Super Star Cluster Velocity Dispersions and Virial Masses in the M82
  Nuclear Starburst
Accepted by the Astrophysical Journal, March 7, 2007
Preprint typeset using LATEX style emulateapj v. 03/07/07
SUPER–STAR CLUSTER VELOCITY DISPERSIONS AND VIRIAL MASSES IN THE M82 NUCLEAR
STARBURST1
Nate McCrady
and James R. Graham
Department of Astronomy, University of California, Berkeley, CA 94720-3411
Accepted by the Astrophysical Journal, March 7, 2007
ABSTRACT
We use high-resolution near-infrared spectroscopy from Keck Observatory to measure the stellar
velocity dispersions of 19 super star clusters (SSCs) in the nuclear starburst of M82. The clusters
have ages on the order of 10 Myr, which is many times longer than the crossing times implied by their
velocity dispersions and radii. We therefore apply the Virial Theorem to derive the kinematic mass
for 15 of the SSCs. The SSCs have masses of 2× 105 to 4× 106 M⊙ , with a total population mass of
1.4 × 107 M⊙ . Comparison of the loci of the young M82 SSCs and old Milky Way globular clusters
in a plot of radius versus velocity dispersion suggests that the SSCs are a population of potential
globular clusters. We present the mass function for the SSCs, and find a power law fit with an index
of γ = −1.91±0.06. This result is nearly identical to the mass function of young SSCs in the Antennae
galaxies.
Subject headings: galaxies: individual (M82) — galaxies: starburst — galaxies: star clusters — in-
frared: galaxies
1. INTRODUCTION
1.1. Starburst Galaxies and Super Star Clusters
Short-duration episodes of intense star formation
known as “starbursts” are responsible for a significant
portion of star formation activity in the present-day Uni-
verse. Heckman (1998) estimates that the four most lu-
minous circumnuclear starbursts (M82, NGC 253, M83
and NGC 4945) account for 25 percent of the high-mass
(> 8 M⊙ ) star formation within 10 Mpc. The star-
burst phenomenon is the present-day manifestation of
the dominant mode of star formation in the early Uni-
verse (Leitherer 2001). At z = 0, high-mass stars form
predominantly in dense clusters and OB associations
(Miller & Scalo 1978). Massive stellar clusters in nearby
starburst galaxies thus provide a laboratory for studying
intense star formation and related feedback processes,
as well as physical conditions analogous to high-redshift
star formation.
Star formation in starbursts is resolved into young,
dense, massive “super–star clusters” (SSCs) that rep-
resent a substantial fraction of new stars formed
in a burst event (Meurer et al. 1995; Zepf et al.
1999). Hubble Space Telescope (HST) observations with
WFPC/WFPC2 in visible light (e.g., O’Connell et al.
1994; Whitmore & Schweizer 1995) have resolved SSCs
in the nearest starburst galaxies, and SSCs appear ubiq-
uitous in mergers and interacting galaxies. Of the
roughly 30 gas-rich mergers observed by HST, all have
young, massive, compact clusters (Whitmore 2001, and
refs.). A spectacular example is the “Antennae” galax-
1 Based on observations made at the W.M. Keck Observatory,
which is operated as a scientific partnership among the California
Institute of Technology, the University of California and the Na-
tional Aeronautics and Space Administration. The Observatory
was made possible by the generous financial support of the W.M.
Keck Foundation.
2 Now at Department of Physics and Astronomy, UCLA, Los
Angeles, CA 90095-1547
3 nate@astro.ucla.edu
ies, NGC 4038/4039, with more than 103 optically-visible
SSCs (Whitmore et al. 1999) and many other clusters
deeply embedded in dust (Gilbert et al. 2000).
The derived masses, radii and ages of SSCs suggest
that they are young globular clusters, and the brightest
and most massive may evolve into a population of glob-
ular clusters similar to that of the Milky Way. The ques-
tion of whether SSCs are in fact the progenitors of glob-
ular clusters depends critically on their masses and their
content of low-mass stars in particular (Meurer et al.
1995). If the stellar initial mass function (IMF) within
the clusters is biased toward high-mass stars (or “top
heavy”), for example by suppression of low mass star
formation, the clusters may not survive the disruptive
nature of mass loss resulting from both stellar evolu-
tion and dynamical processes (e.g. Chernoff & Weinberg
1990; Takahashi & Portegies Zwart 2000).
Local analogues of SSCs — massive, dense young clus-
ters in the Galaxy and Large Magellanic Cloud — con-
tain substantial populations of low-mass stars. The cen-
tral ionizing star cluster in NGC 3603, the most massive
H II region in the Galaxy, has 2000 M⊙ in OB stars alone.
Brandl et al. (1999) find that the mass spectrum of the
cluster is “well populated” down to 0.1 M⊙ . The clus-
ter R136 at the center of the 30 Doradus nebula in the
Large Magellanic Cloud is considered the closest example
of a starburst region (Brandl et al. 1996). In addition to
∼ 103 OB stars, some with masses in excess of 100 M⊙ ,
Sirianni et al. (2000) find a “substantial population” of
low-mass stars down to masses of 0.6 M⊙ in R136. With
a cluster mass of ∼ 2 × 104 M⊙ (Walborn et al. 2002),
R136 is at the lower end of the SSC mass range.
1.2. Mass Estimates
Most mass estimates to date for SSCs beyond the Lo-
cal Group are “photometric masses.” This technique in-
volves measuring the luminosity and broadband color of
a cluster, and comparing the results to the predictions
of spectral synthesis models. Examples include optical
http://arxiv.org/abs/0704.0478v1
2 McCRADY & GRAHAM
studies of clusters in the Antennae galaxies (Whitmore
2000, and refs.) and the nuclear cluster in IC 4449
(Böker et al. 2001). The resulting values are highly de-
pendent on the assumed IMF, age estimates and theo-
retical stellar evolution models. Consequently, the pho-
tometric method provides only very weak constraints on
the IMF in a cluster. The question of how SSCs evolve
or whether they can survive to become globular clusters
cannot be directly addressed with confidence by photom-
etry alone.
Recently, however, several studies have obtained kine-
matic masses for SSCs in starbursts directly from obser-
vations of stellar velocity dispersions. Ho & Filippenko
(1996b) use high-resolution optical spectra to measure
the velocity dispersion of an SSC in the nearby amor-
phous galaxy NGC 1705. They derive a cluster mass of
(8.2± 2.1)× 104 M⊙ . The dwarf starburst galaxy NGC
1569 contains two prominent SSCs. Ho & Filippenko
(1996a) used optical spectroscopy to determine the ve-
locity dispersion and derive a mass of (2 − 6) × 105
M⊙ for SSC-A. Gilbert (2002) uses near-IR spectroscopy
to identify two separate velocity components along the
line of sight at the position of SSC-A, and finds masses
of 3.0× 105 M⊙ for cluster A1 and 3.4× 10
5 M⊙ for clus-
ter A2. Gilbert also finds a velocity dispersion for SSC-B
and derives a mass of 1.8×105 M⊙ . Mengel et al. (2002)
use high-resolution optical and near-IR spectroscopy to
measure the velocity dispersions of six of the brightest
clusters in the merging Antennae galaxies. They derive
mass estimates ranging from 6.5× 105 to 4.7× 106 M⊙ .
In addition to these clusters in starburst galaxies, the
kinematic approach has been applied to several young,
massive clusters in more quiescent galaxies. Böker et al.
(1999) uses near-IR spectra to derive a mass of 6.6× 106
M⊙ for the nuclear star cluster in the giant spiral IC 342.
Larsen et al. (2004) derives virial masses for two SSCs
in the dwarf irregular NGC 4214 and two SSCs in NGC
4449 based on optical spectra, and one young SSC in
the nearby spiral NGC 6946 based on near-IR spectra.
Clusters in the Larsen study have masses between 2×105
and 1.8× 106 M⊙ , typical of SSCs.
Mass estimates based on measured velocity dispersions
are nearly independent of theoretical models, relying on
simple application of the virial theorem. Armed with
the virial mass, one can derive the light-to-mass ratio of
an SSC, which may be compared to predictions of pop-
ulation synthesis models to constrain the cluster’s IMF.
Critical to understanding the IMF is detection of low-
mass stars, the light of which is swamped by high lumi-
nosity supergiants. Measurement of the kinematic mass
provides the only means of detecting and quantifying the
low-mass stellar population of a cluster based on its in-
tegrated light.
1.3. Messier 82
M82 (NGC 3034) provides a useful laboratory. As
one of the nearest starburst galaxies at 3.6 Mpc
(Freedman et al. 1994), M82 presents an obvious reso-
lution advantage: star-forming regions can be studied on
small spatial scales (1′′ = 17.5 pc) and individual SSCs
are resolved by HST. The galaxy’s high inclination of
81◦ (Achtermann & Lacy 1995) and prevalent dust lead
to large, patchy extinction; infrared observations are re-
quired to overcome this obstacle in characterizing the
SSC population.
The light of red supergiant stars (RSGs) dominates
the near-IR continuum throughout the galaxy’s star-
burst core. Satyapal et al. (1997) interpret the compact
sources along the plane of M82 as young star clusters,
the space density of which increase towards the nucleus.
The smooth component of the near-IR emission is itself
likely the integrated contribution from unresolved clus-
ters of RSGs (Förster Schreiber 1998). Based on mid-IR
observations, Lipscy & Plavchan (2004) find that at least
20 percent of the star formation in M82 is occurring in
SSCs. HST/NICMOS images of the region (Figure 1)
show many luminous SSCs within ∼ 300 pc of the nu-
cleus.
The nuclear starburst is “active” in the sense that
the typical age for the starburst clusters is ∼ 107 years
(Satyapal et al. 1997). Evolutionary synthesis models by
Förster Schreiber (1998) suggest the nuclear starburst
(i.e., the central 450 pc) consists of two distinct, short
duration events with ages of about 5 Myr and 10 Myr.
The most intense star formation took place parallel to
the plane of the galaxy with a peak near the nucleus.
O’Connell et al. (1995) image M82 in the V and I bands
with the high-resolution Planetary Camera aboard HST,
identifying over 100 SSCs within a few hundred parsecs
of the nucleus. de Grijs et al. (2001) images a region in
the disk of M82, 1 kpc from the nuclear starburst, with
WFPC2 and NICMOS. They identify 113 SSC candi-
dates which were part of a starburst episode ∼ 600 Myr
ago (a “fossil starburst”), with little star formation in the
past 300 Myr. The clusters in the fossil starburst have
masses of 104−6 M⊙ . Smith & Gallagher (2001, SG01)
estimate an age of 60±20 Myr for the SSC ‘M82-F’, inter-
mediate between the ongoing nuclear burst and the fossil
burst farther out in the disk. M82-F lies ∼ 500 pc west
of the nucleus of M82. McCrady et al. (2005) measures
a mass of 5.6× 105 M⊙ for the cluster based on near-IR
observations, and found evidence for mass segregation.
Early ground-based studies of M82 found evidence of
an abnormal IMF. Rieke et al. (1993) uses population
synthesis models to constrain the IMF based on the near-
IR observations of McLeod et al. (1993). They conclude
that the large K-band luminosity of the M82 starburst
relative to its dynamical mass requires an IMF that is
significantly deficient in low-mass stars (M < 3 M⊙ ).
Doane & Mathews (1993) examine the supernova rate,
molecular gas mass and total dynamic mass and con-
clude that an IMF producing stars of mass > 3 M⊙ easily
matches observations, whereas a power-law IMF (e.g.,
Salpeter 1955) would require an unreasonably small mass
of stars in the region prior to the onset of the burst. In
contrast to these global studies, Satyapal et al. (1997)
use 1′′-resolution near-IR images to identify pointlike
sources and find that at this scale starburst models can
match observations without invoking a high-mass-biased
IMF. High spatial-resolution studies are necessary to in-
vestigate star formation in the cluster-rich M82 star-
burst. In a pilot study for this article, McCrady et al.
(2003) measure the kinematic mass of two clusters using
near-IR spectra and imaging. Based on the light-to-mass
ratios of the clusters, they find that one (MGG-11) ap-
pears to have a top-heavy IMF, whereas the other (MGG-
9) appears consistent with a normal IMF. Measurement
of the SSC mass independent of assumptions regarding
SUPER–STAR CLUSTERS IN M82 3
the L/M ratio are required to further constrain the stel-
lar IMF in the clusters.
1.4. Overview
In this article, we measure the virial masses of the su-
per star cluster population of the inner ∼ 500 pc of the
M82 starburst, extending the work of McCrady et al.
(2003). Our aim is to examine star formation in the
starburst on the scale of individual super star clusters,
regions only a few parsecs in extent, with an eye towards
placing constraints on the IMF of individual SSCs.
We use high-spectral-resolution near-IR spectroscopy
from the W.M. Keck Observatory to measure the stellar
velocity dispersions and dominant stellar spectral type
of the SSCs. We then apply the virial theorem to derive
their masses. Clusters for which the age may be deter-
mined facilitate investigation of the IMF. In § 2 we de-
scribe the kinematic mass, the method we use to measure
the velocity dispersion of stars in a cluster, and discuss
related systematic effects. In §3 we discuss the NIRSPEC
observations, data reduction and spectral extraction. In
§ 4 we measure cluster velocity dispersions and derive the
kinematic masses of the clusters, and present the cluster
mass function for the nuclear starburst region.
2. APPROACH
The mass of a gravitationally-bound star cluster may
be determined by application of the virial theorem
(Spitzer 1987). Specifically, the virial mass is a function
of two observable quantities:
M = 10
where rhp is the half-light radius in projection, σr is
the one-dimensional line-of-sight velocity dispersion and
G is Newton’s gravitational constant. Half-light radii
for the M82 clusters were measured in McCrady et al.
(2003) based on HST/NICMOS images. We assume the
light profile of the cluster traces the mass distribution,
and thus use the measured half-light radius as a proxy
for the half-mass radius. In the case of mass segrega-
tion, however, this assumption breaks down for near-
IR light, and the resulting mass represents a lower-limit
(McCrady et al. 2005). The M82 nuclear SSCs are la-
belled in a NIRSPEC slit-viewing camera (SCAM) mo-
saic shown in Figure 2. HST/NICMOSH-band (F160W)
images of the clusters are shown in Figure 3.
To measure σr for the clusters, we obtain high-spectral-
resolution near-IR integrated light spectra and perform a
cross-correlation analysis with template supergiant stars.
The near-IR spectrum of a young SSC (i.e., ages < 100
Myr) is dominated by the light of cool, evolved super-
giant stars. These highly luminous stars have a large
number of molecular and atomic features in the H band.
The integrated-light spectrum of an SSC resembles the
spectrum of a red supergiant star, the features of which
have been “washed out” by the velocity dispersion of
stars in the cluster (Figure 4). Our cross correlation
method, described in detail in McCrady et al. (2003),
returns both the velocity dispersion of the cluster rel-
ative to a particular template supergiant and a measure
of the similarity of the cluster and supergiant as quan-
tified by the peak value of the cross correlation function
(CCF). We have prepared an atlas of 19 high-resolution
(R ∼ 22, 000) template star spectra in the H band, rang-
ing from spectral types G2 through M5 in luminosity
class I (Kirian et al. 2006). Results of the cross correla-
tion analysis are presented in §4.
Determination of the velocity dispersion by cross cor-
relation analysis is subject to several potential sources
of systematic error. A detailed analysis is presented in
McCrady (2005). We present an overview in the follow-
ing paragraphs.
One potential difficulty is metallicity differences be-
tween the Galactic supergiants used as templates and the
supergiants producing the cluster light. McLeod et al.
(1993, and refs.) cited evidence from emission-line stud-
ies of various elements and concluded that the present-
day ISM in M82 has solar or slightly higher metallicity.
Förster Schreiber et al. (2001) determined that near-IR
stellar absorption features observed in the starburst core
are consistent with the light from solar-metallicity red
supergiants (RSG). Origlia et al. (2004) performed abun-
dance analysis on the nuclear starburst region using spec-
tral synthesis models for near-IR absorption and X-ray
emission. They found an iron abundance roughly half
of the solar value, but enhancement of α-elements to so-
lar or slightly higher levels. This pattern is consistent
with enrichment by recursive bursts of Type II super-
novae. The template supergiants used in our analysis
also have roughly solar metallicity, and thus we expect
that metallicity effects are unlikely to significantly bias
the measured cluster velocity dispersions.
Cross-correlation with a mismatched template spec-
trum can introduce systematic bias to the velocity dis-
persion determination. Tests with supergiant spectra
broadened with a Gaussian to simulate the effect of a
cluster velocity distribution indicate that the cross cor-
relation analysis correctly identifies the “best fit” based
upon the peak value of the CCF. Increasing the level of
added noise decreases the CCF peak, but does not lead to
misidentification of the best template. We have elected
to cross-correlate the cluster spectra with spectra of sin-
gle RSG stars because the light of a young coeval cluster
should be dominated by the light of the most massive
stars. At an age of ∼ 107 years, this would be the light
of evolved massive stars, i.e., the RSG stars. Mixing a
composite spectrum (with the inclusion of intermediate
mass stars) would generate a better match to the overall
spectrum (particularly the depth of absorption features
— see below). But for our purposes, it is more important
to be able to isolate the width of the lines resulting from
the velocity dispersion of cluster stars.
In addition to the dominant light of the RSG stars, we
expect the cluster spectra to contain a substantial con-
tribution from intermediate mass stars still on the main
sequence. In the H band, the spectra of A and late-B
stars (with masses ∼ 2–6 M⊙ ) are essentially featureless,
with the exception of the prominent (and wide) hydro-
gen Brackett series absorption lines. The prevalent neb-
ular emission in the disk of M82 requires us to avoid the
wavelength ranges of these hydrogen lines in our analy-
sis. Over the rest of the spectral range in our analysis,
an admixture of intermediate mass star spectra would
only change the slope of the spectrum (as the near-IR
spectra of these stars are essentially thermal). One step
in our analysis is the removal of any continuum slope,
4 McCRADY & GRAHAM
as the cross-correlation technique is used to measure the
velocity dispersion, information which is contained in the
width of the absorption lines, not in the depth of the lines
or in the continuum. As such, addition of intermediate
mass star spectra would not affect the measured velocity
dispersions or virial masses.
Filtering of the spectra in Fourier space is a source
of systematic error. Extracted spectra (§3) are cross-
correlated with the spectra of template supergiant stars.
The spectra are baseline-subtracted, apodized and both
high- and low-pass filtered in Fourier space. At the high-
frequency end, the cross correlation result is affected by
random noise; high amplitude noise residuals from sky
emission line subtraction are particularly noxious, as the
effects are unpredictable and merely serve to increase
uncertainty. Low frequencies contain information about
spectrum-wide residual variations after baseline subtrac-
tion. One likely source of such a variation is the presence
of light from intermediate-mass main sequence stars in
the integrated cluster light. Very broad hydrogen absorp-
tion features typical of the otherwise largely featureless
H-band spectra of A0V stars (Meyer et al. 1998), for ex-
ample, would not be removed by the low-order baseline
subtraction. Information pertaining to the velocity dis-
persion of the cluster resides in the frequencies between
the extremes.
The frequency filtering applied to the NIRSPEC data
leads to a systematic error of 0− 3 km s−1 , which varies
between echelle orders. The offsetting correction applied
to the results respresents a correction of no more than 20
percent, generally less. Noise in the input spectrum leads
to uncertainty in the correction factor in the range of
0.1−0.5 km s−1 , setting the lower bound on the precision
of the velocity dispersion measurements.
3. OBSERVATIONS
3.1. NIRSPEC Spectra
The spectra used to determine the internal velocity dis-
persions of the SSCs and template stars were taken with
the facility near-infrared echelle spectrometer NIRSPEC
(McLean et al. 1998) on the 10-m Keck II telescope on
Mauna Kea, Hawaii. We used NIRSPEC in the echelle
mode, which yields spectral resolution of R ∼ 22, 000.
The integrated light of super star clusters aged 5 to
80 Myr is dominated by evolved supergiant and bright
giant stars (Gilbert 2002). The near-IR spectrum of cool
evolved stars is replete with atomic and molecular ab-
sorption features — no “continuum” in the traditional
sense (i.e., a Planck thermal spectrum) is evident. Both
the H and K bands offer a large number of features that
the cross correlation analysis effectively averages over in
determination of the mean feature width. There is per-
haps an advantage to the H band, in that warm cir-
cumstellar dust may veil features in the K band. The
NIRSPEC detector experiences significant “persistence”
from exposure to large flux, for example bright sky OH
emission lines or arc lamp lines. Operationally, this dis-
courages changing of filters during an observing night as
the persistent after-images of sky emission lines from a
different filter add significantly to the noise in an echel-
legram. In this analysis, we have opted to observe the
clusters at the shorter wavelength only.
The NIRSPEC-5 (N5) order-sorting filter covers the
wavelength range 1.51–1.75 µm, corresponding approxi-
mately to Johnson H . The N5 echelle data fall in seven
echelle orders, ranging from 44 through 50. All obser-
vations were taken with the echelle and cross-dispersion
gratings set at their blaze angles. This position max-
imizes signal-to-noise for a given exposure time. This
advantage is mitigated by the fact that more than a sin-
gle position is required to cover the free spectral range
at 1.6 µm, and portions of the H band are not observed.
Spectra used in this work were obtained over four ob-
serving seasons, from February 2002 through January
2005. Table 1 presents a summary list of spectroscopic
observations. NIRSPEC observations of evolved stars
used as template spectra are discussed in Kirian et al.
(2006) and McCrady et al. (2003). The minimum air-
mass of M82 (declination +69◦40′) from Mauna Kea is
1.56, and efforts were made to observe at an airmass of
no larger than 2.0 when possible. The slit used has a
width of 0.432′′ (3 pixels) and length of 24′′. Use of the
long slit improves background subtraction, and often al-
lows multiple clusters to be observed simultaneously. Slit
positions were chosen to include multiple objects where
possible to increase observing efficiency. Certain pairs of
targets are closely-separated and only resolvable in good
seeing.
Each individual cluster spectrum has an integration
time of 600 seconds. Bright OH sky emission lines begin
to saturate in longer exposures, increasing the difficulty
of sky subtraction. Total integration time on a cluster is
increased by repeating the observations.
3.2. Reduction and Extraction
The spectra were dark-subtracted, flat-fielded and cor-
rected for cosmic rays and bad pixels. The curved echelle
orders were then rectified onto an orthogonal slit-position
versus wavelength grid based on a wavelength solution
from sky (OH) emission lines. Each pixel in the grid has
a width of δλ = 0.019 nm. We sky-subtracted by fitting
third-order polynomials to the 2D spectra column-by-
column.
The NIRSPEC echelle turret is jostled when the cryo-
genic image rotator undergoes large slews, leading to
stochastic shifts of the wavelength scale of up to sev-
eral pixels. Doppler shift information is lost due to such
shifts. Typically, the absolute wavelength scale is estab-
lished using telluric OH emission. Throughout each data
acquisition cycle the image rotator was either turned off,
or only slow, small amplitude tracking motions were ex-
ecuted. In either case the wavelength solution is stable
to better than a few hundredths of a pixel. Thus the ve-
locity broadening reported here is intrinsic to the source
and is not an instrumental effect.
The cluster spectra were extracted using Gaus-
sian weighting functions matched to the wavelength-
integrated profile of each cluster. To correct for atmo-
spheric absorption in the cluster spectra, we observed a
hot main sequence star at a similar airmass. This cali-
bration star spectrum is divided by a spline function fit
to remove photospheric absorption features (particularly
Brackett series and helium lines) and continuum slope.
The resulting atmospheric absorption spectrum is then
divided into the cluster spectra.
The adopted sky-subtraction method generally com-
pletely removes sky emission lines. However, a high
level of noise is left behind at the position of bright OH
SUPER–STAR CLUSTERS IN M82 5
lines, particularly un- or barely-resolved doublets. These
“noise spikes” must be removed to avoid introduction
of systematic bias in the cross-correlation results. We
smooth the spectrum with a broad (∼ 40 km s−1 ) step
function, and subtract the original spectrum to obtain a
residuals array. Data points greater than 5× the rms are
replaced by the smoothed pixel. The step-function width
and clipping level were chosen to limit replaced pixels to
only those affected by strong sky emission lines. Cer-
tain atmospheric OH emission lines were incompletely
removed in the sky subtraction process. In these cases,
we replaced the pixels affected by residual sky emission
with the median value of the ∼ 5 pixels on either side of
the contaminated range. The fraction of pixels replaced
in a given echelle order typically amounts to a few per-
cent. Tests on an OH emission-free echelle order indicate
that the cross-correlation result is unaffected within the
stated uncertainties.
An atlas of the spectra for 19 SSCs is presented in Fig-
ures 5 and 6. We have included here only the spectra
for echelle orders 46 and 47; plots of all echelle orders
for each cluster are available in McCrady (2005). Each
cluster spectrum represents the summation of multiple
observations (Table 1). The total is normalized by di-
viding by the median value for that echelle order, such
that the spectrum is centered about unity. The resulting
scale is relative flux, which allows direct comparison of
spectra of different clusters. The spectra are offset by
an arbitrary integer amount for presentation of multi-
ple clusters on a single set of axes, and labeled towards
the right (long-wavelength) side. The clusters within a
given echelle order are arranged in the atlas in order of
increasing velocity dispersion.
The signal-to-noise ratio (S/N) of the extracted spec-
tra varies between clusters. The clusters vary in lumi-
nosity over a range of four apparent magnitudes in H
band (McCrady et al. 2003), which is a factor of ∼ 40.
The luminosity differences carry through to the single-
integration S/N as all clusters were observed for 600 sec-
onds per integration. Light losses due to variable seeing
and inefficiencies in fine guiding add additional varia-
tion to the S/N for each cluster. Although faint clusters
were observed more often, not all clusters were observed
to the same S/N as a result of observing constraints.
Differences in the total S/N are evident in the atlas of
cluster spectra. For example, faint SSC-k was observed
only twice and has total S/N ∼ 9 per pixel based on
the CCD equation (Howell 2000, p. 54), which accounts
for Poisson statistics, background, dark current and read
noise. Bright SSC-1c was also observed just twice, but
has total S/N ∼ 28 per pixel. Repeated observations
(13 times) of SSC-r brought the total S/N up to ∼ 37
per pixel; a single observation of faint SSC-r results in
S/N comparable to a single observation of SSC k. These
examples provide a sense of the S/N range of the obser-
vations.
The spectra presented in the atlas have been shifted
to rest wavelength. Across the top of each plot, we have
identified the positions of certain prominent spectral fea-
tures. The H-band spectra of the clusters resemble the
spectra of supergiant stars, and have a large number of
iron and OH absorption lines. Rovibrational ∆v = 3
bandheads of carbon monoxide are recognizable in or-
ders 45 through 49. As seen in the spectra of supergiant
stars (Kirian et al. 2006; Meyer et al. 1998), the strength
of the CO bandheads and OH lines increase at cooler
effective temperatures. Lines from other miscellaneous
metals (Mn, Ti, Si, Ca, C, Ni) and molecules (CN) are
also indicated. At the bottom of each atlas plot is a rep-
resentative sky emission spectrum for that echelle order,
arbitrarily scaled. The brightest OH emission lines leave
a footprint of increased noise in the extracted cluster
spectrum.
The disk of M82 has substantial diffuse emission. The
nuclear starburst displays mottled near-IR continuum
emission (Figure 1). The cross-correlation analysis based
upon the spectra of the clusters is more sensitive to line
emission. Lynds & Sandage (1963) first noted the bipo-
lar, filamentary network of Hα emission extending more
than 1 kpc from the galactic center. Paschen α im-
ages show patchy recombination emission throughout the
nuclear starburst (Alonso-Herrero et al. 2003). K-band
spectra show emission lines of hydrogen (Br γ), He I and
H2. Prominent H-band emission lines are [Fe II] at 1.644
µm and the Br 6 line of hydrogen at 1.7367 µm. In sev-
eral of the slit positions used, nebular emission varies
along the slit and removal is difficult. Remnants of the
lines are apparent in the spectra of certain clusters (e.g.,
SSC-1c in Figure 6).
3.3. Objects Observed
The 20 objects of Table 3 of McCrady et al. (2003)
and the 19 objects of Table 2 do not constitute equal
sets. The intersection of the two tables contains the 15
SSCs for which we have herein derived a mass (see Table
2). The union of the two tables contains 24 objects.
Moreover, Figure 2 identifies 26 objects. An accounting
of the objects observed in this project is as follows.
Five clusters for which we measured photometry and
half-light radius had significant problems with their
echelle spectroscopy. The practical single-exposure time
limit of 600 seconds is set by the saturation point of
atmospheric OH emission lines. Clusters fainter than
[F160W] ∼ 15 mag have S/N < 2 in 600 seconds of typ-
ical seeing. In poor seeing, these faint clusters are often
too difficult to identify for positioning the spectrograph
slit. SSC-1b is a frustrating case, as it is a bright clus-
ter with good S/N in a 600-s exposure. In poor seeing,
however, the light from SSC-1b is blended with the light
of the nearby clusters SSC-1a and SSC-1c. Observations
on 2003 Feb 6 were not used for SSC-1b or SSC-1c be-
cause of inadequate seeing. On the night of 2005 Jan 24,
the seeing was sufficient to resolve SSC-1c, however the
NIRSPEC detector was contaminated by persistence due
to sky emission from use in low-resolution mode by an
unaffiliated observing team earlier in the night. While
we were able to extract SSC-1c, SSC-1b was significantly
contaminated and had to be rejected.
Six other objects identified in Figure 2 have no derived
virial mass. SSC-z is clearly a super star cluster, but
lies just north of the edge of the HST/NICMOS field
(McCrady et al. 2003). In the absence of a resolved im-
age, we have no measurement of the half-light radius.
Object “y” also lies off the edge of the NICMOS field,
just south of SSC-L. Spectra of object “y” are inconclu-
sive due to low S/N in any case. Object “10” is un-
resolved by the NICMOS image, and we therefore have
no measured half-light radius. Interestingly, object “10”
6 McCRADY & GRAHAM
is coincident with a point source in Paschen α images,
suggesting it may be a compact H II emission region sur-
rounding one or several massive stars. SSC-j and SSC-a
are not well fit by empirical King functions, and the half-
light radii of these clusters are undetermined. SSC-h is
likewise not well fit by the empirical King model, as it is
clearly a collection of sources in NIC2 images (Figure 3).
4. ANALYSIS
4.1. Cross Correlation Results
Each cluster was observed multiple times, with seven
echelle orders in the N5 filter per observation. A single
observation of the spectrum in a particular echelle order
is treated as one “experiment” for the cluster. Each of
the experiments for a cluster is cross correlated with the
spectrum from the corresponding spectral order of each
of the template evolved stars. The result of this analy-
sis is an ensemble of cross correlation functions (CCFs)
for each cluster/template star pair. The peak amplitude
of the CCF measures the similarity of the cluster to the
template spectral type (Table 2). For each cluster, we
have identified the template supergiant spectrum which
provides the best match. In most cases, several template
stars match the cluster approximately equally well. The
spectra of template stars with higher surface tempera-
tures (e.g., G-type stars) proved to be poor matches for
the cluster spectra. The CCFs for each cluster and its
best-match template are presented in McCrady (2005).
The velocity dispersions based upon cross correlation
results for the best-match template star are listed in Ta-
ble 2. The quoted uncertainties reflect the formal error
based upon the standard deviation of the mean for the
ensemble of experiments. Systematic errors are treated
in McCrady (2005, see also §2); the stated uncertainties
do not include any allowance for the applied correction
of systematic offsets. In the course of the analysis, each
cluster spectrum is cross correlated with each of the tem-
plate spectra. We find that the velocity dispersions in-
dicated by the best match template are consistent with
velocity dispersions indicated by other templates of sim-
ilar effective temperature to within the uncertainties.
4.2. Derived Virial Masses
Armed with measurements of the cluster half-light
radii and velocity dispersions, we are ready to derive
the virial masses. Table 2 lists the derived mass for 15
SSCs in M82. Most of the SSCs have masses between
2 × 105 and 106 M⊙ ; clusters SSC-L, SSC-7 and SSC-9
haveM > 106 M⊙ . The median uncertainty on the virial
mass measurements is 16 percent. A significant portion
of the error budget is the 8 percent uncertainty in the
adopted distance to M82.
Figure 7 plots the half-light radii versus the velocity
dispersions for the SSCs. We have plotted the locus of
points for certain masses as dashed lines. These lines il-
lustrate that the uncertainty in the velocity dispersion,
σr, has a greater impact on the uncertainty in mass than
does the uncertainty in the half-light radius, rhp. This is
to be expected, as the virial mass (Eq. 1) is proportional
to the square of σr. We have mitigated this effect by
measuring σr to a precision sufficient to balance the er-
ror budget roughly evenly between uncertainties on the
velocity dispersions and the halflight radii.
Application of the virial theorem to determine the
mass of the clusters is based on the assumption that
the clusters are at present bound (self-gravitating) en-
tities. This assumption is supported by a comparison of
the relevant timescales: the crossing time and the age
of the clusters. The crossing time is the typical time re-
quired for a star to cross the cluster, where tcr ≈ rhp/σr
(Binney & Tremaine 1987, p. 190). The SSCs in Table
2 have crossing times in the range of 4 × 104 to 3 × 105
years, while their ages are on the order of ∼ 107 years
(Satyapal et al. 1997). Thus, member stars have made
tens of crossings of the clusters. After just a few cross-
ing times, the stars of a cluster are well mixed (King
1981) and the virial theorem is well satisfied (Aarseth
1974). The assumption that the M82 clusters are cur-
rently gravitationally bound is therefore valid.
To provide context and a sense of scale for the derived
cluster masses, we turn to virial mass measurements of
SSCs and globular clusters in our own and other galax-
ies from the literature. Pryor & Meylan (1993) use ve-
locity dispersions and King-Michie model fits to derive
virial masses of 56 Galactic globular clusters. Their ve-
locity dispersions range from 1 − 19 km s−1 (σ = 6.8
km s−1 ) and masses of 104 to 4 × 106 M⊙ (M = 5.6 ×
105 M⊙ ). The Milky Way globular clusters are plot-
ted in Figure 7 for comparison with the M82 clusters.
(Pryor & Meylan (1993) provide σr and M , from which
we estimated rhp using Eq. 1.) In total, the Milky
Way has about 180 globular clusters (Ashman & Zepf
1998, p. 31). If we assume an average cluster mass of
1.9 × 105 M⊙ (Mandushev et al. 1991), the total mass
of the Galactic population is ∼ 3.4 × 107 M⊙ . The
M82 SSCs in Table 2 have a total mass of ∼ 1.4 × 107
M⊙ , comparable to the aggregate mass of the much older
Galactic globular clusters. (However, we do not mean to
imply that all of the M82 SSCs will remain bound for 12
Gyr; see §5.)
The old globular clusters of the Milky Way are spread
widely in the σ − rh space of Figure 7, but in general
the locus of points is below (lower velocity dispersion
and to the right (larger radius) of the locus of points for
the young M82 SSCs. What can we infer about the two
populations from this plot? It is interesting to consider
the time evolution of a cluster in this parameter space.
Over time, mass loss from individual stars in the course
of their evolution will cause a cluster to lose mass. As
detailed in the Appendix, adiabatic mass loss by a viri-
alized cluster progresses such that the product σr is con-
served. An isolated cluster, evolving through adiabatic
mass loss, would gradually move down and to the right in
Figure 7 as indicated by the plotted vector, crossing the
“isobaric” lines. Over the span of 15 Gyr, a cluster with
a Kroupa IMF would lose around half of its initial mass
(i.e., its mass at 10 Myr) as a result of stellar evolution
(McCrady et al. 2003). Such adiabatic evolution of the
young M82 SSCs over a Hubble Time would place the
clusters in the same region as the bulk of the old globu-
lar clusters in Figure 7. We discuss the implications of
this plot further in §5.
Additional context for our results comes from observed
cluster systems in other galaxies. Dubath & Grillmair
(1997) measured the masses of nine globular clusters in
M31. They find velocity dispersions of 7−27 km s−1 (σ =
SUPER–STAR CLUSTERS IN M82 7
14 km s−1 ), rhp = 2 − 5 pc (rhp = 3.6 pc) and masses
of 4.3− 82× 105 M⊙ (M = 2.3× 10
6 M⊙ ). Larsen et al.
(2002) measure virial masses for four globular clusters in
M33. They find velocity dispersions of 4.4− 6.5 km s−1 ,
rhp = 2 − 8 pc and masses of 1.4 − 6.2 × 10
5 M⊙ . In
general, the old globular clusters in these neighboring
galaxies are larger with lower velocity dispersions. This
pattern is consistent with the notion that the M82 SSCs
are a population of young globular clusters, as adiabatic
mass loss due to stellar evolution would cause the clus-
ters to expand over time (see Appendix). A more direct
comparison is provided by young SSCs in other galaxies.
Mengel et al. (2002) examines five young (age ∼ 8 Myr)
clusters in the merging Antennae galaxies. They find ve-
locity dispersions of 9 − 21 km s−1 , rhp of 3.6 − 4.0 pc,
and masses of 6.4− 47× 105 M⊙ .
As discussed in McCrady et al. (2005), SSC-F shows
evidence of mass segregation. While cluster-wide dynam-
ical mass segregation in these young clusters is unlikely, it
is possible that the most massive stars in a cluster have
either rapidly sunk toward the core or simply formed
nearer the core. In either case, the red supergiant ve-
locity dispersions we measure in the near-IR would be
smaller than the cluster mean and the masses we derive
would represent lower limits. Gasdynamical modeling
by Boily et al. (2005) indicates that inward migration of
massive stars may cause the dimensionless geometric pa-
rameter η in the virial mass formula (Equation 1) to in-
crease by a factor of around two over a few ×107 yr.
In our analysis, we have explicitly assumed that η = 10
as derived in (McCrady et al. 2003). If mass segrega-
tion has in fact led to η > 10 in these M82 clusters, the
masses we derive here would be underestimated by the
corresponding factor.
4.3. Cluster Mass Function
Armed with the virial masses of the SSCs, we can inves-
tigate the cluster mass function for the M82 nuclear star-
burst. The standard manner for making a cluster mass
function is to prepare a histogram of the masses over log-
arithmically spaced bins and fit a power law or lognor-
mal distribution to the slope. Rosolowsky (2005) demon-
strates the shortcomings of this method, citing specifi-
cally the dependence of the power law index to the choice
of bin size and spacing in cases involving a small number
of data points. We choose instead to evaluate the cumu-
lative mass function for the 15 M82 SSCs. Figure 8 plots
the cumulative mass function as N(M ′ > M), which is
the total number of clusters with mass greater than the
reference mass M . In the common case of a power law,
the slope of a standard mass function is dN/dM ∝ Mγ .
For the cumulative mass function, the integration adds
one to the exponent, such that N(M ′ > M) ∝ Mγ+1
(Rosolowsky 2005).
The mass function for the M82 SSCs is well fit by a
power law of index γ = −1.91±0.05. The uncertainty on
the power law index is based on a Monte Carlo simulation
of our mass data. We resampled the cluster masses by
adding normal noise according to the uncertainties on the
mass measurements, then fit for the index of the resulting
cumulative mass function. The distribution of power law
indices was Gaussian with a standard deviation of our
quoted uncertainty. The power law index of γ ∼ −2
indicates that the stellar mass of the cluster population
is divided rather equally between the high-mass clusters
and low-mass clusters. Of the aggregate mass in our
sample of 15 SSCs, roughly 60 percent of the mass is
contained in the three most massive clusters (SSCs L, 9
and 7).
Estimation of the completeness limit for our SSC mass
function is somewhat difficult. Our mass measurements
are based on measured cluster velocity dispersions. For
us to measure a velocity dispersion, the cluster must be
observable in the near-IR and be sufficiently bright and
spatially resolved for us to obtain a usable spectrum.
Limiting factors include the intrinsic mass of the cluster,
the light-to-mass ratio for the cluster, confusion with ad-
jacent clusters or background emission, and line-of-sight
extinction. With the exception of SSC 1b, which suffers
from source confusion, we are confident we have obtained
the spectra of all clusters brighter than apparent mag-
nitude H ∼ 13.8. At the distance of M82, this corre-
sponds to a cluster luminosity of ∼ 1.8 × 105 L⊙ . To
convert to a mass estimate, we can estimate the light-
to-mass ratio for the clusters. For clusters in the age
range of 7–13 Myr, suitable for the M82 nuclear clusters
(McCrady et al. 2003), and a Kroupa (2001) field star
mass function, Starburst99 models predict L/M ∼ 1 in
units of L⊙ /M⊙ . The highly variable extinction in the
dusty, inclined disk of the galaxy could be hiding ad-
ditional bright clusters, on the far side of the disk for
example. Assuming a typical extinction correction for
the clusters of ∼ 0.5 mag in H band, we estimate that
our mass function is largely complete for clusters more
massive than ∼ 3× 105 M⊙ . To characterize the poten-
tial effects of incompleteness, we added fake clusters of
mass (3 ± 0.5)× 105M⊙ to the Monte Carlo simulation.
Each additional undetected cluster with mass near this
completeness limit would decrease the power law index
by ∆γ ∼ −0.02 (i.e., the power law would become more
steeply negative).
5. DISCUSSION
In §4.2, we note that the evolution of an individual M82
SSC via adiabatic mass loss due to stellar evolution over
a Hubble time would reposition the SSC in σ−rh param-
eter space. Such a repositioning would leave any of the
SSCs in our sample in a region consistent with the posi-
tion of the old globular clusters in the Milky Way (Figure
7). In a sense, this represents a necessary but not suffi-
cient condition for the hypothesis that these young SSCs
represent the progenitors of globular clusters. If, instead,
our analysis showed that stellar evolution would move the
clusters to a point in σ− rh parameter space that would
be inconsistent with the position of old globular clus-
ters, it would represent strong evidence that these SSCs
could not be progenitors of globular clusters. In fact,
adiabatically evolving any individual M82 SSC from our
sample for 15 Gyr would leave it solidly within the re-
gion of σ − rh parameter space occupied by old globular
clusters.
But we hasten to note that this result is insufficient
evidence that these SSCs are destined to become a
population of old globular clusters. The M82 nuclear
clusters are young, with ages on the order of 10 Myr
(Förster Schreiber 1998; McCrady 2005). There is grow-
ing evidence in the literature that a significant portion of
8 McCRADY & GRAHAM
young clusters are disrupted on a timescale of approxi-
mately 10 Myr from birth. Observations of massive clus-
ters in the Antennae galaxies (Fall et al. 2005) and M51
(Bastian et al. 2005) and lower mass open clusters in the
solar neighborhood (Lada & Lada 2003) find an excess
of clusters with ages ∼ 10 Myr relative to what would
be expected based on an assumption of constant cluster
formation rate (Bastian & Gieles 2006). The naive in-
terpretation of these findings is that there was a burst
of star cluster formation in the past 10 Myr in each of
these galaxies. But as noted by Fall et al. (2005), the
age distribution of star clusters represents the combined
histories of star cluster formation and disruption within
a galaxy. The relative wealth of clusters aged 10 Myr in
these various nearby galaxies suggests that we are fortu-
nate to be observing them at a special time in their star
formation histories, whereby we fall afoul of the cosmo-
logical principle.
An attractive alternative is that a high percentage of
clusters are disrupted within approximately 10 Myr of
formation, i.e., the e-folding survival time for a popula-
tion of clusters is about 10 Myr (Mengel et al. 2005).
This hypothesis goes by the morbid name of “infant
mortality.” The energy and momentum output of mas-
sive stars via stellar winds and supernovae could remove
residual natal gas from a young massive cluster. If the
gas removal were impulsive (i.e., occured over less than
a crossing time), the cluster could become gravitation-
ally unbound and begin expanding freely. Whether or
not a cluster survives this phase depends largely on the
star formation efficiency in the formation of the cluster
from natal gas (see references in Bastian & Gieles 2006).
Fall et al. (2005) posit that because a cluster with more
mass has both more gas to remove and more massive
stars to provide the energy, the fraction of clusters dis-
rupted may be roughly independent of mass. They find
this conjecture to be consistent with their observation
that the shape of the cluster mass function in the Anten-
nae galaxies is nearly independent of age.
Zhang & Fall (1999) investigated the mass function
of young star clusters in the Antennae galaxies (NGC
4038/9) based on photometric mass estimates, and found
a power law mass function of γ = −2 over the range
104 ≤ M/M⊙ ≤ 10
6, a result confirmed by Fall et al.
(2005). Mengel et al. (2005) found potential evidence
for a turnover or change in slope of the mass function for
the Antennae clusters, but cautions that the random and
systematic uncertainties discourage overinterpretation of
this result. They note that determination of the cluster
mass function from photometric masses requires age de-
terminations for individual clusters, which is particularly
delicate work around ages of ∼ 107 yr when the cluster
luminosity varies greatly with age.
Our virial mass measurements obviate determination
of the ages of individual clusters and assumptions re-
garding the form and cutoff masses of the stellar IMF.
The M82 nuclear clusters in our sample are also young,
and follow a power law mass distribution very similar to
the Antennae clusters. A power law mass distribution
for young SSCs stands in contrast to the lognormal mass
distribution for old globular clusters (Harris 1991), which
imply a preferred mass scale at the peak of ∼ 2×105M⊙
for Milky Way globular clusters. Several processes, oper-
ating on different timescales, have the ability to disrupt
star clusters. As discussed above, infant mortality ap-
pears to disrupt clusters independently of mass, thereby
preserving the shape of the initial cluster mass function.
On longer timescales (∼ 108−109 yrs), the strongly mass
dependent processes of two-body relaxation and exter-
nal perturbations (such as gravitational shocks and dy-
namical friction) can disrupt the clusters (Bastian et al.
2005). Analytical models by Fall & Zhang (2001) find
that the initial form of the high-mass end of the cluster
mass function is preserved over time. Two-body relax-
ation decreases the masses of clusters linearly over time,
flattening the mass function at low masses but little af-
fecting the shape at high masses. By 12 Gyr, the mass
function develops a peak at a mass of about 2× 105M⊙ .
Thus, an initial power law distribution of cluster masses
will develop into a distribution resembling the lognormal
mass function of old globular clusters over 12 Gyr, with
disruption erasing all information regarding the initial
shape of the mass function at the low-mass end.
In a galactic environment, of course, the clusters are
not isolated, and are additionally subject to external
forces such as galactic tides and dynamical friction. The
inner 1 kpc of a galaxy, with its strong tidal fields, is
a particularly dangerous place for star clusters. But as
noted by Fall & Zhang (2001), their models “support the
suggestion that at least some of the star clusters formed
in merging and interacting galaxies can be regarded as
young globular clusters.” As shown in Figure 7, the adia-
batic evolution of a cluster through stellar evolution and
mass loss over a similar time frame will tend to move the
M82 SSCs into the σ − rh parameter space occupied by
old Galactic globular clusters. While we cannot predict
the fate of any individual M82 SSC, our results suggest
that any cluster which should happen to survive for a
Hubble time could resemble the old globular clusters seen
in the Milky Way today.
6. SUMMARY
In this paper, we investigate the SSC population of the
inner ∼ 500 pc of the M82 starburst. The nuclear star-
burst in M82 contains roughly two dozen SSCs that are
prominent in the near-IR. Based on high spectral reso-
lution near-IR spectra, we measure line-of-sight velocity
dispersions for 19 SSCs in the nuclear starburst. We find
dispersions in the range of 7 − 35 km s−1 , comparable
with values for older globular clusters. We apply the
virial theorem to the measured velocity dispersions and
halflight radii to derive the masses of 15 of the SSCs. The
SSC masses lie in the range of 2.5 × 105 M⊙ to 4 × 10
M⊙ , placing them at the high end of the mass distribu-
tion function for old Galactic globular clusters. The total
mass of the 15 measured SSCs is 1.4× 107 M⊙ , which is
of the same order of magnitude as the total mass of the
globular cluster system of the Milky Way. Evolution of
the clusters via gradual mass loss from stellar evolution
would move them into the realm of σ − rh parameter
space occupied by old Milky Way globular clusters. The
cumulative mass function of the clusters follows a power
law with an index of γ = −1.91 ± 0.06. This is very
similar to the mass distribution of young SSCs in the
Antennae galaxies, and lends credence to the suspicion
that SSCs are potential future globular clusters.
We would like to thank the staff of the Keck Ob-
SUPER–STAR CLUSTERS IN M82 9
servatory for their assistance in our observations. We
also thank the anonymous referee for helpful com-
ments regarding implications of this work. NM thanks
John Johnson for invaluable data wrangling advice and
W. D. Vacca, L. Blitz and S. E. Boggs for helpful com-
ments. The authors wish to recognize and acknowledge
the very significant cultural role and reverence that the
summit of Mauna Kea has always had within the in-
digenous Hawaiian community. We are most fortunate
to have the opportunity to conduct observations from
this mountain. This material is based upon work sup-
ported by the National Science Foundation under Grant
No. 0502649, with additional support from NSF Grant
AST–0205999. Any opinions, findings, and conclusions
or recommendations expressed in this material are those
of the authors and do not necessarily reflect the views of
the National Science Foundation.
APPENDIX
APPENDIX
The consequences of mass loss from a virialized star cluster depend upon the rate of loss. We consider specifically
two cases: (1) rapid mass loss, where a star cluster has a sufficiently long relaxation time that v and R are unable to
readjust during the ejection of some quantity of mass, and (2) slow mass loss, where v and R for the cluster continually
readjust to maintain equilibrium.
In the case of rapid mass loss, Hills (1980) derives an expression for the relation between the initial mass and the
amount of mass ejected:
R = R0
M0 −∆M
M0 − 2∆M
. (A1)
Evidently, as ∆M tends to M0/2 the cluster radius tends to infinity and the cluster becomes unbound.
In the case of gradual mass loss, the cluster constantly adjusts to maintain equilibrium. The total energy at any
instant, whether the cluster is in equilibrium or not, is
Mv2 − η
where v is the 3-d rms velocity and η is a non-dimensional form factor. The corresponding change in total energy of
the system is
v2 − 2η
. (A3)
After δm is lost, the cluster must readjust to the new equilibrium. In the new equilibrium configuration the Virial
theorem, E = −T = Ω/2 (Binney & Tremaine 1987, p. 211), can be invoked to express the partial derivative:
, (A4)
which can be integrated from the initial mass, M0, and energy E0,
dE/E = 3
dM/M (A5)
to yield E/E0 = (M/M0)
3. Substituting again from the Virial theorem, which shows that E ∝ Ω ∝ M2/R, we have
have an expression for the radius as a function of mass,
R = R0
. (A6)
which is the adiabatic invariant from Hills (1980), where M ≡ M0 −∆M .
In the equilibrium states both before and after loss of ∆M , the Virial theorem applies, and E = −T (where
T = Mv2/2 is the kinetic energy). Thus:
−Mv2/2
. (A7)
Simplifying and combining terms,
which has the physical solution (M/M0) = (v/v0). If we compare this last result to Equation (A6), we find
and therefore for adiabatic mass loss, vR = v0R0 = constant.
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SUPER–STAR CLUSTERS IN M82 11
TABLE 1
NIRSPEC N5 Observations
Date Objects texp Airmass Seeing Atm Star Remarks
(UT) (min) (sec z) (′′) (SpT)
2002 Feb 23 3, 9, 11 40 1.6 0.5 HD 74604 (B8V) (1)
2003 Jan 19 F, L 70 1.9 0.8 HD 173087 (B5V)
2003 Feb 6 1b, 1c, r 60 1.8 0.7 HD 74604 (B8V)
2003 Feb 6 1a, 3, m 50 1.7 0.7 HD 82327 (B9V) (2)
2003 Feb 6 6, 7 60 1.6 0.7 HD 82327 (B9V)
2003 Feb 6 8, 10, c 120 1.6 0.6 HD 82327 (B9V)
2003 Feb 6 s, t 60 1.9 0.6 HD 146926 (B8V)
2003 Feb 7 a, b 90 2.0 1.5 HD 146926 (B8V) (3)
2003 Dec 5 6, 7 20 1.6 0.5 HD 63586 (A0V)
2003 Dec 5 3, 6, h 40 1.6 0.5 HD 63586 (A0V) (4)
2004 Feb 8 a, y 60 1.9 0.8 HD 146926 (B8V)
2004 Feb 8 r, z 30 2.2 1.0 HD 146926 (B8V)
2004 Feb 9 r, z 40 1.6 1.3+ HD 82327 (B9V) (3)
2004 Feb 9 a, y 30 1.7 1.3+ HD 82327 (B9V) (3)
2005 Jan 24 1a, 1b 20 1.6 0.6 HD 82327 (B9V)
2005 Jan 24 1a, 1c, q 20 1.5 0.6 HD 82327 (B9V)
2005 Jan 24 j, k, q 30 1.5 0.6 HD 82327 (B9V)
Note. — Seeing values are estimates. Remarks. — (1) Only 30 min on object 3.
(2) Only 40 min on object 1a. (3) Seeing very poor & variable. (4) Only 20 min on
object 3.
TABLE 2
Cross-Correlation Results
Best Fit Mean CCF Dispersion Mass∗ tcr
Object Template Peak Value (σ, km s−1 (105 M⊙ ) (10
5 yr)
SSC L HR2289 0.70± 0.05 34.7± 0.4 40.± 6. 0.41± 0.05
SSC F HR2289 0.69± 0.1 12.4± 0.3 5.5± 0.8 1.2± 0.1
SSC a HD237008 0.53± 0.1 10.9± 0.4
SSC 11 HD237008 0.78± 0.07 12.1± 0.4 3.9± 0.6 0.9± 0.1
SSC 9 HD237008 0.70± 0.07 19.8± 0.5 23.± 4. 1.3± 0.2
SSC 8 HD14469 0.52± 0.1 10.5± 0.5 4.0± 0.7 1.5± 0.2
SSC 7 HD237008 0.53± 0.1 18.6± 1. 22.± 4. 1.4± 0.2
SSC 6 HD237008 0.76± 0.09 9.2± 0.3 2.7± 0.4 1.5± 0.2
SSC h HD237008 0.62± 0.07 33.2± 1.0
SSC j HD237008 0.55± 0.10 9.0± 0.8
SSC k HD237008 0.51± 0.1 9.± 1. 5.7± 2. 3.1± 0.5
SSC m HD14469 0.38± 0.1 15.2± 0.8 7.3± 1. 0.9± 0.1
SSC q HD237008 0.53± 0.1 7.9± 0.6 2.8± 0.6 2.5± 0.3
SSC 3 HD237008 0.76± 0.1 8.7± 0.3 2.7± 0.4 1.8± 0.2
SSC 1a HD237008 0.72± 0.07 13.4± 0.4 8.6± 1. 1.5± 0.2
SSC 1c HD237008 0.71± 0.08 12.2± 0.4 5.2± 0.8 1.2± 0.2
SSC r HD237008 0.65± 0.1 8.6± 0.3 3.0± 0.5 2.0± 0.2
SSC t HD237008 0.46± 0.1 7.9± 0.9 2.5± 0.7 2.2± 0.4
SSC z HD237008 0.69± 0.1 9.9± 0.3
∗ Error in mass includes errors in distance to M82, half-light radius and ve-
locity dispersion.
† Crossing time, described in §4.2.
12 McCRADY & GRAHAM
Fig. 1.— Color mosaic of HST ACS/WFC and NICMOS images of the nuclear region in M82. ACS F814W, NICMOS F160W and
NICMOS F222M images are mapped to blue, green and red, respectively. The image is ∼ 25′′ × 65′′ (0.4 × 1.1 kpc) with north up and
east to the left. About two dozen super star clusters are evident, many of which are spatially coincident with and reddened by the band
of variable extinction running from upper left to lower right in the image.
SUPER–STAR CLUSTERS IN M82 13
Fig. 2.— Mosaic of H-band (N5) NIRSPEC SCAM images of the nucleus of M82. Candidate SSCs are labeled for reference. Coordinates
are J2000. Inset image is from HST/NICMOS.
14 McCRADY & GRAHAM
Fig. 3.— HST/NICMOS F160W images of each cluster. Each image is 2.5′′ × 2.5′′, and the position angle of the y-axes is 349.4◦ (i.e.,
North is 10.6◦ left of straight up). The images are log-scaled, as the cores are substantially brighter than the halos.
SUPER–STAR CLUSTERS IN M82 15
Fig. 4.— Comparison of the spectra of SSC-11 and several cool supergiants in echelle order 49. The cluster spectrum displays the same
features as the supergiants, but appears washed out due to the velocity dispersion of its constituent stars. The supergiant stars are plotted
in a temperature sequence, with the hottest star at the top.
16 McCRADY & GRAHAM
Fig. 5.— Atlas of SSC spectra for echelle orders 47 & 46.
SUPER–STAR CLUSTERS IN M82 17
Fig. 6.— Atlas of SSC spectra for echelle orders 47 & 46, continued.
18 McCRADY & GRAHAM
Fig. 7.— Projected halflight radius (rhp) versus velocity dispersion (σr) for M82 SSCs (circles). Dashed lines indicate the locus of points
for cluster mass as labeled. Error bars on the halflight radius do not include the uncertainty on the distance to M82. Galactic globular
clusters (squares) from Pryor & Meylan (1993) are plotted for comparison. The vector indicates time evolution of a cluster due to adiabatic
loss of half its mass (see Appendix).
SUPER–STAR CLUSTERS IN M82 19
Fig. 8.— Cumulative mass function for the M82 SSCs. The dashed line indicates a power law fit where N(M ′ > M) ∝ Mγ+1. The best
fit has a slope of γ = −1.91± 0.06. The estimated completeness point for cluster mass is marked ’C’ (see text). The fitted power law does
not reflect any correction for completeness.
