Deep HST/FOC Imaging of the Central Density Cusp of the Globular Cluster M15

Abstract

Using the Faint Object Camera on the repaired Hubble Space Telescope, we have observed two fields in the globular cluster M15: the central density cusp, and a field at r = 20 ′′ . These are the highest-resolution images ever taken of this cluster's dense core, and are the first to probe the distribution of stars well below the main-sequence turnoff. After correction for incompleteness, we measure a logarithmic cusp slope (d log σ/d log r) of −0.70 ± 0.05 (1-sigma) for turnoff (∼ 0.8M ⊙ ) stars over the radial range from 0. ′′ 3 to 10 ′′ ; this slope is consistent with previous measurements. We also set an approximate upper limit of ∼ 1. ′′ 5 (90% confidence limit) on the size of any possible constant-surface-density core, but discuss uncertainties in this limit that arise from crowding corrections. We find that fainter stars in the cusp also have power-law density profiles: a mass group near 0.7M ⊙ has a logarithmic slope of −0.56 ± 0.05 (1-sigma) over the radial range from 2 ′′ to 10 ′′ . Taken together, the two slopes are not well matched by the simplest core-collapse or black-hole models. We also measure a mass function at r = 20 ′′ , outside of the central cusp. Both of the FOC fields show substantial mass segregation, when compared with a mass function measured with the WFPC2 at r = 5 ′ . In comparing the overall mass functions of the two FOC fields and the r = 5 ′ field, we find that the radial variation of the mass function is somewhat less than that predicted by a King-Michie model of the cluster, but greater than that predicted by a Fokker-Planck model taken from the literature.

An Inverse Look at the Center of M15

“…Hence, we can expect that at such radii the number density of stars recovered by CHASSIS is spuriously high. If the mass function of M15 was flat (which it is not, as reported by Sosin & King 1997), the number density and mass density would be directly linked. Thus, the simplistic assumption of isotropy at all radii is expected to lead to falsely large values of mass densities at radii around 1 pc.…”

“…The errors in the presented mass-to-light profiles correspond to the 1 errors in the estimation of the surface density, compounded by the observational errors in the star count profile obtained from the data in Sosin & King (1997).…”

“…The observed surface brightness in the central region is possibly erroneous owing to seeing difficulties. This is averted by normalizing the surface brightness profile by the value at a radial location where seeing is least likely to be a problem (namely, the outermost radius in the star counts data set) using the star counts data reported by Sosin & King (1997).…”

Structure of Globular Clusters

“…In a similar way, Sosin (1997) investigated the presence of a possible cusp in M30. Also from star counts on images obtained by HST/FOC with filters F430W = FOC B and F480LP = FOC V with a pixel size 0.014"/pix, he determined logarithmic cusp slopes dlogc/dlogr -0.76 ± 0.07, between 0.3"and 12", for stars with mass 0.69 < M < 0.76 M 0 , and dloga/dlogr -0.82 ± 0.11, between 2.0"and 12", for stars with mass 0.57 < M < 0.69 M 0 .…”

“…The implied mass segregation is somewhat less than predicted by a King-Michie model but somewhat greater than predicted by a Fokker-Planck model. Second, Sosin (1997) has investigated the structure of M30. His MFs at r = 0-6", r = 6-12", and at r = 4.6' from the cluster center clearly show substantial mass segregation for all stars between 0.50 and 0.76 M 0 .…”