Département de Physique ENS

Page personnelle de Steven Balbus

Home page of Steven Balbus

Professeur des Universités, Classe Exceptionnelle
Membre IUF, 2010 --

École Normale Supérieure
24, rue Lhomond
Laboratoire de Radioastronomie
75231 PARIS CEDEX 05

email: Steven.Balbus AT lra.ens.fr
Tel.: +33 (0)1 44 32 33 53

I am a theoretical astrophysicist with particular interests in the field of astrophysical gas dynamics. Early in my career I worked on problems of the interstellar medium, clusters of galaxies, and galactic dynamics, but since 1990 I have focused my attention on the behavior of accretion disks. An accretion disk consists of gas in rotation about a central mass, which could be an ordinary star, or a collapsed object such as a white dwarf, neutron star, or black hole. When they are even slightly magnetized, accretion disks are extremely unstable to what is known as the magnetorotational instability. This instability disrupts the gas from smooth laminar flow and renders it turbulent. This is now thought to be the underyling physical mechanism for accretion disk ''viscosity,'' once-upon-a-time a longstanding problem in theoretical astrophysics. I am currently pursuing studies, in a wide variety of fluids, of the consequences of this intrinsically magnetohydrodynamical turbulence.

More recently, I have also become interested in the problem of differential rotation in stellar convective zones, particularly the case of the Sun. I am studying the possibility that the rotation profile of stars with solar-like outer convective envelopes may be a consequence of little more than vorticity generation in a nonbarotropic flow (so-called thermal wind balance), and a near confluence of surfaces of constant angular velocity and constant ''residual'' entropy. Now, read more below in the section Selected Recent Papers...

Update May 2012: I will be moving to the Physics Department of Oxford University as Savilian Professor of Astronomy. The starting date of this appointment is 1 September 2012.


Brochure de rentree et emploi du temps 2010-11 (M1)

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LRA Home.


Notes on the derivation of the Kulsrud's (1983) drift kinetic equation for a collisionless plasma.


Course Notes:

(Updated course notes 11/01/12, final exam from Jan. 2011.)

M2: Magnetohydrodynamics and astrophysical gasdynamics

M2 final from 2011.

1er cours: Introduction à l'Astrophysique.

2me cours: Introduction à l'Astrophysique.

3me cours: Introduction à l'Astrophysique.

4me cours: Introduction à l'Astrophysique.

5me cours: Introduction à l'Astrophysique.

6me cours: Introduction à l'Astrophysique.

7me cours: Introduction à l'Astrophysique.

8me cours: Introduction à l'Astrophysique.

Questions tests.


Hydrodynamics. Updated: 03/05/12.

Sample questions for Hydrodynamics Final.


Review Papers:

Instability, turbulence, and enhanced transport in accretion disks. (Balbus, S. A. and Hawley, J. F. 1998, Reviews of Modern Physics, 70, 1)
An technical introduction to the physics of accretion disk turbulence.

Enhanced angular momentum transport in accretion disks. (Balbus, S. A. 2003, Annu. Rev. Astron. Astrophys., 41, 555)
An update of accretion disk physics with a more detailed treatment of wave transport.

Steven A. Balbus (2009) Magnetorotational instability . Scholarpedia, 4(7):2409.
A brief online review of the magnetorotational instability, suitable for advanced undergraduates and beginning graduate students.

Magnetohydrodynamics of Protostellar Disks. (Balbus, S. A. 2011, in Physical Processes in Circumstellar Disks Around Young Stars, ed. P. J. V. Garcia, [University of Chicago Press: Chicago], p. 237)
A review of MHD processes in low ionization disks.

Selected Recent Papers:

A Simple Model for Solar Isorotation Contours. (Balbus, S. A. 2009, MNRAS, 395, 2056.)
An analytic model for the solar convection zone (SCZ) isorotation contours based on the solution of the thermal wind equation and the assumption that constant entropy and constant rotation surfaces coincide. The latter is a requirement for the SCZ to be marginally stable against magneto-baroclinic instability, just as an adiabatic temperature profile is a requirement for marginal stability against a purely convective instability.

On Differential Rotation and Convection in the Sun. (Balbus, S. A., Bonart, J., Latter, H. N., and Weiss, N. O. 2009, MNRAS, 400, 176.)
A detailed comparison between the solution of the thermal wind equation and GONG data reveals a precise quantitative match, away from the boundary layers at the Sun's outer surface and tachocline. As an alternative to MHD, a purely hydrodynamical explanation is put forth for this result, which obviates the need for entropy and angular velocity surfaces to coincide. Instead, only the "residual" entropy, the entropy left after a (convection-driving) radial profile has been subtracted, coincides with the angular velocity. The figure below shows the fit between theoretical calculation (white curves) and the helioseismology GONG data (dark curves).

Differential Rotation in Fully Convective Stars. (Balbus, S. A. and Weiss, N. O. 2010, MNRAS, 404, 1263.)
A generalization of the mathematical solution for the isorotation contours in the Sun to fully convective stars. The figures below show solutions for a solar-like surface profile (left), and an anti-solar profile (right), which rotates more rapidly at the poles than the equator.

The Effect of the Tachocline on Differential Rotation in the Sun. (Balbus, S. A. and Latter, H. N. 2010, MNRAS, 407, 2565.)
A global mathematical solution for the solar differential rotation profile resulting from localized quadrupolar forcing, represented as a (very simple) inhomogeneous term in the thermal wind equation. The leftmost figure shows the calculated isorotation contours; the second from the left is an image of the same contours taken from GONG data circa 2009 (with thanks to R. Howe); the third from the left shows a superposition of a calculated solution (black) with the data (red). A remarkable and quite unmistakable tachocline structure is apparent in our mathematical solution, which is in good agreement with the helioseismology data. Finally, the rightmost image shows recent results that include the outer boundary layer, this time with a very simple forcing term beyond 0.97 solar radii. (In case of difficulties viewing, click on the individual image.)

Global Model of Differential Rotation in the Sun. (Balbus, S. A., Latter, H., and Weiss, N. 2012, MNRAS, in press.)
A demonstration that the mathematical solution of the previous paper does not require terms external to the thermal wind equation, but emerges naturally when the functional relationship between (residual) entropy and angular velocity takes its most general form. The image below superposes an analytic solution of the thermal wind equation with helioseismology data.

Update: 02 jan 12