Stability of an Ultra-Relativistic Blast Wave in an External Medium with a Steep Power-Law Density Profile

We examine the stability of self-similar solutions for an accelerating relativistic blast wave which is generated by a point explosion in an external medium with a steep radial density profile of a power-law index > 4.134. These accelerating solutions apply, for example, to the breakout of a gamma-ray burst outflow from the boundary of a massive star, as assumed in the popular collapsar model. We show that short wavelength perturbations may grow but only by a modest factor <~ 10.Comment: 12 pages, 3 figures, submitted to Physical Review

Expected Number and Flux Distribution of Gamma-Ray-Burst Afterglows with High Redshifts

If Gamma-Ray-Bursts (GRBs) occur at high redshifts, then their bright afterglow emission can be used to probe the ionization and metal enrichment histories of the intervening intergalactic medium during the epoch of reionization. In contrast to other sources, such as galaxies or quasars, which fade rapidly with increasing redshift, the observed infrared flux from a GRB afterglow at a fixed observed age is only a weak function of its redshift. This results from a combination of the spectral slope of GRB afterglows and the time-stretching of their evolution in the observer's frame. Assuming that the GRB rate is proportional to the star formation rate and that the characteristic energy output of GRBs is ~10^{52} ergs, we predict that there are always ~15 GRBs from redshifts z>5 across the sky which are brighter than ~100 nJy at an observed wavelength of ~2 \mu m. The infrared spectrum of these sources could be taken with the future Next Generation Space Telescope, as a follow-up on their early X-ray localization with the Swift satellite.Comment: 29 pages, 14 figures; submitted to Ap

Are HI Supershells the Remnants of Gamma-Ray Bursts?

Gamma-Ray Bursts (GRBs) are thought to originate at cosmological distances from the most powerful explosions in the Universe. If GRBs are not beamed then the distribution of their number as a function of Gamma-ray flux implies that they occur once per (0.3-40) million years per bright galaxy and that they deposit >10^{53} ergs into their surrounding interstellar medium. The blast wave generated by a GRB explosion would be washed out by interstellar turbulence only after tens of millions of years when it finally slows down to a velocity of 10 km/s. This rather long lifetime implies that there could be up to several tens of active GRB remnants in each galaxy at any given time. For many years, radio observations have revealed the enigmatic presence of expanding neutral-hydrogen (HI) supershells of kpc radius in the Milky Way and in other nearby galaxies. The properties of some supershells cannot be easily explained in terms of conventional sources such as stellar winds or supernova explosions. However, the inferred energy and frequency of the explosions required to produce most of the observed supershells agree with the above GRB parameters. More careful observations and analysis might reveal which fraction of these supershells are GRB remnants. We show that if this link is established, the data on HI supershells can be used to constrain the energy output, the rate per galaxy, the beaming factor, and the environment of GRB sources in the Universe.Comment: 8 pages, final version, ApJ Letters, in pres

Is a Classical Language Adequate in Assessing the Detectability of the Redshifted 21cm Signal from the Early Universe?

The classical radiometer equation is commonly used to calculate the detectability of the 21cm emission by diffuse cosmic hydrogen at high redshifts. However, the classical description is only valid in the regime where the occupation number of the photons in phase space is much larger than unity and they collectively behave as a classical electromagnetic field. At redshifts z<20, the spin temperature of the intergalactic gas is dictated by the radiation from galaxies and the brightness temperature of the emitting gas is in the range of mK, independently from the existence of the cosmic microwave background. In regions where the observed brightness temperature of the 21cm signal is smaller than the observed photon energy, of 68/(1+z) mK, the occupation number of the signal photons is smaller than unity. Neverethless, the radiometer equation can still be used in this regime because the weak signal is accompanied by a flood of foreground photons with a high occupation number (involving the synchrotron Galactic emission and the cosmic microwave background). As the signal photons are not individually distinguishable, the combined signal+foreground population of photons has a high occupation number, thus justifying the use of the radiometer equation.Comment: 4 pages, Accepted for publication in JCA

Development of a Muscle Spindle Model

Abstrac

The Link between Warm Molecular Disks in Maser Nuclei and Star Formation near the Black Hole at the Galactic Center

The discovery of hundreds of young, bright stars within a parsec from the massive black hole at the center of the Galaxy presents a challenge to star formation theories. The requisite Roche densities for the gravitational collapse of gas clouds are most naturally achieved in accretion disks. The water maser sources in Keplerian rotation in the nuclei of NGC4258, NGC1068, and the Circinus galaxy indicate the presence of warm, extended, molecular accretion disks around black holes similar in mass to the one at the Galactic center. Here we argue that the current conditions in the maser nuclei, and those near the Galactic center, represent two consecutive, recurrent phases in the life cycle of the nucleus of a typical gas-rich spiral bulge. The warm molecular disks that give rise to the observed maser emission fragment into stellar-size objects. The stellar masses, their orbital geometry, and the total number of stars thus formed are consistent with the values identified at the Galactic center. The stars tend to form in compact groups resembling the IRS 13 complex that dominates the stellar light in the neighborhood of the black hole.Comment: ApJ Letters, in pres

Deviations from the local field approximation in negative streamer heads

Negative streamer ionization fronts in nitrogen under normal conditions are investigated both in a particle model and in a fluid model in local field approximation. The parameter functions for the fluid model are derived from swarm experiments in the particle model. The front structure on the inner scale is investigated in a 1D setting, allowing reasonable run-time and memory consumption and high numerical accuracy without introducing super-particles. If the reduced electric field immediately before the front is >= 50kV/(cm bar), solutions of fluid and particle model agree very well. If the field increases up to 200kV/(cm bar), the solutions of particle and fluid model deviate, in particular, the ionization level behind the front becomes up to 60% higher in the particle model while the velocity is rather insensitive. Particle and fluid model deviate because electrons with high energies do not yet fully run away from the front, but are somewhat ahead. This leads to increasing ionization rates in the particle model at the very tip of the front. The energy overshoot of electrons in the leading edge of the front actually agrees quantitatively with the energy overshoot in the leading edge of an electron swarm or avalanche in the same electric field.Comment: The paper has 17 pages, including 15 figures and 3 table

Hypervelocity Stars from the Andromeda Galaxy

Hypervelocity stars (HVSs) discovered in the Milky Way (MW) halo are thought to be ejected from near the massive black hole (MBH) at the galactic centre. In this paper we investigate the spatial and velocity distributions of the HVSs which are expected to be similarly produced in the Andromeda galaxy (M31). We consider three different HVS production mechanisms: (i) the disruption of stellar binaries by the galactocentric MBH; (ii) the ejection of stars by an in-spiraling intermediate mass black hole; and (iii) the scattering of stars off a cluster of stellar-mass black holes orbiting around the MBH. While the first two mechanisms would produce large numbers of HVSs in M31, we show that the third mechanism would not be effective in M31. We numerically calculate 1.2*10^6 trajectories of HVSs from M31 within a simple model of the Local Group and hence infer the current distribution of these stars. Gravitational focusing of the HVSs by the MW and the diffuse Local Group medium leads to high densities of low mass (~ solar mass) M31 HVSs near the MW. Within the virialized MW halo, we expect there to be of order 1000 HVSs for the first mechanism and a few hundred HVSs for the second mechanism; many of these stars should have distinctively large approach velocities (< -500 km/s). In addition, we predict ~5 hypervelocity RGB stars within the M31 halo which could be identified observationally. Future MW astrometric surveys or searches for distant giants could thus find HVSs from M31.Comment: 14 pages, 6 figures, changed to match version accepted by MNRA

Observable Signatures of EMRI Black Hole Binaries Embedded in Thin Accretion Disks

We examine the electromagnetic (EM) and gravitational wave (GW) signatures of stellar-mass compact objects (COs) spiraling into a supermassive black hole (extreme mass-ratio inspirals or EMRIs), embedded in a thin, radiation-pressure dominated, accretion disk. At large separations, the tidal effect of the secondary CO clears a gap. We show that the gap refills during the late GW-driven phase of the inspiral, leading to a sudden EM brightening of the source. The accretion disk leaves an imprint on the GW through its angular momentum exchange with the binary, the mass increase of the binary members due to accretion, and its gravity. We compute the disk-modified GWs both in an analytical Newtonian approximation and in a numerical effective-one-body approach. We find that disk-induced migration provides the dominant perturbation to the inspiral, with weaker effects from the mass accretion onto the CO and hydrodynamic drag. Depending on whether a gap is present, the perturbation of the GW phase is between 10 and 1000 radians per year, detectable with the future Laser Interferometer Space Antenna (LISA) at high significance. The Fourier transform of the disk-modified GW in the stationary phase approximation is sensitive to disk parameters with a frequency trend different from post-Newtonian vacuum corrections. Our results suggest that observations of EMRIs may place new sensitive constraints on the physics of accretion disks.Comment: 42 pages, 8 figures, 3 tables, submitted to Phys. Rev.

Toward an Ising Model of Cancer and Beyond

Theoretical and computational tools that can be used in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies to control cancer growth is desired. To develop such a predictive model, one must account for the complex mechanisms involved in tumor growth. Here we review resarch work that we have done toward the development of an "Ising model" of cancer. The review begins with a description of a minimalist four-dimensional (three in space and one in time) cellular automaton (CA) model of cancer in which healthy cells transition between states (proliferative, hypoxic, and necrotic) according to simple local rules and their present states, which can viewed as a stripped-down Ising model of cancer. This model is applied to model the growth of glioblastoma multiforme, the most malignant of brain cancers. This is followed by a discussion of the extension of the model to study the effect on the tumor dynamics and geometry of a mutated subpopulation. A discussion of how tumor growth is affected by chemotherapeutic treatment is then described. How angiogenesis as well as the heterogeneous and confined environment in which a tumor grows is incorporated in the CA model is discussed. The characterization of the level of organization of the invasive network around a solid tumor using spanning trees is subsequently described. Then, we describe open problems and future promising avenues for future research, including the need to develop better molecular-based models that incorporate the true heterogeneous environment over wide range of length and time scales (via imaging data), cell motility, oncogenes, tumor suppressor genes and cell-cell communication. The need to bring to bear the powerful machinery of the theory of heterogeneous media to better understand the behavior of cancer in its microenvironment is presented.Comment: 55 pages, 21 figures and 3 tables. To appear in Physical Biology. Added reference