[Paper Review] The Stellar Initial Mass Function and Beyond

Richard B. Larson|arXiv (Cornell University)|May 27, 2002

Astrophysics and Star Formation Studies3 citations

TL;DR

This paper reviews the stellar initial mass function (IMF), proposing that the characteristic stellar mass near one solar mass arises from Jeans-mass clumps in molecular clouds, while the Salpeter power-law IMF at high masses likely results from accretion and dynamical processes in dense star clusters. The key contribution is the synthesis of observational and simulation evidence supporting a universal IMF with a characteristic mass and power-law tail, and the suggestion that massive black holes may form via runaway mergers in dense clusters.

ABSTRACT

A brief review is given of the basic observed features of the stellar IMF, and also of some of the theoretical ideas and simulations that may help to explain these features. The characteristic stellar mass of order one solar mass may derive from the typical masses of the observed star-forming clumps in molecular clouds, and the typical clump mass may in turn be determined mainly by the Jeans mass, as is true in many numerical simulations of cloud collapse and fragmentation. The Salpeter power law that approximates the IMF at higher masses is less well understood, but it may result from the effects of continuing gas accretion by the more massive forming stars together with the effects of interactions and mergers in dense forming stellar systems. The mass of the most massive star that forms in a cluster is observed to increase systematically with the mass of the cluster, and the most massive clusters may form stars that are massive enough to collapse completely to black holes.

Motivation & Objective

• To synthesize observational and theoretical evidence on the stellar initial mass function (IMF) and its underlying physical origins.
• To evaluate whether the IMF is universal or variable across different environments, such as star clusters and galactic regions.
• To investigate the physical mechanisms—particularly gas accretion and stellar mergers—that may produce the observed power-law IMF at high masses.
• To explore the connection between the IMF and the formation of massive black holes in dense stellar systems.
• To assess the role of clump masses in molecular clouds as the origin of the characteristic stellar mass near one solar mass.

Proposed method

• Analyzes observational data on field stars and young clusters to constrain the IMF across different mass ranges.
• Reviews numerical simulations of cloud collapse and fragmentation, emphasizing the role of the Jeans mass in determining clump masses.
• Evaluates the Salpeter power-law (slope x = 1.35) and alternative approximations like Kroupa’s three-part power-law IMF for masses above and below 0.5 M☉.
• Examines the dependence of the maximum stellar mass on cluster mass, using observational trends to infer accretion and merger processes.
• Models the dynamics of dense star clusters to explain the formation of very massive stars and black holes via runaway mergers.
• Considers X-ray and dynamical evidence for intermediate-mass black holes in young clusters as indirect support for the proposed formation mechanisms.

Experimental results

Research questions

• RQ1 What physical processes determine the characteristic stellar mass near one solar mass in the IMF?
• RQ2 Why does the IMF follow a Salpeter-like power law at high masses, and what mechanisms sustain this behavior?
• RQ3 To what extent is the IMF universal, or does it vary with environment, metallicity, or cluster mass?
• RQ4 How do accretion and stellar mergers in dense clusters contribute to the formation of massive stars and black holes?
• RQ5 Can the observed mass dependence of the most massive star on cluster mass be explained by dynamical processes and accretion?

Key findings

• The characteristic stellar mass near one solar mass likely arises from the typical masses of pre-stellar clumps in molecular clouds, which are governed by the Jeans mass in simulations.
• The Salpeter power-law IMF (slope x = 1.35) at high masses is not fully understood but may result from continued gas accretion and dynamical interactions in dense stellar systems.
• The IMF flattens at low masses (x ≈ 0 for 0.08–0.5 M☉) and declines in the brown dwarf regime (x = –0.7), indicating that most stellar mass is in stars near one solar mass.
• Observations show the maximum stellar mass in a cluster increases with cluster mass, though not as steeply as predicted by the Salpeter law, suggesting accretion and merger processes are at work.
• Very massive stars and black holes may form via runaway mergers in dense, massive young clusters, with X-ray observations supporting the existence of intermediate-mass black holes in such systems.
• Theoretical models suggest that central black holes in galaxies may grow through repeated mergers of star clusters and their embedded black holes, potentially explaining the observed black hole–bulge mass relation.