Direct Evidence for Stellar Initial Mass Function Variation in the Milky Way

Abstract

Because direct measurements require resolved stellar populations including low-mass stars, determining the stellar initial mass function (IMF) has been a historically difficult problem even within our own Galaxy and impossible everywhere else. As a result, even though it is predicted that the IMF should vary depending upon the properties of each individual star-forming molecular cloud, it is standard to assume a Universal IMF. Using recent observations from {\em Gaia}, it is now possible to test for IMF variation using resolved stellar populations in open clusters and a parameterization that separates properties of the IMF from subsequent dynamical evolution. Here, we show that the IMF is not Universal but instead varies across individual Galactic stellar populations, reflecting evolution in the average conditions of molecular clouds over cosmic time. This evolution is consistent with the predictions of a simple astrophysical model in which the IMF is environmentally-dependent and the Milky Way reflects typical galactic behavior in recent cosmic history. Thus, observational evidence now agrees with long-standing theoretical and numerical predictions.

Figures (6)

• Figure 1: (Left) Theory predicts (blue, solid) that an increase in the sound speed will increase the break masses compared with a Kroupa IMF (red) but not the slopes. A simulation increasing the input stellar radiation field by a factor of 100 Guszejnov2022 shows a similar increase in break masses, although the temperatures and sound speed within the simulated cloud exhibit a complex profile rather than a single value. (Right) Evolution of the stellar mass function over time (dashed) for an open cluster with a Kroupa IMF (solid), showing the effects of tidal stripping and stellar evolution, based on the semi-analytical approximations in Lamers2013 (see also Gieles2008PortegiesZwart2010Lamers2013). The time required for individual clusters to reach remaining mass fractions of $\mu = 0.5$, 0.2, and 0.1 will vary depending upon cluster parameters. The slopes and high-mass cutoff evolve over time, but the break mass is not affected. Thus, an observed change in break mass must be due to the IMF rather than subsequent evolution.
• Figure 2: Variation in best-fit Kroupa (left) and Chabrier (right) mass functions as open cluster stellar populations are dynamically depleted according to the Lamers2013 prescription, for both a Kroupa (top) and Chabrier (bottom) initial mass function. Depletion prior to mass segregation (yellow) primarily alters the normalization. After mass segregation, further depletion increases the characteristic mass for the best-fit Chabrier mass function, but the break mass for a Kroupa mass function is nearly invariant. This occurs regardless of whether the true underlying IMF is Kroupa-like or Chabrier-like. Thus, the choice of a Kroupa mass function breaks the degeneracy between dynamical evolution and IMF variation which exists for a Chabrier fit.
• Figure 3: Mass functions of NGC 6067 at various stages of the analysis all yield similar break points, demonstrating that the existence and location of the break mass are features of the data rather than induced by analytical techniques. (a) Raw stellar counts already exhibit a break mass at $1.23 \pm 0.02,M_\odot$. (b) Applying a correction for Gaia selection changes the slopes but not the break mass. (c) Applying a further correction for unresolved binaries yields a break mass of $1.28 \pm 0.14,M_\odot$ for the mass function used in this work. (d) If an incorrect cluster age of 4 Gyr is used instead of the correct $1.25$ Gyr, the break mass remains unchanged.
• Figure 4: Observed stellar mass functions for four different open clusters from the Hunt2023 catalog. The break masses are different for each cluster. This cannot be due to subsequent stellar evolution or dynamical disruption, and thus must be caused by variation in the IMF.
• Figure 5: (left) The break mass observed in Gaia clusters (points, with running median and interquartile range in red, dashed for few clusters in window) increases with cluster age. (right) As expected, selection biases artificially steepened the slope and added scatter. After correcting for the bias, the slope decreases but the correlation strengthens, revealing the true underlying break mass-age relation. The trend is consistent with the sound speed evolution of a typical galaxy Steinhardt2023b, which will produce an increasing break mass for older clusters. A Kroupa IMF (dashed), defined to have a break mass of $0.5 M_\odot$, is shown for comparison.