arXiv subjects

A. Sandoval-Villalbazo

Publications and source records attributed to A. Sandoval-Villalbazo.

50 records · Page 3Linked to original sources

arXiv2006

Hyperbolic heat equation in Kaluza's magnetohydrodynamics

This paper shows that a hyperbolic equation for heat conduction can be obtained directly using the tenets of linear irreversible thermodynamics in the context of the five dimensional space-time metric originally proposed by T. Kaluza back in 1922. The associated speed of propagation is slightly lower than the speed of light by a factor inversely proportional to the specific charge of the fluid element. Moreover, consistency with the second law of thermodynamics is achieved. Possible implications in the context of physics of clusters of galaxies of this result are briefly discussed.

gr-qc↗

arXiv2005

Light scattering test regarding the relativistic nature of heat

The dynamic structure factor of a simple relativistic fluid is calculated. The coupling of acceleration with the heat flux present in Eckart's version of irreversible relativistic thermodynamics is examined using the Rayleigh-Brillouin spectrum of the fluid. A modification of the width of the Rayleigh peak associated to Eckart's picture of the relativistic nature of heat is predicted and estimated.

gr-qc↗

arXiv2005

Relativistic non-equilibrium thermodynamics revisited

Relativistic irreversible thermodynamics is reformulated following the conventional approach proposed by Meixner in the non-relativistic case. Clear separation between mechanical and non-mechanical energy fluxes is made. The resulting equations for the entropy production and the local internal energy have the same structure as the non-relativistic ones. Assuming linear constitutive laws, it is shown that consistency is obtained both with the laws of thermodynamics and causality.

gr-qc↗

arXiv2004

Hypercubes circumscribed in hyperspheres: a constant growth ratio for volumes at large dimensions

This note shows that an interesting property arises when considering the relation between the hypersphere volumes at dimensions $n+1$ and $n$, if the hyperspheres circumscribe unitary hypercubes in $n+1$ and $n$ dimensions, respectively . In the limit of large $n$, the ratio $\frac{V_{n+1}}{V_{n}}$ is constant and equal to the irrational number $\sqrt{\frac{πe}{2}}$. Some consequences of this result are explored.

math.MG↗

arXiv2004

The statistical nature of the second order corrections to the thermal SZE

This paper shows that the accepted expressions for the second order corrections in the parameter $z$ to the thermal Sunyaev-Zel'dovich effect can be accurately reproduced by a simple convolution integral approach. This representation allows to separate the second order SZE corrections into two type of components. One associated to a single line broadening, directly related to the even derivative terms present in the distortion intensity curve, while the other is related to a frequency shift, which is in turn related to the first derivative term.

astro-ph↗

arXiv2004

A simple model for hydromagnetic instabilities in the presence of a constant magnetic field

In this paper we study a simple model consisting of a dilute fully ionized plasma in the presence of the gravitational and a constant magnetic field to analyze the propagation of hydromagnetic instabilities. In particular we show that the so called Jeans instability is in principle affected by the presence of the magnetic field. A brief discussion is made attempting to assess this influence in the stage of the evolution of the Universe where structures were formed. The most logical conclusion is that if magnetic fields existed in those times their magnitudes were too small to modify Jeans' mass. Our results places limits of the possible values of seed magnetic fields consistent with the formation structures in the Universe. These values are within the range of the results obtained by other authors.

astro-ph↗

arXiv2004

Jeans instability in the linearized Burnett regime

Jeans instability is derived for the case of a low density self-gravitating gas beyond the Navier-Stokes equations. The Jeans instability criterium is shown to depend on a Burnett coefficient if the formalism is taken up to fourth order in the wave number. It is also shown that previously known viscosity corrections to the Jeans wave-number are enhanced if the full fourth order formalism is applied to the stability analysis.

astro-ph↗

arXiv2004

On a parity property in the thermal Sunyaev-Zel'dovich effect

The main issue in this paper is to discuss a parity property that appears in the expressions for the distorted spectrum of the thermal Sunyaev-Zel'dovich effect. When using the convolution integrals method involving scattering laws we argue that the distorted spectrum contains a new term, which is an odd power of the frequency. Such a term, absent in the conventional approaches, implies a crossover frequency which differs in value form the ones reported in the literature by a significant, in principle observable, amount. Also, such term casts doubt on the demanding need of computing complicated relativistic calculations. The relationship of our approach with the existing calculations is discussed.

astro-ph↗

arXiv2003

The thermal and kinematic Sunyaev-Zel'dovich effects revisited

This paper shows that a simple convolution integral expression based on the mean value of the isotropic frequency distribution corresponding to photon scattering off electrons leads to useful analytical expressions describing the thermal Sunyaev-Zel'dovich effect. The approach, to first order in the Compton parameter is able to reproduce the Kompaneets equation describing the effect. Second order effects in the parameter $z=\frac{kT_{e}}{mc^{2}}$ induce a slight increase in the crossover frequency.

astro-ph↗

arXiv2003

Note on the Sunyaev-Zel'dovich thermal effect

In a previous publication we have derived an expression for the full distorted spectrum arising when the photons of the cosmic background radiation are absorbed and emitted by an optically thin gas. The expression simply adds up the effects of the joint probability that an electron absorbs an incoming photon of frequency}$\barν${\small and emits it with a frequency}$ν${\small . We here show that such an expression is identical to the Kompaneets equation describing the thermal Sunyaev-Zel'dovich effect. This clearly shows that the two pictures, diffusion and absorption-emission are mathematically equivalent to first order in the Compton parameter. Other consequences of this result are also discussed.

astro-ph↗

arXiv2003

Hydrodynamic time correlation functions in the presence of a gravitational field

This paper shows that the ordinary Brillouin spectrum peaks associated to scattered radiation off acoustic modes in a fluid suffer a shift in their values due to gravitational effects. The approach is based in the ordinary linearized Navier-Stokes equations for a fluid coupled to a Newtonian gravitational potential. The formalism leads to a dispersion relation that contains both gravitational and dissipative effects. It is also shown that the Brillouin peaks tend to condense into a single peak when the fluid modes approach the critical Jeans wave number.

astro-ph↗

arXiv2003

A convolution integral representation of the thermal Sunyaev-Zel'dovich effect

Analytical expressions for the non-relativistic and relativistic Sunyaev-Zel'dovich effect (SZE) are derived by means of suitable convolution integrals. The establishment of these expressions is based on the fact that the SZE disturbed spectrum, at high frequencies, possesses the form of a Laplace transform of the single line distortion profile (structure factor). Implications of this description of the SZE related to light scattering in optically thin plasmas are discussed.

astro-ph↗

arXiv2002

Cosmological bulk viscosity, the Burnett regime, and the BGK equation

Einstein's field equations in FRW space-times are coupled to the BGK equation in order to derive the stress energy tensor including dissipative effects up to second order in the thermodynamical forces. The space-time is assumed to be matter-dominated, but in a low density regime for which a second order (Burnett) coefficient becomes relevant. Cosmological implications of the solutions, as well as the physical meaning of transport coefficients in an isotropic homogeneous universe are discussed.

gr-qc↗

arXiv2002

The Sunyaev-Zel'dovich effect revisited

The well known Sunyaev-Zel'dovich (SZ) effect is reexamined using a Doppler shift type mechanism arising from the scattering of photons by electrons in an optically thin gas. The results are in excellent agreement with the observational data as well as with the results obtained using the diffusive pictures. A comparison of the results here obtained with other approaches is thoroughly discussed, as well as some important extensions of this method to other aspects of the SZ effect

astro-ph↗