Probabilistic distributions of M/L values for ultrafaint dwarf spheroidal galaxies: stochastic samplings of the initial mass function

• Published in: Monthly notices of the Royal Astronomical Society Vol. 420; no. 2; pp. 1183 - 1187
• Main Author: Hernandez, X.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.02.2012; Oxford University Press
• Subjects: Astronomy; Dwarf stars; galaxies: stellar content; Spheroids; Stars & galaxies; stars: luminosity function, mass function; stars: statistics; stars: statistics; galaxies: stellar content; stars: luminosity function, mass function
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1111/j.1365-2966.2011.20099.x

We explore the ranges and distributions which will result for the intrinsic stellar mass-to-light ratio (M/L) values of single stellar populations, at fixed initial mass function (IMF), age and metallicity, from the discrete stochastic sampling of a probabilistic IMF. As the total mass of a certain stellar population tends to infinity, the corresponding M/L values quickly converge to fixed numbers associated with the particulars of the IMF, age, metallicity and star formation histories in question. When going to small stellar populations, however, a natural inherent spread will appear for the M/L values, which will become probabilistic quantities. For the recently discovered ultrafaint local dwarf spheroidal galaxies, with total luminosities dropping below 103 L V /L ⊙, it is important to asses the amplitude of the probabilistic spread in inherent M/L values mentioned above. The total baryonic masses of these systems are usually estimated from their observed luminosities, and the assumption of a fixed, deterministic M/L value, suitable for the infinite population limit of the assumed ages and metallicities of the stellar populations in question. This total baryonic masses are crucial for testing and calibrating of structure formation scenarios, as the local ultrafaint 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. We find that for total numbers of stars in the range of what is observed for the local ultrafaint dwarf spheroidals, the 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 is obtained for the corresponding infinite stellar population limit M/L. This can serve to 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, when going to the ultrafaint limit.