A New Window on Primordial non-Gaussianity

We know very little about primordial curvature perturbations on scales smaller than about a Mpc. Measurements of the mu-type distortion of the CMB spectrum provide the unique opportunity to probe these scales over the unexplored range from 50 to 10^4 Mpc^-1. This is a very clean probe, in that it relies only on well-understood linear evolution. We point out that correlations between mu-distortion and temperature anisotropies can be used to test Gaussianity at these very small scales. In particular the mu-T cross correlation is proportional to the very squeezed limit of the primordial bispectrum and hence measures fNL^loc, while mu-mu is proportional to the primordial trispectrum and measures tauNL. We present a Fisher matrix forecast of the observational constraints.Comment: 5 pages, one figure. v2: added clarifying comments and references, fixed typo

Modifications to the Cosmic 21-cm Background Frequency Spectrum by Scattering via electrons in Galaxy Clusters

The cosmic 21-cm background frequency spectrum related to the spin-flip transition of neutral Hydrogen present during and before the era of reionization is rich in features associated with physical processes that govern transitions between the two spin states. The intervening electrons in foreground galaxy clusters inversely Compton scatter the 21-cm background spectrum and modify it just as the cosmic microwave background (CMB) spectrum is modified by inverse-Compton scattering. Towards typical galaxy clusters at low redshifts, the resulting modification is a few tenths milli-Kelvin correction to the few tens milli-Kelvin temperature of 21-cm signal relative to that of the cosmic microwave background black body spectrum. The modifications are mostly associated with sharp changes in the cosmic 21-cm background spectrum such as due to the onset of a Lyman-$\alpha$ radiation field or heating of neutral gas. Though low frequency radio interferometers that are now planned for 21-cm anisotropy measurements are insensitive to the mean 21-cm spectrum, differential observations of galaxy clusters with these interferometers can be utilized to indirectly establish global features in the 21-cm frequency spectrum. We discuss the feasibility to detect the spectrum modified by clusters and find that for upcoming interferometers, while a detection towards an individual cluster is challenging, one can average signals over a number of clusters, selected based on the strength of the Sunyave-Zel'dovich effect at high radio frequencies involving CMB scattering alone, to establish the mean 21-cm spectrum.Comment: 6 pages, 3 figures, PRD in press; expanded and title changed from v1. Final version in pres

Nonlinear self-adjointness and conservation laws

The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the strict self-adjointness and quasi self-adjointness introduced earlier by the author. It is shown that the equations possessing the nonlinear self-adjointness can be written equivalently in a strictly self-adjoint form by using appropriate multipliers. All linear equations possess the property of nonlinear self-adjointness, and hence can be rewritten in a nonlinear strictly self-adjoint. For example, the heat equation $u_t - \Delta u = 0$ becomes strictly self-adjoint after multiplying by $u^{-1}.$ Conservation laws associated with symmetries can be constructed for all differential equations and systems having the property of nonlinear self-adjointness

Inverse Compton scattering in mildly relativistic plasma

We investigated the effect of inverse Compton scattering in mildly relativistic static and moving plasmas with low optical depth using Monte Carlo simulations, and calculated the Sunyaev-Zel'dovich effect in the cosmic background radiation. Our semi-analytic method is based on a separation of photon diffusion in frequency and real space. We use Monte Carlo simulation to derive the intensity and frequency of the scattered photons for a monochromatic incoming radiation. The outgoing spectrum is determined by integrating over the spectrum of the incoming radiation using the intensity to determine the correct weight. This method makes it possible to study the emerging radiation as a function of frequency and direction. As a first application we have studied the effects of finite optical depth and gas infall on the Sunyaev-Zel'dovich effect (not possible with the extended Kompaneets equation) and discuss the parameter range in which the Boltzmann equation and its expansions can be used. For high temperature clusters ($k_B T_e \gtrsim 15$ keV) relativistic corrections based on a fifth order expansion of the extended Kompaneets equation seriously underestimate the Sunyaev-Zel'dovich effect at high frequencies. The contribution from plasma infall is less important for reasonable velocities. We give a convenient analytical expression for the dependence of the cross-over frequency on temperature, optical depth, and gas infall speed. Optical depth effects are often more important than relativistic corrections, and should be taken into account for high-precision work, but are smaller than the typical kinematic effect from cluster radial velocities.Comment: LateX, 30 pages and 11 figures. Accepted for publication in the Astrophysical Journa

On the Energy Required to Eject Processed Matter from Galaxies

We evaluate the minimum energy input rate that starbursts require for expelling their newly processed matter from their host galaxies. Special attention is given to the pressure caused by the environment in which a galaxy is situated, as well as to the intrinsic rotation of the gaseous component. We account for these factors and for a massive dark matter distribution, and develop a self-consistent solution for the interstellar matter gas distribution. Our results are in excellent agreement with the results of Mac Low & Ferrara (1999) for galaxies with a flattened disk-like ISM density distribution and a low intergalactic gas pressure ($P_{IGM}/k$ $\leq$ 1 cm$^{-3}$ K). However, our solution also requires a much larger energy input rate threshold when one takes into consideration both a larger intergalactic pressure and the possible existence of a low-density, non-rotating, extended gaseous halo component.Comment: 7 pages, 4 figures, 1 table, Accepted for publication in Ap

Supernova Remnant in a Stratified Medium: Explicit, Analytical Approximations for Adiabatic Expansion and Radiative Cooling

We propose simple, explicit, analytical approximations for the kinematics of an adiabatic blast wave propagating in an exponentially stratified ambient medium, and for the onset of radiative cooling, which ends the adiabatic era. Our method, based on the Kompaneets implicit solution and the Kahn approximation for the radiative cooling coefficient, gives straightforward estimates for the size, expansion velocity, and progression of cooling times over the surface, when applied to supernova remnants (SNRs). The remnant shape is remarkably close to spherical for moderate density gradients, but even a small gradient in ambient density causes the cooling time to vary substantially over the remnant's surface, so that for a considerable period there will be a cold dense expanding shell covering only a part of the remnant. Our approximation provides an effective tool for identifying the approximate parameters when planning 2-dimensional numerical models of SNRs, the example of W44 being given in a subsequent paper.Comment: ApJ accepted, 11 pages, 2 figures embedded, aas style with ecmatex.sty and lscape.sty package

Analytical Study on the Sunyaev-Zeldovich Effect for Clusters of Galaxies. II. comparison of covariant formalisms

We study a covariant formalism for the Sunyaev-Zeldovich effects developed in the previous papers by the present authors, and derive analytic expressions for the redistribution functions in the Thomson approximation. We also explore another covariant formalism recently developed by Poutanen and Vurm. We show that the two formalisms are mathematically equivalent in the Thomson approximation which is fully valid for the cosmic microwave background photon energies. The present finding will establish a theoretical foundation for the analysis of the Sunyaev-Zeldovich effects for the clusters of galaxies.Comment: Accepted version, 7 pages, 1 figure, accepted by Physical Review D for publicatio

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

Primordial magnetic field and spectral distortion of cosmic background radiation

The role played by a primordial magnetic field during the pre-recombination epoch is analysed through the cyclotron radiation (due to the free electrons) it might produce in the primordial plasma. We discuss the constraint implied by the measurement or lack thereof COBE on this primordial field.Comment: to appear in International Journal of Mod. Phy