# SPHERICALLY SYMMETRIC, COLD COLLAPSE: THE EXACT SOLUTIONS AND A COMPARISON WITH SELF-SIMILAR SOLUTIONS

## Abstract

We present the exact solutions for the collapse of a spherically symmetric cold (i.e., pressureless) cloud under its own self-gravity, valid for arbitrary initial density profiles and not restricted to the realm of self-similarity. These solutions exhibit a number of remarkable features, including the self-consistent formation of and subsequent accretion onto a central point mass. A number of specific examples are provided, and we show that Penston’s solution of pressureless self-similar collapse is recovered for polytropic density profiles; importantly, however, we demonstrate that the time over which this solution holds is fleetingly short, implying that much of the collapse proceeds non-self-similarly. We show that our solutions can naturally incorporate turbulent pressure support, and we investigate the evolution of overdensities—potentially generated by such turbulence—as the collapse proceeds. Finally, we analyze the evolution of the angular velocity and magnetic fields in the limit that their dynamical influence is small, and we recover exact solutions for these quantities. Our results may provide important constraints on numerical models that attempt to elucidate the details of protostellar collapse when the initial conditions are far less idealized.

- Authors:

- Astronomy Department and Theoretical Astrophysics Center, University of California, Berkeley, CA 94720 (United States)

- Publication Date:

- OSTI Identifier:
- 22664012

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Astrophysical Journal; Journal Volume: 835; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ANGULAR VELOCITY; CLOUDS; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; DENSITY; EXACT SOLUTIONS; GALAXIES; GRAVITATION; LIMITING VALUES; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; MASS; SPHERICAL CONFIGURATION; STARS; SYMMETRY; TURBULENCE

### Citation Formats

```
Coughlin, Eric R., E-mail: eric_coughlin@berkeley.edu.
```*SPHERICALLY SYMMETRIC, COLD COLLAPSE: THE EXACT SOLUTIONS AND A COMPARISON WITH SELF-SIMILAR SOLUTIONS*. United States: N. p., 2017.
Web. doi:10.3847/1538-4357/835/1/40.

```
Coughlin, Eric R., E-mail: eric_coughlin@berkeley.edu.
```*SPHERICALLY SYMMETRIC, COLD COLLAPSE: THE EXACT SOLUTIONS AND A COMPARISON WITH SELF-SIMILAR SOLUTIONS*. United States. doi:10.3847/1538-4357/835/1/40.

```
Coughlin, Eric R., E-mail: eric_coughlin@berkeley.edu. Fri .
"SPHERICALLY SYMMETRIC, COLD COLLAPSE: THE EXACT SOLUTIONS AND A COMPARISON WITH SELF-SIMILAR SOLUTIONS". United States.
doi:10.3847/1538-4357/835/1/40.
```

```
@article{osti_22664012,
```

title = {SPHERICALLY SYMMETRIC, COLD COLLAPSE: THE EXACT SOLUTIONS AND A COMPARISON WITH SELF-SIMILAR SOLUTIONS},

author = {Coughlin, Eric R., E-mail: eric_coughlin@berkeley.edu},

abstractNote = {We present the exact solutions for the collapse of a spherically symmetric cold (i.e., pressureless) cloud under its own self-gravity, valid for arbitrary initial density profiles and not restricted to the realm of self-similarity. These solutions exhibit a number of remarkable features, including the self-consistent formation of and subsequent accretion onto a central point mass. A number of specific examples are provided, and we show that Penston’s solution of pressureless self-similar collapse is recovered for polytropic density profiles; importantly, however, we demonstrate that the time over which this solution holds is fleetingly short, implying that much of the collapse proceeds non-self-similarly. We show that our solutions can naturally incorporate turbulent pressure support, and we investigate the evolution of overdensities—potentially generated by such turbulence—as the collapse proceeds. Finally, we analyze the evolution of the angular velocity and magnetic fields in the limit that their dynamical influence is small, and we recover exact solutions for these quantities. Our results may provide important constraints on numerical models that attempt to elucidate the details of protostellar collapse when the initial conditions are far less idealized.},

doi = {10.3847/1538-4357/835/1/40},

journal = {Astrophysical Journal},

number = 1,

volume = 835,

place = {United States},

year = {Fri Jan 20 00:00:00 EST 2017},

month = {Fri Jan 20 00:00:00 EST 2017}

}