Crucial aspects of the initial mass function

Abstract

Context. Our understanding of stellar systems depends on the adopted interpretation of the initial mass function, IMF φ(m). Unfortunately, there is not a common interpretation of the IMF, which leads to different methodologies and diverging analysis of observational data. Aims. We study the correlation between the most massive star that a cluster would host, m max , and its total mass into stars, M, as an example where different views of the IMF lead to different results. Methods. We assume that the IMF is a probability distribution function and analyze the m max − M correlation within this context. We also examine the meaning of the equation used to derive a theoretical M −m max relationship, N × mup mmax φ(m) dm = 1 with N the total number of stars in the system, according to different interpretations of the IMF. Results. We find that only a probabilistic interpretation of the IMF, where stellar masses are identically independent distributed random variables, provides a self-consistent result. Neither M nor the total number of stars in the cluster, N, can be used as IMF scaling factors. In addition,m max is a characteristic maximum stellar mass in the cluster, but not the actual maximum stellar mass. A M −m max correlation is a natural result of a probabilistic interpretation of the IMF; however, the distribution of observational data in the N (or M) − m max plane includes a dependence on the distribution of the total number of stars, N (and M), in the system, Φ N (N), which is not usually taken into consideration. Conclusions. We conclude that a random sampling IMF is not in contradiction to a possible m max − M physical law. However, such a law cannot be obtained from IMF algebraic manipulation or included analytically in the IMF functional form. The possible physical information that would be obtained from the N (or M) − m max correlation is closely linked with the Φ M (M) and Φ N (N) distributions; hence it depends on the star formation process and the assumed definition of stellar cluster.

ASteCA: Automated Stellar Cluster Analysis

“…The first step in determining P(A|B i ) is to define how the B i models are generated. The well-known age-metallicity degeneracy is, as stated in HVG08 and Cerviño et al (2011), geometrical in nature 21 , and the result of considering only the shapes of the isochrones when fitting an observed SC, instead of also taking the density of stars along them into account. There are two ways of accounting for the star density in a given isochrone: through a mass density parameter as done in HVG08 or, as done in MDC10, generating correctly populated B i models as synthetic clusters; we have chosen to apply the latter.…”

Cygnus OB2 DANCe: A high-precision proper motion study of the Cygnus OB2 association

“…Even if the groups we observed have experienced significant disruptive mass loss they would be unlikely to have been as massive as ∼10,000 M⊙ in the past. This argues against there being a relationship between cluster mass and the mass of the most massive star within it (see also Parker & Goodwin 2007;Cerviño et al 2013). …”

An analysis of star formation withHerschelin the Hi-GAL Survey

“…Cluster configurations are expected to have an initial distribution of stellar masses along the main sequence, known as stellar initial mass function (IMF). The IMF is used to indicate both the observed distribution by number of the stellar masses observed in a particular star ensemble and the theoretical probability density function of stellar masses that can be formed in a generic star ensemble (Cerviño, M. et al 2013). One remarkable aspect is that the majority of the stellar system directly measured (field stars, open clusters, associations, and globular clusters) follows a similar IMF.…”