Probabilistic distributions of $M/L$ values for ultra-faint dwarf spheroidal galaxies: stochastic samplings of the IMF

Abstract

As the total mass of stellar populations of fixed IMF, age and metallicity tends to infinity, resulting intrinsic $M/L$ values quickly converge to fixed numbers associated to the particulars of the stars in question. When going to very small stellar populations, the stochastic sampling of the IMF will yield an inherent spread for the $M/L$ values, which will become probabilistic quantities. For the recently discovered ultra-faint dwarf spheroidal galaxies, with total luminosities dropping below 10^3 L_V/L_o, it is important to asses the amplitude of the probabilistic spread in inherent $M/L$ values. The total baryonic masses of these systems are usually estimated from their luminosities, assuming fixed, deterministic $M/L$ values, suitable for the infinite population limit. These total baryonic masses are crucial for the testing of structure formation scenarios, as the local ultra-faint dwarf spheroidals represent the most extreme galactic scales known. Also subject to reliable $M/L$ values, is the use of these systems as possible discriminants between dark matter and modified gravity theories. By simulating large collections of stellar populations, each consisting of a particular collection of individual stars, we compute statistical distributions for the resulting $M/L$ values. For total numbers of stars in the range of what is observed for the ultra-faint dwarf spheroidals, inherent $M/L$ values of stellar populations can be expected to vary by factors of upwards of 3, interestingly, systematically skewed towards higher values than what corresponds to the infinite population limit. This can explain part of the spread in reported baryonic masses for these systems, which also appear as shifted systematically towards high dark to baryonic mass ratios at fixed stellar velocity dispersions.

6 pages, 4 figures, accepted in MNRAS

References in corpus (6)

• The Kinematics of the Ultra-Faint Milky Way Satellites: Solving the Missing Satellite Problem
• A Possible Origin of the Mass-Metallicity Relation of Galaxies
• Dwarf Spheroidals in MOND
• An inhomogeneous model for the Galactic halo: a possible explanation for the spread observed in s- and r-process elements
• The Star Formation History and Extended Structure of the Hercules Milky Way Satellite
• A robust statistical estimation of the basic parameters of single stellar populations. I. Method

Cited by in corpus (5)

• Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions
• "Galaxy," Defined
• Approximate Bayesian Computation for Astronomical Model Analysis: A Case Study in Galaxy Demographics and Morphological Transformation at High Redshift
• The statistical challenge of constraining the low-mass IMF in Local Group dwarf galaxies
• Theoretical lower limits on sizes of ultra faint dwarf galaxies from dynamical friction