## virial theorem

Overview page. Subjects: Astronomy and Astrophysics.

A way of estimating the total mass of an object such as a galaxy or a cluster of galaxies from the movement of its individual members. The theorem states that the average gravitational...

## virial theorem

Overview page. Subjects: Astronomy and Astrophysics.

A way of estimating the total mass of an object such as a galaxy or a cluster of galaxies from the movement of its individual members. The theorem states that the average gravitational...

## virial theorem

in** A Dictionary of Astronomy**

P ublished online February 2018 .

Reference Entry. Subjects: Astronomy and Astrophysics; Astronomical Instrumentation, Methods, and Techniques; Galaxies. 165 words.

A way of estimating the total mass of an object such as a galaxy or a cluster of galaxies from the movement of its individual members. The theorem states that the average gravitational...

## Virial theorem for radiating accretion discs

in** Monthly Notices of the Royal Astronomical Society**

May 2012; p ublished online April 2012 .

Journal Article. Subjects: Astronomy and Astrophysics. 2448 words.

A continuum version of the virial theorem is derived for a radiating self-gravitating accretion disc around a compact object. The central object is point-like, but we can avoid the...

## Mayer virial expansions and Groeneveld’s theorems

in** Advanced Statistical Mechanics**

December 2009; p ublished online February 2010 .

Chapter. Subjects: Mathematical and Statistical Physics. 6326 words.

This chapter introduces the concept of the low density virial expansion of the equation of state, and derives the Mayer diagram theory for computing this expansion. Groeneveld's theorems...

## virial theorem

in** A Dictionary of Astronomy**

January 2012; p ublished online January 2012 .

Reference Entry. Subjects: Astronomy and Astrophysics. 161 words.

A way of estimating the total mass of an object such as a galaxy or a cluster of galaxies from

## virial theorem

in** A Dictionary of Physics**

March 2019; p ublished online March 2019 .

Reference Entry. Subjects: Physics. 122 words.

A result concerning systems consisting of a number of particles that relates the average *kinetic energy over time to the average ...

## virial theorem

in** The Oxford Companion to Cosmology**

January 2008; p ublished online January 2008 .

Reference Entry. Subjects: Astronomy and Astrophysics. 4 words.

## Six myths on the virial theorem for interstellar clouds

in** Monthly Notices of the Royal Astronomical Society**

October 2006; p ublished online September 2006 .

Journal Article. Subjects: Astronomy and Astrophysics. 6142 words.

The interstellar medium is highly dynamic and turbulent. However, little or no attention has been paid in the literature to the implications that this fact has on the validity of at least...

## Virial theorem and generalization of the Fermi-liquid theory for the homogeneous degenerate electron system

in** Progress of Theoretical and Experimental Physics**

P ublished online February 2013 .

Journal Article. Subjects: Condensed Matter Physics. 2945 words.

Using the general thermodynamic equalities and the virial theorem, it is shown that the ground state energy of the homogeneous electron liquid is uniquely defined by the one-particle...

## Bayes versus the virial theorem: inferring the potential of a galaxy from a kinematical snapshot

in** Monthly Notices of the Royal Astronomical Society**

January 2014; p ublished online November 2013 .

Journal Article. Subjects: Astronomy and Astrophysics. 15059 words.

We present a new framework for estimating a galaxy's gravitational potential, Φ, from its stellar kinematics by adopting a fully non-parametric model for the galaxy's unknown action-space...

## Investigation of force-freeness of a solar emerging magnetic field via application of the virial theorem to magnetohydrodynamic simulations

in** Publications of the Astronomical Society of Japan**

December 2014; p ublished online October 2014 .

Journal Article. Subjects: Astrometry and Celestial Mechanics; Astronomical Instrumentation, Methods, and Techniques; Solar Physics. 4393 words.

Force-freeness of a solar magnetic field is a key to reconstructing the invisible coronal magnetic structure of an emerging flux region on the Sun where active phenomena such as flares and...

## Applications

in** Stellar Magnetism**

February 2012; p ublished online May 2012 .

Chapter. Subjects: Astronomy and Astrophysics. 19793 words.

This chapter discusses in greater detail some of the topics introduced in Chapter 2. It covers magnetosonic waves; magnetohydrodynamic shocks; self-gravitating systems and the virial...

## Hamilton-Jacobi Theory

in** Lagrangian and Hamiltonian Dynamics**

June 2018; p ublished online August 2018 .

Chapter. Subjects: Mathematical and Statistical Physics. 9343 words.

This chapter focuses on Liouville’s theorem and classical statistical mechanics, deriving the classical propagator. The terms ‘phase space volume element’ and ‘Liouville operator’ are...

## Tan Relations and the Contact Parameter

in** Bose-Einstein Condensation and Superfluidity**

January 2016; p ublished online March 2016 .

Chapter. Subjects: Condensed Matter Physics. 3916 words.

This chapter is devoted to the derivation of various thermodynamic relations, known as Tan relations, involving the so-called contact parameter. This physical quantity, which determines the...

## Self-gravitation and negative heat capacity

in** Thermodynamics**

September 2016; p ublished online January 2017 .

Chapter. Subjects: Mathematical and Statistical Physics. 3460 words.

The basic thermodynamics of self-gravitating systems is explained. First the virial theorem is introduced, and it is shown that a gravitating cloud bound by its own gravity is unstable, and...

## The three body problem

in** Advanced Mechanics**

July 2013; p ublished online December 2013 .

Chapter. Subjects: Atomic, Molecular, and Optical Physics. 3006 words.

This chapter derives the consequences of scale invariance in the three body problem. Jacobi co-ordinates are introduced. The orbits are geodesics in a certain metric. The three body problem...

## Nonlocal Gravity and Dark Matter

in** Nonlocal Gravity**

May 2017; p ublished online July 2017 .

Chapter. Subjects: Astronomy and Astrophysics; Mathematical and Statistical Physics. 11499 words.

The implications of linearized NLG for the gravitational physics of the Solar System, spiral galaxies and nearby clusters of galaxies are critically examined in this chapter. In the...

## Virial sequences for thick discs and haloes: flattening and global anisotropy

in** Monthly Notices of the Royal Astronomical Society**

May 2012; p ublished online April 2012 .

Journal Article. Subjects: Astronomy and Astrophysics. 9024 words.

Stellar haloes and thick discs are tracer populations and make only a modest contribution to the overall gravity field. Here, we exploit the virial theorem to provide formulae for the ratio...

## velocity dispersion

Overview page. Subjects: Astronomy and Astrophysics.

The spread of velocities of stars or galaxies in a cluster. Galaxies in a cluster have individual orbital velocities about the cluster's centre of mass, which depend on the total cluster...

## Deep Impurities with Collision Delay

in** Interacting Systems far from Equilibrium**

December 2017; p ublished online February 2018 .

Chapter. Subjects: Condensed Matter Physics. 3762 words.

The linearised nonlocal kinetic equation is solved analytically for impurity scattering. The resulting response function provides the conductivity, plasma oscillation and Fermi momentum. It...