# On exact polytropic equilibria of self-gravitating gaseous and radiative systems: their application to molecular cloud condensation

@article{Honda2003OnEP, title={On exact polytropic equilibria of self-gravitating gaseous and radiative systems: their application to molecular cloud condensation}, author={Mitsuru Honda and Yasuko S. Honda}, journal={Monthly Notices of the Royal Astronomical Society}, year={2003}, volume={341}, pages={164-168} }

We propose a novel mathematical method to construct an exact polytropic sphere in self-gravitating hydrostatic equilibrium, improving the non-linear Poisson equation. The central boundary condition for the present equation requires a ratio of gas pressure to total one at the centre, which is uniquely identified by the whole mass and molecular weight of the system. The special solution derived from the Lane-Emden equation can be reproduced. This scheme is now available for modelling the…

## 5 Citations

Approximate analytical solutions of the Lane–Emden equation for a self-gravitating isothermal gas sphere

- Physics
- 2009

The isothermal Lane-Emden equation arises in many astrophysical problems, in particular in modelling of a self-gravitating, polytropic gas in a spherically symmetric configuration. In this work, the…

A theoretical model for electromagnetic characterization of a spherical dust molecular cloud equilibrium structure

- Physics
- 2015

Abstract A theoretical model is developed to study the equilibrium electromagnetic properties of a spherically symmetric dust molecular cloud (DMC) structure on the Jeans scales of space and time. It…

A polytropic approach to semi-relativistic isothermal gas spheres at arbitrary temperature

- Physics
- 2010

We use the standard polynomial expansion technique to show the existence of a relation between the polytropic model and the description of gas spheres at finite temperature. A numerical analysis is…

Polytropic atmospheres and the scaling of potential vorticity

- Physics
- 2005

SummaryPotential vorticity P is in widespread use as a diagnostic in atmospheric dynamics. Here, we employ the concepts of polytropic change of state and polytropic temperature for investigating the…

Symmetry Reduction of Lane-Emden Equation for Polytropes

- Physics, Mathematics
- 2008

We describe an ansatz for symmetry reduction of the Lane-Emden equation for an arbitrary polytropic index n, admitting only one symmetry generator. For the reduced first order differential equation…

## References

SHOWING 1-10 OF 23 REFERENCES

The Structure of Self-gravitating Polytropic Systems with n around 5

- Physics
- 2001

We investigate the structure of self-gravitating polytropic stellar systems. We present a method that allows us to obtain approximate analytical solutions, ψn+(x) of the nonlinear Poisson equation…

Self-similar collapse of isothermal spheres and star formation.

- Physics
- 1977

We consider the problem of the gravitational collapse of isothermal spheres by applying the similarity method to the gas-dynamic flow. We argue that a previous solution obtained by Larson and Penston…

Polytropic gas spheres: an approximate analytic solution of the Lane-Emden equation

- Physics
- 1996

Polytropic models play a very important role in galactic dynamics and in the theory of stellar structure and evolution. However, in general, the solution of the Lane-Emden equation can not be given…

Series solutions for polytropes and the isothermal sphere

- Physics
- 2001

The Lane–Emden equation for polytropic index and its limit of the isothermal sphere equation are singular at some negative value of the radius squared. This singularity prevents the real power series…

A Radiation Hydrodynamic Model for Protostellar Collapse. I. The First Collapse

- Physics
- 1998

Dynamical collapse of a molecular cloud core and the formation of a star are investigated by performing radiation hydrodynamic calculations in spherical symmetry. The angle-dependent and…

A Radiation Hydrodynamic Model for Protostellar Collapse. II. The Second Collapse and the Birth of a Protostar

- Physics
- 2000

We carry out radiation hydrodynamic calculations to study physical processes in the formation of a 1 M☉ protostar. Following our previous work, calculations pursue the whole evolution from the…

Similarity Solution for Formation of a Circumstellar Disk through the Collapse of a Flattened Rotating Cloud

- Physics
- 1998

We present similarity solutions that describe the runaway collapse of a rotating isothermal disk and its subsequent inside-out collapse. The similarity solutions contain the sound speed cs and the…

Molecular cloud condensation as a tracer of low-mass star formation

- PhysicsNature
- 1994

STARS form inside dense clouds of molecular gas, but the details of the process, such as the quantity of gas that goes into stars and the rate at which the gas collapses, are still unknown. The…

Solar Core Homology, Solar Neutrinos, and Helioseismology

- Physics
- 1996

Precise numerical standard solar models (SSMs) now agree with one another and with helioseismological observations in the convective and outer radiative zones. Nevertheless, these models obscure how…

The structure of clusters of galaxies observed with Einstein

- Physics
- 1984

Imaging observations from the Einstein Observatory are used to determine properties of galactic clusters and the intracluster gas. The hydrostatic-isothermal gas model is applied to obtain the…