Ω p. Fig. 6 shows the molecular gas distribution obtained for the values of Ω p =30, 35, 40, 45 km s 1 kpc 1, and at first sight these are very similar. The most notable difference is a general shift of the global structure which turns clockwise as Ω p increases. The final test to determine the pattern speed by this method is the comparison of the molecular gas distribution with a data set of observations at different wavelengths. The overlay of the isodensity contours of the red image (Fig. 7) and the Hα image (Fig. 8) on the modelled intesity map (grey scale) obtained from the self gravitating model are displayed for the same values of Ω p as in Fig. 6. In both cases the best fit is obtained for an Ω p =40km s 1 kpc 1. A quantitative comparison of the results of the simulations and the red image by a linear regression method gives correlation coeficients of 0.68, 0.73, 0.87 and 0.75 for the values Ω p =30, 35, 40, 45 km s 1 kpc 1 respectively. We use the red image to find the best fit to the main bar, and the Hα image to compare the morphology of the spiral structure. In Fig. 4 we showed the radii of the main resonances for Ω p = 40 km s 1 kpc 1 : the co rotation radius, where the angular velocity of the matter Ω is equal to the pattern speed of the density wave, is located at a radius of 50 ( 5 kpc) in the middle of the optical disc. Two inner Lindblad resonances are obtained due to the peaked rotation curve near the centre of the galaxy. They are located at radii 0.25 and 0.75 kpc respectively. The outer Lindblad resonance is in the outer disc at a radius of 10 kpc. The inner region of NGC 157 presents a complex morphology. The distribution of the most brilliant HII regions is concentrated in the two inner spiral arms and the bar is almost devoid of star formation with the exception of three hot spots. Braine & Combes (1992) noted as unexpected the large quantity of gas in the central regions of the galaxy, in contrast with the absence of star formation. The existence of a bar and two inner Lindblad resonances could explain this phenomenon: within the inner ILR gas orbits

7 M.J. Sempere & M. Rozas: Dynamical model of the grand-design spiral galaxy NGC Fig. 6a d. Particle plots showing molecular cloud distribution in the disc of NGC157 for several runs corresponding to different values of Ω p: a 30 km s 1 kpc 1, b 35 km s 1 kpc 1, c 40 km s 1 kpc 1, the best fit, and d 45 km s 1 kpc 1. The scale of the frames is the same than for Fig. 1a. are parallel to the main axis of the bar; between the two ILRs gas orbits follow the x 2 orbits, perpendicular to the bar, and in the region between the outer ILR and corotation orbits are again parallel to the bar (the x 1 family of orbits). Since gas can dissipate energy by collisions, gas orbits rotate gradually from parallel to perpendicular as the resonances are crossed. At the crossing of the ILRs the collision rate of molecular clouds increases due to the change of orientation of the clouds orbits and there is an enhancement of the gas density at these places that promotes the formation of GMC s and subsequently of the star formation events. As predicted by Friedli & Benz (1995) energy released by star formation could modify the Schmidt law along the bar impeding more star formation. Fig. 9 displays an overlay of the Hα (grey scale) and the red image (isodensity contours) in the two inner kpc of the galaxy. The three hot spots in the bar are located at the nucleus and between the two ILRs, in good agreement with the predictions of the theory. Above the nucleus a fainter HII region can be made out at the same radius than the two hot spots. This peculiar distribution could be a very patchy circumnuclear ring. NGC 157 is a starburst galaxy and as showed by Arsenault (1989) circumnuclears rings and barred features in late type spirals, are associated to starburst nucleii. Fig. 7c shows the overlay of the red image and the best fit of the simulations. The main bar and the arms are sucessfully reproduced in the model. The H α counterpart in Fig. 8c. emphasizes the close fit of the main two arm structure in the entire galaxy disc. The third arm that is well reproduced in the simulations does not appear in the H α image. As predicted in Elmegreen et al. (1992), the formation of the three arm component would require several revolutions after the formation of the asymmetric two arm system. The three arm component is younger and

8 412 M.J. Sempere & M. Rozas: Dynamical model of the grand-design spiral galaxy NGC 157 Fig. 7a d. Overlay of the density gas distribution (grey scale) corresponding to the values of Ω p: a 30 km s 1 kpc 1, b 35 km s 1 40 km s 1 kpc 1, the best fit, and d 45 km s 1 kpc 1, on the inferred projected mass distribution of NGC 157 (solid contours). kpc 1, c weaker than the predominant two arm structure and the lack of massive star formation could be due to this fact. From the determination of the position of the main resonances in other SBAbc galaxies as NGC 4321 and NGC 7479, we have found a very different kinematical characteristics that determines a large variety of bar properties and star formation processes. Although NGC 4321 has been classified as late type, its kinematical behaviour correspond more to that of an early type galaxy. On the contrary NGC 7479 show the bar characteristics and pattern speed predicted for a late type by Combes & Elmegreen (1992). NGC 157 could be an intermediate case since its rotation curve follows the general trend of late types but it posseses a local maximun at the centre. This first step in the determination of the resonances in NGC 157 seems to be in good agreement with the theoretical predictions of the Density Wave Theory (DWT), but more observations in other wavelengths, particularly from the centre of this galaxy, are necessary to complete our understanding of physical process involving the presence of a density wave.

9 M.J. Sempere & M. Rozas: Dynamical model of the grand-design spiral galaxy NGC Fig. 8a d. Overlay of the density gas distribution (grey scale) corresponding to the values of Ω p: a 30 km s 1 kpc 1, b 35 km s 1 40 km s 1 kpc 1, the best fit, and d 45 km s 1 kpc 1, on the Hα image of NGC 157 (grey contours). kpc 1, c 5. Conclusions We have determined the location of the main resonances in the disc of NGC 157 by means of hydrodynamical simulations of the molecular component of the interstellar medium. Our method is based on a global morphological fit of the simulated gas response to a density wave with real observations at different wavelengths. The most sensitive parameters in the numerical simulations are the pattern speed of the wave, Ω p, and the mass distribution in the galaxy, which produces the rotation curve. Since we have obtained the mass distribution from a red image of the galaxy with some assumptions about mass to light ratios the only free parameter that we vary in our simulations is Ω p. We have run two models: the first one is a model of cloud inelastic collisions, without self gravity, in which the effects of star formation are simulated. The second model considers partially inelastic collisions, supresses the star formation events and includes the gas self gravity in order to analyse in more detail the gas behaviour in the centre and the arms of the galaxy, where gas self gravity can play an important role.

10 414 M.J. Sempere & M. Rozas: Dynamical model of the grand-design spiral galaxy NGC 157 an extremely patchy circumnuclear ring of star formation. The nuclear starburst in this galaxy seems to be in agreement with previous surveys of nuclear activity in barred galaxies (Arsenault 1989) which found that starburst are predominant in late type galaxies with barred and ringed features. The most brilliant HII regions are located along the two symmetric inner arms and round the bar forming an inner pseudo ring. The arms seem to break at a well defined radius and form an outer pseudo ring. The outer ring develops between the corotation and the OLR. NGC 157 has been classified as a late type galaxy (SBA(rs)bc). Nevertheless, in previous determinations of the position of the resonances in other two galaxies, NGC 4321 and NGC 7479, classified as SBAbc, we have found a very different dynamical behaviour. It seems more adequate to classify spiral galaxies on the basis of both its kinematical and morphological properties. Fig. 9. The inner 2 kpc region of the Hα image of NGC 157 superposed to the response of the molecular gas in the best fit of the numerical simulations Ω p=40 km s 1 kpc 1. We can see a nuclear hot spot and two HII regions between the two inner ILRs. We summarize our results as follows: The best morphological fit is found for a value of Ω p = 40 km s 1 kpc 1 which places the co rotation radius at a radius of 5 kpc (50 from the nucleus). With this value of Ω p two ILRs are present located at 0.25 and 0.75 kpc from the nucleus respectively, and the OLR is at a distance of 10 kpc. The red image shows a weak bar and an inner stellar oval misaligned with the major axis of the bar could be present. Nevertheless we must be cautious because dust absorption could distort the ellipticity of the isophotes and only an infrarred image could confirm its presence. Two spiral arms extend from the ends of the bar out to a radius where they became floculent. A third weaker arm stretches out from the bar in the inner disc. With the pattern speed obtained in the simulations, the stellar oval would be circumscribed by the sustained by the x 2 orbits. The main bar ends well inside the corotation radius and its extent seems limited by the disc scale length (Combes & Elmegreen 1993). The arms bifurcate at the corotation and we are able to reproduce in our simulations the third inner arm with a single pattern speed. This result is in good agreement with Elmegreen & Elmegreen (1992), who interpret this feature as an m=1 wave driven by the non axisymmetry of the two main arms, rotating with the same pattern speed. We have analysed the main features of the Hα image relating them to the global dynamics of the galaxy. The positions of the main resonances determine the distribution of the HII regions: the two hot spots below the nucleus and a fainter HII region above it, are located between the ILRs forming Acknowledgements. This paper has been improved thanks to the valuable remarks and comments of the referee, Dr. Daniel Friedli. We gratefully acknowledge the Yerkes Observatory hospitality and specially the direct support of L.M. Hobbs. We thank Dr. J.E. Beckman for helpful comments on the manuscript. The William Herschel Telescope is operated on the island of La Palma by the Royal Greenwich Observatory in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias. This work was partially supported by the Spanish DGICYT (Dirección General de Investigación Científica ytécnica) Grants Nos. PB and PB References Afanasiev V.L., Burenkov A.N., Zasov A.V., Sil chenko O.K., 1988, Afz, 28, 2 Arsenault R., 1989, A&A, 217, 66 Athanassoula E., García Gómez C., Bosma A., 1993, A&AS, 102, 229 Braine J., Combes F., 1992, A&A, 264, 433 Burbidge E.M., Burbidge G.R., Prendergast K.H., 1961, ApJ, 134, 874 Casoli F., Combes F., 1982, A&A, 198, 43 Combes F., Gerin M., 1985, A&A, 150, 327 Combes F., Debbasch F., Friedli D., Pfenniger D., 1990, A&A, 233, 82 Combes F., Elmegreen B.G., 1993, A&A, 271, 391 Elmegreen D.M., 1981, ApJS, 47, 229 Elmegreen D.M., Elmegreen B.G., 1984, ApJS, 54, 127 Elmegreen B.G., Elmegreen D.M., Montenegro L., 1992, ApJS, 79, 37 Elmegreen D.M., Elmegreen B.G., 1995, ApJ, 445, 591 Friedli D., Martinet L., In: Thuan T.X., Balkowsky C., Tran Thanh Van J., (eds.) Physics of Nearby Galaxies. Nature or Nurture?. Editions Frontières, Gif sur Yvette, France, p. 527 Friedli D., Martinet L., 1993, A&A, 277, 27 Friedli D., Benz W., 1993, A&A, 268, 65 Friedli D., Benz W., 1995, A&A, 301, 649 García-Burillo S., Combes F., Gerin M., 1993, A&A, 274, 148 García-Burillo S., Sempere M.J., Combes F., 1994, A&A, 287, 419 Grosbøl P.J., 1985, A&AS, 60, 261 Ho L.C., Filippenko A.V., Sargent W.L.W., 1995, ApJS, 98, 477 Ho L.C., Filippenko A.V., Sargent W.L.W., In: Barred Galaxies. Proc IAU Symposium 157 (in press)

11 M.J. Sempere & M. Rozas: Dynamical model of the grand-design spiral galaxy NGC Kennicutt R.C., In: Shlosman I. (eds.). Mass Transfer Induced Activity in Galaxies. Cambridge University Press, Cambridge, p.131 Martin P., Roy J-R., 1995, ApJ, 445, 161 Martin P., In: Barred Galaxies. Proc IAU Symposium 157 (in press) del Río et al, 1996, (in preparation) Rozas M., Beckman J.E., Knapen J. H., In: Barred Galaxies. Proc IAU Symposium 157 (in press) Rozas M., Beckman J.E., Knapen J.H., 1996a, A&A, (in press) Rozas M., Knapen J.H., Beckman J.E. 1996b, A&A, (submitted) Sanders R.H., Tubbs A.D., 1980, ApJ, 235, 803 Sanders R.H., Huntley J.M., 1976, ApJ, 209, 53 Sellwood J.A., Sparke L.S., 1988, MNRAS, 231, 25 Sellwood J.A., Wilkinson A., 1993, Rep. Prog. Phys., 56, 173 Sempere M.J., García Burillo S., Combes F., Knapen J.H., 1994, A&A, 296, 45 Sempere M.J., Combes F., Casoli F., 1995, A&A, 299, 371 Shaw M.A., Combes F., Axon D.J., Wright G.S., 1993, A&A, 273, 31 Shlosman I., Frank J., Begelman M.C., 1989, Nat, 338, 45 Shlosman I., Begelman M.C., Frank J., 1990, Nat, 345, 679 Staveley Smith L., Davies R.D., 1987, MNRAS, 224, 953 Tagger M., Sygnet J.F., Athanassoula E., Pellat R., 1987, Apj, 318, L43 Tinney C.G., Scoville N.Z., Sanders D.B., Soifer B.T., 1990, ApJ, 362, 473 Young J.S., Xie S., Tacconi L., et al., 1995, ApJS, 98, 219 Vaucouleurs G. de, Vaucouleurs A. de, Corwin H.G., et al., 1991, Third Reference Catalogue of Bright Galaxies. Springer Verlag, New York. Wada K., Habe A., 1992, MNRAS, 258, 82 This article was processed by the author using Springer-Verlag LaT E X A&A style file L-AA version 3.