Constraints on the Stellar Mass Function from Stellar Dynamics at the Galactic Center

Abstract

We consider the dynamical evolution of a disk of stars orbiting a central black hole. In particular, we focus on the effect of the stellar mass function on the evolution of the disk, using both analytic arguments and numerical simulations. We apply our model to the ring of massive stars at '0.1 pc from the Galactic center, assuming that the stars formed in a cold, circular disk, and find that our model requires the presence of a significant population of massive (>100 M ) stars in order to explain the observed eccentricities of 0.2Y 0.3. Moreover, in order to limit the damping of the heavier stars' eccentricities, we also require fewer low-mass stars than expected from a Salpeter mass function, giving strong evidence for a significantly ''top-heavy'' mass function in the rings of stars seen near to the Galactic center. We also note that the maximum possible eccentricities attainable from circular initial conditions at ages of <10 Myr are around 0.4Y 0.5, and we suggest that any rings of stars found with higher eccentricities were probably not formed from circular disks.

Short- and long-term evolution of a stellar disc around a massive black hole: the role of the cusp, stellar evolution and binaries

“…Here we explore the dynamical evolution of such stellar disks, and focus on disks similar to that observed in the Galactic center. Alexander et al (2007) have been the first to describe the behavior of a stellar disk around a MBH. They used an analytic approach, and then verified and calibrated them through the use of Nbody simulations.…”

“…Here we follow-up on the initial analytic work by Alexander et al (2007), and extend it to include the role of a realistic detailed mass-function, the effects of stellar evolution, the impact of binary-heating and additional heating by a stellar cusp. This approach allows us to better understand and identify the role played by each of these processes and components, as well as to study the long-term evolution of realistic disks, which is more difficult (and computationally expensive) to study using full N-body simulations.…”

Misaligned accretion on to supermassive black hole binaries

“…Although stars formed in a circular disc are likely to follow circular orbits, scattering events between individual stars can throw them onto orbits that allow them to directly interact with the binary (e.g. Alexander et al 2007;Amaro-Seoane et al 2013). …”

Young stars in the Galactic center

“…The observed radial density profile is consistent with ρ(r) ∝ r −2 as predicted for in situ gas disks and is much steeper than the ρ(r) ∝ r −0.75 predicted for in-falling cluster scenarios (Lin & Pringle 1987;Berukoff & Hansen 2006;Levin 2007;Lu et al 2009;Bartko et al 2009). The simplest in situ formation scenarios initially produce circular orbits since gas that flows in at low or moderate rates circularizes prior to the onset of star formation (Nayakshin & Cuadra 2005;Alexander et al 2007;Löckmann et al 2009). The observed eccentricity distribution peaks at e=0.3 Yelda et al 2013).…”

“…These models predict extreme gas conditions compared to the disk of the Milky Way with higher temperatures, pressures, densities, and ambient radiation fields (Nayakshin 2006;Alexander et al 2007Alexander et al , 2008Cuadra et al 2008;Mapelli et al 2012). Analysis of the observed luminosity function of the spectroscopically identified young stars and careful correction for incompleteness has resulted in two different estimates for the IMF.…”