S. Mendoza

Understanding local dwarf spheroidals and their scaling relations under MOdified Newtonian Dynamics

We use a specific form of the interpolation function in the MOND formalism, which optimally accounts for the internal structure of dwarf spheroidal (dSph) galaxies, to explore the consequences it has on the scaling relations seen in these systems. The particular form of the interpolation function we used leads to a law of gravity that does not degrade the good fit of the MOND proposal on galactic scales, and in fact, slightly improves the accordance with observations on dSph scales. This formalism yields a good description of gravitational phenomena without the need of invoking any still undetected and hypothetically dominant dark matter, in the weak field regime probed by local dSph galaxies. Isothermal equilibrium density profiles then yield projected surface density profiles for the local dSph galaxies in very good agreement with observational determinations, for values of the relevant parameters as inferred from recent observations of these Galactic satellites. The observed scaling relations for these systems are also naturally accounted for within the proposed scheme, including a previously unrecognised correlation of the inferred mass-to-light ratios of local dSphs with the ages of their stellar populations, which is natural in modified gravity schemes in the absence of dark matter. The results shed some light on the form that the MOND interpolating function may have in the most challenging regime, which occurs at moderate accelerations and intermediate mass-weighted lengths.

A natural approach to extended Newtonian gravity: tests and predictions across astrophysical scales

In the pursuit of a general formulation for a modified gravitational theory at the non-relativistic level and as an alternative to the dark matter hypothesis, we construct a model valid over a wide variety of astrophysical scales. Through the inclusion of Milgrom’s acceleration constant into a gravitational theory, we show that very general formulae can be constructed for the acceleration felt by a particle. Dimensional analysis shows that this inclusion naturally leads to the appearance of a mass-length scale in gravity, breaking its scale invariance. A particular form of the modified gravitational force is constructed and tested for consistency with observations over a wide range of astrophysical environments, from Solar system to extragalactic scales. We show that over any limited range of physical parameters, which define a specific class of astrophysical objects, the dispersion velocity of a system must be a power law of its mass and size. These powers appear linked together through a natural constraint relation of the theory. This yields a generalized gravitational equilibrium relation valid for all astrophysical systems. A general scheme for treating spherical symmetrical density distributions is presented, which in particular shows that the Fundamental Plane of elliptical galaxies, the Newtonian virial equilibrium, the Tully–Fisher and the Faber–Jackson relations, as well as the scalings observed in local dwarf spheroidal galaxies, are nothing but particular cases of that relation when applied to the appropriate mass-length scales. We discuss the implications of this approach for a modified theory of gravity and emphasize the advantages of working with the force, instead of altering Newton’s second law of motion, in the formulation of a gravitational theory.

Gravitational waves and lensing of the metric theory proposed by Sobouti

Aims. We investigate in detail two physical properties of the metric \( f(R) \) theory developed by Sobouti (2007, A&A, 464, 921). We first look for the possibility of producing gravitational waves which travel at the speed of light. We then check the possibility of producing extra bending in the lenses produced by the theory. Methods. We do this by using standard weak field approximations to the gravitational field equations that appear in Soboutis theory. Results. We show that the metric theory of gravitation proposed by Sobouti (2007) predicts the existence of gravitational waves travelling at the speed of light in vacuum. In fact, this is proved in general terms for all metric theories of gravity which can be expressed as powers of Riccis scalar. We also show that an extra additional lensing as compared to that predicted by standard general relativity is produced. Conclusions. These two points are generally considered to be of crucial importance in the development of relativistic theories of gravity that could provide an alternative description to the dark matter paradigm.

Gravitational lensing with f (χ) = χ3/2 gravity in accordance with astrophysical observations

In this article we perform a second order perturbation analysis of the gravitational metric theory of gravity f(χ) = χ 3/2 developed by Bernal et al. (2011). We show that the theory accounts in detail for two observational facts: (1) the phenomenology of flattened rotation curves associated to the Tully-Fisher relation observed in spiral galaxies, and (2) the details of observations of gravitational lensing in galaxies and groups of galaxies, without the need of any dark matter. We show how all dynamical observations on flat rotation curves and gravitational lensing can be synthesised in terms of the empirically required metric coefficients of any metric theory of gravity. We construct the corresponding metric components for the theory presented at second order in perturbation, which are shown to be perfectly compatible with the empirically derived ones. It is also shown that under the theory being presented, in order to obtain a complete full agreement with the observational results, a specific signature of Riemann’s tensor has to be chosen. This signature corresponds to the one most widely used nowadays in relativity theory. Also, a computational program, the MEXICAS (Metric EXtended-gravity Incorporated through a Computer Algebraic System) code, developed for its usage in the Computer Algebraic System (CAS) Maxima for working out perturbations on a metric theory of gravity, is presented and made publicly available.

Internal shocks in relativistic jets with time-dependent sources

We present a ballistic description of the formation and propagation of the working surface of a relativistic jet. Using simple laws of conservation of mass and linear momentum at the working surface, we obtain a full description of the working surface flow parametrized by the initial velocity and mass injection rate. This allows us to compute analytically the energy release at any time in the working surface. We compare this model with the results obtained numerically through a new hydrodynamical code applied to the propagation of a relativistic fluid in one dimension in order to test the limits of our study. Finally, we compare our analytical results with observed light curves of five long gamma ray bursts and show that our model is in very good agreement with observations using simple periodic variations of the injected velocity profiles. This simple method allows us to recover initial mass discharge and energy output ejected during the burst.

Analytic solutions to the accretion of a rotating finite cloud towards a central object - I. Newtonian approach

We construct a steady analytic accretion flow model for a finite rotating gas cloud that accretes material to a central gravitational object. The pressure gradients of the flow are considered to be negligible, and so the flow is ballistic. We also assume a steady flow and consider the particles at the boundary of the spherical cloud to be rotating as a rigid body, with a fixed amount of inwards radial velocity. This represents a generalization to the traditional infinite gas cloud model described by Ulrich. We show that the streamlines and density profiles obtained deviate largely from the ones calculated by Ulrich. The extra freedom in the choice of the parameters on the model can naturally account for the study of protostars formed in dense clusters by triggered mechanisms, where a wide variety of external physical mechanisms determine the boundary conditions. Also, as expected, the model predicts the formation of an equatorial accretion disc about the central object with a radius different from the one calculated by Ulrich.

Formation of internal shock waves in bent jets

We discuss the circumstances under which the bending of a jet can generate an internal shock wave. The analysis is carried out for relativistic and non-relativistic astrophysical jets. The calculations are carried out byusing the method of characteristics for the case of steady simple waves. This generalizes the non-relativistic treatment first used by Icke in 1991. We show that it is possible to obtain an upper limit to the bending angle of a jet in order not to create a shock wave at the end of the curvature. This limiting angle has a value of ∼75° for non-relativistic jets with a polytropic index K = 4/3, ∼135° for non-relativistic jets with κ=5/3 and ∼50° for relativistic jets with κ=5/3. We also discuss under which circumstances jets will form internal shock waves for smaller deflection angles.

Analytic solutions to the accretion of a rotating finite cloud towards a central object – II. Schwarzschild space–time

We construct a general relativistic model for the accretion flow of a rotating finite cloud of non-interacting particles infalling on to a Schwarzschild black hole. The streamlines start at a spherical shell, where boundary conditions are fixed with wide flexibility, and are followed down to the point at which they either cross the black hole horizon or become incorporated into an equatorial thin disc. Analytic expressions for the streamlines and the velocity field are given, in terms of Jacobi elliptic functions, under the assumptions of stationarity and ballistic motion. A novel approach allows us to describe all of the possible types of orbit with a single formula. A simple numerical scheme is presented for calculating the density field. This model is the relativistic generalization of the Newtonian one developed by Mendoza, Tejeda & Nagel, and, due to its analytic nature, it can be useful in providing a benchmark for general relativistic hydrodynamical codes and for exploring the parameter space in applications involving accretion on to black holes when the approximations of steady state and ballistic motion are reasonable ones.

A hydrodynamical model for the FERMI-LAT -ray light curve of Blazar PKS 1510-089

ABSTRACT A physical description of the formation and propagation of working surfaces insidethe relativistic jet of the Blazar PKS 1510-089 are used to model its γ-ray variabilitylight curve using FERMI-LAT data from 2008 to 2012. The physical model is basedon conservation laws of mass and momentum at the working surface as explainedby Mendoza et al. (2009). The hydrodynamical description of a working surface isparametrised by the initial velocity and mass injection rate at the base of the jet. Weshow that periodic variations on the injected velocity profiles are able to account forthe observed luminosity, fixing model parameters such as mass ejection rates of thecentral engine injected at the base of the jet, oscillation frequencies of the flow andmaximum Lorentz factors of the bulk flow during a particular burst.Keywords: Blazars– PKS 1510-089– Relativistic Jets – Relativistic Hydrodynamics 1 INTRODUCTIONAmong all types of AGN, Blazars (Blazar class is defined asradio loud sources conformed by the BL Lac objects and theFlat Spectrum Radio Quasars -FSRQ, see e.g. Fossati et al.1997; Ghisellini et al. 1998, and references therein) repre-sent the most energetic class. They are known to have themost powerful jets (e.g. Lister et al. 2009) and also showa highly variable Spectral Energy Distribution (SED) fromthe radio to the γ-rays wavelengths (see Abdo et al. 2010b;D’Ammando et al. 2011, and references therein).The FSRQ PKS 1510-089 is known to be one ofthe most powerful astrophysical objects with a highlycollimated relativistic jet that has shown apparent superlu-minal velocities between 20c to 46c and with a semi-angleaperture for the jet ∼ 0.2

The Connection Between Entropy and the Absorption Spectra of Schwarzschild Black Holes for Light and Massless Scalar Fields

We present heuristic arguments suggesting that if EM waves with wavelengths somewhat larger than the Schwarzschild radius of a black hole were fully absorbed by it, the second law of thermodynamics would be violated, under the Bekenstein interpretation of the area of a black hole as a measure of its entropy. Thus, entropy considerations make the well known fact that large wavelengths are only marginally absorbed by black holes, a natural consequence of thermodynamics. We also study numerically the ingoing radial propagation of a scalar field wave in a Schwarzschild metric, relaxing the standard assumption which leads to the eikonal equation, that the wave has zero spatial extent. We find that if these waves have wavelengths larger that the Schwarzschild radius, they are very substantially reflected, fully to numerical accuracy. Interestingly, this critical wavelength approximately coincides with the one derived from entropy considerations of the EM field, and is consistent with well known limit results of scattering in the Schwarzschild metric. The propagation speed is also calculated and seen to differ from the value c, for wavelengths larger than Rs, in the vicinity of Rs. As in all classical wave phenomena, whenever the wavelength is larger or comparable to the physical size of elements in the system, in this case changes in the metric, the zero extent ’particle’ description fails, and the wave nature becomes apparent.