The limiting mass of cold white dwarfs was first calculated by E. Stoner in an approximate model of a uniform star and was soon reduced by ~20% in papers by S. Chandrasekhar and L. D. Landau based on an exact solution of the equations for the stellar equilibrium. Here we examine uniform models of white dwarfs taking general relativity effects and the influence of finite temperature into account. Solutions are obtained in the form of finite analytic formulas and, for masses differing by no more than ~20% from the exact solutions, found by numerical integration of the differential equations for the stellar equilibrium.
We present the first set of constant rest-mass ultra-massive oxygen/neon white dwarf cooling tracks with masses larger than 1.29 Msun which fully take into account the effects of general relativity on their structural and evolutionary properties. We have computed the full evolution sequences of 1.29, 1.31, 1.33, 1.35, and 1.369 Msun white dwarfs with the La Plata stellar evolution code, LPCODE. For this work, the standard equations of stellar structure and evolution have been modified to include the full effects of general relativity. For comparison purposes, the same sequences have been compu…
In [1], the thermal equilibrium of static, spherically symmetric perfect fluids in General Relativity was studied. I would like to elaborate three points relevant to the results of [1]. The first point is only a clarification, summarized in theorem 1 below, of results that appear in [1]. The following two points correct the error in [1], stating that the condition for thermodynamic stability, found in [1], is referring to the microcanonical ensemble, while it was referring to the canonical one. In theorems 2 and 3, specific cases for which equivalence of dynamical and thermodynamic stability h…
Recently, several white dwarfs have been proposed with masses significantly above the Chandrasekhar limit, known as Super-Chandrasekhar White Dwarfs, to account for the overluminous Type Ia supernovae. In the present work, Equation of State of a completely degenerate relativistic electron gas in magnetic field based on Landau quantization of charged particles in a magnetic field is developed. The mass-radius relations for magnetized White Dwarfs are obtained by solving the Tolman-Oppenheimer-Volkoff equations. The effects of the magnetic energy density and pressure contributed by a density-dep…
Due to the highly degeneracy of electrons in white dwarf stars, we expect that the relativistic effects play very important role in these stars. In the present article, we study the properties of the condensed matter in white dwarfs using Newtonian and relativistic polytropic fluid sphere. Two polytropic indices (namely n=3 and n=1.5) are proposed to investigate the physical characteristics of the models. We solve the Lane-Emden equations numerically.. The results show that the relativistic effect is small in white dwarf stars.
Our knowledge of white dwarf planetary systems predominately arises from the region within a few Solar radii of the white dwarfs, where minor planets break up, form rings and discs, and accrete onto the star. The entry location, angle and speed into this Roche sphere has rarely been explored but crucially determines the initial geometry of the debris, accretion rates onto the photosphere, and ultimately the composition of the minor planet. Here we evolve a total of over 10^5 asteroids with single-planet N-body simulations across the giant branch and white dwarf stellar evolution phases to quan…
Over the last couple of decades, there are direct and indirect evidences for massive compact objects than their conventional counterparts. A couple of such examples are super-Chandrasekhar white dwarfs and massive neutron stars. The observations of more than a dozen peculiar over-luminous type Ia supernovae predict their origins from super-Chandrasekhar white dwarf progenitors. On the other hand, recent gravitational wave detection and some pulsar observations argue for massive neutron stars, lying in the famous mass-gap between lowest astrophysical black hole and conventional highest neutron …
It has been hypothesized that advanced technological civilizations will construct giant space colonies and supporting infrastructures to orbit about their home stars. With data from recent satellites that operate at infrared and optical wavelengths (Spitzer, WISE, TESS, Kepler), in company with a few modest assumptions, it is now possible to begin to constrain observationally the frequency of such space-based civilizations in our Milky Way Galaxy.
White dwarf-neutron star binaries generate detectable gravitational radiation. We construct Newtonian equilibrium models of corotational white dwarf-neutron star (WDNS) binaries in circular orbit and find that these models terminate at the Roche limit. At this point the binary will undergo either stable mass transfer (SMT) and evolve on a secular time scale, or unstable mass transfer (UMT), which results in the tidal disruption of the WD. The path a given binary will follow depends primarily on its mass ratio. We analyze the fate of known WDNS binaries and use population synthesis results to e…
The recent formulation of the relativistic Thomas-Fermi model within the Feynman-Metropolis-Teller theory for compressed atoms is applied to the study of general relativistic white dwarf equilibrium configurations. The equation of state, which takes into account the β-equilibrium, the nuclear and the Coulomb interactions between the nuclei and the surrounding electrons, is obtained as a function of the compression by considering each atom constrained in a Wigner-Seitz cell. The contribution of quantum statistics, weak, nuclear, and electromagnetic interactions is obtained by the determination …
Here we extend the exploration of significantly super-Chandrasekhar magnetised white dwarfs by numerically computing axisymmetric stationary equilibria of differentially rotating magnetised polytropic compact stars in general relativity (GR), within the ideal magnetohydrodynamic regime. We use a general relativistic magnetohydrodynamic (GRMHD) framework that describes rotating and magnetised axisymmetric white dwarfs, choosing appropriate rotation laws and magnetic field profiles (toroidal and poloidal). The numerical procedure for finding solutions in this framework uses the 3+1 formalism of …
The properties of uniformly rotating white dwarfs are analyzed within the framework of general relativity. Hartle's formalism is applied to construct self-consistently the internal and external solutions to the Einstein equations. The mass, the radius, the moment of inertia and quadrupole moment of rotating white dwarfs have been calculated as a function of both the central density and rotation period of the star. The maximum mass of rotating white dwarfs for stable configurations has been obtained.
CONTEXT. Little is known about the planetary systems around single white dwarfs although there is strong evidence that they do exist. AIMS. We performed a pilot study with the extreme-AO system on the Spectro-Polarimetric High-contrast Exoplanet REsearch (SPHERE) on the Very Large Telescopes (VLT) to look for giant planets around a young white dwarf, GD 50. METHODS. We were awarded science verification time on the new ESO instrument SPHERE. Observations were made with the InfraRed Dual-band Imager and Spectrograph in classical imaging mode in H band. RESULTS. Despite the faintness of the targe…
We present fully general relativistic (GR) simulations of binary white dwarf-neutron star (WDNS) inspiral and merger. The initial binary is in a circular orbit at the Roche critical separation. The goal is to determine the ultimate fate of such systems. We focus on binaries whose total mass exceeds the maximum mass (Mmax) a cold, degenerate EOS can support against gravitational collapse. The time and length scales span many orders of magnitude, making fully general relativistic hydrodynamic (GRHD) simulations computationally prohibitive. For this reason, we model the WD as a "pseudo-white dwar…
We simulate head-on collisions from rest at large separation of binary white dwarf -- neutron stars (WDNSs) in full general relativity. Our study serves as a prelude to our analysis of the circular binary WDNS problem. We focus on compact binaries whose total mass exceeds the maximum mass that a cold degenerate star can support, and our goal is to determine the fate of such systems. A fully general relativistic hydrodynamic computation of a realistic WDNS head-on collision is prohibitive due to the large range of dynamical time scales and length scales involved. For this reason, we construct a…
PSR J1738+0333 is one of the four millisecond pulsars known to be orbited by a white dwarf companion bright enough for optical spectroscopy. Of these, it has the shortest orbital period, making it especially interesting for a range of astrophysical and gravity related questions. We present a spectroscopic and photometric study of the white dwarf companion and infer its radial velocity curve, effective temperature, surface gravity and luminosity. We find that the white dwarf has properties consistent with those of low-mass white dwarfs with thick hydrogen envelopes, and use the corresponding ma…
We consider a particular effect which can be expected in scenarios of deviations from Special Relativity induced by Planckian physics: the loss of additivity in the total energy of a system of particles. We argue about the necessity to introduce a length scale to control the effects of non-additivity for macroscopic objects and consider white dwarfs as an appropriate laboratory to test this kind of new physics. We study the sensitivity of the mass-radius relation of the Chandrasekhar model to these corrections by comparing the output of a simple phenomenological model to observational data of …
Ultra-massive H-rich (DA spectral type) white dwarf stars ($M_{\star} > 1.05 M_{\odot}$) are expected to be substantially crystallized by the time they reach the ZZ Ceti instability strip ($T_{\rm eff} \sim 12\,000$ K). Crystallization leads to a separation of $^{16}$O and $^{20}$Ne (or $^{12}$C and $^{16}$O) in the core of ultra-massive WDs, which strongly impacts their pulsational properties. An additional factor to take into account when modeling the evolution and pulsations of WDs in this range of masses are the relativistic effects, which induce changes in the cooling times and the stella…
Static and uniformly rotating, cold and hot white dwarfs are investigated both in Newtonian gravity and general theory of relativity, employing the well-known Chandrasekhar equation of state. The mass-radius, mass-central density, radius-central density etc relations of stable white dwarfs with $μ=A/Z=2$ and $μ=56/26$ (where $A$ is the average atomic weight and $Z$ is the atomic charge) are constructed for different temperatures. It is shown that near the maximum mass the mass of hot rotating white dwarfs is slightly less than for cold rotating white dwarfs, though for static white dwarfs the …
We are studying the influence of stellar multiplicity on exoplanet systems, in particular systems that have been detected via radial-velocity searches. We are in particular interested in the closest companions as they would have a strong influence on the evolution of the original planet forming disks. In this study we present new companions detected during our ongoing survey of exoplanet hosts with VLT/SPHERE. We are using the extreme adaptive optics imager SPHERE at the ESO/VLT to search for faint (sub)stellar companions. We utilized the classical coronagraphic imaging mode to perform a snaps…
Pulsars with compact companions in close eccentric orbits are unique laboratories for testing general relativity and alternative theories of gravity. Moreover, they are excellent targets for future gravitational wave experiments like LISA and they are also highly important for understanding the equation of state of super-dense matter and the evolution of massive binaries. Here we report on optical observations of the 1.02 M_sun companion to the pulsar PSR J1141-6545. We detect an optical counterpart with apparent magnitudes V=25.08(11) and R=24.38(14), consistent with the timing position of th…
We present a general solution of the Einstein gravitational field equations for the static spherically symmetric gravitational interior spacetime of an isotropic fluid sphere. The solution is obtained by transforming the pressure isotropy condition, a second order ordinary differential equation, into a Riccati type first order differential equation, and using a general integrability condition for the Riccati equation. This allows us to obtain an exact non-singular solution of the interior field equations for a fluid sphere, expressed in the form of infinite power series. The physical features …
Radio pulsars in short-period eccentric binary orbits can be used to study both gravitational dynamics and binary evolution. The binary system containing PSR J1141$-$6545 includes a massive white dwarf (WD) companion that formed before the gravitationally bound young radio pulsar. We observe a temporal evolution of the orbital inclination of this pulsar that we infer is caused by a combination of a Newtonian quadrupole moment and Lense-Thirring precession of the orbit resulting from rapid rotation of the WD. Lense-Thirring precession, an effect of relativistic frame-dragging, is a prediction o…
Gravitational deflection of starlight around the Sun during the 1919 total solar eclipse provided measurements that confirmed Einstein's general theory of relativity. We have used the Hubble Space Telescope to measure the analogous process of astrometric microlensing caused by a nearby star, the white dwarf Stein 2051 B. As Stein 2051 B passed closely in front of a background star, the background star's position was deflected. Measurement of this deflection at multiple epochs allowed us to determine the mass of Stein 2051 B -- the sixth nearest white dwarf to the Sun -- as 0.675 +/- 0.051 sola…
Massive, highly magnetized white dwarfs with fields up to $10^9$ G have been observed and theoretically used for the description of a variety of astrophysical phenomena. Ultramagnetized white dwarfs with uniform interior fields up to $10^{18}$ G, have been recently purported to obey a new maximum mass limit, $M_{\rm max}\approx 2.58~M_\odot$, which largely overcomes the traditional Chandrasekhar value, $M_{\rm Ch}\approx 1.44~M_\odot$. Such a much larger limit would make these astrophysical objects viable candidates for the explanation of the superluminous population of type Ia supernovae. We …
Monte Carlo (MC) method played an essential role in many areas of human activity and has found application in many branches of physical science. This paper proposes a computational technique based on MC algorithms to solve Lane-Emden (LE) type equations. We analyze four LE equations arising in astrophysics: the positive and negative indices of the polytropic gas spheres, the isothermal gas sphere, and the white dwarf equation. We calculated eleven models (i.e., eleven LE equations) of the positive index polytropes, nine for the negative index polytrope, the isothermal gas sphere, and the white…
In this work we investigate the structure of white dwarfs using the Tolman-Oppenheimer-Volkoff equations and compare our results with those obtained from Newtonian equations of gravitation in order to put in evidence the importance of General Relativity (GR) for the structure of such stars. We consider in this work for the matter inside white dwarfs two equations of state, frequently found in the literature, namely, the Chandrasekhar and Salpeter equations of state. We find that using Newtonian equilibrium equations, the radii of massive white dwarfs ($M>1.3M_{\odot}$) are overestimated in com…
White dwarfs are compact objects that stand against gravitational collapse by their internal pressure of degenerate matter. In this work we aimed to perform an introductory study on these stars, using two equations of state (EOS): (I) an ideal Fermi gas and (II) the one by Baym Pethick and Sutherland (BPS). In addition, we analyzed these two equations of state in two scenarios, the Newtonian and the one from General Relativity, which allowed us to analyze the effects of curved space-time. We also studied a rotating white dwarf, finding a metric for this case. With these two cases, with rotatio…
The mass-radius relation of white dwarfs is largely determined by the equation of state of degenerate electrons, which causes the stellar radius to decrease as mass increases. Here we observationally measure this relation using the gravitational redshift effect, a prediction of general relativity that depends on the ratio between stellar mass and radius. Using observations of over three thousand white dwarfs from the Sloan Digital Sky Survey and the Gaia space observatory, we derive apparent radial velocities from absorption lines, stellar radii from photometry and parallaxes, and surface grav…
