Fluid Flows to Black Holes

The following sections are included:

• Preface

• Chandrasekhar Centennial Symposium (October 15–17, 2010)

• Contents

The complexities of three countries — India, England, and the US — helped produce a scientist of rare stature and greatness.

The simple is the seal of the true. And beauty is the splendor of truth.

Once the astrophysics community had come to grips with a calculation performed by a 19-year-old student sailing off to graduate school, the heavens could never again be seen as a perfect and tranquil dominion.

The following sections are included:

• Introduction

• Ramanujan Institute

• The Goddess of Namakkal

• The Lost Notebook

• Ramanujan as an inspiration

The extraordinary achievements of Subrahmanyan Chandrasekhar (Chandra) have guided and inspired many younger astrophysicists. The brief survey seeks to highlight a few specific cases in India where, through his writings, lectures and discussions, Chandra made a lasting impact. It will be argued that although at a general, somewhat superficial level, Chandra is a light beacon to be followed, very few Indian astrophysicists reached a level where they could engage Chandra in a scientific discussion on a topic that interested him.

Chandrasekhar’s own books, papers, and oral history interviews make clear that he was generally more interested in the present and future of astrophysics than in its past. Nevertheless, late in his life and after his death, historians of science have somewhat entangled him in two supposedly controversial issues, one concerning precursors of his mass limit for degenerate stars and the other his relationship with Eddington. Neither story is an entirely happy one.

The Chandrasekhar limit is of key importance for the evolution of white dwarfs in binary systems and for the formation of neutron stars and black holes in binaries. Mass transfer can drive a white dwarf in a binary over the Chandrasekhar limit, which may lead to a Type Ia supernova (in case of a CO white dwarf) or an Accretion-Induced Collapse (AIC, in the case of an O-Ne-Mg white dwarf; and possibly also in some CO white dwarfs) which produces a neutron star. The direct formation of neutron stars or black holes out of degenerate stellar cores that exceed the Chandrasekhar limit, occurs in binaries with components that started out with masses ≥ 8 M_⊙.

This paper first discusses possible models for Type Ia supernovae, and then focusses on the formation of neutron stars in binary systems, by direct core collapse and by the AIC of O-Ne-Mg white dwarfs in binaries. Observational evidence is reviewed for the existence of two different direct neutron-star formation mechanisms in binaries: (i) by electron-capture collapse of the degenerate O-Ne-Mg core in stars with initial masses in the range of 8 to about 12 M_⊙, and (ii) by iron-core collapse in stars with inital masses above this range. Observations of neutron stars in binaries are consistent with a picture in which neutron stars produced by e-capture collapse have relatively low masses, ˜1.25M_⊙, and received hardly any velocity kick at birth, whereas neutron stars produced by iron-core collapses are more massive and received large velocity kicks at birth. Many of the globular cluster neutron stars and also some of the neutron stars in low-mass binaries in the Galactic disk are likely to have been produced by AIC of O-Ne-Mg white dwarfs in binaries. AIC is expected to produce normal strongly magnetized neutron stars, which in binaries can evolve into millisecond pulsars through the usual recycling scenario.

Stable relativistic stars form a two-parameter family, parametrized by mass and angular velocity. Limits on each of these quantities are associated with relativistic instabilities discovered by Chandrasekhar: A radial instability, to gravitational collapse or explosion, marks the upper and lower limits on their mass; and an instability driven by gravitational waves may set an upper limit on their spin. Our summary of relativistic stability theory given here is based on and includes excerpts from the book Rotating Relativistic Stars, by the present authors (Friedman & Sterigioulas 2011).

We review here some of the major open issues and challenges in black hole physics today, and the current progress on the same. It is pointed out that to secure a concrete foundation for the basic theory as well as astrophysical applications for black hole physics, it is essential to gain a suitable insight into these questions. In particular, we discuss the recent results investigating the final fate of a massive star within the framework of the Einstein gravity, and the stability and genericity aspects of the gravitational collapse outcomes in terms of black holes and naked singularities. Recent developments such as spinning up a black hole by throwing matter into it, and physical effects near naked singularities are considered. It is pointed out that some of the new results obtained in recent years in the theory of gravitational collapse imply interesting possibilities and understanding for the theoretical advances in gravity as well as towards new astrophysical applications.

The discovery of dynamical friction was Chandrasekhar’s best known contribution to the theory of stellar dynamics, but his work ranged from the fewbody problem to the limit of large N (in effect, galaxies). Much of this work was summarised in the text “Principles of Stellar Dynamics“ (Chandrasekhar 1942, 1960), which ranges from a precise calculation of the time of relaxation, through a long analysis of galaxy models, to the behaviour of star clusters in tidal fields. The later edition also includes the work on dynamical friction and related issues. In this review we focus on progress in the collisional aspects of these problems, i.e. those where few-body interactions play a dominant role, and so we omit further discussion of galaxy dynamics. But we try to link Chandrasekhar’s fundamental discoveries in collisional problems with the progress that has been made in the 50 years since the publication of the enlarged edition.

Stellar dynamics occupied Chandrasekhar’s interest for a brief interlude between his more prolonged studies of stellar structure and radiative transfer. This paper traces the history of one of his ideas – namely, that the shape of the galactic potential controls the orientation of the stellar velocity dispersion tensor. It has its roots in papers by Eddington (1915) and Chandrasekhar (1939), and provoked a fascinating dispute between these two great scientists – less well-known than their famous controversy over the white dwarf stars. In modern language, Eddington claimed that the integral curves of the eigenvectors of the velocity dispersion tensor provide a one-dimensional foliation into mutually orthogonal surfaces. Chandrasekhar challenged this, and explicitly constructed a counter-example. In fact, the work of neither of these great scientists was without flaws, though further developments in stellar dynamics were to ultimately draw more on Eddington’s insight than Chandrasekhar’s. We conclude with a description of modern attempts to measure the orientation of the velocity dispersion tensor for populations in the Milky Way Galaxy, a subject that is coming into its own with the dawning of the age of precision astrometry.

I outline methods for calculating the solution of Monte Carlo Radiative Transfer (MCRT) in scattering, absorption and emission processes of dust and gas, including polarization. I provide a bibliography of relevant papers on methods with astrophysical applications.

Over the course of roughly a decade, from the late 1950s through the early 1960s, Chandraskhar made fundamental contributions to basic plasma physics, and the effect of magnetic fields on the dynamics of astrophysical plasmas. This paper reviews recent progress and outstanding problems in Astrophysical magnetohydrodynamics, the application of MHD to astrophysical systems, with particular emphasis on the role of Chandra’s early contributions to the field. Specific topics discussed include magnetic field amplification by dynamo processes inside stars, the magnetorotational instability and angular momentum transport in accretion disks, MHD turbulence in the interstellar medium of galaxies, and kinetic MHD effects in weakly collisional plasmas. Chandra’s contributions in all of these areas endure.

Tracking the evolution of high redshift seed black hole masses to late times, we examine the observable signatures today. These massive initial black hole seeds form at extremely high redshifts from the direct collapse of pre-galactic gas discs. Populating dark matter halos with seeds formed in this fashion, we follow the mass assembly history of these black holes to the present time using a Monte-Carlo merger tree approach. Utilizing this formalism, we predict the black hole mass function at high redshifts and at the present time; the integrated mass density of black holes in the Universe; the luminosity function of accreting black holes as a function of redshift and the scatter in observed, local M_bh – σ relation. Comparing the predictions of the ‘light’ seed model with these massive seeds we find that significant differences appear predominantly at the low mass end of the present day black hole mass function. However, all our models predict that low surface brightness, bulge-less galaxies with large discs are least likely to be sites for the formation of massive seed black holes at high redshifts. The efficiency of seed formation at high redshifts has a direct influence on the black hole occupation fraction in galaxies at z = 0. This effect is more pronounced for low mass galaxies. This is the key discriminant between the models studied here and the Population III remnant ‘light’ seed model. We find that there exists a population of low mass galaxies that do not host nuclear black holes. Our prediction of the shape of the M_bh – σ relation at the low mass end and increased scatter has recently been corroborated by observations.

The Universe is the grandest conceivable scale on which the human mind can strive to understand nature. The amazing aspect of cosmology, the branch of science that attempts to understand the origin and evolution of the Universe, is that it is largely comprehensible by applying the same basic laws of physics that we use for other branches of physics. The observed cosmic microwave background (CMB) is understood by applying the basic laws of radiative processes and transfer, masterfully covered in the classic text by S. Chandrasekhar, in the cosmological context. In addition to the now widely acclaimed temperature anisotropy, there is also linear polarization information imprinted on the observed Cosmic Microwave background. CMB polarization already has addressed, and promises to do a lot more to unravel the deepest fundamental queries about physics operating close to the origin of the Universe.

An enigmatic prediction of Einstein’s general theory of relativity is gravitational waves. With the observed decay in the orbit of the Hulse-Taylor binary pulsar agreeing within a fraction of a percent with the theoretically computed decay from Einstein’s theory, the existence of gravitational waves was firmly established. Currently there is a worldwide effort to detect gravitational waves with inteferometric gravitational wave observatories or detectors and several such detectors have been built or are being built. The initial detectors have reached their design sensitivities and now the effort is on to construct advanced detectors which are expected to detect gravitational waves from astrophysical sources. The era of gravitational wave astronomy has arrived. This article describes the worldwide effort which includes the effort on the Indian front— the IndIGO project —, the principle underlying interferometric detectors both on ground and in space, the principal noise sources that plague such detectors, the astrophysical sources of gravitational waves that one expects to detect by these detectors and some glimpse of the data analysis methods involved in extracting the very weak gravitational wave signals from detector noise.

Non radial oscillations of neutron stars are associated with the emission of gravitational waves. The characteristic frequencies of these oscillations can be computed using the theory of stellar perturbations, and they are shown to carry detailed information on the internal structure of the emitting source. Moreover, they appear to be encoded in various radiative processes, as for instance, in the tail of the giant flares of Soft Gamma Repeaters. Thus, their determination is central to the theory of stellar perturbation. A viable approach to the problem consists in formulating this theory as a problem of resonant scattering of gravitational waves incident on the potential barrier generated by the spacetime curvature. This approach discloses some unexpected correspondences between the theory of stellar perturbations and the theory of quantum mechanics, and allows us to predict new relativistic effects.

This paper describes a brief history of the development of the Chandra X-ray observatory, based on the talk which was presented on October 17, 2010 at the Chandrasekhar Centennial Symposium held in the campus of the University of Chicago.

Five noted scientists, all close colleagues and friends of Subrahmanyan Chandrasekhar, share thoughts and memories of the man whose centennial we celebrate.

The following sections are included:

• Index