Accelerating star formation of dense clumps

TL;DR

We address how star formation accelerates within dense clumps and their embedded protoclusters, where a linear age tracer is lacking. By mapping clump evolution onto a normalized timescale $t$ using the cumulative distribution function of dust temperature $T_{ m dust}$, the study analyzes ATLASGAL and ALMAGAL data to reveal an exponentially accelerating growth of the star-forming mass, with $M_{ m vir} \propto e^{t}$ (best-fit $M_{ m vir} = 200\,e^{t}\,M_\odot$) and $M_{ m core}^{\max} \propto e^{t}$ (best-fit $M_{ m core}^{\max} = 0.9\,e^{t}\,M_\odot$). The clump bolometric luminosity follows $L_{ m bol}^{\rm clump} = a\,e^{t} + b\,e^{3.5t}$, implying an early accretion-dominated phase and a later, stellar-luminosity-dominated phase; the CMF becomes top-heavy with slope $\alpha \approx 1$. The accelerating framework naturally reproduces the observed evolution of the CMF, the mass growth of the most massive protostars, and the dense-gas star formation law, and is physically plausible under a scenario of hierarchical subcluster formation and filamentary accretion that yields self-similar growth from stellar to protocluster scales. This unified view links clump-scale processes to larger-scale star formation laws and highlights the role of internal dynamics and anisotropic inflows in driving rapid protocluster assembly.

Abstract

We present a statistical framework that establishes an accelerating star formation scenario for dense clumps using ATLASGAL and ALMAGAL samples. By employing the cumulative distribution function of dust temperature as a monotonic evolutionary indicator, we linearize clump evolution into a normalized timescale, enabling direct comparison across different samples. The virial mass of clumps increases exponentially with this normalized time, revealing an accelerating buildup of star-forming gas within protoclusters. The evolution of the maximum core mass further shows that the growth timescales of protoclusters and their embedded most massive protostars are comparable, implying a self-similar acceleration of star formation from the stellar to the protocluster scale. This unified framework naturally reproduces the observed evolution of luminosity, the core mass function, the mass growth of the most massive protostars, and the dense gas star formation law on clump scales, establishing a coherent picture of accelerating star formation across scales.

Figures (3)

• Figure 1: Distribution of ATLASGAL clumps 2018MNRAS.473.1059U. (a) Probability density function (PDF) of dust temperature ($T_{\rm dust}$). (b) Cumulative distribution function (CDF) of $T_{\rm dust}$. The two y-axes indicate the linear mapping between the CDF of $T_{\rm dust}$ and the evolutionary age ($t$). (c) Distribution of clump mass ($M_{\rm cl}$) versus $T_{\rm dust}$ (blue dots); orange dots represent clumps with virial mass measurements. (d) Same as panel (c), but with the x-axis replaced by $t$. (e) Distribution of virial mass ($M_{\rm vir}$) versus $T_{\rm dust}$. (f) Same as panel (e), but with the x-axis replaced by $t$. The evolutionary age $t$ is normalized (in units of $t_0$) such that the exponential fit between $M_{\rm vir}$ and $t$ (bla) follows the relation $M_{\rm vir} \propto e^{t}$.
• Figure 2: Upper: Distribution of $\log_{10}(M_{\rm core}^{\rm max})$ as a function of $t$ for the ALMAGAL sample. Black error bars indicate the mean and standard deviation of $\log_{10}(M_{\rm core}^{\rm max})$ within each time bin, while blue error bars represent the standard error of the mean (i.e., ${\rm stderr}={\rm std}/\sqrt{N}$, with $N$ being the number of sources in each bin). The red line shows the exponential fit between $M_{\rm core}^{\rm max}$ and $t$. Lower: Distribution of $L_{\rm bol}$ as a function of $t$ for the ATLASGAL sample. The red line represents the best-fit model of Eq. \ref{['eq_lumiform']}. The dashed and solid black lines indicate the contributions from intrinsic stellar luminosity and accretion luminosity, respectively (see Sect. \ref{['sec_lumi']}).
• Figure 3: Upper: A schematic illustration showing how shifted ICMFs (colored curves) combine to produce a top-heavy CMF (black curve). The upper shifted ICMFs represent newly formed cores, while the accretion process shifts the mass function of older cores toward higher masses, forming right-shifted ICMFs. Lower: Cumulative functions of the observed CMFs for three time bins, together with the corresponding modeled CMFs (see upper panel), where the $x$-axis values are linearly scaled to match the observations.