On gravitational fields of stars in f(R) gravity theories

Einstein's general relativity is a classical theory of gravitation: it is a postulate on the coupling between the four-dimensional, continuos spacetime and the matter fields in the universe, and it yields their dynamical evolution. It is believed that general relativity must be replaced by a quantum theory of gravity at least at extremely high energies of the early universe and at regions of strong curvature of spacetime, cf. black holes. Various attempts to quantize gravity, including conceptually new models such as string theory, have suggested that modification to general relativity might show up even at lower energy scales. On the other hand, also the late time acceleration of the expansion of the universe, known as the dark energy problem, might originate from new gravitational physics. Thus, although there has been no direct experimental evidence contradicting general relativity so far - on the contrary, it has passed a variety of observational tests - it is a question worth asking, why should the effective theory of gravity be of the exact form of general relativity? If general relativity is modified, how do the predictions of the theory change? Furthermore, how far can we go with the changes before we are face with contradictions with the experiments? Along with the changes, could there be new phenomena, which we could measure to find hints of the form of the quantum theory of gravity? This thesis is on a class of modified gravity theories called f(R) models, and in particular on the effects of changing the theory of gravity on stellar solutions. It is discussed how experimental constraints from the measurements in the Solar System restrict the form of f(R) theories. Moreover, it is shown that models, which do not differ from general relativity at the weak field scale of the Solar System, can produce very different predictions for dense stars like neutron stars. Due to the nature of f(R) models, the role of independent connection of the spacetime is emphasized throughout the thesis.

Hot gaseous coronae of early-type galaxies and their radio luminosity function

Recent X-ray observations have revealed that early-type galaxies (which usually produce extended double radio sources) generally have hot gaseous haloes extending up to approx102kpc1,2. Moreover, much of the cosmic X-ray background radiation is probably due to a hotter, but extremely tenuous, intergalactic medium (IGM)3. We have presented4–7 an analytical model for the propagation of relativistic beams from galactic nuclei, in which the beams' crossing of the pressure-matched interface between the IGM and the gaseous halo, plays an important role. The hotspots at the ends of the beams fade quickly when their advance becomes subsonic with respect to the IGM. This model has successfully predicted (for typical double radio sources) the observed8 current mean linear-size (approx2Dsime350 kpc)4,5, the observed8–11 decrease in linear-size with cosmological redshift4–6 and the slope of the linear-size versus radio luminosity10,12–14 relation6. We have also been able to predict the redshift-dependence of observed numbers and radio luminosities of giant radio galaxies7,15. Here, we extend this model to include the propagation of somewhat weaker beams. We show that the observed flattening of the local radio luminosity function (LRLF)16–20 for radio luminosity Papproximately 1024 W Hz-1 at 1 GHz can be explained without invoking ad hoc a corresponding break in the beam power function Phi(Lb), because the heads of the beams with Lb < 1025 W Hz-1 are decelerated to sonic velocity within the halo itself, which leads to a rapid decay of radio luminosity and a reduced contribution of these intrinsically weaker sources to the observed LRLF.

3D MHD simulations of subsurface convection in OB stars

During their main sequence evolution, massive stars can develop convective regions very close to their surface. These regions are caused by an opacity peak associated with iron ionization. Cantiello et al. (2009) found a possible connection between the presence of sub-photospheric convective motions and small scale stochastic velocities in the photosphere of early-type stars. This supports a physical mechanism where microturbulence is caused by waves that are triggered by subsurface convection zones. They further suggest that clumping in the inner parts of the winds of OB stars could be related to subsurface convection, and that the convective layers may also be responsible for stochastic excitation of non-radial pulsations. Furthermore, magnetic fields produced in the iron convection zone could appear at the surface of such massive stars. Therefore subsurface convection could be responsible for the occurrence of observable phenomena such as line profile variability and discrete absorption components. These phenomena have been observed for decades, but still evade a clear theoretical explanation. Here we present preliminary results from 3D MHD simulations of such subsurface convection.

Swing amplification of nonaxisymmetric perturbations in stars and gas in a sheared galactic disk

We present a study of the growth of local, nonaxisymmetric perturbations in gravitationally coupled stars and gas in a differentially rotating galactic disk. The stars and gas are treated as two isothermal fluids of different velocity dispersions, with the stellar velocity dispersion being greater than that for the gas. We examine the physical effects of inclusion of a low-velocity dispersion component (gas) on the growth of non-axisymmetric perturbations in both stars and gas, as done for the axisymmetric case by Jog & Solomon. The amplified perturbations in stars and gas constitute trailing, material, spiral features which may be identified with the local spiral features seen in all spiral galaxies. The formulation of the two-fluid equations closely follows the one-fluid treatment by Goldreich & Lynden-Bell. The local, linearized perturbation equations in the sheared frame are solved to obtain the results for a temporary growth via swing amplification. The problem is formulated in terms of five dimensionless parameters-namely, the Q-factors for stars and gas, respectively; the gas mass fraction; the shearing rate in the galactic disk; and the length scale of perturbation. By using the observed values of these parameters, we obtain the amplifications and the pitch angles for features in stars and gas for dynamically distinct cases, as applicable for different regions of spiral galaxies. A real galaxy consisting of stars and gas may display growth of nonaxisymmetric perturbations even when it is stable against axisymmetric perturbations and/or when either fluid by itself is stable against non-axisymmetric perturbations. Due to its lower velocity dispersion, the gas exhibits a higher amplification than do the stars, and the amplified gas features are slightly more tightly wound than the stellar features. When the gas contribution is high, the stellar amplification and the range of pitch angles over which it can occur are both increased, due to the gravitational coupling between the two fluids. Thus, the two-fluid scheme can explain the origin of the broad spiral arms in the underlying old stellar populations of galaxies, as observed by Schweizer and Elmegreen & Elmegreen. The arms are predicted to be broader in gas-rich galaxies, as is indeed seen for example in M33. In the linear regime studied here, the arm contrast is shown to increase with radius in the inner Galaxy, in agreement with observations of external galaxies by Schweizer. These results follow directly due to the inclusion of gas in the problem.

Temperature profiles of accretion discs around rapidly rotating strange stars in general relativity: A comparison with neutron stars

We compute the temperature profiles of accretion discs around rapidly rotating strange stars, using constant gravitational mass equilibrium sequences of these objects, considering the full effect of general relativity. Beyond a certain critical value of stellar angular momentum (J), we observe the radius ( $r_{\rm orb}$) of the innermost stable circular orbit (ISCO) to increase with J (a property seen neither in rotating black holes nor in rotating neutron stars). The reason for this is traced to the crucial dependence of ${\rm d}r_{\rm orb}/{\rm d}J$ on the rate of change of the radial gradient of the Keplerian angular velocity at $r_{\rm orb}$ with respect to J. The structure parameters and temperature profiles obtained are compared with those of neutron stars, as an attempt to provide signatures for distinguishing between the two. We show that when the full gamut of strange star equation of state models, with varying degrees of stiffness are considered, there exists a substantial overlap in properties of both neutron stars and strange stars. However, applying accretion disc model constraints to rule out stiff strange star equation of state models, we notice that neutron stars and strange stars exclusively occupy certain parameter spaces. This result implies the possibility of distinguishing these objects from each other by sensitive observations through future X-ray detectors.

A DYNAMO MODEL OF MAGNETIC ACTIVITY IN SOLAR-LIKE STARS WITH DIFFERENT ROTATIONAL VELOCITIES

We attempt to provide a quantitative theoretical explanation for the observations that Ca II H/K emission and X-ray emission from solar-like stars increase with decreasing Rossby number (i.e., with faster rotation). Assuming that these emissions are caused by magnetic cycles similar to the sunspot cycle, we construct flux transport dynamo models of 1M(circle dot) stars rotating with different rotation periods. We first compute the differential rotation and the meridional circulation inside these stars from a mean-field hydrodynamics model. Then these are substituted in our dynamo code to produce periodic solutions. We find that the dimensionless amplitude f(m) of the toroidal flux through the star increases with decreasing rotation period. The observational data can be matched if we assume the emissions to go as the power 3-4 of f(m). Assuming that the Babcock-Leighton mechanism saturates with increasing rotation, we can provide an explanation for the observed saturation of emission at low Rossby numbers. The main failure of our model is that it predicts an increase of the magnetic cycle period with increasing rotation rate, which is the opposite of what is found observationally. Much of our calculations are based on the assumption that the magnetic buoyancy makes the magnetic flux tubes rise radially from the bottom of the convection zone. Taking into account the fact that the Coriolis force diverts the magnetic flux tubes to rise parallel to the rotation axis in rapidly rotating stars, the results do not change qualitatively.

Black holes in the early universe, in compact binaries, and as energy sources inside solar-type stars

This thesis consists of three separate studies of roles that black holes might play in our universe.

In the first part we formulate a statistical method for inferring the cosmological parameters of our universe from LIGO/VIRGO measurements of the gravitational waves produced by coalescing black-hole/neutron-star binaries. This method is based on the cosmological distance-redshift relation, with "luminosity distances" determined directly, and redshifts indirectly, from the gravitational waveforms. Using the current estimates of binary coalescence rates and projected "advanced" LIGO noise spectra, we conclude that by our method the Hubble constant should be measurable to within an error of a few percent. The errors for the mean density of the universe and the cosmological constant will depend strongly on the size of the universe, varying from about 10% for a "small" universe up to and beyond 100% for a "large" universe. We further study the effects of random gravitational lensing and find that it may strongly impair the determination of the cosmological constant.

In the second part of this thesis we disprove a conjecture that black holes cannot form in an early, inflationary era of our universe, because of a quantum-field-theory induced instability of the black-hole horizon. This instability was supposed to arise from the difference in temperatures of any black-hole horizon and the inflationary cosmological horizon; it was thought that this temperature difference would make every quantum state that is regular at the cosmological horizon be singular at the black-hole horizon. We disprove this conjecture by explicitly constructing a quantum vacuum state that is everywhere regular for a massless scalar field. We further show that this quantum state has all the nice thermal properties that one has come to expect of "good" vacuum states, both at the black-hole horizon and at the cosmological horizon.

In the third part of the thesis we study the evolution and implications of a hypothetical primordial black hole that might have found its way into the center of the Sun or any other solar-type star. As a foundation for our analysis, we generalize the mixing-length theory of convection to an optically thick, spherically symmetric accretion flow (and find in passing that the radial stretching of the inflowing fluid elements leads to a modification of the standard Schwarzschild criterion for convection). When the accretion is that of solar matter onto the primordial hole, the rotation of the Sun causes centrifugal hangup of the inflow near the hole, resulting in an "accretion torus" which produces an enhanced outflow of heat. We find, however, that the turbulent viscosity, which accompanies the convective transport of this heat, extracts angular momentum from the inflowing gas, thereby buffering the torus into a lower luminosity than one might have expected. As a result, the solar surface will not be influenced noticeably by the torus's luminosity until at most three days before the Sun is finally devoured by the black hole. As a simple consequence, accretion onto a black hole inside the Sun cannot be an answer to the solar neutrino puzzle.

Dynamical stability of nascent neutron stars

This thesis presents a study of the dynamical stability of nascent neutron stars resulting from the accretion induced collapse of rapidly rotating white dwarfs.

Chapter 2 and part of Chapter 3 study the equilibrium models for these neutron stars. They are constructed by assuming that the neutron stars have the same masses, angular momenta, and specific angular momentum distributions as the pre-collapse white dwarfs. If the pre-collapse white dwarf is rapidly rotating, the collapsed object will contain a high density central core of size about 20 km, surrounded by a massive accretion torus extending to hundreds of kilometers from the rotation axis. The ratio of the rotational kinetic energy to gravitational binding energy, β, of these neutron stars is all found to be less than 0.27.

Chapter 3 studies the dynamical stability of these neutron stars by numerically evolving the linearized hydrodynamical equations. A dynamical bar-mode instability is observed when the β of the star is greater than the critical value β_d ≈ 0.25. It is expected that the unstable mode will persist until a substantial amount of angular momentum is carried away by gravitational radiation. The detectability of these sources is studied and it is estimated that LIGO II is unlikely to detect them unless the event rate is greater than 10^-6/year/galaxy.

All the calculations on the structure and stability of the neutron stars in Chapters 2 and 3 are carried out using Newtonian hydrodynamics and gravity. Chapter 4 studies the relativistic effects on the structure of these neutron stars. New techniques are developed and used to construct neutron star models to the first post-Newtonian (1PN) order. The structures of the 1PN models are qualitatively similar to the corresponding Newtonian models, but the values of β are somewhat smaller. The maximum β for these 1PN neutron stars is found to be 0.24, which is 8% smaller than the Newtonian result (0.26). However, relativistic effects will also change the critical value β_d. A detailed post-Newtonian stability analysis has yet to be carried out to study the relativistic effects on the dynamical stability of these neutron stars.

New Insights from Aperiodic Variability of Young Stars

Nearly all young stars are variable, with the variability traditionally divided into two classes: periodic variables and aperiodic or "irregular" variables. Periodic variables have been studied extensively, typically using periodograms, while aperiodic variables have received much less attention due to a lack of standard statistical tools. However, aperiodic variability can serve as a powerful probe of young star accretion physics and inner circumstellar disk structure. For my dissertation, I analyzed data from a large-scale, long-term survey of the nearby North America Nebula complex, using Palomar Transient Factory photometric time series collected on a nightly or every few night cadence over several years. This survey is the most thorough exploration of variability in a sample of thousands of young stars over time baselines of days to years, revealing a rich array of lightcurve shapes, amplitudes, and timescales.

I have constrained the timescale distribution of all young variables, periodic and aperiodic, on timescales from less than a day to ~100 days. I have shown that the distribution of timescales for aperiodic variables peaks at a few days, with relatively few (~15%) sources dominated by variability on tens of days or longer. My constraints on aperiodic timescale distributions are based on two new tools, magnitude- vs. time-difference (Δm-Δt) plots and peak-finding plots, for describing aperiodic lightcurves; this thesis provides simulations of their performance and presents recommendations on how to apply them to aperiodic signals in other time series data sets. In addition, I have measured the error introduced into colors or SEDs from combining photometry of variable sources taken at different epochs. These are the first quantitative results to be presented on the distributions in amplitude and time scale for young aperiodic variables, particularly those varying on timescales of weeks to months.

Quakes in solid quark stars

A starquake mechanism for pulsar glitches is developed in the solid quark star model. It is found that the general glitch natures (i.e., the glitch amplitudes and the time intervals) could be reproduced if solid quark matter, with high baryon density but low temperature, has properties of shear modulus mu(c) = 10(30-34) erg/cm(3) and critical stress sigma(c) = 10(18similar to24) erg/cm(3). The post-glitch behavior may represent a kind of damped oscillations. (C) 2004 Elsevier B.V. All rights reserved.