An Inverse Look at the Center of M15

Abstract

The observed radial and transverse velocities of individual stars in the globular cluster M15 are used as inputs to a fully nonparametric code (CHASSIS) in order to estimate the equilibrium stellar distribution function and the threedimensional mass density profile, from which are estimated the mass-to-light ratio, enclosed mass, and velocity dispersion profiles. In particular, the paper explores the possible existence of a central black hole in M15 via several runs that use the radial velocity data set, which offers kinematic measurements closer to the center of the cluster than the proper-motion data. These runs are distinguished from each other in the choice of the initial seed for the cluster characteristics; however, the profiles identified by the algorithm at the end of each run concur with each other within error bars, thus confirming the robustness of CHASSIS. The recovered density profiles are noted to exhibit unequivocal flattening interior to about 0.0525 pc. Also, the enclosed mass profile is very close to being a power-law function of radius <0.1 pc and is not horizontal. Simplistically speaking, these trends negate the possibility of the central mass being concentrated in a black hole, the lower bound on the radius of the sphere of influence of which would be k0.041 pc had it existed. However, proper analysis suggests that the mass enclosed within the inner 0.01 pc could be in the form of a black hole of mass $10 3 M under two different scenarios, which are discussed. The line-ofsight velocity dispersion is visually found to be very similar to the observed dispersion profile. The enclosed mass and velocity dispersion profiles calculated from runs done with the proper-motion data are found to be consistent with the profiles obtained with the radial velocity data.

Comparing X-Ray and Dynamical Mass Profiles in the Early-Type Galaxy NGC 4636

“…At the outset, we note that deviation from isotropy in the true velocity space configuration of the system would urge CHASSIS to overestimate the mass density, at radii where anisotropy prevails (Chakrabarty & Portegies Zwart 2004;Chakrabarty 2006). If in reality, velocity anisotropy describes the phase-space distribution from which the measured GC kinematic data are drawn, then the recovered mass density distribution would be spuriously enhanced in amplitude at these radii.…”

Low-resolution spectroscopy of main sequence stars belonging to 12 Galactic globular clusters

“…The most metal-poor cluster in our sample is M 15, with [Fe/H] = −2.34 (Carretta et al 2009c), it has a blue HB and it is a core-collapsed GGC, which is suspected to harbour a black hole in its centre (see Ho et al 2003;McNamara et al 2003;van den Bosch et al 2006;Chakrabarty 2006;Kiselev et al 2008, and references therein). It is at present quite far away from the Galactic center (Table 4).…”

The Distribution of Dark Matter in the Halo of the Early-Type Galaxy NGC 4636

“…Within CHASSIS, the effect of imposing isotropy in velocity space, where anisotropy prevails, is to recover spuriously high mass-density values (Chakrabarty 2006). Though in general it is difficult to quantify the extent of this bias since it depends on the structure of the unknown distribution function, in the case of NGC 4636, we can surmise that the effect of anisotropy is not significant at the 1σ level.…”

“…We use the algorithm CHASSIS (Chakrabarty & Saha 2001) to analyze the available kinematics of the same sample of 174 GCs that is used in the Jeans equation approach of Dirsch et al (2005). This algorithm has been calibrated against the N -body realization of two star clusters (Chakrabarty & Portegies Zwart 2004), and applied to estimate the central mass structure of the Galaxy (Chakrabarty & Saha 2001) and the GC M15 (Chakrabarty 2006). It is also used to estimate the dark-matter content in NGC 3379, using planetary nebulae kinematics (Chakrabarty 2008, in preparation).…”