Dynamical model of the grand-design spiral galaxy NGC 157
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Astron. Astrophys. 317, 405–415 (1997)
ASTRONOMY
AND
ASTROPHYSICS
Dynamical model of the grand-design spiral galaxy NGC 157
M.J. Sempere1,2,? and M. Rozas2
1
University of Chicago, Yerkes Observatory, Williams Bay, WI 53191-0258, USA
2
IAC, Instituto de Astrofı́sica de Canarias, E-38200 La Laguna, Tenerife, Spain
Received 20 November 1995 / Accepted 7 June 1996
Abstract. Numerical simulations of the interstellar medium un- void of HII regions with the exception of three hot–spots that
der the action of a density wave provide an accurate method appear near the centre of the galaxy, one at the nucleus, and the
for determining the positions of the main resonances in grand– two others at a radius of ∼ 0.4 kpc, between the ILR1 and the
design spiral galaxies. Barred spiral galaxies are among the best ILR2 . These circumnuclear Hα features could be the signature
candidates for a single and well defined wave mode, because of a patchy ring.
bars are standing waves which may share the same pattern speed NGC 157 has been classified as a late–type galaxy
as the spiral structure. (SAB(rs)bc); its kinematical behaviour as well as the distri-
In line with our previous work on determination of the bution of HII regions along the bar and its nuclear starburst are
pattern speed in barred spiral galaxies (M 51, NGC 4321 and in agreement with recent surveys of star formation in bars (Ar-
NGC 7479) by the method employed in this article, we have senault, 1989) and classification of bar types in early and late
applied it to the grand–design spiral NGC 157 and compared type galaxies (Combes & Elmegreen 1993).
the results with previous determinations of the position of the
resonances in this galaxy. NGC 157 is an interesting case to test Key words: galaxies: kinematics and dynamics – galaxies: spi-
the theoretical predictions on star formation and nuclear activity ral – galaxies: individual: NGC 157 – galaxies: SM – radio lines:
and their relation with the existence and position of the main galaxies
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 Ωp = 40 km s−1 kpc−1 is derived from
our numerical model and this places the corotation resonance 1. Introduction
at a radius of RCR ∼ 5 kpc (∼ 5000 ), in the middle of the disc
Interest in barred systems has increased recently since infrared
and close to the point where the two inner arms suffer a bi-
images of galaxies are revealing the existence of ovals and
furcation and broadening. This result differs slightly from the
barred potentials in at least a 60% of disc galaxies (Sellwood
optical determination by Elmegreen et al. (1992) and Elmegreen
& Wilkinson 1993; Ho et al. 1995). Bars have been postulated
& Elmegreen (1995), who identified the location of the corota-
as one of the possible mechanisms responsible for the origin
tion radius at the endpoint of the ridges of star formation, at a
of density waves. Numerical simulations (Sanders & Huntley
radius RCR = 0.44 R25 (∼ 5600 ).
1976; Combes & Gerin 1985) have shown how even a weak
With this pattern speed two inner Lindblad resonances are
barred potential can trigger a spiral perturbation in the gaseous
predicted at radii RILR1 = 0.25 kpc and RILR2 = 0.75 kpc re-
component and exert strong tidal torques which transfer angular
spectively. The bar ends well inside the corotation limited by the
momentum outwards.
disc scale length (∼ 3500 ) and a stellar nuclear oval misaligned
In particular, the patterns in isolated grand–design galax-
with the major axis of the bar could be confined within the ILR2 .
ies can be satisfactorily explained on the basis of a predom-
The Hα image features and the starburst nucleus of
inant and well defined wave mode driven by a bar. A bar it-
NGC 157 are related to the global dynamics of the galaxy and
self, is a standing m = 2 wave mode which in many models
therefore to the positions of the resonances. The Hα image
shares the same pattern speed as the spiral structure. How-
shows a ringlike region of star formation located between the
ever, several numerical simulations show that if the central
corotation and the outer Lindblad resonance (OLR). An inner
mass concentration is very high (producing a very peaked ro-
pseudo–ring appears surrounding the main bar which is almost
tation curve in the centre), two wave modes with different pat-
Send offprint requests to: M.J. Sempere tern speeds can coexist for some time in a galaxy disc (Sell-
? wood & Sparke 1988; Friedli & Martinet 1992). In this case,
Present address: Observatorio Astronómico Nacional. Campus
Universitario. E-28871 Alcalá de Henares (Madrid), Spain the spiral could be the driven response to the large amplitude406 M.J. Sempere & M. Rozas: Dynamical model of the grand-design spiral galaxy NGC 157
bar, through three mode coupling (Tagger et al 1987). Never- The nuclear activity in spiral galaxies has been long sus-
theless, this behaviour would be transient and more appropiate pected to be related to the bar and ring features. In a survey
to describe the kinematics of early–type galaxies. The possibil- of different morphological types of spiral galaxies carried out
ity of different pattern speeds in the central region of a galaxy by Arsenault (1989) it is clearly found an excess of barred and
(∼ 1 kpc), where bars within bars can coexist, has been shown in ringed galaxies in STBs and AGNs. Moreover, AGNs are found
numerical simulations by Friedli & Martinet (1993) and could to belong typically to early–types and STBs to late–types. The
not be rouled out in the case of misaligned bars. These systems central mass distribution is the main property that differences
of nested bars have been invoked as a mechanism of gas fueling early– and late–type galaxies and therefore the shape of their
in active galactic nuclei (AGNs) and starburst galaxies (STBs) rotation curves. Star formation activity is linked to the pertur-
(Shlosman et al. 1989, 1990). bation of orbits at the ILRs. An effective star formation at the
The problem of how bars form and evolve and its influence ILRs would stop the feeding of a central engine, and is more
on the global evolution of a galaxy disc is directly associated likely to happen in molecular gas rich late–type spirals. That
with the determination of the bar pattern speed and the location leads to the suggestion that an effective nuclear starburst phase
of the main resonances in the disc. Since the evolution of a bar is is an inhibition mechanism to a more powerful type of activity
essentially a function of accreted mass (Friedli & Benz 1993) like in AGNs.
the pattern speed will vary with time. The Hubble sequence NGC 157 is a good candidate to make observation com-
could under these circunstances be a dynamical classification parisons with the theoretical predictions for barred galaxies. It
where galaxies evolve from late– to early–types. Bars in early– joins all the previous discussed features: it is an isolated grand–
and late–type galaxies would have different dynamical charac- design spiral galaxy with a weak bar, a circumnuclear ring and
teristics. a starburst nucleus. Likewise, it possesses a spectacular burst of
star formation in its disc and inner and outer pseudo–rings.
Many observational and numerical studies have been re-
We have tried to find the connection between the global
cently developed to shed light on this matter. Combes &
dynamics and the star formation morphology, through the de-
Elmegreen (1993), using of self–consistent N–body numerical
termination of the position of the main resonances in its disc.
simulations show how the pattern speed of the bar depends crit-
ically on the bulge to disc mass ratio and the disc scale–length. In Sect. 2 we present a detailed description of NGC 157.
Bars in late type galaxies would be limited by the scale–length Sect. 3 is devoted to the description of the numerical model.
of the disc rather than by resonances, and early–type galaxies Finally, in Sect. 4, we discuss the main results of comparing
would possess bars limited by the corotation resonance. the observed galaxy disc with the simulated one and we inter-
pret the location of the resonances derived from the numerical
Friedli & Benz (1993; 1995) have carried out 3–D self– simulations when compared to the features of the red and Hα
consistent numerical simulations of the secular evolution of images.
isolated barred galaxies, including stars, gas, star formation and
radiative cooling. They find that bars can modify the dynam-
ical evolution of galaxies. The gravitational coupling between 2. Global properties
stellar bars and interstellar medium can provide gas fueling to NGC 157 is a grand–design spiral galaxy that has been classi-
the nucleus that ultimately leads to the destruction of the bar be- fied as SAB(rs)bc by de Vaucouleurs et al. (1991) and as arm
cause of the appearance of a strong and extended inner Lindblad class 12 by Elmegreen & Elmegreen (1984). Its appearance
resonance. The influence of bars in star formation is extensively changes notably if we analyse optical pictures taken at different
analysed and it is predicted that bars do not affect the global SFR wavelengths.
in the disc but they can modify severely circumnuclear star for-
In the near–infrared atlas of spiral galaxies by Elmegreen
mation. Compared to unbarred spirals of the same type, barred
(1981), the bar of NGC 157 is clearly contrasted. On the con-
galaxies have a higher probability of exhibiting star formation
trary, the blue–band image of NGC 157 (see Elmegreen et al.
round the nucleus and a higher formation rate of massive stars in
1992) shows a symmetric spiral structure in the inner disc which
the inner regions, more evident in early type galaxies (Kennicutt
is broken in the outer disc with the bifurcation and broadening
1994; Martin 1995; Ho et al. 1995).
of the two inner symmetric arms, but no bar is discernible.
In the bar region, energy release leads to a significant alter- In a deprojected red (R–band) image of the galaxy (Fig. 1a,
ation of the power–law relation between SFR and gas surface 1b) a weak bar with a PAb = 93◦ and whose semi–major axis
density, and a non–linear behaviour can take place here: an in- extends ∼ 3.5 kpc, can be seen. An intense dust lane crosses
crease in the gas mass does not result in a corresponding increase it at the east side. The isophotes at this place are affected by
in SF (Friedli & Benz 1995). dust extinction and the bar seems to be divided in two parts. An
Recent surveys of barred galaxies show a general trend: inner oval structure is guessed in the inner kpc but the presence
young bars in late type galaxies present intense star formation of dust in this region does not allow us to affirm it conclusively.
along their major axis (Martin 1995). On the contrary, for early– The spiral structure seems to be three armed in the inner region
type barred spirals a very small number of HII regions are ob- and multiarmed in the outer disc.
served in their bars, distributed as nuclear hotspots or circum- In a previous study of the optical tracers of spiral wave
nuclear rings. resonances in galaxies using blue–band images, Elmegreen etM.J. Sempere & M. Rozas: Dynamical model of the grand-design spiral galaxy NGC 157 407
Fig. 1. a R–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 In an analysis of the radial distribution of the HII regions
within the region limited by the 3:1 resonance. The m = 3 spiral in external galaxies, Athanassoula et al. (1993) found no gen-
is interpreted as due to the asymmetry in the two predominant eral correlation between the position of the corotation and the
spiral arms, that produce an m = 1 component driven by the outer Lindblad resonance (OLR) determined by Elmegreen et
two–arm spiral and with the same pattern speed. The formation al. (1992), and the radial density peaks of star formation. In the
of the three arm component would require several revolutions particular case of NGC 157 they found that the corotation is sit-
after the formation of the asymmetric two–arm system and it uated just at the radius of a surface brightness maximum. This
would be much weaker than the two–arm component. study could be not conclusive, because the determination of the
The Hα CCD image recently obtained by Rozas et al. resonances by optical tracers involves a high degree of uncer-
(1996a) (Fig. 2) shows a nicely delineated pattern of the arms tainty. On the other hand, the resonances need not be confined
extending to the edge of the optical disc. The main HII re- to narrow regions, but may show considerable radial extent due,
gions are concentrated along the inner spiral arms and in an for example, to the distortion of the orbits produced by a bar
inner pseudo–ring enclosing the main bar. There is also a quasi– (Garcı́a–Burillo et al. 1994).
ringlike structure at the outer disc, that Elmegreen & Elmegreen
The CO(1–0) emission observed by Tinney et al. (1990)
(1992) identify with the corotation circle. On the contrary, the
displays a pronounced non–axisymmetry. The total H2 mass
bar is almost devoid of HII regions with the exception of a cen-
calculated is MH2 = 3.5×109 M and the ratio of the far infrared
tral hot–spot at the nucleus and a very patchy circumnuclear
continuum luminosity to the CO luminosity, LF IR /LCO =38.
ring. An estimate of the star formation rate (SFR) at the star-
In the survey carried out by Young et al. (1995) the measured
burst nucleus of NGC 157 gives a value of ∼ 1 M yr−1
global CO flux of this galaxy is 500±90 Jy km s−1 and they
The distribution of the HII regions and their luminosities
fit the CO distribution by a model with smooth radial fall–off
and other physical properties have been analysed in Rozas et
that peaking at the centre of the galaxy disc. Braine & Combes
al. (1996a,b). There are no significant differences in the lumi-
(1992) calculate a log MH2 = 8.78 for the nucleus (inner kpc).
nosity functions of the HII regions in the arms and the interarm
They note the fact that this galaxy does not present strong Hα
disc, and there is evidence of a population of highly luminous
emission in the centre although it has a high optical surface
density–limited regions in the arms.
brightness and strong CO. In the IRAS survey NGC 157 is found
We have also measured the symmetry in the Hα images to be an intermediate IRAS luminosity galaxy with LF IR =
of the distribution of star formation of the two principal arms 27.5 × 109 L .
(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 The integrated H i flux (corrected beam dilution) obtained
not in the arms where intense peaks of star formation in one arm by Staveley–Smith & Davies (1987) is FI=62.6± 5.5 Jy km s−1
are not reproduced spatially in the other. and MHI ' 109.9 M . These authors note the asymmetry of the408 M.J. Sempere & M. Rozas: Dynamical model of the grand-design spiral galaxy NGC 157
performed two different runs of numerical simulations of the
dynamical behaviour of the molecular interstellar medium fol-
lowing:
– 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 morpholog-
ical fit between the molecular gas and the stellar disc potential,
since the observations indicate that the distribution of molecu-
lar 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
Fig. 2. Hα deprojected image of NGC 157. Strong star formation is of the potential than a R–band image. Our method is only a first
located along two symmetric inner arms, an inner ring surrounding step that can help us in later observations and in applying a more
the bar and distributed in a quasi–ringlike structure in the outer disc accurate numerical model to study new features.
The bar is devoid of HII regions with the exception of three nuclear The two main input parameters of the numerical simulations
spots and two brilliant concentrations at the edges of the bar and the are the pattern speed of the bar+spiral perturbation, Ωp , and the
beginning of the spiral arms. The circles are the predicted positions of
adopted mass distribution (or rotation curve). The accuracy of
ILR1 , ILR2 and corotation obtained for the best fit of the numerical
our method is based on the sensitivity of the model to the value
model.
of the pattern speed: very small variations of this parameter can
H i disribution and point out the presence of MCG–02–02–056 change apreciably the final global morphologies.
at a distance 8.0 9 SE. We have performed in the following steps, in our comparison
The first attempt to determine a rotation curve was car- of theory with observations:
ried out by Burbidge et al. (1961), who found an extended in-
– We need to derive the stellar potential for both runs of nu-
ternal region of rigid–body rotation. However, more recently
merical simulations. The best tracer for this purpose would
Afanasiev et al. (1988) derived a new rotation curve from high
be an infrared image (unfortunately not available), but red
resolution Hα data, which shows a two–humped feature with a
images are fairly good tracers of the mass distribution in
rapidly rotating nucleus (' 110 km s−1 ) in the inner 0.5 kpc.
normal spiral galaxies where dust absorption does not af-
We will use in this paper the Hα and R–band images taken by
fect dramatically the red wavelengths. However, we have
M. Rozas et al. with the 4.2m William Herschel telescope at the
to point out that NGC 157 has a lot of dust uniformly dis-
Roque de los Muchachos Observatory (Spain) to compare with
tributed all over its disc, with the exception of the central
the results of our numerical simulations. A detailed description
region (∼ 1 kpc). This fact could be expected since this
of the observations can be found in Rozas et al. (1996a).
galaxy presents a strong maximum of molecular gas emis-
We have used a distance to the galaxy of 22.5 Mpc (cor- sion at this place and neutral gas is associated to dust. In the
responding to an Ho =75 km s−1 Mpc−1 ). At this distance V-R diagramme no peculiar features as rings can be appre-
100 ' 109pc. The adopted deprojection angles are i= 45◦ and ciate. The only remarkable feature is an intense dust lane
PA=35◦ (Grosbøl 1985). that crosses the east side of the bar (del Rı́o, private com-
As conventional, our diagrammes are oriented with the kine- munication). We can assume that the M/L ratio does not
matical minor and major axes parallel to the x and y axes, re- varies abruptly with radius.
spectively. An R–band image of the galaxy with a spatial resolution of
0.00 279/pixel and a seeing of 0.00 8 was used to derive the mass
3. Numerical models distribution via the simplest hypotheses for the radial vari-
ation of the M/L ratio. In a first step, the foreground stars
The numerical models applied to NGC 157 have been used are removed and the image is deprojected onto the plane of
for the determination of the pattern speed in several grand– the galaxy. Finally, the stellar surface density is computed
design galaxies: M 51, Garcı́a–Burillo et al. (1993); NGC 4321, from the brigthness distribution. The corresponding grav-
Garcı́a–Burillo et al. (1993) and Sempere et al. (1994); itational potential and rotation curve are calculated using
NGC 7479, Sempere et al. (1995). For the present study we a Fast Fourier Transform. The FFT method uses a two–M.J. Sempere & M. Rozas: Dynamical model of the grand-design spiral galaxy NGC 157 409
Fig. 3. We show the comparison of the rotation curves in NGC 157 as Fig. 4. The angular frequencies Ω, Ω−κ/2 and Ω+κ/2 in km s−1 kpc−1
derived from Hα data by Afanasiev et al. (1989) (stars) and from our versus radius in kpc. The positions of the main resonances are shown
model (solid line). for an Ωp = 40 km s−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.
dimensional cartesian grid of 256×256 pixels of angular
size 0.5500 × 0.5500 which is equivalent to a spatial reso-
lution of 59 pc. The numerical simulations begin adopting introduced gradually with a delay of a 25% the total time of
a constant M/L ratio and then the rotation curve derived the run (7.2 × 108 years) and with a constant pattern speed
from the model is compared with the best curve obtained Ωp .
from interstellar Hα emission observations (Afanasiev et – In the first model a total number of 4 × 104 clouds are dis-
al. 1988). tributed according to a mass spectrum ranging from 103 to
In this first step, they are slightly different and we need 106 M (Casoli & Combes 1982). The initial radial distri-
to modify softly the M/L relation in the inner region (0.5 bution is an exponential disc of scale length ad = 3.5 kpc
kpc) to obtain the final adopted rotation curve that fits the and the distribution perpendicular to the plane is gaussian,
observed curve (Fig. 3). It was not necessary to add any as expected from the equilibrium of a multi–component sys-
dark matter component. The modelled rotation curve and tem.
the observed one present minor differences at some radius The clouds move as test particles in the stellar potential
possibly due to the dust absorption, but the general shape is computed from the R–band image, and interact via inelastic
well reproduced. collisions which can produce coalescence, mass exchange
Fig. 4 shows the circular angular velocity Ω and the Lindblad or fragmentation, the total mass being conserved during the
precession frequencies, Ω−κ/2, and Ω+κ/2, versus radius. run. The energy lost by collisions is re–injected via simu-
The potential is extended in the z direction, perpendicular lated star formation events: when a cloud reaches a mass
to the plane, under the assumption of cylindrical symmetry ≥ 3 × 105 M (giant molecular cloud), it is automatically
(i.e., x and y forces independent of z), since we are con- fragmented into small clouds with a velocity dispersion of
cerned only with the molecular gas of thickness 0.5 kpc. 10 km s−1 after a GMC life–time of 4 × 107 years.
For the vertical forces, we assume that each stellar plane The total simulation time of a run is 7.2 × 108 years
obeys the equilibrium of an infinite layer with a density law (∼ 2 galaxy rotations). After this time molecular gas has
ρ = ρ0 sech2 (z/H), where we have adopted H = 2 kpc as been trapped into the potential well created by the non–
the characteristic height. axisymmetric structure and has reached a quasi–stationary
Finally, the total stellar potential is divided in its axisym- state.
metric and non–axisymmetric parts. The symmetric part is – In the second model we introduced the self gravity of the
the azimuthal average of the total potential for each radius. gas in order to better analyse the behaviour of the gas in
The non–axisymmetric component is obtained by subtrac- the centre of the galaxy. NGC 157 has a total molecular gas
tion of the axisymmetric part from the total potential and mass Mg = 3.5 × 109 M and the total stellar mass inferred
represents the contribution of the spiral arms and stellar bar from our red image is M∗ = 4.5 × 1010 M . The influence
to the potential. due to gas self–gravitation in the global disc could not be
In both runs of numerical simulations we begin by launch- very important because Mg /M∗ = 0.08 < 0.1 (Wada &
ing molecular clouds in the axisymmetric potential with its Habe 1992; Friedli & Benz 1993). Nevertheless, as we have
rotational velocity and giving the clouds a small velocity previously noted in Sect. 2, Braine & Combes (1992) find
dispersion of 10 km s−1 . The non-axisymetric potential is a big amount of molecular gas in the central kpc, where410 M.J. Sempere & M. Rozas: Dynamical model of the grand-design spiral galaxy NGC 157
Fig. 5a and b. Molecular cloud dis-
tribution obtained from the numeri-
cal simulations for two extreme val-
ues of Ωp : 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 A spiral structure similar to that observed is obtained only
gravitational instability (Wada & Habe 1992). for a restricted values of Ωp . Fig. 6 shows the molecular gas
To obtain a clear picture of the simulation plots we have distribution obtained for the values of Ωp =30, 35, 40, 45 km
suppressed the star formation events to follow better the s−1 kpc−1 , and at first sight these are very similar. The most
particle orbits. We have chosen arbitrarily all clouds with notable difference is a general shift of the global structure which
the same mass: 103 M . Clouds interact via partially in- turns clockwise as Ωp increases.
elastic collisions. The value of the inelasticity parameter in The final test to determine the pattern speed by this method
the direction parallel to the relative velocity between two is the comparison of the molecular gas distribution with a data
colliding clouds is ∼ 0.65 and 1 in the perpendicular direc- set of observations at different wavelengths. The overlay of the
tion to assure the conservation of the angular moment. The isodensity contours of the red image (Fig. 7) and the Hα image
gravitational forces due to the gas have been computed by (Fig. 8) on the modelled intesity map (grey scale) obtained from
an FFT method and added to the imposed stellar potential the self gravitating model are displayed for the same values of
(Combes et al 1990). The total mass of the molecular gas Ωp as in Fig. 6.
in the optical disc is MH2 = 3.5 × 109 (Tinney et al. 1990) In both cases the best fit is obtained for an Ωp = 40 km s−1
within the R25 radius. −1
kpc . A quantitative comparison of the results of the simu-
lations and the red image by a linear regression method gives
4. Comparison between the model and the observations correlation coeficients of 0.68, 0.73, 0.87 and 0.75 for the values
Ωp =30, 35, 40, 45 km s−1 kpc−1 respectively. We use the red
To compare the results of our models with the red and Hα im-
image to find the best fit to the main bar, and the Hα image to
ages we produced simulated maps of the molecular gas under
compare the morphology of the spiral structure.
the assumption that the interstellar medium is optically thin in
clouds (i.e. molecular cloud crowding factor is low for all the In Fig. 4 we showed the radii of the main resonances for Ωp =
velocity clouds). We have computed and projected in the sky 40 km s−1 kpc−1 : the co–rotation radius, where the angular
plane the position and radial velocity of each particle after a velocity of the matter Ω is equal to the pattern speed of the
total run time. density wave, is located at a radius of 5000 (' 5 kpc) in the
A data cube is built by convolving the expected emission of middle of the optical disc. Two inner Lindblad resonances are
the clouds using a telescope beam halfwidth of 12 00 . The cell obtained due to the peaked rotation curve near the centre of the
size of the cube is 600 × 600 in the spatial dimensions and 3 km galaxy. They are located at radii 0.25 and 0.75 kpc respectively.
s−1 in velocity. The outer Lindblad resonance is in the outer disc at a radius of
Figures 5 and 6 show the final configurations of the molec- ' 10 kpc.
ular gas for several runs of the first model of inelastic collisions The inner region of NGC 157 presents a complex morphol-
with different Ωp values ranging from 15 to 60 km s−1 kpc−1 . ogy. The distribution of the most brilliant HII regions is concen-
Fig. 5 displays the results for the two extreme cases: Ωp = 15 trated in the two inner spiral arms and the bar is almost devoid
and Ωp = 60 km s−1 kpc−1 respectively. It can be seen that the of star formation with the exception of three hot–spots. Braine
final gas distribution obtained for these values of Ωp does not fit & Combes (1992) noted as unexpected the large quantity of gas
the global morphology of the galaxy. In particular, the bar plus in the central regions of the galaxy, in contrast with the absence
spiral arms structure is very different from the real structure, and of star formation.
it is not quasi–stationary, disappearing rapidly after one rotation The existence of a bar and two inner Lindblad resonances
period. could explain this phenomenon: within the inner ILR gas orbitsM.J. Sempere & M. Rozas: Dynamical model of the grand-design spiral galaxy NGC 157 411
Fig. 6a–d. Particle plots showing molecular cloud distribution in the disc of NGC157 for several runs corresponding to different values of Ωp :
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 tween the two ILRs, in good agreement with the predictions of
gas orbits follow the x2 orbits, perpendicular to the bar, and the theory. Above the nucleus a fainter HII region can be made
in the region between the outer ILR and corotation orbits are out at the same radius than the two hot–spots. This peculiar dis-
again parallel to the bar (the x1 family of orbits). Since gas tribution could be a very patchy circumnuclear ring. NGC 157
can dissipate energy by collisions, gas orbits rotate gradually is a starburst galaxy and as showed by Arsenault (1989) cir-
from parallel to perpendicular as the resonances are crossed. At cumnuclears rings and barred features in late–type spirals, are
the crossing of the ILRs the collision rate of molecular clouds associated to starburst nucleii.
increases due to the change of orientation of the clouds orbits
and there is an enhancement of the gas density at these places Fig. 7c shows the overlay of the red image and the best fit of
that promotes the formation of GMC’s and subsequently of the the simulations. The main bar and the arms are sucessfully repro-
star formation events. As predicted by Friedli & Benz (1995) duced in the model. The Hα counterpart in Fig. 8c. emphasizes
energy released by star formation could modify the Schmidt– the close fit of the main two–arm structure in the entire galaxy
law along the bar impeding more star formation. disc. The third arm that is well reproduced in the simulations
does not appear in the Hα image. As predicted in Elmegreen
Fig. 9 displays an overlay of the Hα (grey scale) and the red et al. (1992), the formation of the three arm component would
image (isodensity contours) in the two inner kpc of the galaxy. require several revolutions after the formation of the asymmet-
The three hot–spots in the bar are located at the nucleus and be- ric two–arm system. The three arm component is younger and412 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 Ωp : 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 , on the inferred projected mass distribution of NGC 157 (solid contours).
weaker than the predominant two–arm structure and the lack of & Elmegreen (1992). NGC 157 could be an intermediate case
massive star formation could be due to this fact. since its rotation curve follows the general trend of late–types
From the determination of the position of the main reso- but it posseses a local maximun at the centre.
nances in other SBAbc galaxies as NGC 4321 and NGC 7479,
we have found a very different kinematical characteristics that This first step in the determination of the resonances in
determines a large variety of bar properties and star formation NGC 157 seems to be in good agreement with the theoreti-
processes. Although NGC 4321 has been classified as late–type, cal predictions of the Density Wave Theory (DWT), but more
its kinematical behaviour correspond more to that of an early– observations in other wavelengths, particularly from the centre
type galaxy. On the contrary NGC 7479 show the bar charac- of this galaxy, are necessary to complete our understanding of
teristics and pattern speed predicted for a late–type by Combes physical process involving the presence of a density wave.M.J. Sempere & M. Rozas: Dynamical model of the grand-design spiral galaxy NGC 157 413
Fig. 8a–d. Overlay of the density gas distribution (grey scale) corresponding to the values of Ωp : 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 , on the Hα image of NGC 157 (grey contours).
5. Conclusions Since we have obtained the mass distribution from a red image
of the galaxy with some assumptions about mass to light ratios
We have determined the location of the main resonances in the only free parameter that we vary in our simulations is Ωp .
the disc of NGC 157 by means of hydrodynamical simulations We have run two models: the first one is a model of cloud inelas-
of the molecular component of the interstellar medium. Our tic collisions, without self–gravity, in which the effects of star
method is based on a global morphological fit of the simulated formation are simulated. The second model considers partially
gas response to a density wave with real observations at differ- inelastic collisions, supresses the star formation events and in-
ent wavelengths. The most sensitive parameters in the numerical cludes the gas self–gravity in order to analyse in more detail the
simulations are the pattern speed of the wave, Ωp , and the mass gas behaviour in the centre and the arms of the galaxy, where
distribution in the galaxy, which produces the rotation curve. gas self–gravity can play an important role.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 predomi-
nant 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.
Acknowledgements. This paper has been improved thanks to the valu-
able remarks and comments of the referee, Dr. Daniel Friedli. We grate-
Fig. 9. The inner 2 kpc region of the Hα image of NGC 157 superposed
fully acknowledge the Yerkes Observatory hospitality and specially the
to the response of the molecular gas in the best fit of the numerical
direct support of L.M. Hobbs. We thank Dr. J.E. Beckman for helpful
simulations Ωp =40 km s−1 kpc−1 . We can see a nuclear hot–spot and
comments on the manuscript. The William Herschel Telescope is op-
two HII regions between the two inner ILRs.
erated on the island of La Palma by the Royal Greenwich Observatory
in the Spanish Observatorio del Roque de los Muchachos of the Insti-
tuto de Astrofı́sica de Canarias. This work was partially supported by
We summarize our results as follows: the Spanish DGICYT (Dirección General de Investigación Cientı́fica
y Técnica) Grants Nos. PB91-0525 and PB94-1101.
– The best morphological fit is found for a value of Ωp =
40 km s−1 kpc−1 which places the co–rotation radius at a
radius of ' 5 kpc (5000 from the nucleus). With this value
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