The Secular Bar-Mode Instability in Rapidly Rotating Stars Revisited

Uniformly rotating, homogeneous, incompressible Maclaurin spheroids that spin sufficiently rapidly are secularly unstable to nonaxisymmetric, bar-mode perturbations when viscosity is present. The intuitive explanation is that energy dissipation by viscosity can drive an unstable spheroid to a stable, triaxial configuration of lower energy - a Jacobi ellipsoid. But what about rapidly rotating compressible stars? Unlike incompressible stars, which contain no internal energy and therefore immediately liberate all the energy dissipated by viscosity, compressible stars have internal energy and can retain the dissipated energy as internal heat. Now compressible stars that rotate sufficiently rapidly and also manage to liberate this dissipated energy very quickly are known to be unstable to bar-mode perturbations, like their incompressible counterparts. But what is the situation for rapidly rotating compressible stars that have very long cooling timescales, so that all the energy dissipated by viscosity is retained as heat, whereby the total energy of the star remains constant on a secular (viscous) evolution timescale? Are such stars also unstable to the nonlinear growth of bar modes, or is the viscous heating sufficient to cause them to expand, drive down the ratio of rotational kinetic to gravitational potential energy T/|W| ~ 1/R, where R is the equatorial radius, and turn off the instability before it gets underway? If the instability still arises in such stars, at what rotation rate do they become unstable, and to what final state do they evolve? We provide answers to these questions in the context of the compressible ellipsoid model for rotating stars. The results should serve as useful guides for numerical simulations in 3+1 dimensions for rotating stars containing viscosity.Comment: Accepted for publication in ApJ 613, 1213-1220, 200

Religious Freedom as if Religion Matters: A Tribute to Justice Brennan

On April 22, 1998, Professor of Law, Stephen L. Carter of Yale Law School, delivered the Georgetown Law Center’s eighteenth Annual Philip A. Hart Memorial Lecture: Religion-Centered Free Exercise: A Tribute to Justice Brennan. Stephen L. Carter is the William Nelson Cromwell Professor of Law at Yale, where he has taught since 1982. Among his courses are law and religion, the ethics of war, contracts, evidence, and professional responsibility. His most recent book is The Violence of Peace: America’s Wars in the Age of Obama (2011). Among his other books on law and politics are God’s Name in Vain: The Wrongs and Rights of Religion in Politics; Civility: Manners, Morals, and the Etiquette of Democracy; The Dissent of the Governed: A Meditation on Law, Religion, and Loyalty; The Confirmation Mess: Cleaning up the Federal Appointments Process; and The Culture of Disbelief: How American Law and PoliticsTrivialize Religious Devotion. Professor Carter writes a column for Bloomberg View and is a regular contributor to Newsweek and The Daily Beast. He blogs about professional football for the Washington Post. Professor Carter also writes fiction. His novel The Emperor of Ocean Park spent eleven weeks on the New York Times best-seller list. His next novel, The Impeachment of Abraham Lincoln, will be published in 2012. His novella “The Hereditary Thurifer” recently appeared in the crime anthology, The Dark End of the Street. Professor Carter was formerly a law clerk for Supreme Court Justice Thurgood Marshall, as well as for Judge Spottswood W. Robinson, III, of the United States Court of Appeals for the District of Columbia Circuit. He is a graduate of Stanford University and Yale Law School, and has received eight honorary degrees