Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.stsci.edu/~marel/abstracts/psdir/M15paper2err_6.ps Äàòà èçìåíåíèÿ: Sat Nov 30 01:22:01 2002 Äàòà èíäåêñèðîâàíèÿ: Sat Dec 22 15:55:28 2007 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: http astrokuban.info astrokuban

Astronomical Journal, submitted.
Addendum: ``Hubble Space Telescope Evidence for an Intermediate­Mass
Black Hole in the Globular Cluster M15---
II. Kinematical Analysis and Dynamical Modeling 1 ''
Joris Gerssen, Roeland P. van der Marel
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218
Karl Gebhardt
Department of Astronomy, Mail Code C4100, University of Texas at Austin, Austin, TX 78712
Puragra Guhathakurta 2,3
Herzberg Institute of Astrophysics, National Research Council of Canada, 5071 West Saanich
Road, Victoria, BC V9E 2E7, Canada
Ruth C. Peterson 4
UCO/Lick Observatory, Department of Astronomy and Astrophysics, University of California at
Santa Cruz, 1156 High Street, Santa Cruz, CA 95064
Carlton Pryor
Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway,
NJ 08854­8019
1 Based on observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope
Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA
contract NAS 5­26555. These observations are associated with proposal #8262.
2 Herzberg Fellow.
3 Permanent address: UCO/Lick Observatory, University of California, Santa Cruz, 1156 High Street Santa Cruz,
California 95064.
4 Also at: Astrophysical Advances, Palo Alto, CA 94301.

-- 2 --
In our paper we reported the existence of a dark and compact mass component near the
center of M15, based on an analysis of new data from the Hubble Space Telescope. Possible
explanations for this mass component include: (1) a single intermediate­mass black hole (BH);
or (2) a collection of dark remnants (e.g., neutron stars) that have sunk to the cluster center
due to mass segregation. We assessed the plausibility of the latter possibility by comparing the
kinematical data for M15 to the predictions of the most sophisticated and most recently published
Fokker­Planck models for M15 (Dull et al. 1997, hereafter D97). We showed that the mass­to­light
ratio (M/L) profile in Figure 12 of D97 implies too few dark remnants near the cluster center
to explain the observed kinematics of M15. This supported the view that M15 harbors an
intermediate­mass BH. We address here how this conclusion is a#ected by the recent discovery of
an error in Figure 12 of D97. We show that the presence of an intermediate­mass BH continues to
be a viable interpretation of the data, but that its presence ceases to be uniquely implied.
After the completion of our paper, the authors of the D97 paper discovered an unfortunate
error in their Figures 9 and 12. The labeling along the abscissa of these figures is incorrect due to
a coding error in SM plotting routines (H. Cohn and B. Murphy, private communication, 2002).
The units along the top axis should have read `arcmin' instead of `pc', and the labeling in arcmin
along the bottom axis is incorrect. The net result is that the radial scale of these figures in the
D97 paper is too compressed by a factor 2.82. The true total mass of the centrally concentrated
population of dark remnants in the Fokker­Planck models is therefore considerably larger than
what was implied by the M/L profile shown in Figure 12 of the D97 paper.
Figure 1 shown here is similar to Figure 12 of our paper, but it now shows the data­model
comparison with the corrected D97 M/L profile. Models without a BH are now found to
be statistically acceptable (within 1#), although inclusion of an intermediate­mass BH, with
MBH = 1.7 +2.7
-1.7 â 10 3 M# , still provides a marginally better fit to the data (although not a
statistically significant one). Hence, the Fokker­Planck models for M15 discussed by D97 do
in fact have enough dark remnants near the cluster center to explain the observed kinematics.
However, the D97 models still have a number of important shortcomings, as discussed in §5.4
of our paper. Most importantly, D97 assumed that all neutron stars that form in the cluster
are retained. By contrast, the observed distribution of pulsar kick velocities indicates that the
retention factor should only be a few percent; most authors agree that it should be no more than
10% (see references in §5.4 of our paper). In this sense, the D97 models provide an upper limit on
the number and mass of dark remnants in M15. The same is true for N­body models constructed
recently by Baumgardt et al. (2002), the results of which are qualitatively similar to those of D97.
More realistic evolutionary models that include neutron star escape will require a more massive
and more statistically significant BH to fit the data than that suggested by Figure 1. Alternatively,
one can assume that there are more stars in the high­mass end of the initial mass function, or that
the transition between stars that evolve to white dwarfs as compared to neutron stars occurs at a
higher initial mass (H. Cohn and B. Murphy, private communication, 2002). Independent evidence
does not exist to support these assumptions, although they cannot be ruled out.
The evidence for a central BH in M15 is less convincing than it was on the basis of our earlier
analyses. However, because of the somewhat unrealistic assumptions about neutron star retention
in the models of D97 and Baumgardt et al. (2002), and because of the independent evidence for a

-- 3 --
BH in another cluster (G1; Gebhardt, Rich & Ho 2002), the presence of a BH in M15 continues to
be a viable interpretation of the data. The best fit BH mass with the corrected D97 M/L profile
is MBH = 1.7 +2.7
-1.7 â 10 3 M# (see Figure 1); with a constant M/L it is MBH = 3.2 +2.2
-2.2 â 10 3 M# (see
§5.4 of our paper). A model that includes both neutron star escape and mass segregation would
probably yield a value between these numbers. So if M15 has a BH, its mass is consistent with
the correlation between velocity dispersion and BH mass that has been inferred for galaxies (see
Figure 14 of our paper). This continues to suggest the possible existence of an important new link
between the structure, evolution and formation of globular clusters, galaxies, and their central
BHs (see §6 of our paper, and also Gebhardt et al. 2002). However, with the presently available
models and data it is neither uniquely implied nor ruled out that M15 has an intermediate­mass
BH.
We thank Haldan Cohn, Brian Murphy, Phyllis Lugger, Piet Hut and Steve McMillan for
stimulating discussions.
REFERENCES
Baumgardt, H., Hut, P., Makino, J., McMillan, S., & Portegies Zwart, S. 2002, ApJL, submitted
Dull, J. D., Cohn, H. N., Lugger, P. M., Murphy, B. W., Seitzer, P. O., Callanan, P. J., Rutten,
R. G. M., & Charles, P. A. 1997, ApJ, 481, 267 (D97)
Gebhardt, K., Rich, R. M., & Ho, L. 2002, ApJ, 578, L41
This preprint was prepared with the AAS L A T E X macros v4.0.

-- 4 --
Fig. 1.--- Data­model comparison for spherical dynamical models with an isotropic velocity
distribution, an M/L profile inferred from Fokker­Planck models, and a central black hole of mass
MBH . The M/L profile is a corrected version of the one shown by D97. (a; left panel) The
likelihood quantity # defined in equation (4) of our paper as function of MBH . The minimum in
# identifies the best fit black hole mass. Horizontal dashed lines indicate the 1 and 2# confidence
regions. (b; right panel) The RMS projected line­of­sight velocity #RMS as a function of projected
radius R. The heavy jagged curve surrounded by heavy dashed curves is the observed profile, as in
Figure 9d of our paper. The smooth thin curves are the predictions for models with MBH ranging
from 0 to 10 â 10 3 M# in steps of 10 3 M# .