Stellar initial mass function in the 100-pc solar neighbourhood

Abstract

The stellar initial mass function (IMF) is among the most fundamental distributions in astrophysics, defined as the mass spectrum of stars produced in a single star-formation event. Even in the solar neighbourhood, where measurements can be conducted via star counting, disentangling the IMF from observational effects remains challenging. In this work we introduce a new parametrisation of the stellar IMF in the 100-pc solar neighbourhood, leveraging the high-precision astrometric and photometric data from \textsl{Gaia} DR3: we model the colour-magnitude diagram of the field star population while accounting for observational uncertainties, Malmquist bias, Lutz-Kelker bias, variations in the mass-luminosity relation arising from metallicity differences, and the effects of unresolved binaries. In particular, we synthesise the binary population with a process imitating the dynamical evolution observed in star clusters to enforce that all components are drawn from the same IMF, while simultaneously recovering the observed present-day mass-ratio distribution. We determine an averaged stellar IMF over $0.25<m<1.0~M_{\odot}$ that aligns with canonical IMFs but achieves significantly tighter constraints: $α_1=0.75^{+0.06}_{-0.04}$, $α_2=2.07^{+0.04}_{-0.03}$, and a break point at $m_{\mathrm{break}}=0.40^{+0.01}_{-0.01}$ $\mathrm{M_{\odot}}$. Our inference also yields an averaged binary fraction over $0.25<m<1.0~M_{\odot}$ of approximately 26\%, and constrains the \textsl{Gaia} DR3 angular resolution to $1.11^{+0.11}_{-0.08}$ arcsec. We also provide the $ξ$-parameter for our IMF, which is $0.5070_{-0.0096}^{+0.0068}$, to facilitate direct comparison with other IMF determinations.

Figures (21)

• Figure 1: Detection rate (selection function) for stars within different $M_{\mathrm{G}}$ and distance ranges, assuming different density profile models. Left: exponential disk density model. Right: constant density model. See \ref{['sec:app_vmax']} for details.
• Figure 2: colour-magnitude diagram for stars in the 100-pc solar neighbourhood. The scatter with gray colour map illustrates the density distribution for all GCNS sample, overlapped with the object density distribution resulting from our sample selection procedure in \ref{['sec:MS sample']}. Black dashed lines denote the selection standards for Main-sequence stars in penoyre2022, while black dotted lines denote the iso-mass lines for $0.15~\mathrm{M_{\odot}}$ and unevolved $1.0~\mathrm{M_{\odot}}$ stars from PARSEC model.
• Figure 3: Schematic flow diagram of the population synthesis methodology employed in this study. The model assumes that all stars form in embedded clusters with an initial binary fraction of 100%, where both components are sampled from the same IMF and paired randomly (uppermost panel). Subsequent cluster-mode dynamical evolution disrupts a subset of binary systems ($\mathrm{phot_{dis}}$), transforming the period and mass-ratio distributions to their present-day configurations. Surviving binaries are then classified according to Gaia DR3's angular resolution into resolved ($\mathrm{phot_{rb}}$) and unresolved ($\mathrm{phot_{ub}}$) systems. The photometric properties of unresolved binaries are recalculated to account for their combined flux. The notation $X \sim p(X)$ in this paper means that $X$ is drawn from the probability distribution $p(X)$.
• Figure 4: Dynamical evolution operator from marks2011a. The function reflects the survival rate of binary systems under certain binding energy in the dynamical evolution. The plot shows the variation of the functional form when different characteristic cluster densities $\mathrm{log_{10}}(\rho/\mathrm{M_{\odot}~pc^{-3}})$ are set up.
• Figure 5: Relation of the characteristic cluster density in our dynamical evolution operator and subsequent present-day binary fraction.