Table Of ContentNGC 2915. II. A Dark Spiral Galaxy
With A Blue Compact Dwarf Core
Gerhardt R. Meurer
Department of Physics and Astronomy,
6 The Johns Hopkins University
9 Baltimore, MD 21218-2695
9
Electronic-mail: [email protected]
1
n
a
J Claude Carignan
1
3 D´epartement de Physique and Observatoire du Mont M´egantic,
Universit´e de Montr´eal
1
C.P. 6128, Succ. “A”,
v
1 Montr´eal, Qu´ebec, Canada H3C 3J7
9 Electronic-mail: [email protected]
1
1
0
6 Sylvie F. Beaulieu and Kenneth C. Freeman
9
/ Mount Stromlo and Siding Spring Observatories
h
p The Australian National University
-
o Private Bag, P.O. Weston Creek, ACT 2611, Australia
r Electronic-mail: [email protected], [email protected]
t
s
a
: Submitted to The Astronomical Journal
v
i
X
r
a
ABSTRACT
This paper presents Australia Telescope Compact Array HI synthesis observations of
the weak blue compact dwarf (BCD) galaxy NGC 2915. It is shown that NGC 2915 has
the HI properties of a late type spiral galaxy (Sd - Sm), including a double horn global
profile, and HI spiral arms. The HI extends out to over five times the Holmberg radius,
and 22 times the exponential scale length in the B band. The optical counterpart
corresponds to a central HI bar. The HI distribution and kinematics are discussed
in detail. A rotation curve is derived and fitted with a mass model consisting of a
stellar disk, a neutral gas disk, and a dark matter (DM) halo. The DM halo dominates
at nearly all radii. The total mass to blue light ratio, /L = 76 within the last
T B
M
measuredpoint. ThusNGC2915isoneofthedarkestdiskgalaxiesknown. Thecomplex
HI dynamics of the central region results in a high uncertainty of many of the fitted
1
parameters. Nevertheless it is clear that the core of the DM halo is unusually dense
(ρ 0.1 pc−3) and compact (R 1 kpc). The neutral gas component, with mass
0 ⊙ c
≈ M ≈
Mg = 1.27 109 ⊙ is probably more massive than the stellar disk. Split and broad HI
lines (veloc×ity diMspersion 35kms−1) are seen in the central region. Pressure support
≈
is probably significant, and it isnot clear whether the coreis inequilibrium. Beyond the
optical disk the average HI line of sight velocity dispersion is 8 kms−1, which is normal
for disk galaxies. NGC 2915 does not obey the Tully-Fisher (1977) relation, being
underluminous for its V = 88 kms−1 by a factor of nine. It also does not obey the star
rot
formationthreshold modelofKennicutt (1989),when onlytheneutralgasisconsidered.
A simple HI surface density threshold of ΣHI,crit 1021cm−2 adequately describes
≈
the location of current star formation. Although the HI properties of NGC2915 are
extreme relative to normal galaxies they appear less extreme in comparison to other
BCDS, which have similar radial profiles of HI density and velocity dispersion, and HI
extending well beyond the optical disk.
2
1. Introduction ties. The dynamics of the ISM are analyzed in
4.. The rotation curve is measured, pressure
§
Thequestforunderstandingdarkmatter(DM) support corrections applied and mass models fit-
halos of galaxies using HI as a probe is pre- ted. Section 5. presents a discussion of the re-
§
dominantly weighted towards spiral and dwarf sults including a comparison with other galax-
irregular galaxies. The HI rich blue compact ies, a discussion of the Tully-Fisher (1977) rela-
dwarf (BCD; Thuan and Martin, 1981) class has tion and the star-formation threshold law. Our
been largely ignored, and is under represented conclusions are summarized in 6.. In the Ap-
§
in HI synthesis studies. This may be because pendix we discuss a possible interaction partner
their small optical angular sizes, often smaller of NGC 2915.
than typical synthesized beam sizes, suggests
that they will not be well resolved at λ21 cm.
2. Observations and Data Reduction
Also, only 8% of the BCDs in Thuan and Mar-
tin’s sample have double horn profiles indicative NGC 2915 was observed with three configura-
of extended rotating disks, suggesting that they tions of the Australia Telescope Compact Array
are not ideal candidates for DM studies. Some using all six antennas. However, baselines with
important HI synthesis observations of BCDs, antenna6, (whichgives thelongestbaselines-up
andsimilargalaxies, havebeenmade(e.g. Taylor to 6 km) were discarded since they produced in-
et al., 1993; 1995; 1996; Hunter et al., 1994) but significant correlation amplitudes. The dual po-
their primary aims were other than to search for larizationATreceiverwasemployedwiththecor-
DM. relator set to 256 channels per polarization, and
Here we presentHI observations of NGC 2915 with each channel separated by 15.7 KHz (3.31
whose optical properties were presented by Meu- km/s). The observing logs for the three config-
rer et al. (1994; paper I). There it was shown to urations are given in Table 1. The integration
be a weak BCD, that is its integrated star for- time was 20 s per visibility measurement. Some
mation rate is only 0.05 ⊙ yr−1. Most of this data in each run were lost to equipment failure
M
star formation is near the very center of the gal- and weather.
axywithsomeenhancedstarformationalongthe The data were reduced using standard soft-
majoraxistotheSEofthecenter. NGC2915 re- ware in the AIPS package (ATNF version). The
solves into stars; the brightest of these yields the relevant tasks usedarenoted herein parenthesis.
distance D = 5.3 1.3 Mpc. At this distance 1′′ Bad or suspect data were edited out (TVFLAG,
corresponds to 26±pc, and 1′ corresponds to 1.54 SPFLAG). Temporal gain and phase drifts were
kpc. Previous single dish HI observations indi- calibrated (CALIB) using the secondary calibra-
cate that it has a very extended HI disk (Becker tor, 0906-682 which was observed at 50 min. in-
et al. 1988). The HI observations presented here tervals for 3–6 min. Spectral variations in the
were made primarily to determine NGC 2915’s calibration were determined from the observa-
HI rotation curve, and from it, constrain the tions of 1934-638 and 0407-658 (BPASS). The
structure of its DM halo. In addition we wish absolute flux level was set by the primary cali-
to examine how the HI properties of this BCD brator1934-638(SETJY,GETJY;fluxreference:
differ from other types of galaxies, and whether Walsh, 1992). The calibration was checked for
they give any indication of what regulates star the1.5kmarraydatasetusing0407-658 whichis
formation in BCDs. also a flux standard (Walsh, 1992). The calibra-
The observations are presented in 2.. Sec- tion agreed to within 2% with the adopted 1934-
§
tion 3. presents an overview of the HI proper- 638 calibration. The calibrations were applied
§
3
and the two polarization channels combined to 3. Overview of HI properties
form Stokes “I” data sets (SPLIT). The contin-
uum was fitted and subtracted in the UV plane A cursory examination of the HI properties
(UVLSF) and the resultant continuum and line of NGC 2915 shows that they are very differ-
data sets were averaged in time (UVAVG) to one ent from its optical properties. Figure 2 (plate
minute per visibility. The line data sets were XXXX) shows three HI surface density maps,
shifted to the heliocentric rest frame (CVEL), plottedasgreyscales. PanelashowstheNAmo-
and the data from the three runs were com- ment0map(45′′ beam);panelb,theUNmoment
bined (DBCON). The data were imaged and 0map(27′′ 23′′ beam),andpanelc,theXGAUS
×
“cleaned” (MX; Schwab, 1984; see also Clark, peak amplitude map. NGC 2915 clearly has a
1980; H¨ogbom, 1974) to about the noise level spiral morphology, and this is most readily ap-
per resultant channel to make both uniform and parent in the NA map. There appears to be two
natural weighted data cubes (hereafter UN and armswhichcanbetracedbacktotheendsofcen-
NA respectively). For the NA cube, two spectral tral bar structure. Figure 3 shows a contour plot
channels at a time were averaged at the imaging of the NAmoment 0 map, while theUN moment
stage. The UN data was imaged at full spectral 0 contours are shown in Fig. 4 (Plate XXXX)
resolution. The beam sizes at the 50% level are overlaid on an I band image obtained with the
W = 45′′ (circular) for the NA data cube and Anglo-Australian Telescope. This clearly shows
50
W = 27′′ 23′′ (PA = 0◦)fortheUNcube. The that the HI, including the spiral arms, extends
50
×
final cubes were made by reconvolving the clean well beyond the optical extent of NGC 2915.
component images with two-dimensional Gaus- The prominent central bar is about 2.5′ (3.9
sian beams having the above sizes. Planes of the
kpc) long. It is most clearly seen in panel a
resultant NA data cube are shown in Fig. 1. of Fig. 2. The velocity field, analyzed in 4.1.,
§
From each cube, maps of total intensity, mean shows the signature of an oval distortion demon-
velocity, and line broadening were constructed strating that this is a real bar, and not a highly
fromthezeroth, first,andsecondmomentsofthe inclined disk. Thebar is resolved into two clouds
data cubes (w.r.t. velocity; MOMNT). The mo- in the UN data as can be seen in the bottom
ment maps and data cubes were then corrected two panels of Fig. 2 and Fig. 4. Each of these
for the fall-off in primary beam response with clouds has a neutral gas mass1 of 2.5 107
∼ ×
distance from the pointing center (PBCOR). Ta- ⊙ (1.4 107 ⊙ if a local background is sub-
M × M
ble 2 summarizes some of the properties of the tracted) which is the majority of the mass in the
NA and UN data sets including the beam size, bar. They are located 17′′ NW and 36′′ SE of
pixel size and noise level in the resultant data cluster 1 (paper I). They encompass many of
cubes. the embedded objects discussed in paper I and
bracket the brighter central clusters as well as
In order to check the moment analysis results,
some of the peculiar structure on the SE side of
single Gaussian fits to the UN data cube were
the galaxy. The faint “jets”, first mentioned by
made (XGAUS). As a further check, and to ex-
S´ersic et al. (1977) (cf. Fig. 2 paper I) project
aminethelineprofilesindetailtheUNdatacube
outwards from the core of these clouds. The
was block averaged into 30′′ 30′′ pixels, and all
× XGAUS map in panel c of Fig. 2 is very noisy,
the resulting profiles were examined and fit with
and clearly shows only the highest S/N features.
a multiple Gaussian fitting algorithm using the
In this map the morphology is reminiscent of a
IRAF program SPLOT.
1The neutral gas mass is the HI mass multiplied by 1.33
to correct for theneutral Hecontent.
4
spiral with a bar interior to a detached ring. horned nature of the profile is the classic profile
of a rotating disk. The bump near V is due to
The optically visible portion of NGC 2915 co- sys
the large central concentration of HI.
incides in position, orientation, and size to the
central bar. Thus while the exponential optical Figure 8 shows the line of sight velocity dis-
surface brightness profile (for R > 35′′) implies persion, b, map from the XGAUS profile fitting.
a disk structure, the HI data suggests that the Itshowsthatbincreasesbyseveraltensofkms−1
stars are in a bar configuration. This interpre- towards the center of NGC 2915. This is a much
tation is consistent with the optical morphology larger gradient than typically observed in spi-
(paper I) which shows enhanced star formation ral and irregular galaxies (Kamphuis, 1992; Lo
primarily in the center of the galaxy, but also et al., 1993). These maps indicate that pressure
alongtheopticalmajoraxis,orthebarridgeline. support may be important to the dynamics of
Such a distribution of star formation is common NGC 2915. The line profiles are discussed in de-
in barred galaxies (Friedli & Benz, 1995, and ref- tail in 4.2., whilethepressuresupport,or asym-
§
erences therein). metric drift, corrections to therotation curve are
Thereisalarge“hole” 130′′ 180′′ (3.4 4.6 discussed in 4.3..
§
kpc)located 310′′ (8.9 kpc∼)tothe×eastofthe×gal- Table 2 presents some properties measured
axy’s center. Examination of a position-velocity from our data. From the global HI profiles we
cut through this structure does not reveal split measured the total line flux SdV, the corre-
line profiles, indicating that it is probably not a sponding HI mass, HI, the Rvelocity widths at
M
kinematic shell, but an interarm clearing. The 50% and 20% of the maximum intensity, W
50
HI in NGC 2915 does not appear to be very and W20 respectively, and the systemic veloc-
porous,asisfoundtobethecaseinmanynearby ity V . That SdV from the UN and NA
sys
disk galaxies, such as HoII (Puche et al., 1992). global profiles agRree so well, indicates that the
This may be largely a result of resolution; the UN data is not missing much short spacing flux
HoII data have a resolution of 66 pc, and typical compared to theNA data. TheHI mass, HI =
M
bubble sizes are a few hundred pc, while the lin- 9.6 0.2 108 ⊙ from the NA data, is signifi-
± × M
ear resolution of our data is ten times worse (640 cantly higher than that derived by Becker et al.
pc). (1988), = 7.0 108 (after adjusting to our
HI
M ×
adopted distance) usinga low resolution HI map
The velocity field from the NA and UN mo-
derived from Parkes 64m observations. We sus-
ment 1 maps are shown in Figs. 5 and 6 (Plate
pect that the flux difference is due to the lower
XXXX) respectively. They clearly show the ex-
signaltonoiseratiooftheirobservationsandper-
pected pattern of a rotating disk. The disk must
haps inadequacies in their beam profile correc-
be warped as indicated by the twisting of the
tion. The systemic velocities measured from the
kinematic major and minor axes. Thus although
global profile, V (global), and the tilted ring
there are closed velocity contours, it is not read- sys
analysis, V (dynamical) (see 4.1.), agree well
ily apparent whether these are due to a declining sys §
with each other, and also with the optical ve-
rotation curve, or the warped disk. The rotation
locity V (optical) = 468 5kms−1 reported in
curve is derived in detail in 4.1.. The NA and sys
±
§ paper I.
UN global velocity profiles are shown in Fig. 7.
These were made from the data cubes by sum- From the total intensity maps we measure
ming the flux in each channel within a “blanking RHI, the radius where the face-on HI column
aperture”. The aperture was defined by eye us- density N(HI) = 5 1019cm−2, and N (max),
HI
×
ing the total intensity map as a guide. The twin the maximum HI face-on column density. The
5
correction to face-on is for the mean inclination It was found that the NA-MOMNT and UN-
i = 59◦, as derived below. The remaining prop- XGAUS solutions are stable to small perturba-
erties in Table 2 compare the HI and optical tions. However the inner three rings of the UN-
properties (paper I). is compared to the B MOMNT field (R < 90′′) are not. No unique
HI
M
bandluminosity, L ,andR iscomparedtothe solutions could be found. This is due to the
B HI
Holmberg radius R and B band exponential kinks in the central isovelocity contours seen in
Ho
scale length α−1. The resultant ratios quantify Fig. 6. Therefore we adopt the UN-XGAUS re-
B
what is already clear: NGC 2915 is gas-rich and sults for R 90′′, the UN-MOMNT results for
very extended in HI. 90′′ < R 3≤90′′ andtheNAresultsforR > 390′′.
≤
Finally each half (approaching and receding) of
4. ISM Dynamics the galaxy was analyzed separately. This final
step allows the uncertainty of the parameters to
4.1. Tilted ring analysis be estimated from the level of asymmetry in the
velocity field; the errors in the parameters are
The HI rotation curve was derived using the taken to be the absolute difference between the
now standard tilted ring algorithm, ROTCUR
value for the full ring and either the receding or
(Begeman1989), inamannersimilartothatout-
approaching half, whichever is larger. The V
rot
lined by Martimbeau et al. (1994). The UN and
errorsestimatedbythismethodarealwayslarger
NA first moment maps, and the UN-XGAUS ve-
than or equal to the formal errors from the least
locity field were analyzed separately, using ring
squares fitting. The formal errors in i and φ are
widths of 25′′, and 45′′ for the UN and NA data
occasionally larger than the asymmetry of field
respectively. There are up to six parameters for
errors. In these cases the former is adopted.
each ring; thecentral coordinates X ,Y , thesys-
c c
The results in terms of i, φ and V for each
temicvelocity V ,theinclinationi, theposition rot
sys
data set are shown in Fig. 9. The adopted fit pa-
angle φ of the kinematic major axis (receding
rameters are tabulated in Table 3. The HI disk
side),andtherotationvelocity, V . Theparam-
rot shows a strong warp in both φ (∆φ = 40◦) and
eters were derived using five iterations of the al-
i (∆i = 25◦). The warp is strongest, especially
gorithm. In the first iteration all parameters are
in i, for R 150′′, with relatively mild warp-
allowed to be free. This iteration gives a feel for ing (∆φ = ≤15◦, ∆i = 4◦) beyond this radius.
how the parameters vary with radius R. In the
The adopted rotation curve shows a rapid rise
second iteration, i and φ are held fixed while the
to V 80 kms−1 at R = 202.5′′. It then re-
other parameters areallowed tovary. Theaim of rot ≈
mains approximately constant until rising again
this iteration is to find the best average value of
forR > 290′′. Figure10showsapositionvelocity
X ,Y , and V , which are then held fixed at a
c c sys
cut through the NA data cube along the major
constant value for all subsequent iterations. The
axis (φ = 70◦). The second rise can be seen di-
resultant mean Vsys values are reported in Ta- −
rectly on both sides of the galaxy, demonstrating
ble 2 as V (dynamical). In the third iteration,
sys
that it is real.
new radial profiles of i,φ, and V are derived.
rot
Smooth curves are drawn through these profiles Figure 11 shows the residual maps from the
and the interpolated values of these parameters ring fits. Local deviations from the fit have
are used as the initial guess for these parameters ∆Vr <∼ 15 kms−1. The residuals in the in-
| |
in the fourth iteration, which is meant to test ner portion show rings of mostly negative and
how stable the solutions are to small changes in mostly positive residuals at R 65′′ and 150′′
≈
the initial guesses. respectively. This indicates that V varies with
sys
R, suggesting that the inner portions of the gal-
6
axy are not in equilibrium. Kamphuis (1992) Theaverage line split is ∆V = 41 kms−1. A few
r
finds V variations in normal spiral galaxies, representative profiles and their SPLOT fits are
sys
but at large radii. In the center where V is shown in Fig. 13.
rot
low these deviations are large enough to cause
Couldthebroadprofilesbeduetobeamsmear-
the isovelocity contour twists and the problems
ing of the observed steep rotation curve? This
in the UN-MOMNT fit noted above. The resid-
is not likely, because the knee in the rotation
uals along the minor axis have opposing signs up
curve is four to six beam widths from the cen-
to 10kms−1 oneithersideofthecenter (+to
ter, and thus the central velocity gradient is not
≈ ±
the NE, to the SW). This is a signature of an
that steep. Beam smearing only shows its ef-
−
oval distortion2: the kinematic major and minor
fects over one to two beam widths. We verified
axes are non-orthogonal (Bosma, 1981). The ef-
this by simulations of the data including the ef-
fectcanalsobediscernedinFigs 5,6. Thedistor-
fects of beam smearing on the UN data cube. A
tion probably arises from the central bar, and is change in V of 80 kms−1 in one beam width
strongest for the rings with 200′′ <∼ R <∼ 450′′. can result inrotb = 27 kms−1. But we can rule
It shows that the orbits are not strictly circular
out such a steep rotation curve, because it would
fortheserings,although oneshouldbearinmind
require the knee in the rotation curve to be at
that the residuals are small compared to the am- R = 50′′. Only higher resolution observations
plitude of V 80 kms−1 at these radii.
rot candetermineiftherearelargevelocitygradients
≈
within any given beam. However any such gradi-
4.2. Line profiles
ents are likely to beturbulent in nature since the
broad (b 20kms−1) line region is eight beam
The results of the automatic Gaussian fitting ≥
diameters wide.
are shown in Fig. 8 which gives a map of b values
fromXGAUS.Thebmapisnotsymmetricabout Figure 14 compares the SPLOT b measure-
the center of NGC 2915. There is stronger line ments with the azimuthally averaged b from the
broadening on the SE side than the NW. The MOMNT and XGAUS results. It shows that the
broadening is centered on the SE HI cloud (see SPLOT and XGAUS results are in good agree-
Fig. 4). ment,indicatingthattheadditionalbeamsmear-
ing in the 30′′ pixel data has not substantially
XGAUS was set to make only single Gaussian
increased b with respect to the full resolution
fits. The SPLOT measurements were designed
UN data. The MOMNT analysis, on the other
to test the XGAUS results and measure complex
hand, yieldsb substantially lower than the Gaus-
line profiles. The position of the splot fits are
sian fits. This is due to an artificial bias in
shown in Fig. 12, with the positions of profiles
the MOMNT analysis technique; MOMNT only
best fit by multiple Gaussians highlighted. The
uses the data where the signal is above a cer-
HIprofilesarepredominantlysinglepeaked. The
main region of split lines is confined to within 2′ tain threshold in a smoothed version of the data
cube. This systematically excludes the profile
of the center, which is also where the lines be-
wings, and thus the results are biased towards
come the broadest. Profiles at the position of
lower b.
both HI clouds are split. Thus the total HI
width distribution (including splitting) is a bit The dotted line in Fig. 14 shows the two pixel
more symmetric than the b map shown in Fig. 8. resolution of the UN data cube (b = 2.8 kms−1).
Most profilesare well sampledby ourdata, those
2Sincethelinewidthsalongtheminoraxisarenotelevated having b <∼ 2.8 kms−1 mostly have low signal
relativetothemajoraxis,itisnotlikelythatresidualsare
to noise ratios. A notable exception is shown
dueto a galactic wind.
7
in Fig. 13f. At large R, the mean b is around whereσ istheasymmetricdriftcorrectiongiven
D
8kms−1,whichistypicalfordiskgalaxies (Kam- by
phuis, 1992). Figure 13 shows that at this width
∂ln(Σ ) ∂ln(b) ∂ln(h )
the profiles remain well sampled. σ2 = Rb2 g +2 z .
D − (cid:20) ∂R ∂R − ∂R (cid:21)
(2)
4.3. Asymmetric drift correction
Usuallythecontributionsofeachofthegradients
The broadening of the HI profiles in the cen- are zero or negative, making the correction posi-
tral region is significant compared to the mea- tive. We do not have a direct measurement of hz
sured rotation, as can be seen by comparing but will assume ∂ln(hz)/∂R = 0. The other two
Fig. 14 with Fig. 9. The random motions of the terms can be estimated from the radial profiles
gas may then provide significant dynamical sup- of ln(b) and ln(Σg) which are shown in Fig. 15.
portin the central region. It is not clear that the Both profiles have a core-halo structure and are
gasthereisindynamicalequilibrium. Indeedthe well fit by a function consisting of a Gaussian
asymmetry of the b map suggests that it is not. centered at R = 0 on top of a polynomial (in R)
Nevertheless, here we will assume that gas is in background:
equilibriumand account for thepressuresupport
ln(b) = 2.40+6.57 10−4R
by estimating an “asymmetric drift” correction ×
following Oort (1965; see his eq. 10). We assume +1.23exp( R/85.1 2/2) (3)
−{ }
that the gas velocity ellipsoid (i.e. pressure) is ln(Σ ) = 0.812+1.057 10−3R
g
isotropic. This greatly simplifies the correction3. 7.13 10−6R×2
Inacylindricalcoordinatesystem, theradial(R) − ×
+1.51exp( R/56.2 2/2) (4)
accelerationKR abouttherotationaxiszisgiven −{ }
by whereR is in arcsec, b is in kms−1, and Σ is the
K = Vrot2 b2∂(ln[ρb2]), gas surface density in ⊙pc−2. The fitgs were
− R R − ∂R M
unweighted and have an rms of 0.05 and 0.07 in
where ρ is the density. If there were no pressure ln(b) and ln(Σ ) respectively. These fits (con-
g
support the orbits would be circular with veloci- verted to linear units) are shown in Fig. 15, as
ties Vc given by wellastheσD curveresultingfromdifferentiating
thefits. ThelasttwocolumnsofTable3tabulate
V2
c = KR. σD and the corrected circular velocities, Vc. As
R −
expected the σ corrections are quite significant
D
The density can be written as ρ = Σ /(2h ), for R 152′′. We can now proceed to model the
g z ≤
where h is the vertical scale height and Σ the mass distribution, with the caveat that the HI
z g
gassurfacedensity(heretakenasHIplusneutral may not be equilibrium at these radii.
He). The circular velocity is then
4.4. Mass models
V2 = V 2+σ2 (1)
c rot D
Three component mass models were fit to the
3Binney and Tremaine (1978) treat the case of the asym- rotation curve. The components are the stellar
metricdriftincollisionlesssystems(starsonly)whichhave disk, a neutral ISM (HI) disk, and a dark mat-
non-isotropic velocity ellipsoids.
ter (DM) halo. The stellar mass distribution is
determined from the surface brightness profiles
in paper I, and has one free parameter /L .
B
M
The mass distribution of the HI disk (ncluding
8
neutral He) is determined from the observations are for a very compact and dense core, the most
presented here, andthereare nofreeparameters. extreme of the models generated here.
The DM halo is assumed to have a spherically
Model B is a fit to V instead of V ; in effect
rot c
symmetric density distribution given by
it ignores the pressure support. The difference
ρ0 between Models A and B is thus indicative of
ρ= (5)
1+(R/R )γ the uncertain dynamical state of the central re-
c
gion. Neglecting the asymmetric drift correction
wherethefreeparameters are thecentral density
results in a larger, less dense core. The effect on
ρ and the core radius R . Here we adopt γ = 2.
0 c
the inferred core parameters is quite dramatic, a
For this densitydistributiontherotational veloc-
factor of about 1.5 in R and more than 2 in ρ .
ity at large R, V∞, and halo velocity dispersion c 0
Since we may have underestimated σ , it is pos-
σ are given by (Lake et al. 1990): D
0
sible that NGC 2915’s halo is even more dense
V2 = 4πGρ R2 =4.9σ . and compact than that of Model A. Like model
∞ 0 c 0
A, model B yields /L = 0.0.
B
Fitting was done with a χ2 minimization tech- M
Model C shows a fit where the DM halo is
nique. Thus the fitted parameters depend not
a non-singular isothermal sphere (e.g. Binney &
only on the input data, but also the associated
Tremaine 1987). For this density distribution
errors.
2 V∞
We experimented with numerous schemes for σ = R πGρ = .
0 c 0
3 √2
assigning errors to the V values in Table 3. p
c
These included adopting the V errors, com- This is the form of the DM distribution usu-
rot
bining the V errors with likely σ errors, and ally favored by Carignan and collaborators (e.g.
rot D
taking local averages of the errors over several Puche&Carignan,1991, andreferencestherein).
rings. In the end we adopt a uniform error in It is clear that model A is a better fit over all
V of 3 kms−1. This corresponds to the average radii,butmodelCproducesasgoodorbetterofa
c
error in V for R > 90′′. The other methods fitfor R 6kpc. Thedifferencebetween Models
rot
≤
invariably assign less weight to the inner points A and C illustrates the uncertainty due to which
than to the outer points. The χ2 minimization arbitraryformofthehalodistributionisadopted.
then effectively sacrifices the fit in the inner re- The isothermal sphere and the analytic form of
gions in order to make a marginal improvement eq. 5 have significantly different scaled density
at large R. Only equal weighting produces a rea- profiles over their first few R . Thus model C
c
sonablefitatallR. Sofortheadoptedfitsweare has very different parameter values than A and
no longer doing true χ2 minimization, but effec- B. It has a much less dense core, and it is the
tivelyanon-weightedleastsquaresminimization. only one of the three with a non-zero /L as
B
M
Four models are discussed. They are illustrated the best fit.
in Fig. 16, and their parameters are tabulated in
Models A-C give the best fit value with all
Table 4. Each panel of Fig. 16 shows the fitted
parameters free. The resulting limits on /L
B
rotationcurveandthecontributionofeachofthe M
are lower than one would expect for the red
components.
color of the outlying diffuse stellar population
Model A is the best fit to the V data. All in NGC 2915. For Model D we return to the
c
three parameters are allowed to be free, with the analytic halo models given by eq. 5 and fix
only constraint that they be 0. The resulting /L = 1.2, which represents approximately
B
≥ M
fit has /L = 0.0, i.e. the disk is not needed themaximumthediskcomponentcancontribute
B
M
to fit the rotation curve. The halo parameters tomatch theinnermostV datapoint. Thismass
c
9
to light ratio is in the range expected for the bar and a strong warp. These are normal prop-
colors of NGC 2915 (1 <∼ M/LB <∼ 3; Bruzual erties of spiral galaxies (Holmberg 1958; Bosma
and Charlot, 1993). The resultant halo parame- 1991). NGC2915appearstobeatwoarmedsys-
ters turn out to be identical to model B. In this tem. The arm structure is not flocculent like the
casethediskcontribution toV (R)is ofthesame transient features seen in simulations of shearing
c
order as the σ corrections. Likewise models of disks (e.g. Gerola & Seiden, 1978), despite oc-
D
typeC,butwithnoσ corrections, produceneg- curring in the flat (shearing) part of the rotation
D
ligible disk contributions. Thus the strength of curve. The arms are therefore probably due to a
the disk component critically depends on the σ spiral density wave. Although the kinematic sig-
D
corrections. Fits using the R band light profile nature of such a wave is not apparent, this may
(paper I) are not significantly better in fitting be due to the quality of the data (low signal to
the rotation curve than the B profile used here. noise, insufficient resolution).
Model D is our preferred fit, since the limits on
NGC2915’sHIextendswellbeyondRHowhich
/L are implausibly low for models A and B,
B is common for galaxies with high /L ra-
M HI B
and model D is clearly a better fit than model C. M
tio (Huchtmeier & Seiradakis, 1985; Hoffman
Note that models A, B and D have very sim- et al., 1993; van Zee et al. 1995). Its Σ pro-
g
ilar values V∞ with low uncertainties. This is file has a core-halo structure. This is less com-
because V∞ essentially determines the level of mon for spiral galaxies which typically exhibit
the flat part of the rotation curve, which is con- an HI deficit or plateau in the center (Wevers
strained much better than the inner portions. et al. 1986; Warmels, 1988), although similar
V∞ is lower for model C because the isother- cores have been found in irregular galaxies (e.g.
mal sphere reaches a maximum Vc of 1.1V∞, and NGC 55; Puche et al., 1991). NGC 2915’s veloc-
does not approach V∞ until R >∼ 10Rc (Binney ity dispersion profile also stands out for the high
& Tremaine 1987). value, b 40 kms−1, in the center. This is much
≈
higher than seen in normal (non-bursting) disk
None of the models can produce the exact
galaxies, which typically reach a central maxi-
shape of the rotation curve, especially the up-
mum of b 15 kms−1, droppingto 6 to8 kms−1
turn in V at large R. We performed fits where
rot ≈
at large radii (e.g. Dickey et al., 1990; see also
γ in eq. 5 is a free parameter. These yield
comparisons of Kamphuis, 1992; Lo et al. 1993).
γ = 1.93 and are not a significant improvement
overModelA.The 8kms−1 modulationsinthe NotethatalthoughNGC2915hasanormalb = 8
± kms−1 beyond the optical radius, it is unclear
V profile occur where the b profile and residual
c
how itandother galaxies withextended HI disks
maps show significant non-circular motions. One
maintain this velocity dispersion beyond any ap-
should not over-interpret them as necessarily re-
parent heat sources.
flecting structure in the mass distribution.
The HI properties of NGC 2915 are less ab-
5. Discussion normal compared to the relatively few BCD and
amorphous galaxies imaged in HI. These galax-
5.1. Comparison with other galaxies ies typically contain extended HI disks well be-
yond the optical radius, core-halo Σ profiles
HI
NGC 2915 is an intriguing galaxy because its and b profiles reaching 25 to 40 kms−1 in the
optical properties are those of a weak BCD (pa-
center (Taylor et al. 1994; 1995; Hunter et al.
perI)whileitsHImorphologyandglobalprofiles 1994; Meurer 1994; Brinks 1988; Viallefond &
are those of an Sd-Sm disk galaxy (cf. Roberts
Thuan, 1983). The properties of NGC 2915
and Haynes, 1994; Shostak, 1978). It has both a
are also reminiscent of the starburst IBm gal-
10
