MASS FUNCTION OF HALOS: A NEW ANALYTICAL APPROACH

2004 ◽  
Vol 13 (07) ◽  
pp. 1345-1349 ◽  
Author(s):  
JOSÉ A. S. LIMA ◽  
LUCIO MARASSI
Keyword(s):  
Power Law ◽  
Free Parameter ◽  
Analytical Approach ◽  
Mass Function ◽  
New Method ◽  
Power Law Distribution ◽  
The Press ◽  
The Universe ◽  
Special Case

A generalization of the Press–Schechter (PS) formalism yielding the mass function of bound structures in the Universe is given. The extended formula is based on a power law distribution which encompasses the Gaussian PS formula as a special case. The new method keeps the original analytical simplicity of the PS approach and also solves naturally its main difficult (the missing factor 2) for a given value of the free parameter.

scholarly journals On the temporal evolution of the stellar mass function of Galactic clusters

2009 ◽  
Vol 5 (S266) ◽  
pp. 81-86
Author(s):  
Guido De Marchi ◽  
Francesco Paresce ◽  
Simon Portegies Zwart
Keyword(s):  
Power Law ◽  
Globular Clusters ◽  
Dynamical Evolution ◽  
Mass Function ◽  
Stellar Mass ◽  
Initial Mass Function ◽  
Dissolution Time ◽  
Power Law Distribution ◽  
Galactic Clusters ◽  
Characteristic Mass

AbstractWe show that we can obtain a good fit to the present-day stellar-mass functions of a large sample of young and old Galactic clusters with a tapered Salpeter power-law distribution function with an exponential truncation of the form dN/dm ∝ mα [1 − exp(−m/mc)β]. The average value of the power-law index α is ~−2.2, very close to the Salpeter value of −2.3, while the characteristic mass, mc, is in the range 0.1–0.6M⊙ and does not seem to vary in any systematic way with the present cluster parameters such as metal abundance, total cluster mass or central concentration. However, the characteristic mass shows a remarkable correlation with the dynamical age of the cluster, namely mc/M⊙ ≃ 0.15 + 0.5 × t3/4dyn, where tdyn is the dynamical time, taken as the ratio of cluster age and dissolution time. The small scatter around this correlation is likely due to uncertainties on the estimated value of tdyn. We attribute the observed trend to the onset of mass segregation through two-body relaxation in a tidal environment, causing preferential loss of low-mass stars from the cluster and hence a drift of the characteristic mass towards higher values. If dynamical evolution is indeed at the origin of the observed trend, it seems plausible that globular clusters, now with mc ≃ 0.35M⊙, were born with a stellar mass function very similar to that measured today in the youngest Galactic clusters and with a value of mc around 0.15 M⊙. This is consistent with the absence of a turn-over in the mass function of the Galactic bulge down to the observational limit at ~0.2M⊙ and argues for the universality of the initial mass function of Population I and II stars.

scholarly journals A dual power-law distribution for the stellar initial mass function

2018 ◽  
Vol 478 (2) ◽  
pp. 2113-2118 ◽  
Author(s):  
Karl Heinz Hoffmann ◽  
Christopher Essex ◽  
Shantanu Basu ◽  
Janett Prehl
Keyword(s):  
Power Law ◽  
Mass Function ◽  
Initial Mass Function ◽  
Initial Mass ◽  
Power Law Distribution ◽  
Stellar Initial Mass Function ◽  
Dual Power

PRESS–SCHECHTER MASS FUNCTION AND THE NORMALIZATION PROBLEM

2007 ◽  
Vol 16 (02n03) ◽  
pp. 445-452 ◽  
Author(s):  
L. MARASSI ◽  
J. A. S. LIMA
Keyword(s):  
Initial Density ◽  
Mass Function ◽  
Density Fluctuations ◽  
Number Density ◽  
Nonextensive Statistics ◽  
The Press ◽  
Normalization Problem ◽  
Log Normal ◽  
Log Normal Distribution ◽  
The Universe

The Press–Schechter (PS) formalism yields the number density of bound objects formed during the evolution of the Universe, which should be compared to the great clusters of galaxies now observed. This basic approach has an intrinsic problem of normalization (the so-called missing factor 2). We argue here that such a problem is related to specific choices of the statistical distribution describing the initial density fluctuations. The fudge factor 2 occurs even in the context of the q-nonextensive statistics which is the simplest one-parametric extension of the Gaussian distribution. In general, other distributions require different corrections, such as the log-normal distribution. However, by assuming that the perturbations can be described by the Burr distribution, we prove that the PS approach in this case is not plagued with the normalization problem.

scholarly journals Galactic consequences of clustered star formation

2009 ◽  
Vol 5 (S266) ◽  
pp. 417-420
Author(s):  
M. R. Haas ◽  
P. Anders
Keyword(s):  
Star Formation ◽  
Power Law ◽  
Sampling Method ◽  
Mass Function ◽  
Star Cluster ◽  
Initial Mass Function ◽  
High Mass ◽  
Power Law Distribution ◽  
Chemical Enrichment ◽  
Low Mass

AbstractIf all stars form in clusters and both stars and clusters follow a power-law distribution which favours the creation of low-mass objects, the numerous low-mass clusters will be deficient in high-mass stars. Therefore, the stellar mass function integrated over the entire galaxy (the integrated galactic initial mass function; IGIMF) will be steeper at the high-mass end than the underlying stellar IMF. We show how the steepness of the IGIMF depends on the sampling method and on the assumptions made regarding the star cluster mass function. We also investigate the O-star content, integrated photometry and chemical enrichment of galaxies that result from several IGIMFs compared to more standard IMFs.

SYMMETRIES ABOUT BIG RIP IN SO(1, 1) PHANTOM UNIVERSE

2006 ◽  
Vol 21 (37) ◽  
pp. 2845-2852 ◽  
Author(s):  
YI-HUAN WEI
Keyword(s):  
Dark Energy ◽  
Power Law ◽  
Dark Energy Model ◽  
Inverse Power ◽  
Late Time ◽  
Linear Potential ◽  
Big Rip ◽  
Inverse Power Law ◽  
The Universe ◽  
Special Case

We study the SO(1, 1) dark energy model with the inverse power law potential, V = V0Φ-n, and find for n<2 the model has the late-time phantom property and the universe will evolve to the future Big Rip. The inverse linear potential is a special case, for which the field and the scalar factor are respectively T-invariant and CT-invariant about the Big Rip.

scholarly journals Using the Modified Lognormal Power-law Distribution to Model the Mass Function of NGC 1711

2020 ◽  
Vol 895 (1) ◽  
pp. 66
Author(s):  
Deepakshi Madaan ◽  
Sophia Lianou ◽  
Shantanu Basu
Keyword(s):  
Power Law ◽  
Mass Function ◽  
Power Law Distribution

scholarly journals The structure of co-publications multilayer network

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Ghislain Romaric Meleu ◽  
Paulin Yonta Melatagia
Keyword(s):  
Power Law ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Small World ◽  
Generation Model ◽  
Small World Network ◽  
Power Law Distribution ◽  
Multilayer Networks ◽  
Multilayer Network ◽  
Scientific Papers

AbstractUsing the headers of scientific papers, we have built multilayer networks of entities involved in research namely: authors, laboratories, and institutions. We have analyzed some properties of such networks built from data extracted from the HAL archives and found that the network at each layer is a small-world network with power law distribution. In order to simulate such co-publication network, we propose a multilayer network generation model based on the formation of cliques at each layer and the affiliation of each new node to the higher layers. The clique is built from new and existing nodes selected using preferential attachment. We also show that, the degree distribution of generated layers follows a power law. From the simulations of our model, we show that the generated multilayer networks reproduce the studied properties of co-publication networks.

scholarly journals On the emergent system mass function: the contest between accretion and fragmentation

2020 ◽  
Vol 500 (2) ◽  
pp. 1697-1707
Author(s):  
Paul C Clark ◽  
Anthony P Whitworth
Keyword(s):  
Star Formation ◽  
Standard Deviation ◽  
Mass Distribution ◽  
Power Law ◽  
Accretion Rate ◽  
Mass Function ◽  
High Mass ◽  
New Model ◽  
System Formation ◽  
Low Mass

ABSTRACT We propose a new model for the evolution of a star cluster’s system mass function (SMF). The model involves both turbulent fragmentation and competitive accretion. Turbulent fragmentation creates low-mass seed proto-systems (i.e. single and multiple protostars). Some of these low-mass seed proto-systems then grow by competitive accretion to produce the high-mass power-law tail of the SMF. Turbulent fragmentation is relatively inefficient, in the sense that the creation of low-mass seed proto-systems only consumes a fraction, ${\sim }23{{\ \rm per\ cent}}$ (at most ${\sim }50{{\ \rm per\ cent}}$), of the mass available for star formation. The remaining mass is consumed by competitive accretion. Provided the accretion rate on to a proto-system is approximately proportional to its mass (dm/dt ∝ m), the SMF develops a power-law tail at high masses with the Salpeter slope (∼−2.3). If the rate of supply of mass accelerates, the rate of proto-system formation also accelerates, as appears to be observed in many clusters. However, even if the rate of supply of mass decreases, or ceases and then resumes, the SMF evolves homologously, retaining the same overall shape, and the high-mass power-law tail simply extends to ever higher masses until the supply of gas runs out completely. The Chabrier SMF can be reproduced very accurately if the seed proto-systems have an approximately lognormal mass distribution with median mass ${\sim } 0.11 \, {\rm M}_{\odot }$ and logarithmic standard deviation $\sigma _{\log _{10}({M/M}_\odot)}\sim 0.47$).

scholarly journals Power-law behavior of transcription factor dynamics at the single-molecule level implies a continuum affinity model

2021 ◽  
Author(s):  
David A Garcia ◽  
Gregory Fettweis ◽  
Diego M Presman ◽  
Ville Paakinaho ◽  
Christopher Jarzynski ◽  
...  
Keyword(s):  
Transcription Factor ◽  
Single Molecule ◽  
Power Law ◽  
Dwell Time ◽  
Specific Binding ◽  
Power Law Distribution ◽  
Single Molecule Level ◽  
Binding Behavior ◽  
Chromatin Template ◽  
Nuclear Domains

Abstract Single-molecule tracking (SMT) allows the study of transcription factor (TF) dynamics in the nucleus, giving important information regarding the diffusion and binding behavior of these proteins in the nuclear environment. Dwell time distributions obtained by SMT for most TFs appear to follow bi-exponential behavior. This has been ascribed to two discrete populations of TFs—one non-specifically bound to chromatin and another specifically bound to target sites, as implied by decades of biochemical studies. However, emerging studies suggest alternate models for dwell-time distributions, indicating the existence of more than two populations of TFs (multi-exponential distribution), or even the absence of discrete states altogether (power-law distribution). Here, we present an analytical pipeline to evaluate which model best explains SMT data. We find that a broad spectrum of TFs (including glucocorticoid receptor, oestrogen receptor, FOXA1, CTCF) follow a power-law distribution of dwell-times, blurring the temporal line between non-specific and specific binding, suggesting that productive binding may involve longer binding events than previously believed. From these observations, we propose a continuum of affinities model to explain TF dynamics, that is consistent with complex interactions of TFs with multiple nuclear domains as well as binding and searching on the chromatin template.

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