The MLP distribution: a modified lognormal power-law model for the stellar initial mass function

Basu, Shantanu; Gil, María Ángeles; Auddy, Sayantan

doi:10.1093/mnras/stv445

Cited by 24 publications

(26 citation statements)

References 24 publications

(38 reference statements)

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“…• The fitting of the column density PDF of supercritical clouds or subcritical clouds with linear perturbations is best done by a modified lognormal power law (MLP) function (Basu et al 2015). The MLP is a pure lognormal in one limit and pure power law in another, depending on the values of its three parameters.…”

Section: Resultsmentioning

confidence: 99%

“…The MLP distribution is a threeparameter PDF given in closed form as (Basu et al 2015). Here Σ is the column density of the molecular cloud, and the three parameters describing the MLP distribution are α, µ 0 and σ 0 .…”

Section: The Column Density Pdfs For Supercritical Cloudsmentioning

confidence: 99%

“…Here Σ is the column density of the molecular cloud, and the three parameters describing the MLP distribution are α, µ 0 and σ 0 . The power-law tail is represented by α, while µ 0 and σ 0 describe the body of the distribution (see Basu et al (2015) for details). Here, we find the set of parameters for the MLP distribution that fits the normalized column density PDF.…”

Section: The Column Density Pdfs For Supercritical Cloudsmentioning

confidence: 99%

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The effect of magnetic fields and ambipolar diffusion on the column density probability distribution function in molecular clouds

Auddy

Basu

Kudoh

2017

Monthly Notices of the Royal Astronomical Society

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Simulations generally show that non-self-gravitating clouds have a lognormal column density (Σ) probability distribution function (PDF), while self-gravitating clouds with active star formation develop a distinct power-law tail at high column density. Although the growth of the power law can be attributed to gravitational contraction leading to the formation of condensed cores, it is often debated if an observed lognormal shape is a direct consequence of supersonic turbulence alone, or even if it is really observed in molecular clouds. In this paper we run three-dimensional magnetohydrodynamic simulations including ambipolar diffusion with different initial conditions to see the effect of strong magnetic fields and nonlinear initial velocity perturbations on the evolution of the column density PDFs. Our simulations show that column density PDFs of clouds with supercritical mass-to-flux ratio, with either linear perturbations or nonlinear turbulence, quickly develop a power-law tail such that dN/d log Σ ∝ Σ −α with index α ≃ 2. Interestingly, clouds with subcritical mass-to-flux ratio also proceed directly to a power-law PDF, but with a much steeper index α ≃ 4. This is a result of gravitationally-driven ambipolar diffusion. However, for nonlinear perturbations with a turbulent spectrum (v 2 k ∝ k −4 ), the column density PDFs of subcritical clouds do retain a lognormal shape for a major part of the cloud evolution, and only develop a distinct power-law tail with index α ≃ 2 at greater column density when supercritical pockets are formed.

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Section: Resultsmentioning

confidence: 99%

Section: The Column Density Pdfs For Supercritical Cloudsmentioning

confidence: 99%

Section: The Column Density Pdfs For Supercritical Cloudsmentioning

confidence: 99%

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The effect of magnetic fields and ambipolar diffusion on the column density probability distribution function in molecular clouds

Auddy

Basu

Kudoh

2017

Monthly Notices of the Royal Astronomical Society

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“…The question of the origin of the mass distribution of stars, the initial mass function (IMF), is a long standing issue (e.g., Salpeter 1955;Kroupa 2001;Chabrier 2003;Bastian et al 2010;Offner et al 2014) and several authors have attempted to provide explanations either using analytical modeling of the gas fragmentation (Inutsuka 2001;Padoan et al 1997;Hennebelle & Chabrier 2008), numerical simulations of a fragmenting cloud (Girichidis et al 2011;Bonnell et al 2011;Ballesteros-Paredes et al 2015) or statistical description of accretion (Basu & Jones 2004;Basu et al 2015;Maschberger et al 2014). In general, these models have been resonably succesful in reproducing the high mass tail of the IMF and obtained powerlaw mass spectra with a slope close to the Salpeter value.…”

Section: Introductionmentioning

confidence: 99%

How First Hydrostatic Cores, Tidal Forces, and Gravoturbulent Fluctuations Set the Characteristic Mass of Stars

Hennebelle¹,

Lee²,

Chabrier

2019

ApJ

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The stellar initial mass function (IMF) is playing a critical role in the history of our universe. We propose a theory and that is based solely on local processes, namely the dust opacity limit, the tidal forces and the properties of the collapsing gas envelope. The idea is that the final mass of the central object is determined by the location of the nearest fragments, which accrete the gas located further away, preventing it to fall onto the central object. To estimate the relevant statistics in the neighbourhood of an accreting protostar, we perform high resolution numerical simulations. We also use these simulations to further test the idea that fragmentation in the vicinity of an existing protostar is determinant in setting the peak of the stellar spectrum. We develop an analytical model, which is based on a statistical counting of the turbulent density fluctuations, generated during the collapse, that are at least equal to the mass of the first hydrostatic core, and sufficiently important to supersede tidal and pressure forces to be self-gravitating. The analytical mass function presents a peak located at roughly 10 times the mass of the first hydrostatic core in good agreement with the numerical simulations. Since the physical processes involved are all local, i.e. occurs at scales of a few 100 AU or below, and do not depend on the gas distribution at large scale and global properties such as the mean Jeans mass, the mass spectrum is expected to be relatively universal.

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“…A recent IMF theory from that family (Basu et al 2015) generates a log-normal distribution with a power-law tail via the process of quenched accretion with the exponential distribution of accretion timescales. However, that theory neither provides a justification for the exponential distribution nor does it proposes a quantitative argument for the slope of the power-law tail.…”

Section: Introductionmentioning

confidence: 99%

Explaining the Stellar Initial Mass Function With the Theory of Spatial Networks

Klishin

Chilingarian

2016

ApJ

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The distributions of stars and prestellar cores by mass (initial and dense core mass functions, IMF/DCMF) are among the key factors regulating star formation and are the subject of detailed theoretical and observational studies. Results from numerical simulations of star formation qualitatively resemble an observed mass function, a scale-free power law with a sharp decline at low masses. However, most analytic IMF theories critically depend on the empirically chosen input spectrum of mass fluctuations which evolve into dense cores and, subsequently, stars, and on the scaling relation between the amplitude and mass of a fluctuation. Here we propose a new approach exploiting techniques from the field of network science. We represent a system of dense cores accreting gas from the surrounding diffuse interstellar medium (ISM) as a spatial network growing by preferential attachment and assume that the ISM density has a self-similar fractal distribution following the Kolmogorov turbulence theory. We effectively combine gravoturbulent and competitive accretion approaches and predict the accretion rate to be proportional to the dense core mass: µ dM dt M. Then we describe the dense core growth and demonstrate that the power-law core mass function emerges independently of the initial distribution of density fluctuations by mass. Our model yields a power law solely defined by the fractal dimensionalities of the ISM and accreting gas. With a proper choice of the low-mass cut-off, it reproduces observations over three decades in mass. We also rule out a low-mass star dominated "bottom-heavy" IMF in a single star-forming region.

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The MLP distribution: a modified lognormal power-law model for the stellar initial mass function

Cited by 24 publications

References 24 publications

The effect of magnetic fields and ambipolar diffusion on the column density probability distribution function in molecular clouds

The effect of magnetic fields and ambipolar diffusion on the column density probability distribution function in molecular clouds

How First Hydrostatic Cores, Tidal Forces, and Gravoturbulent Fluctuations Set the Characteristic Mass of Stars

Explaining the Stellar Initial Mass Function With the Theory of Spatial Networks

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