Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2010.00603

Evolution of the density PDF in star forming clouds: the role of gravity

Etienne Jaupart·Gilles Chabrier
View original source ↗Read source document ↗Export metadata ↓

Abstract

We derive an analytical theory of the PDF of density fluctuations in supersonic turbulence in the presence of gravity in star-forming clouds. The theory is based on a rigorous derivation of a combination of the Navier-Stokes continuity equations for the fluid motions and the Poisson equation for the gravity. It extends upon previous approaches first by including gravity, second by considering the PDF as a dynamical system, not a stationary one. We derive the transport equations of the density PDF, characterize its evolution and determine the density threshold above which gravity strongly affects and eventually dominates the dynamics of turbulence. We demonstrate the occurence of {\it two} power law tails in the PDF, with two characteristic exponents, corresponding to two different stages in the balance between turbulence and gravity. Another important result of this study is to provide a procedure to relate the observed {\it column density} PDFs to the corresponding {\it volume density} PDFs. This allows to infer, from the observation of column-densities, various physical parameters characterizing molecular clouds, notably the virial parameter. Furthermore, the theory offers the possibility to date the clouds in units of ${t}_{\rm coll}$, the time since a statistically significant fraction of the cloud started to collapse. The theoretical results and diagnostics reproduce very well numerical simulations and observations of star-forming clouds. The theory provides a sound theoretical foundation and quantitative diagnostics to analyze observations or numerical simulations of star-forming regions and to characterize the evolution of the density PDF in various regions of molecular clouds.

Explore related subjects

astro-ph.GAastro-ph.SR

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Etienne Jaupart, Gilles Chabrier. 2020-11-03. Evolution of the density PDF in star forming clouds: the role of gravity. https://doi.org/10.3847/2041-8213%2Fabbda8

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Self-lensing binaries in globular clusters -- predictions for ELT

Self-lensing (SL) represents a powerful technique for detecting compact objects in binary systems through gravitational microlensing effects, when a compact companion transits in front of its luminous partner. We present the first comprehensive study of SL probability within globular cluster (GC) environments, utilizing synthetic stellar populations from MOCCA simulations to predict detection rates for the Extremely Large Telescope (ELT). Our analysis incorporates finite-size lens effects for white dwarf (WD) lenses and the specific observational characteristics of the ELT/MICADO instrument. We find that present-day GCs contain 1-50 SL sources with magnifications $μ_\mathrm{sl} > 1+10^{-8}$, strongly dependent on initial binary fraction, with systems dominated by WD lenses paired with low-mass main-sequence companions. The predicted populations exhibit characteristic bimodal magnitude distributions with peaks at $m \approx 24$ and 32 mag at 10 kpc distance, and typical Einstein ring crossing times of $τ_\mathrm{eff} \sim 2$ hours. ELT observations should achieve detection efficiency of 0.015-10 sources in $\sim150$ nearby GC after a year of observations depending on distance and survey strategy, with nearby clusters ($D \lesssim 10$ kpc) offering the highest yields. Multi-year monitoring campaigns with daily cadence provide order-of-magnitude improvements over single observations through enhanced photometric precision and increased detection probability. Our results demonstrate that coordinated ELT surveys of Galactic GCs represent a viable approach for probing hidden binary populations and compact object demographics in dense stellar environments, with comprehensive programs potentially yielding up to 10-100 well-characterized SL sources after first 5 years of observations suitable for statistical studies of binary evolution in extreme environments.

astro-ph.GA↗
arXiv2026

Galaxy morphology dependent (black hole mass)-(velocity dispersion) relations: implications for gravitational wave forecasts and cosmological simulations

The correlation between black hole mass, $M_{\rm bh}$, and stellar velocity dispersion, $σ_0$, is revisited using 137 galaxies with quantitative bar strengths and enhanced morphological awareness. Interpreted within the `Triangal' evolutionary framework, gas-rich and gas-poor assembly pathways emerge in the $M_{\rm bh}$-$σ_0$ diagram. To quantify these scaling relations, a symmetric Bayesian hierarchical regression code, dubbed the Symmetric COvariance Population Estimator (SCOPE), is introduced. Unlike conditional estimators (e.g., LINMIX), SCOPE derives the intrinsic population covariance, natively accommodating asymmetric measurement errors while guaranteeing directional invariance between axes. Primeval, dust-poor S0 galaxies (including dwarf early-type galaxies with $R_{\rm e,gal}$ ~ 1 kpc) follow a shallow relation ($M_{\rm bh}\proptoσ_0^{2.5\text{--}3.1}$). Explained via the virial theorem, this flattening reframes expectations for intermediate-mass black holes. In contrast, tracing the `Disc Down-sizing' sequence - where dry mergers erase discs - yields a steep relation for massive elliptical and ellicular galaxies ($M_{\rm bh}\proptoσ_0^{7.8\pm1.4}$). Applying a single, monolithic scaling relation across all morphologies inadvertently averages over different formation histories, potentially skewing AGN virial $f$-factor calibrations and systematically under-predicting the ultra-massive black holes needed to generate the nanohertz gravitational wave background. Furthermore, strongly barred, dust-poor S0 galaxies appear offset to higher $σ_0$, while this dynamical signature is lost in the complexities of spiral galaxies. Ultimately, these morphology-dependent relations provide physically-motivated benchmarks for cosmological simulations and a framework for disentangling regimes driven by AGN feedback from those driven by mergers.

astro-ph.GA↗
arXiv2026

Profile Analysis of the Multiwavelength 2.1-year Oscillations of PG 1553+113

We investigate the morphology of the oscillation profiles of the blazar PG~1553+113 in relation to its well-known $\sim$2.1 yr periodicity. We identify individual cycles in the $γ$-ray, X-ray, UV, and optical light curves and characterize their temporal profiles using analytical models for single- and multi-peaked events. We find that the oscillations are generally described by a broad activity envelope with shorter-timescale substructure, showing that the $\sim$2.1 yr signal is not a strictly sinusoidal or self-similar modulation. The internal morphology varies across cycles and energy bands. This is particularly evident in X-rays, where all analyzed cycles show a strong formal preference for multi-component profiles, unlike the $γ$-ray band, where several cycles admit statistically comparable empirical descriptions. The contemporaneous MWL oscillations show broadly aligned activity episodes, but the timing and relative amplitudes of secondary components are not systematically repeated. This suggests that a common long-term modulation affects the broadband emission, while additional local or energy-dependent processes shape individual cycles. Such a picture is compatible with a geometric, jet-related contribution to the broad recurrent envelope, with intrinsic variability superimposed on it. We also identify new cycles with a dominant peak accompanied by weaker twin-peak-like features, similar to structures previously discussed in a supermassive black hole binary scenario for PG~1553+113. Although our results do not provide definitive evidence for this interpretation, the recurrence of comparable morphologies in newly analyzed cycles keeps this scenario viable.

astro-ph.GA↗