Apparent Sizes and Spectral Line Profiles for Spherical and Disk Masers: Solutions to the Full Equations

Calculations are performed for the spectral line profiles and images of astrophysical maser radiation that emerges from isolated spheres and thin disks viewed edge-on. In contrast to previous investigations where various approximations are made, the full equations are solved here for the frequency-dependent radiative transport that includes the thermal motion of the molecules. The spectral line profiles for spheres and disks are found to rebroaden to the full thermal Doppler breadth with increasing saturation in essentially the same way as is well known to occur for a linear maser. The variation with frequency in the apparent angular sizes of masing spheres and thin disks is found to be negligible at frequencies within the spectral line where the flux is significant. Calculations also are performed for spherical and disk masers that are not isolated, but for which the seed radiation for the masers is incident from one side as would occur when a strong continuum source is on the far side of the masers. Again, the spectral line profiles are found to rebroaden to the full thermal breadths with increasing saturation and there are no significant variations in the apparent angular sizes with frequency. However, the full rebroadening does occur at somewhat higher saturation and the variation of the apparent angular sizes as a function of the degree of saturation is quite different from that of the isolated masers. Spheres and disks have served as idealized geometries with which to examine possible deviations from the linear approximation for astrophysical masers.Comment: accepted for Astrophysical Journa

Polarization of Astronomical Maser Radiation. IV. Circular Polarization Profiles

Profile comparison of the Stokes parameters $V$ and $I$ is a powerful tool for maser data analysis, providing the first direct methods for unambiguous determination of (1) the maser saturation stage, (2) the amplification optical depth and intrinsic Doppler width of unsaturated masers, and (3) the comparative magnitudes of Zeeman splitting and Doppler linewidth. Circular polarization recently detected in OH 1720 MHz emission from the Galactic center appears to provide the first direct evidence for maser saturation.Comment: 14 pages, 1 Postscript figures (included), uses aaspp4.sty. To appear in Astrophysical Journa

Selfgravitating Gas Spheres in a Box and Relativistic Clusters: Relation between Dynamical and Thermodynamical Stability

We derive a variational principle for the dynamical stability of a cluster as a gas sphere in a box. Newtonian clusters are always dynamically stable and, for relativistic clusters, the relation between dynamical and thermodynamical instabilities is analyzed. The boundaries between dynamically and thermodynamically stable and unstable models are found numerically for relativistic stellar systems with different cut off parameters. A criterion based on binding energy curve is used for determination of the boundary of dynamical stability.Comment: 10 figure

Exact analytical solution of the collapse of self-gravitating Brownian particles and bacterial populations at zero temperature

We provide an exact analytical solution of the collapse dynamics of self-gravitating Brownian particles and bacterial populations at zero temperature. These systems are described by the Smoluchowski-Poisson system or Keller-Segel model in which the diffusion term is neglected. As a result, the dynamics is purely deterministic. A cold system undergoes a gravitational collapse leading to a finite time singularity: the central density increases and becomes infinite in a finite time t_coll. The evolution continues in the post collapse regime. A Dirac peak emerges, grows and finally captures all the mass in a finite time t_end, while the central density excluding the Dirac peak progressively decreases. Close to the collapse time, the pre and post collapse evolution is self-similar. Interestingly, if one starts from a parabolic density profile, one obtains an exact analytical solution that describes the whole collapse dynamics, from the initial time to the end, and accounts for non self-similar corrections that were neglected in previous works. Our results have possible application in different areas including astrophysics, chemotaxis, colloids and nanoscience

Cosmological expansion and local physics

The interplay between cosmological expansion and local attraction in a gravitationally bound system is revisited in various regimes. First, weakly gravitating Newtonian systems are considered, followed by various exact solutions describing a relativistic central object embedded in a Friedmann universe. It is shown that the ``all or nothing'' behaviour recently discovered (i.e., weakly coupled systems are comoving while strongly coupled ones resist the cosmic expansion) is limited to the de Sitter background. New exact solutions are presented which describe black holes perfectly comoving with a generic Friedmann universe. The possibility of violating cosmic censorship for a black hole approaching the Big Rip is also discussed.Comment: 17 pages, LaTeX, to appear in Phys. Rev.

Various Modes of Helium Mixing in Globular Cluster Giants and Their Possible Effects on the Horizontal Branch Morphology

It has been known for a long time that some red giants in globular clusters exhibit large star-to-star variations in the abundances of light elements that are not exhibited by field giants. This fact can be taken as evidence that the extra mixing mechanism(s) that operate in globular cluster giants may be consequences of star-star interactions in the dense stellar environment. In order to constrain the extra mixing mechanism(s), we study the influence of helium enrichment along the red giant branch (RGB) on the evolution of stars through the horizontal branch. Three possible modes of helium enrichment are considered, associated with close encounters of stars in the globular clusters. We show that as a consequence of the variations in the core mass as well as in the total mass due to mass loss, the color of horizontal branch models are distributed over almost all range of horizontal branch. The results are discussed in relation to the scenario for the origin of the abundance anomalies and for the effects on the morphology of horizontal branch. We argue that the star-star interactions can explain not only the source of angular momentum of rapid rotation but also provide a mechanism for the bimodal distribution of rotation rates in some globular clusters. We also propose the time elapsed from the latest core collapse phase during the gravo-thermal oscillations as the second parameter to explain the variations in HB morphology among the globular clusters.Comment: 57 pages, 16 figures, to be published on June 2006 in Ap

Cosmic Black-Hole Hair Growth and Quasar OJ287

An old result ({\tt astro-ph/9905303}) by Jacobson implies that a black hole with Schwarzschild radius $r_s$ acquires scalar hair, $Q \propto r_s^2 \mu$, when the (canonically normalized) scalar field in question is slowly time-dependent far from the black hole, $\partial_t \phi \simeq \mu M_p$ with $\mu r_s \ll 1$ time-independent. Such a time dependence could arise in scalar-tensor theories either from cosmological evolution, or due to the slow motion of the black hole within an asymptotic spatial gradient in the scalar field. Most remarkably, the amount of scalar hair so induced is independent of the strength with which the scalar couples to matter. We argue that Jacobson's Miracle Hair-Growth Formula${}^\copyright$ implies, in particular, that an orbiting pair of black holes can radiate {\em dipole} radiation, provided only that the two black holes have different masses. Quasar OJ 287, situated at redshift $z \simeq 0.306$, has been argued to be a double black-hole binary system of this type, whose orbital decay recently has been indirectly measured and found to agree with the predictions of General Relativity to within 6%. We argue that the absence of observable scalar dipole radiation in this system yields the remarkable bound $|\,\mu| < (16 \, \hbox{days})^{-1}$ on the instantaneous time derivative at this redshift (as opposed to constraining an average field difference, $\Delta \phi$, over cosmological times), provided only that the scalar is light enough to be radiated --- i.e. m \lsim 10^{-23} eV --- independent of how the scalar couples to matter. This can also be interpreted as constraining (in a more model-dependent way) the binary's motion relative to any spatial variation of the scalar field within its immediate vicinity within its host galaxy.Comment: 20 page

Dynamical Processes in Globular Clusters

Globular clusters are among the most congested stellar systems in the Universe. Internal dynamical evolution drives them toward states of high central density, while simultaneously concentrating the most massive stars and binary systems in their cores. As a result, these clusters are expected to be sites of frequent close encounters and physical collisions between stars and binaries, making them efficient factories for the production of interesting and observable astrophysical exotica. I describe some elements of the competition among stellar dynamics, stellar evolution, and other processes that control globular cluster dynamics, with particular emphasis on pathways that may lead to the formation of blue stragglers.Comment: Chapter 10, in Ecology of Blue Straggler Stars, H.M.J. Boffin, G. Carraro & G. Beccari (Eds), Astrophysics and Space Science Library, Springe

Relativistic Dynamics and Extreme Mass Ratio Inspirals

It is now well-established that a dark, compact object (DCO), very likely a massive black hole (MBH) of around four million solar masses is lurking at the centre of the Milky Way. While a consensus is emerging about the origin and growth of supermassive black holes (with masses larger than a billion solar masses), MBHs with smaller masses, such as the one in our galactic centre, remain understudied and enigmatic. The key to understanding these holes - how some of them grow by orders of magnitude in mass - lies in understanding the dynamics of the stars in the galactic neighbourhood. Stars interact with the central MBH primarily through their gradual inspiral due to the emission of gravitational radiation. Also stars produce gases which will subsequently be accreted by the MBH through collisions and disruptions brought about by the strong central tidal field. Such processes can contribute significantly to the mass of the MBH and progress in understanding them requires theoretical work in preparation for future gravitational radiation millihertz missions and X-ray observatories. In particular, a unique probe of these regions is the gravitational radiation that is emitted by some compact stars very close to the black holes and which could be surveyed by a millihertz gravitational wave interferometer scrutinizing the range of masses fundamental to understanding the origin and growth of supermassive black holes. By extracting the information carried by the gravitational radiation, we can determine the mass and spin of the central MBH with unprecedented precision and we can determine how the holes "eat" stars that happen to be near them.Comment: Update from the first version, 151 pages, accepted for publication @ Living Reviews in Relativit

Relativistic Binaries in Globular Clusters

Galactic globular clusters are old, dense star systems typically containing 10\super{4}--10\super{7} stars. As an old population of stars, globular clusters contain many collapsed and degenerate objects. As a dense population of stars, globular clusters are the scene of many interesting close dynamical interactions between stars. These dynamical interactions can alter the evolution of individual stars and can produce tight binary systems containing one or two compact objects. In this review, we discuss theoretical models of globular cluster evolution and binary evolution, techniques for simulating this evolution that leads to relativistic binaries, and current and possible future observational evidence for this population. Our discussion of globular cluster evolution will focus on the processes that boost the production of hard binary systems and the subsequent interaction of these binaries that can alter the properties of both bodies and can lead to exotic objects. Direct {\it N}-body integrations and Fokker--Planck simulations of the evolution of globular clusters that incorporate tidal interactions and lead to predictions of relativistic binary populations are also discussed. We discuss the current observational evidence for cataclysmic variables, millisecond pulsars, and low-mass X-ray binaries as well as possible future detection of relativistic binaries with gravitational radiation.Comment: 88 pages, 13 figures. Submitted update of Living Reviews articl