Early-Type Disk Galaxies: Structure and Kinematics

0.52 MB·English

by  A. V. Zasov

Early-Type Disk Galaxies: Structure and Kinematics
A. V. Zasov
Sternberg Astronomical Institute, Moscow State University,
Universitetski˘ı pr. 13, Moscow, 119899 Russia
A. V. Moiseev
Special Astrophysical Observatory, Russian Academy of Sciences,
Nizhni˘ı Arkhyz, 369167 Karacha˘ı-Cherkessian Republic, Russia
A. V. Khoperskov and E. A. Sidorova
Volgograd State University, Volgograd, 400068 Russia
Spectroscopic observations of three lenticular (S0) galaxies (NGC 1167, NGC 4150, and
8
NGC 6340) and one SBa galaxy (NGC 2273) have been taken with the 6-m telescope of the
0
SpecialAstrophysicalObservatoryoftheRussianAcademyofSciencesaimedtostudythestructure
0
and kinematic properties of early-typedisk galaxies. The radial profiles of the stellar radial veloci-
2
tiesandthevelocitydispersion aremeasured. N-bodysimulationsareusedtoconstructdynamical

n models of galaxies containing a stellar disk, bulge, and halo. The masses of individual components
a are estimated for maximum-mass disk models. A comparison of models with estimated rotational
J velocities and thestellar velocity dispersion suggests thatthestellar disks in lenticulargalaxies are

5 “overheated”;i.e.,thereisasignificantexcessvelocitydispersionovertheminimumlevelrequiredto
2 maintain thestabilityofthedisk. Thissupportsthehypothesisthatthestellar disksof S0galaxies
weresubject tostronggravitational perturbations. Therelativethicknessof thestellar disksin the

] S0galaxies we consider substantially exceed thetypical disk thickness of spiral galaxies.
h
p
-
o 1. INTRODUCTION directly or indirectly leading to a reduction in the
r amount of gas and a “halt” of active star forma-
t
s tion. Environmental effects evidently play a key
Early-typedisk galaxiesaregalaxiesofmorpho-
a
role in this case, as is demonstrated by the lower
[ logical types S0–S0/a (lenticular galaxies) and Sa
percentageofearlygalaxiesindistantclusters(the
withpropertiessimilartothoseoflenticulargalax-
1 Butcher–Oemler effect [1, 2]), and the lower con-
ies. The structure of early-type disk galaxies is
v temporary rates of the current star formation in
similar to that of later-type spirals: they have a
9
galaxies located in denser environments [6]. How-
6 massive stellar disk and, in many cases, also a dy-
ever, early-type galaxies also include quite a few
9 namically decoupled stellar circumnuclear disk, a
field galaxies, which may have different histories.
3 developed bulge, and a dark halo that determines
. therotationalvelocityoftheirouterregions. They The problem of the gas content in lenticular
1
0 differ from most later-type spirals in their higher galaxies is equally interesting. Even when HI is
8 (on average) bulge luminosities, the low contrast present in detectable amounts, its total mass is at
0 or even total lack of their spiral arms, the very least an order of magnitude lower than would be
v: low surface density of gas(HI), and, consequently, expected to result from a simple return to the in-
i their extremely weak star formation. terstellar medium of gas ejected by evolved disk
X Explaining the observed features of early-type stars [4]. The scarcity of data on the thickness of
r disk galaxies poses a number of problems. First thestellardisksinlenticulargalaxiesmakesitdiffi-
a
and foremost, it is unclear whether lenticular cult to comparethem with other galaxiesin terms
galaxies representa logicalextension of the Sd–Sa of the volume gas density or the gas pressure in
morphological sequence of galaxies, which reflects the disk plane.
the conditions for their formation and the nature The relative mass fraction of the dark halos in
of their ensuing “quiescent” evolution, or whether early disk galaxies also remains an open question.
their peculiarities are caused by their interaction This is due, first and foremost, to difficulties in
with the environment (mergers, accretion of small estimating rotation curves at large galactocentric
satellites, loss of gas due to the pressureof the ex- distances based on stellar absorption lines. Fairly
ternal medium). extended HI rotation curves have been obtained
Indeed, lenticular galaxiesinclude many objects for a small number of lenticular galaxies. Accord-
whose structure suggests an appreciable external ing toNoordermeer[5]andNoordermeeretal.[6],
influence (e.g., dynamically and chemically decou- the rotationalvelocities in these galaxiesoften de-
pledcircumnucleardisks,peculiaritiesoftheradial crease toward the periphery, but they still imply
brightness profile, or peculiar structural features, the presence of fairly massive dark halos.
such as polar rings). S0 galaxies in rich clusters The largescatterof datain the Tully–Fisher re-
appear to form as a result of the direct effect of lation (luminosity–rotation velocity diagram) for
the intergalactic gas on the interstellar medium, lenticular galaxies suggests substantial inhomo-
geneity of their properties (see, e.g., [7] and ref- locity and stellar velocity dispersion at the largest
erences therein). It also follows from the analy- possible galactocentric distances, preferably along
sis of the velocity dispersions of old stars in the the mainaxesof the galaxy,to makeit possible to
galaxy disks, which shows that in some early-type determine the velocity dispersion along both the
disk galaxies, the stellar velocity dispersion sub- radial and vertical directions.
stantially exceeds the minimum level required for In this paper, we describe spectroscopic obser-
the gravitational stability of the disk, whereas, in vations and the results of our construction of dy-
later-type spiral galaxies, the velocity dispersion namical models for four early-type disk galaxies.
of the disk stars usually appears to be close to its Table1liststhe basicparametersofthesegalaxies
threshold value [8]. However, the relatively low we have adopted. Figure 1 shows images of two
accuracy of the estimated velocity dispersions for of the galaxies with low-contrast structure taken
disk stars beyond the bright bulges and problems withthe6-mtelescopeoftheSpecialAstrophysical
withdecomposingthevelocitydispersionintor,ϕ, Observatory of the Russian Academy of Sciences.
and z components lead us to treat this conclusion Table 2 gives a log of the observations.
as being tentative. ThegalaxyluminositiesinTable1correspondto
Acomparisonoftheobservationaldatawithdy- the total B magnitudes from the HYPERLEDA
T
namicalmodels inwhich the velocity dispersionof database [11]. The last column gives the radius
the disk stars—both in the plane of the disk and of the exponential stellar disk R which was
max
perpendicular to this plane—is close to the criti- adoptedingalaxymodels. Thisradiuscorresponds
cal values for the dynamical stability of the disk to the isophotalradiusR =D /2,orthe radius
25 25
provides insight into its dynamical evolution. A beyond which the photometric profile steepens.
comparisonof model (c ) andobserved(c ) line-
ℓ obs
of-sight velocity dispersions for old disk stars can
reveal one of three possible situations. 2. DESCRIPTION OF INDIVIDUAL
(1) c < c . If interpreted in terms of disk GALAXIES
obs ℓ
stability, it would imply that the mass of the disk
adopted in the model is overestimated, and that NGC 1167. This galaxy contains a substan-
the disk must be “less massive” in order to sat-
tial amount of HI. According to the observations
isfy the conditions of dynamical stability against
of Noordermeer et al. [14], the total HI mass is
perturbations in the plane of the disk and against 1.7×1010 M⊙, but the gas is distributed over a
bending perturbations.
very large area, so that the average surface den-
(2) cobs =cℓ within the measurement errors. In sity hHIi within the optical radius R25 is less than
this case, it appears that dynamical instabilities 2 M⊙/pc2. The gas density remains below the
during the formation of the bulk of the disk mass critical value required for gravitational instability
have brought the stellar disk to a marginally sta- of the gaseous layer at all galactocentric distances
ble state, where the stellar velocity dispersion is r, explaining the lack of observed star-forming re-
determined by the surface density of the disk, its gions in the galaxy. HI observations show an ex-
rotational velocity as a function of galactocentric tendedrotationcurve,whichslowlydecreasesafter
distancer,anditsinternalstructure. Thisappears reaching its maximum and extends over 10 radial
tobethemostcommoncaseamongnoninteracting disk scales [5, 6]. The maximum rotational veloc-
spiral galaxies. ity of the disk is almost 400 km/s, making this
(3) c > c ; i.e., the observed stellar velocity one of the most rapidly rotating and massive disk
obs ℓ
dispersionexceedsthemodelvaluescorresponding galaxies known.
to marginal disk stability. In this case, there is The total bulge luminosity of this galaxy is
reason to believe that disk stars have acquired an about one-third of the disk luminosity [15]. The
excess(i.e.,abovethelevelrequiredforstabilityof bulge has a steep photometric profile (our V-band
the disk) energy of random motions during their measurements yield a Sersic parameter of n ≃ 3)
evolution,sothatthediskhasbecomeoverheated. so that its brightness dominates the central re-
This can be viewed as evidence that the stellar gion, which has a size of several kpc. Starting
populationofthedisksubsystemofthegalaxyhas from r =15′′−20′′ (5.0−6.5 kpc), the photometric
beensubjecttostronggravitationalperturbations, profilebecomesexponential,andhencethebulge’s
for example, asa resultof mergersof massivestel- contribution to the observed brightness becomes
lar or gaseous satellites, or of close interactions small.
with nearby neighbors. In principle, the dynam- The images taken with the 6-m telescope of the
ical heating in the inner part of the galaxy can SpecialAstrophysicalObservatoryrevealasystem
alsobe relatedtothe disruptionofahigh-contrast of ring-like arcs or spirals, which were also noted
stellar bar. by Noordermeer [5]. The spirals are remarkably
Constructingdynamicalgalaxymodels thatcan thin and smooth, without characteristic irregular-
yield estimates of the disk-to-halo mass ratio or ities and bright knots (usually due to local star-
diskthicknessrequiresestimatesoftherotationve- forming regions in the galaxy’s spiral arms), sug-
NGC1167 NGC6340
60′′ 60′′
FIG. 1: V-band images of the galaxies NGC 1167 (left) and NGC 6340 (right) on logarithmic brightness scales,
showingtherawimages(top)andtheimagesafterthemodelsurfacebrightnessdistributionsubtracted(bottom).
TABLEI: Adopted parameters of thefour galaxies
Galaxy Type Tilt Distance, Luminosity, Radial scale Rmax,
angle i Mpc 1010L⊙ of thedisk rd, kpc kpc
NGC 1167 S0 36◦ [6] 67 10 8.0 [6] 31.9
NGC 2273 SBa 50◦ [9] 25.7 1.48 3.7 [10] 15
NGC 4150 S0 56◦ [11] 14 0.33 0.84 [12] 3.34
NGC 6340 S0/a 26◦ 19.8 1.21 2.4 [13] 9.6
TABLE II: Log of spectroscopic observations
Galaxy Slit Date Texp, s Seeing PA
direction
NGC 1167 Major axis 25/26.10.2005 8400 3′′ 70◦
Minor axis 24/25.11.2005 9600 2.2 160
NGC 2273 Major axis 26/27.11.2005 8400 2.5 58
Minor axis 25/26.12.2005 4800 2.6 148
NGC 4150 Major axis 02/03.02.2005 9600 2.8 146
Minor axis 03/04.02.2005 7200 1.4 57
NGC 6340 Major axis 06/07.05.2005 7200 3 120
Minor axis 02/03.06.2006 9000 2.1 30
gesting a lack of O stars in these structures. The nature of the thin, smooth arms remains unclear.
Accordingtopreliminaryestimatesweobtainedby shape can be seen in the central part of the disk,
analyzing images ofthe galaxy,the B−V color in- which are most likely located outside the plane of
dex is slightly (0.05m−0.1m) bluer in the spirals the disk. However, the most striking features are
than in the surrounding disk, suggesting ongoing thin fragments of rings or spiral structures simi-
or recent star formation. If the initial stellar mass lar to those observedin NGC 1167,but somewhat
functioninthesespiralsisanomalouslysteepslope, morefuzzyandconfinedbyanarrowerzoneofthe
thiscouldexplainthelackofmassivestarscapable disk. The galaxy has a bright bulge with a lumi-
of producing extended, bright HII regions. nosity almost half the disk luminosity. However,
Thereareno other galaxiesofcomparablelumi- the bulge is fairly strongly concentrated: its effec-
nosity in the neighborhood of NGC 1167. tive radii in the I and V bands are re = 8.6′′ [13]
and r = 3.1′′ [21]. The kinematics of the stellar
NGC 2273. This is a relativelyisolatedgalaxy e
population in the inner region of the galaxy were
ofmoderateluminosity withaSeyfertnucleus and
analyzed by Bottema [22] and Corsini et al. [23].
an unusually clear and symmetric structure in the
centralregion,with a radiusof≈25′′ (a brightbar Two-dimensional spectroscopy of the circumnu-
clear region of the galaxy revealed a chemically
and a pseudo-ring) and faint fuzzy spirals beyond
decoupled nucleus consisting of old stars with a
it. The photometric profile of the galaxy cannot
relatively high abundance of heavy elements, and
bedescribedbyasimpleexponentiallaw: itsteep-
ens at r > 80′′−100′′ [10, 15]. Like NGC 1167, probablyacircumnuclearpolarringlocatedwithin
r = 500 pc [24, 25]. Following Sil’chenko [24], we
NGC2273containsafairlylargeamountofgas[6,
16]. At r < 40′′, the brightness profile is domi- adopt for this galaxy a distance of 19.8 Mpc.
nated by the bulge. The total hydrogen mass is
MHI = 2.42×109 M⊙, but the average gas sur-
face density is roughlyas low as it is in NGC 1167 3. OBSERVATIONS
(hHIi=2.2M⊙/pc2)[6]. Moiseevetal.[9]andthe
SAURONteam[17]analyzedtheopticalspectraof
We observed the galaxies with the SCORPIO
the galaxy in order to study the two-dimensional
multimode instrument [26] mounted at the pri-
velocitydistributionofgasandstars. Inthebarre-
mary focus of the 6-m telescope of the Special As-
gion(r <30′′),gas(butnotthestars!) exhibitsap-
trophysical Observatory. We studied stellar kine-
preciable circular motions [9]. The rotation curve
matics using the slit spectrograph mode with a
of the galaxy appears to have a local maximum 6′ ×1′′ slit and a 2048× 2048 pixel EEV 42–40
near the center (r ≃ 10′′), but Noordermeer et
CCD as the detector. The scale along the slit was
al. [6] believe that this may be due to noncircular 0.36′′/pixel. Observations were made in the wave-
gas motions. A small circumnuclear disk coinci- lengthrange4800−5540˚A,whichcontainsnumer-
dentwiththemolecular-gasdisk[9]canbeseenat
ous absorption lines of the old stellar populations
the center of the galaxy, visible in emission lines. in the galaxies. The spectralresolutionwas 2.2 ˚A,
NGC 4150. This isalow-luminosityS0galaxy which corresponds to an instrumental profile with
with a smooth photometric profile, which is fit σ = 55 km/s in terms of the velocity dispersion.
well by an exponential law from the very cen- The log of observations in Table 2 gives the dates
ter out to at least r = 80′′ [12]. The central of the observations, the exposures (T ), the av-
exp
region shows traces of dust observed against the erage seeing, and the positional angle PA of the
bright stellar background. UV observations re- slit. We used an IDL-based software package to
veal a bright nucleus, indicative of the presence reduce the data. See [26] for a brief description of
of young stars [18]. The inner part of the galaxy the algorithms employed.
exhibits small amounts of molecular and atomic Weusedtheclassicalcross-correlationtechnique
gas [4]. Distance estimates for this galaxy are un- to calculate the radial velocities and velocity dis-
certain. Karachentsev et al. [19] suggested that persion of the stellar component; the algorithms
NGC 4150is locatedatthe peripheryofthe Virgo and software employed are similar to those de-
cluster at a distance of about 20 Mpc. Sage and scribedbyMoiseev[27]. Astemplatesforthecross
Welch[4]adoptedadistanceof9.7Mpc. Weadopt correlation, we used spectra of G8–K4 giants ob-
here a distance of 14 Mpc. The kinematics of the served on the same nights as the galaxies. To
inner region of the galaxy was studied earlier as increase the signal-to-noise ratio, we used adap-
part of the SAURON project [20]. The circumnu- tive binning (co-adding) of the spectra along the
clear region (r < 5′′) appears to host a counter- slit, with the integrationwindow exponentially in-
rotating disk. creasing with galactocentric distance. This tech-
NGC 6340. It is an S0/a galaxy, a member nique makes it possible to compensate for the ra-
of a group, although there are no other galaxies dial exponential decrease in the surface brightness
of comparable luminosity in its immediate vicin- in the galaxy disks. Figures 2 and 3 show the
ity. The image of the galaxy features a bright results of our measurements of the variations of
inner disk—lens—and low-contrast, outer spiral the radial velocities and the velocity dispersions
arms. Long, conspicuous dust lanes of unusual along the major and minor axes of the galaxies.
5200
NGC 1167 (PA = 70°) 2000 NGC 2273 (PA = 58°)
5100
s s 1900
m/ 5000 m/
k k
V, 4900 V, 1800
4800 1700
200 140
120
150 100
s s
m/ m/ 80
c, kobs 100 c, kobs 6400
50
20
0 0
–40 –20 0 20 40′′ –50 0 50′′
r r
NGC 4150 (PA = 146°)
300 1350 NGC 6340 (PA = 120°)
1300
V, km/s 225000 V, km/s1250
1200
150
1150
250
100
200
80
m/s 60 m/s 150
k k
c, obs 40 c, obs 100
20 50
0 0
–60 –40 –20 0 20 40′′ –20 0 20 40′′
r r
FIG. 2: Distribution of radial velocities and the velocity dispersion along the major axes of the galaxies. The
solid curvesshow theSAURONdata.
For comparison, these figures also show the dis- velocity within ±5′′ of the center is immediately
tributions of these parameters for NGC 2273 and obvious,andisapparentlyduetothepresenceofa
NGC4150obtainedbytakingappropriatesections circumnuclear polar ring. The radial-velocity gra-
acrossthe two-dimensionalSAURON velocity and dient is not zero at large galactocentric distances
velocity-dispersion maps [17, 20]. It is obvious alongthe minoraxis,andvariesby about40km/s
from this comparison that any systematic bias of alongthediskradiuswithin2′ (whichisequivalent
our velocity-dispersion estimates does not exceed to about 6 kpc along the major axis). This be-
the measurement errors. The difference between havior points toward a noticeable misalignment of
the radial-velocity curves along the major axis of the kinematic and photometric axes of the galaxy.
NGC 2273 is apparently due to the better spatial According to preliminary estimates based on two
resolution of the SAURON data. spectral sections, the PA of the kinematic minor
Note that some of our observations were made axis of the galaxy should be close to 0◦. How-
under unfavorable photometric conditions (some ever, the low accuracy of the measured velocity
cloudiness), which prevented us from taking spec- gradientsalongthespectrographslitpreventedre-
traoftheouterregionsofNGC6340alongthema- construction of the detailed shape of the rotation
jor axis. However, the high accuracy of the mea- curve for this galaxy.
surements along the minor axis enabled us to ob- SCORPIO can be used to obtain not only spec-
tainadetailedradial-velocityprofileforthestellar tra,butalsodirectimagesofobjectsinthe fieldof
population. The non-monotonic behavior of the view. Short-exposure (10−30 s) V images were
EARLY-TYPE DISK GALAXIES 85

5060 NGC 1167 (PA = 160°) 1900 NGC 2273 (PA = 148°)
5040
1880
5020
s s
m/5000 m/1860
k k
V, 4980 V, 1840
4960
1820
4940
1800
4920
140
200
120
s 150 s 100
m/ m/
k k 80
, bs 100 , bs 60
o o
c c 40
50
20
0 0
–40 –20 0 20 40′′ –40 –20 0 20 40 60′′
r r
NGC 4150 (PA = 57°) 1320
260
NGC 6340 (PA = 30°)
1300
m/s240 m/s1280
V, k V, k1260
220
1240
1220
200
140
100
120
80
100
s s
m/ 60 m/ 80
k k
, obs 40 , obs 60
c c 40
20
20
0 0
–20 0 20 40′′ –50 0 50′′
r r
FIG. 3: Sameas Fig. 2, but along the minor axes of thegalaxies.
used to aim the spectrograph slit at the galac- rotationcurves(maximum-diskmodels). We com-
tic nucleus to within 0.2′′−0.3′′. We also took pared the observations to both the rotation curve
deeper imagesshownin Fig.1 forthe twogalaxies calculated for this model and the minimum veloc-
NGC 1167 and NGC 6340, which exhibited un- ity dispersions for a collisionless disk that would
usualspiralstructureonshortexposures. The im- be sufficient to maintain its stability against ra-
ages were obtained by subtracting from the ob- dial and bending perturbations. An analysis of
served surface brightness the surface brightness in the dynamical evolution of the disks which follow
an axisymmetric model with a smooth brightness from numerical simulations can be used to obtain
distribution consistingof a disk andbulge with el- stable models without resort to approximate and
liptical isophotes. insufficiently trustworthy local analytical criteria.
Weusedathree-componentmodel(disk,halo,and
bulge) whose component parametersyieldeda cir-
cular velocity of
4. GENERAL PRINCIPLES OF
MODELING
Vc(r)=q(Vcdisc(r))2+(Vcbulge(r))2+(Vchalo(r))2,
We constructed dynamical models of the galax- (1)
ies having the maximum possible disk masses and where Vdisk(r), Vbulge(r), and Vhalo(r) are the
c c c
modelrotationcurvesconsistentwiththeobserved corresponding contributions of individual compo-
nents to the circular velocity. line-of-sight velocity dispersions:
The dynamical models of collisionless (stellar)
c (r)=(c2cos2(i)+c2 sin2(i)cos2(α)+
disks are based on numerical integration of the ℓ z ϕ
equations of motion of N gravitationally interact- +c2sin2(i)sin2(α))0.5, (3)
r
ing particles using the TREEcode program, tak-
whereiistheinclinationofthedisktotheplaneof
ing into account the external field of the “hard”
theskyandαistheanglebetweentheslitdirection
bulge and halo. This means that the parameters
andthe majoraxisprojectedontothe planeofthe
of the spheroidal subsystems are considered to be
galaxy.
stationary, and are described by free parameters
The technique of constructing a galaxy model
of the model. For NGC 4150, we also considered
whose disk is at the limit of stability against both
a model with a “live” bulge, which enabled us to
gravitationalperturbationsintheplaneofthedisk
take into account the bulge contribution not only
and bending perturbations is described by Khop-
to the gravitationalpotential, but also to the stel-
erskov et al. [28, 31] and Tyurina et al. [32].
lar velocity dispersion. However,we found no fun-
The corresponding computations covered five to
damental differences: the velocity dispersion re-
ten orbital-rotation periods at the outer disk rim,
mained virtually unchanged beyond the effective
ensuringthe establishmentofa stationarystate in
bulge radius.
whichthevelocitydispersionhasvirtuallystopped
Wespecifiedthedisksurfacedensityintheform
changingandhasmaintaineditsaveragevalueover
several rotational periods. We used an iterative
algorithm with the initial velocity dispersion suc-
σ(r)=σ ·exp(−r/r ) (2)
0 d cessively approximating the stability limit, as de-
veloped by Khoperskov et al. [28]. The iterative
at galactocentric distances r ≤ R (Table 1).
max approach is based on a series of successive com-
Here,rd istheradialdiskscaleestimatedfromthe putations involving N = 2 × 105 particles, each
brightness distribution of the galaxy.
starting with an initial velocity dispersion that is
To reduce ambiguity in choosing a model that somewhat closer to the critical value than in the
was consistent with the observed rotation curve, previouscase. Tothisend,wechosetheinitialdis-
we further assumed that the radial scale for the tributionofthevelocitydispersionsc (r)andc (r)
r ϕ
disk surface-density variations in the region cov- to be between the initial and final values obtained
ered by measurements is close to the radial scale in the previous simulation.
rd of the disk brightness known from optical pho- We also performed control computations with
tometry (Table 1). N = 106 particles to monitor computational ef-
We started the modeling with the initial fectsintheinferredradialdistributionsofthedisk
disk in an unstable (subcritical) state with a parameters at the stability limit. The results cor-
Schwartzschild (ellipsoidal) velocity distribution, roborated our earlier conclusion [28] that models
such that the resulting collisionless disk was close with N >∼ 105 are adequate to determine the sta-
to the stability threshold. Hence, the result- bility limit.
ing models represent models of the maximum, Ingeneral,wesubdividedtheconstructionofthe
marginally stable disks. The real disks may have model stable equilibrium disks into the following
smaller masses than those obtained in our models stages.
without violating the stability condition. Estima- (1) Estimating the components of the velocity
tions of the masses of stellar disks based on the dispersion along three axes [see (3)] by analyzing
condition that they be gravitationally stable [22, the observed velocity dispersions along the ma-
28, 29] show that the maximum-disk model con- jor and minor axes of the galaxy. As the addi-
structed without allowance for the velocity dis- tionalcondition requiredfor this task,we adopted
persion may overestimate the circular disk veloc- the Lindblad relation between the radial and az-
ities by 20–30%. Note, that the estimates of imuthal components of the velocity dispersion,
the disk masses obtained using another method, which was tested in numerous numerical simula-
namely hydrodynamical modeling of the gas mo- tions: c /c = 2Ω/κ, where κ is the epicyclic fre-
r ϕ
tionsintheregionofspiralarms,suggestthatonly quency.
the inferred disk mases of slowly rotating galaxies (2)Determiningthecircular-velocitycurveV (r)
c
(Vc < 150−200 km/s) will be substantially lower fromtheobservedrotationalvelocitiesofthestars,
than their “maximum” masses [30]. Vobs(r), and the velocity dispersion c (r). How-
⋆ r
Weconstructedanequilibriumdynamicalmodel ever, when available, we adopted the gas rotation
tocalculateradialprofilesofthecircularrotational curve as the initial circular-velocity curve.
velocities V , the rotational velocities of the stars (3)Decomposingtherotationcurveintocompo-
c
V (particles in the model), and the velocity dis- nents representing the bulge, disk of finite thick-
persions c , c , and c , which ensure the marginal ness and halo (the maximum-disk model).
r ϕ z
stability of the disk. To compare our models with (4) Choosing the initial conditions for the de-
the observational data, we calculated the model scription of the disk in the subcritical state, with
the derived component parameters used as a first almost three compared to the marginally stable
approximation. state. A comparison of our maximum-disk model
(5) Numerically computing the dynamical evo- with the observed distribution of the velocity dis-
lution of the disk to obtain a model for the persionalongtheminoraxisconfirmsthatthedisk
marginally stable disk whose circular-velocity is significantly overheated.
curve agrees with the curve obtained from the ob- Below we analyze only the galaxy models with
servations. the maximum disk mass.
(6)Computingtheradialdependenceoftheline- We determined the disk half-thickness z from
0
of-sight velocity dispersionfor the resulting model the dynamical model, with the stellar density dis-
with allowance for the inclination of the disk. tribution in the z direction approximated by the
(7) Comparing the model and observed line-of- law ̺ ∝ ch−2(z/z ), which is valid for a self-
0
sight velocity dispersions. gravitatingisothermaldisk. Theaveragediskhalf-
(8) Computing the disk parameters: its mass, thicknessofthisgalaxyisz ≈2.8kpcifcalculated
0
average thickness (for the observed velocity dis- for the maximum-disk model. Thus, the disk is
persion), and mass-to-luminosity ratio. Estimat- fairly thick, both in absolute terms and compared
ing the fractional mass of the dark halo. to its radial scale: z /r = 0.35. For comparison,
0 d
We did not compare the model velocity disper- thehalf-densityhalf-thicknessofthestellardiskin
sions for disk stars with the corresponding ob- the solarneighborhoodisabout350pc [33],which
serveddispersionsforcentralregionsofthegalaxy, corresponds to z ≈400 pc.
0
since both the form of the rotation curve and the NGC 2273. As in the previous case, an HI
velocitydispersionofthediskstarsaredetermined rotation curve is available for NGC 2273 [5, 16].
very uncertainly in the bulge region. We used velocity-field measurements kindly pro-
vided by E. Noordermeer to construct the rota-
tion curve outside the galaxy bulge with the fixed
5. MODELS OF THE GALAXIES disk inclinations adopted in this paper (Table 1).
Figure 5 shows the rotation curves and velocity-
NGC 1167. We constructed three models for dispersiondistributionsbasedontheobservational
this galaxy (a, b, c) to see the effect of the choice data. The HI rotation curve exhibits a local max-
of parameters on the final result. Here, n1167- imum at a galactocentric distance of several kpc,
a is the maximum-disk model; n1167-c can be but the model curve reproduces it poorly. The
thought of as the minimum-disk model, which stellar-velocityfield in the very central part of the
corresponds to an R mass-to-luminosity ratio of galaxy also suggests the possible presence of a lo-
M/L ≈ 1.5, which is certainly lower than the cal maximum, but much closer to the center—at
R
mass-to-luminosity ratios of stellar systems with- a galactocentric distance of ≃250 pc [34], which
out active star formation and with normal stel- corresponds to the circumnuclear disk.
lar population; and n1167-b has an intermediate A remarkable dynamical feature of this galaxy
disk mass. All three models reproduce the rota- is that the observed gas velocity (small circles in
tion curve of the galaxy fairly well. Fig. 5a) at r > 3 kpc differs only slightly from
Figure 4a compares the observed rotational ve- the rotational velocity of the stars (straight and
locities with the rotational velocities for the mod- slanted crosses in Fig. 5a). In the case of an ax-
els. The n1167-a and n1167-b models differ ap- isymmetric, stationary disk, no model with a dy-
preciably only in the central region, due to their namicallycoolgaseousdiskcanreproducethis be-
different bulge concentrations. The central disk havior: fortheusuallyadoptedgasvelocitydisper-
surface densities are almost the same in these sionof10km/s,thestellarrotationcurveshouldbe
two models: 1400 and 1340 M⊙/pc2. The halo lower than the gas rotation curve by 20–30 km/s.
mass is somewhathigher in the secondmodel: the The SAURON-VII data [17] also confirm the high
halo-to-disk mass ratios within R are equal to rotationalvelocityofthestellarcomponent(thedi-
max
(M /M ) = 0.67 and (M /M ) = amondandtrianglecorrespondingtotheSAURON
h d n1167-a h d n1167-b
0.83. In the n1167-c model, the mass of the halo archive data in Fig. 5a).
exceeds that of the disk. The observed similarity of the rotational veloc-
Figure4bshowsthedistributionsoftheobserved ities of the old stars and gas can, in principle, be
and model estimates of the line-of-sight velocity explained if the turbulent velocity of the gaseous
dispersion for the marginal-disk model n1167-a. medium is close to the stellar velocity dispersion
It is obvious that the velocity dispersion in this (30–70 km/s). In this case, the HI forms a thick
model is substantially lower than the correspond- disk that is roughly the same as the disk of old
ing observed values. The velocity dispersion be- stars. However,the originofsucha dynamicalpe-
comes even lower if we decrease the disk mass culiarity of the atomic-gas layer is by no means
(curve shown by diamonds in Fig. 4b). In the evident. The galaxy lacks a sufficient number of
n1167-c model, the observed disk is overheated in young stars to impart the required energy to the
terms of the velocity dispersion c by a factor of gas. The similarity in the old-star and gas rota-
ℓ
V, km/s (‡) V, km/s
NGC 1167
400 NGC 2273
(a)
350
200
300
250 150
200
100
150
100
50
50
0 5 10 15 20 25 30 35 40 r, kpc 0 5 10 15 20
r, kpc
Ò, km/s Ò, km/s
NGC 1167
200 (b) 150 NGC 2273 (b)
150
100
100
50
50
0 5 10 15 r, kpc 0 5 10 r, kpc
FIG.4: NGC1167. Shownarethe(a)rotationalveloc- FIG.5: NGC2273. Shownarethe(a)rotationalveloc-
ity of the stellar disk according to our measurements ity of the stellar disk according to our measurements
Vobs (the straight and slanted crosses show measure- Vobs (straight and slanted crosses show the measure-
⋆ ⋆
mentsmadeoneithersideofthecenter),gasrotational ments made on either side of the center), HI rota-
velocity [5] (open circles), Hα rotational velocities [5] tional velocity [5] (small open circles), rotational ve-
(open triangles), the circular velocity Vc according to locity based on the same data calculated for a model
thedataof Noordermeeret al. [14] (open squares), Vc with fixed disk inclinations (large open circles), Hα
for then1167-amodel (dotted curve),thecorrespond- rotational velocities [5] (small filled circles near the
ingstellar-diskrotationalvelocityforthismodel(filled center), the model rotation curve (solid), the rotation
triangles), Vc for the n1167-b model (dashed curve), curve that agrees best with the measured rotational
and the corresponding stellar-disk rotational velocity velocities andstellar velocity dispersions (dotted),the
forthismodel(asterisks);(b)stellarvelocitydispersion SAURON-VIIdataforVHβ (diamonds) andV⋆ (trian-
cobs accordingtoourobservationsalongthemajoraxis gle)(seetext);(b)stellarvelocitydispersionaccording
(crosses) and minor axis (small filled circles), line-of- toourobservationsalong themajor axis(crosses) and
sightvelocitydispersionofdiskstarsinthemaximum- minoraxis(smallfilledcircles), theline-of-sight veloc-
disk model along the major axis (filled squares) and ity dispersion of the disk stars in the maximum-disk
minor axis (dotted curve), and the corresponding ve- model along the major axis (filled squares) and minor
locity dispersion along the major axis for the n1167-c axis(dottedcurve),andthevelocitydispersionaccord-
model with a low-mass disk (diamonds). The vertical ingto[17](filledtriangles). Theverticaldashedarrow
dashed arrow indicates the conventional boundary of indicates the conventionalboundary of thebulge.
the bulge.
tional velocities is more likely due to the complex tion in this galaxy is low, M /M = 0.09, but the
b d
internal structure observed in the central part of observedstellarkinematicscannotbeexplainedby
the galaxy (a high-contrast bar and short spiral allowing for the bulge.
arms), which may be responsible for non-circular Figure 6b shows the velocity dispersion esti-
gas motions. In this case, the rotational velocity mates along the major and minor axes for the
of the stellar disk should be preferred over that of galaxy model considered together with the obser-
thegaseousdiskwhenconstructingamodelforthe vationaldata. Again,thestellardiskisappreciably
galaxy. overheated. The disk of the galaxy is fairly thick,
Figure 5b compares the observed line-of-sight with a vertical-to-radialscale ratio of no less than
stellar velocity dispersions c and the velocity 0.32. The velocity dispersion of the “live” bulge
obs
dispersions c obtained for the marginally stable inthemodelagreeswiththeobservedvelocitydis-
ℓ
disk model. In this model, the component masses persion at r <0.8 kpc.
within r = 12 kpc are Mh/Md = 0.5, Mb/Md = The photometric data imply a very short (less
0.13, and Md = 8.05×1010 M⊙. The estimated than1kpc)radialdiskscaleforthisgalaxy. Given
velocity dispersion corresponding to the stability the slow radial decrease of the stellar velocity dis-
limit decreases with decreasing disk mass fraction persion, this implies that the thickness of the stel-
of the model. The significant difference between lar disk increases significantly with galactocentric
cℓ and cobs in the central region of the galaxy (up distance, so that the z0 estimate listed in Table 3
to 40 km/s) appears to be due to stars of the dy- below should not be taken too literally. The disk
namically “hotter” bulge; i.e., it does not refer to half-thickness within 1 kpc from the center of this
the disk. Atgalactocentricdistancesr =2−5kpc, galaxydoesnotexceed400pc(whichisstillgreater
the observed velocity dispersion is close to the ex- than the corresponding parameter for the Milky
pectedvelocitydispersionforthismodel. Thedisk Way),butitbecomesequaltotheradialdiskscale
componentmaybeslightly“overheated”atthepe- at a galactocentric distance of several kpc. Start-
riphery of the stellar system (r = 7−11 kpc), but ing from r ≈ 4−5 kpc, the disk proper appears
we must bear in mind the largescatter of the esti- to be absent. Indeed, the photometric profile be-
mated velocity dispersions. We can thus conclude comes flat at these galactocentric distances [12].
that a model with a marginally stable disk having NGC 6340. As in NGC 4150, rotation was
a close-to-maximum mass is consistent with the
measuredonlyforthestellarcomponent. Onlythe
observational data for this galaxy.
gradientofthe rotationalvelocity alongthe major
Notethattheadoptedparametersforthemodel axis can be confidently estimated (see Section 3).
with a marginally stable disk can reproduce both The estimates of the stellar velocity dispersion re-
the rotation curve and the formation of a bar in ported both here and in the earlier paper of Bot-
the galaxy. In numerical simulations, a bar forms tema[35]arecharacterizedbyalargescatter. The
in the inner part of the disk during one to two ro- dispersionat the center of the galaxyis 130 km/s,
tational periods as the disk approaches the quasi- but this refers to the bulge, not the disk. The
stationary state, as a result of the disk’s instabil- velocity dispersion decreasesconsiderably with in-
ity against the bar-forming mode. However, the creasing r. Judging from the photometric profile
observed spiral structure (fragments of thin rings) ofthegalaxy[13],thediskdominatesinbrightness
cannot be reproduced in collisionless models; a beginning from r ≈1.7 kpc.
coolcomponent(gas)isevidentlyrequiredforsuch
Figure 7a shows the model rotation curves and
structure to form.
measured rotational velocities of the stellar disk.
The average vertical disk scale height in As we pointed out above,the stellar-velocitymea-
NGC 2273calculated in the maximum-disk model surements for this galaxy prevent the reconstruc-
is 0.8 kpc, which is twice this parameter in the tion of the form of the rotation curve. Due to the
Milky Way Galaxy. lack of direct estimates of the rotational velocity
NGC 4150. Figure 6a illustrates the radial of the gaseous component for this galaxy, we ac-
distributions of the rotational velocity of the stel- ceptedanoverallformoftherotationcurveforthe
lar disk (various symbols), the circular rotational disk of this galaxy that makes it consistent with
velocity calculated for the maximum-disk model the adopted radial scale r . The maximum of the
d
(solid bold curve), and the results of decompos- curve was conventionally set to be equl to the HI
ing the circular velocity for this model (thin solid rotationalvelocityaccordingtotheHYPERLEDA
curves). The dynamical model of this galaxy was database—V = 219 km/s (after reducing the
max
calculated with a “live” bulge, where the distribu- latter to the adopted inclination i = 26◦ inferred
tions of mass and particle velocities could evolve from the outer isophotes).
with time. Figure 7b shows the radial dependences of the
In the maximum-disk model, the decomposition line-of-sight velocity dispersion. At galactocentric
of the rotation curve yields a central disk surface distances 2–8 kpc, the average estimated velocity
density of σ0 ≈ 1330 M⊙/pc2 and a component- dispersionbasedonmeasurementsmadealongthe
mass ratio of M /M =0.6. The bulge mass frac- minor axis is no less than 60 km/s, suggesting
h d