Continuous gravitational wave from magnetized white dwarfs
Surajit Kalita, Banibrata Mukhopadhyay
备注：
5 pages including 4 figures and 1 table; based on the talk given in the IAU Symposium 357: White Dwarfs as probes of fundamental physics and tracers of planetary, stellar & galactic evolution, Hilo, Hawaii, October 21-25, 2019; to appear in the proceedings of IAU Symposium 357
发表信息：
Proceedings of the International Astronomical Union, 15(S357) (2019) 79-83
Recent evidence of super-Chandrasekhar white dwarfs (WDs), from the observations of over-luminous type Ia supernovae (SNeIa), has been a great astrophysical discovery. However, no such massive WDs have so far been observed directly as their luminosities are generally quite low. Hence it immediately raises the question of whether there is any possibility of detecting them directly. The search for super-Chandrasekhar WDs is very important as SNeIa are used as standard candles in cosmology. In this article, we show that continuous gravitational wave can allow us to detect such super-Chandrasekhar WDs directly.
The topic of magnetized super-Chandrasekhar white dwarfs is in the limelight, particularly in the last few years, since our proposal of their existence. By full-scale general relativistic magnetohydrodynamic (GRMHD) numerical analysis, we confirm in this work the existence of stable, highly magnetized, significantly super-Chandrasekhar white dwarfs with mass more than 3 solar mass. While a poloidal field geometry renders the white dwarfs oblate, a toroidal field makes them prolate retaining an overall quasi-spherical shape, as speculated in our earlier work. These white dwarfs are expected to …
We clarify important physics issues related to the recently established new mass limit for magnetized white dwarfs which is significantly super-Chandrasekhar. The issues include, justification of high magnetic field and the corresponding formation of stable white dwarfs, contribution of the magnetic field to the total density and pressure, flux freezing, variation of magnetic field and related currents therein. We also attempt to address the observational connection of such highly magnetized white dwarfs.
We address the issue of stability of recently proposed significantly super-Chandrasekhar white dwarfs. We present stable solutions of magnetostatic equilibrium models for super-Chandrasekhar white dwarfs pertaining to various magnetic field profiles. This has been obtained by self-consistently including the effects of the magnetic pressure gradient and total magnetic density in a general relativistic framework. We estimate that the maximum stable mass of magnetized white dwarfs could be more than 3 solar mass. This is very useful to explain peculiar, overluminous type Ia supernovae which do no…
Over the past couple of decades, researchers have predicted more than a dozen super-Chandrasekhar white dwarfs from the detections of over-luminous type Ia supernovae. It turns out that magnetic fields and rotation can explain such massive white dwarfs. If these rotating magnetized white dwarfs follow specific conditions, they can efficiently emit continuous gravitational waves and various futuristic detectors, viz. LISA, BBO, DECIGO, and ALIA can detect such gravitational waves with a significant signal-to-noise ratio. Moreover, we discuss various timescales over which these white dwarfs can …
The evolution of the remnant of the merger of two white dwarfs is still an open problem. Furthermore, few studies have addressed the case in which the remnant is a magnetic white dwarf with a mass larger than the Chandrasekhar limiting mass. Angular momentum losses might bring the remnant of the merger to the physical conditions suitable for developing a thermonuclear explosion. Alternatively, the remnant may be prone to gravitational or rotational instabilities, depending on the initial conditions reached after the coalescence. Dipole magnetic braking is one of the mechanisms that can drive s…
We investigate the luminosity and cooling of highly magnetized white dwarfs with electron-degenerate cores and non-degenerate surface layers where cooling occurs by diffusion of photons. We find the temperature and density profiles in the surface layers or envelope of white dwarfs by solving the magnetostatic equilibrium and photon diffusion equations in a Newtonian framework. We also obtain the properties of white dwarfs at the core-envelope interface, when the core is assumed to be practically isothermal. With the increase in magnetic field, the interface temperature increases whereas the in…
We show that the soft gamma-ray repeaters (SGRs) and anomalous X-ray pulsars (AXPs) can be explained as recently proposed highly magnetized white dwarfs (B-WDs). The radius and magnetic field of B-WDs are perfectly adequate to explain energies in SGRs/AXPs as the rotationally powered energy. While the highly magnetized neutron stars require an extra, observationally not well established yet, source of energy, the magnetized white dwarfs, yet following Chandrasekhar's theory (C-WDs), exhibit large ultra-violet luminosity which is observationally constrained from a strict upper limit.
We consider a relativistic, degenerate, electron gas under the influence of a strong magnetic field, which describes magnetized white dwarfs. Landau quantization changes the density of states available to the electrons, thus modifying the underlying equation of state. In the presence of very strong magnetic fields a maximum of either one, two or three Landau level(s) is/are occupied. We obtain the mass-radius relations for such white dwarfs and their detailed investigation leads us to propose the existence of white dwarfs having a mass ~2.3M_Sun, which overwhelmingly exceeds the Chandrasekhar …
Type Ia supernovae (SNe Ia) play a crucial role as standardizable cosmological candles, though the nature of their progenitors is a subject of active investigation. Recent observational and theoretical work has pointed to merging white dwarf binaries, referred to as the double-degenerate channel, as the possible progenitor systems for some SNe Ia. Additionally, recent theoretical work suggests that mergers which fail to detonate may produce magnetized, rapidly-rotating white dwarfs. In this paper, we present the first multidimensional simulations of the post-merger evolution of white dwarf bin…
Several recently discovered peculiar type Ia supernovae seem to demand an altogether new formation theory that might help explain the puzzling dissimilarities between them and the standard type Ia supernovae. The most striking aspect of the observational analysis is the necessity of invoking super-Chandrasekhar white dwarfs having masses ~ 2.1-2.8M_sun, M_sun being the mass of Sun, as their most probable progenitors. Strongly magnetized white dwarfs having super-Chandrasekhar masses were already established to be potential candidates for the progenitors of peculiar type Ia supernovae. Owing to…
In this work we compute models for relativistic white dwarfs in the presence of strong magnetic fields. These models possibly contribute to super-luminous SNIa. With an assumed axi-symmetric and poloidal magnetic field, we study the possibility of existence of super-Chandrasekhar magnetized white dwarfs by solving numerically the Einstein-Maxwell equations, by means of a pseudo-spectral method. We obtain a self-consistent rotating and non-rotating magnetized white dwarf models. According to our results, a maximum mass for a static magnetized white dwarf is 2.13 $\rm{M_{\odot}}$ in the Newtonia…
We compute static equilibria of white dwarf stars containing strong poloidal magnetic field, and present the modification of white dwarf mass-radius relation caused by the magnetic field. We find that a maximum white dwarf mass of about $1.9$~$M\odot$ may be supported if the interior field is as strong as approximately $10^{10}$ T. This mass is over 30 per cent larger than the traditional Chandrasekhar Limit. The equation of state of electron degenerate matter can be strongly modified due to Landau quantization at such high magnetic fields. We find, however, that this does not significantly af…
Over the last decade or so, we have been developing the possible existence of highly magnetized white dwarfs with analytical stellar structure models. While the primary aim was to explain the nature of the peculiar overluminous type Ia supernovae, later on, these magnetized stars were found to have even wider ranging implications including those for white dwarf pulsars, soft gamma-ray repeaters and anomalous X-ray pulsars, as well as gravitational radiation. In particular, we have explored in detail the mass-radius relations for these magnetized stars and showed that they can be significantly …
We sketch a possible evolutionary scenario by which a highly magnetized super-Chandrasekhar white dwarf could be formed by accretion on to a commonly observed magnetized white dwarf. This is an exploratory study, when the physics in cataclysmic variables (CVs) is very rich and complex. Based on this, we also explore the possibility that the white dwarf pulsar AR Sco acquired its high spin and magnetic field due to repeated episodes of accretion and spin-down. We show that strong magnetic field dramatically decreases luminosity of highly magnetized white dwarf (B-WD), letting them below the cur…
Recent detection of gravitational wave from nine black hole merger events and one neutron star merger event by LIGO and VIRGO shed a new light in the field of astrophysics. On the other hand, in the past decade, a few super-Chandrasekhar white dwarf candidates have been inferred through the peak luminosity of the light-curves of a few peculiar type Ia supernovae, though there is no direct detection of these objects so far. Similarly, a number of neutron stars with mass $>2M_\odot$ have also been observed. Continuous gravitational wave can be one of the alternate ways to detect these compact ob…
We investigate the evolution of isolated, zero and finite temperature, massive, uniformly rotating and highly magnetized white dwarf stars under angular momentum loss driven by magnetic dipole braking. We consider the structure and thermal evolution of white dwarf isothermal cores taking also into account the nuclear burning and neutrino emission processes. We estimate the white dwarf lifetime before it reaches the condition either for a type Ia supernova explosion or for the gravitational collapse to a neutron star. We study white dwarfs with surface magnetic fields from $10^6$ to $10^{9}$~G …
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 …
A simple cooling model of white dwarf stars is re-analyzed in Palatini $f(R)$ gravity. Modified gravity affects the white dwarf structures and consequently their ages. We find that the resulting super-Chandrasekhar white dwarfs need more time to cool down than sub-Chandrasekhar ones, or when compared to the Newtonian models.
We explore the possibility that soft gamma-ray repeaters (SGRs) and anomalous X-ray pulsars (AXPs) are powered by highly magnetized white dwarfs (B-WDs). We take a sample of SGRs and AXPs and provide the possible parameter space in mass, radius, and surface magnetic field based on their observed properties (period and its derivative) and the assumption that these sources obey the mass-radius relation derived for the B-WDs. The radius and magnetic field of B-WDs are adequate to explain energies in SGRs/AXPs as the rotationally powered energy. In addition, B-WDs also adequately explain the perpl…
The evolution of an accreting white dwarf (WD) with strong magnetic field toward a type Ia supernova (SN Ia) may differ from the classical single-degenerate (SD) channel. In this paper, we perform binary population synthesis (BPS) simulations for the SD channel with a main-sequence (MS) companion, including the strongly magnetized WD accretion. Under a reasonable assumption that the fraction of such systems is $\sim 15$%, the resulting delay time distribution (DTD) roughly follows the $t^{-1}$ power-law distribution. Within the (WD/MS) SD channel, the contribution from the highly magnetized WD…
Rotating magnetized white dwarfs are studied within the framework of general relativity using Hartle's formalism. Matter inside magnetized white dwarfs is described by an equation of state of particles under the action of a constant magnetic field which introduces anisotropic pressures. Our study is done for values of magnetic field below $10^{13}$ G -a threshold of the maximum magnetic field obtained by the cylindrical metric solution- and typical densities of WDs. The effects of the rotation and magnetic field combined are discussed, we compute relevant magnitudes such as the moment of inert…
We study the strongly magnetized white dwarf configurations in a self-consistent manner as a progenitor of the over-luminous type-Ia supernovae. We compute static equilibria of white dwarf stars containing a strong magnetic field and present the modification of white dwarf mass-radius relation caused by the magnetic field. From a static equilibrium study, we find that a maximum white dwarf mass of about 1.9 M$_\odot$ may be supported if the interior poloidal field is as strong as approximately $10^{10}$ T. On the other hand if the field is purely toroidal the maximum mass can be more than 5 M$…
In the present work we investigate the r-mode instability windows, spindown and spindown rates of sub- and super-Chandrasekhar magnetized white dwarfs in presence of Landau quantization of the electron gas and magnetic braking. The gravitational wave strain amplitudes due to r-mode instability is also calculated. The dominant damping mechanism is taken to be the shear viscosity arising due to scattering of the degenerate electrons from the ion liquid. We find that the critical frequencies of Landau quantized magnetized white dwarfs are the lowest, those of non-Landau quantized ones are higher …
Recently a substantial part of globular cluster population has been established as GeV gamma-ray sources by the Fermi-LAT telescope. We investigate possible production of the high energy gamma-rays by relativistic electrons injected from the population of fast rotating, magnetized White Dwarfs within the globular cluster. These electrons comptonize the radiation field within the globular cluster. We conclude that gamma-rays produced by electrons accelerated by the whole population of White Dwarfs within a specific cluster are on the level of detectability of the future Cherenkov telescope arra…
Generally the virial theorem provides a relation between various components of energy integrated over a system. This helps us to understand the underlying equilibrium. Based on the virial theorem we can estimate, for example, the maximum allowed magnetic field in a star. Recent studies have proposed the existence of highly magnetized white dwarfs, with masses significantly higher than the Chandrasekhar limit. Surface magnetic fields of such white dwarfs could be more than 10^9 G with the central magnitude several orders higher. These white dwarfs could be significantly smaller in size than the…
We describe one of the so-called low magnetic field magnetars SGR 0418+5729, as a massive fast rotating highly magnetized white dwarf following Malheiro et. al. 2012. We give bounds for the mass, radius, moment of inertia, and magnetic field for these sources, by requesting the stability of realistic general relativistic uniformly rotating configurations. Based on these parameters, we improve the theoretical prediction of the lower limit of the spin-down rate of SGR 0418+5729. In addition, we compute the electron cyclotron frequencies corresponding to the predicted surface magnetic fields.
There is solid observational evidence on the existence of massive, $M\sim 1~M_\odot$, highly magnetized white dwarfs (WDs) with surface magnetic fields up to $B\sim 10^9$ G. We show that, if in addition to these features, the star is fast rotating, it can become a rotation-powered pulsar-like WD and emit detectable high-energy radiation. We infer the values of the structure parameters (mass, radius, moment of inertia), magnetic field, rotation period and spin-down rates of a WD pulsar death-line. We show that WDs above the death-line emit blackbody radiation in the soft X-ray band via the magn…
Recent literature has seen an ongoing discussion on the limiting mass of strongly magnetized white dwarfs, since such objects may prove to be a source of over-luminous type-Ia supernovae. In an earlier paper, we have presented the mass-radius relation of white dwarfs with a strong poloidal magnetic field in Newtonian gravity. The inclusion of effects such as general relativistic gravity and many-body corrections to the equation of state can alter the mass-radius relation and the maximum mass. In this work we estimate the extent to which these effects may modify the earlier results. We find tha…
We explore the luminosity L of magnetized white dwarfs and its effect on the mass-radius relation. We self-consistently obtain the interface between the electron degenerate gas dominated inner core and the outer ideal gas surface layer or envelope by incorporating both the components of gas throughout the model white dwarf. This is obtained by solving the set of magnetostatic equilibrium, photon diffusion and mass conservation equations in the Newtonian framework, for different sets of luminosity and magnetic field. We appropriately use magnetic opacity, instead of Kramer's opacity, wherever r…
In recent years a number of white dwarfs has been observed with very high surface magnetic fields. We can expect that the magnetic field in the core of these stars would be much higher (~ 10^{14} G). In this paper, we analytically study the effect of high magnetic field on relativistic cold electron, and hence its effect on the stability and the mass-radius relation of a magnetic white dwarf. In strong magnetic fields, the equation of state of the Fermi gas is modified and Landau quantization comes into play. For relatively very high magnetic fields (with respect to the energy density of matte…
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 …
Ultra-massive white dwarfs ($ 1.05 \rm M_\odot \lesssim M_{WD}$) are particularly interesting objects that allow us to study extreme astrophysical phenomena such as type Ia supernovae explosions and merger events. Traditionally, ultra-massive white dwarfs are thought to harbour oxygen-neon (ONe) cores. However, recent theoretical studies and new observations suggest that some ultra-massive white dwarfs could harbour carbon-oxygen (CO) cores. Although several studies have attempted to elucidate the core composition of ultra-massive white dwarfs, to date, it has not been possible to distinguish …
White dwarfs are the most common endpoints of stellar evolution. They are often found in close binary systems in which the white dwarf is accreting matter from a companion star, either via an accretion disc or channelled along the white dwarf magnetic field lines. The nature of this binary depends on the masses and the separation of the two stellar components, as well as other parameters such as the white dwarf magnetic field and the nature of the stars. This chapter looks at the formation of white dwarfs and intrinsic properties, before looking at the different populations of accreting white …
The effect of magnetic fields in the Equations of State (EoS) of compact objects is the splitting of the pressure in two components, one parallel and the other perpendicular to the magnetic field. This anisotropy suggests the necessity of using structure equations considering the axial symmetry of the magnetized system. In this work, we consider an axially symmetric metric in spherical coordinates, the $γ$-metric, and construct a system of equations to describe the structure of spheroidal compact objects. In addition, we connect the geometrical parameter $γ$ linked to the spheroid's radii, wit…
The purpose of this thesis is to obtain more realistic equations of state to describe the matter forming magnetized white dwarfs, and use them to solve its structure equations. The equations of state are determined by considering the weak magnetic field approximation $B<B_c$ ($B_c=4.41\times10^{13}\text{ G}$) for the electron gas of the star. The magnetic field introduces anisotropic pressures, even for the moderate values present in white dwarfs. Also, we consider the energy and pressure correction due to the Coulomb interaction of the electron gas with the ions located in a crystal lattice. …
Ultra-massive white dwarfs ($\rm M_{WD} \gtrsim 1.05\, M_{\odot}$) are considered powerful tools to study type Ia supernovae explosions, merger events, the occurrence of physical processes in the Super Asymptotic Giant Branch (SAGB) phase, and the existence of high magnetic fields. Traditionally, ultra-massive white dwarfs are expected to harbour oxygen-neon (ONe) cores. However, new observations and recent theoretical studies suggest that the progenitors of some ultra-massive white dwarfs can avoid carbon burning, leading to the formation of ultra-massive white dwarfs harbouring carbon-oxygen…
We perform calculations of white dwarfs endowed with strong magnetic fields. White dwarfs are the progenitors of supernova Type Ia explosions and they are widely used as candles to show that the Universe is expanding and accelerating. However, observations of ultraluminous supernovae have suggested that the progenitor of such an explosion should be a white dwarf with mass above the well-known Chandrasekhar limit $\sim \,$1.4 $\rm{M_{\odot}}$. In corroboration with other works, but by using a fully general relativistic framework, we obtained also strongly magnetized white dwarfs with masses $\r…
An extended magnetosphere of a strongly magnetized accreting white dwarf (known as a polar) prevents the formation of an accretion disk and the matter is channelled to the magnetic pole(s). A few such sources show quasi-periodic oscillations in their optical light curves. These high-frequency oscillations are thought to be generated from the post-shock accretion column. The kinetic energy of the accretion flow is finally emitted from this post-shock region and the involved radiation processes decide the state of the matter. Here we study the structure and the dynamical properties of such accre…
We consider a relativistic, degenerate electron gas at zero-temperature under the influence of a strong, uniform, static magnetic field, neglecting any form of interactions. Since the density of states for the electrons changes due to the presence of the magnetic field (which gives rise to Landau quantization), the corresponding equation of state also gets modified. In order to investigate the effect of very strong magnetic field, we focus only on systems in which a maximum of either one, two or three Landau level(s) is/are occupied. This is important since, if a very large number of Landau le…
This is the summary of the parallel session entitled "White Dwarf Pulsars and Rotating White Dwarf Theory", chaired by Yukikatsu Terada in Thirteenth Marcel Grossmann Meeting. The origin of cosmic rays remains a mystery, even over 100 years since their discovery. Neutron stars (NSs) are considered textbook cases of particle acceleration sites in our Galaxy, but many unresolved numerical problems remain. Searches for new acceleration sites are crucial for astrophysics. The magnetized white dwarfs (MWDs) have the same kind of rotating magnetosphere as NSs, and may be the source of up to 10% of g…
Accretion-driven spin-up of a magnetized white dwarf in a close binary system is discussed. We address a situation in which the magnetic field of the white dwarf is screening during the accretion phase and re-generating due to the field diffusion through the accreted material after it. We find this scenario to be effective for a formation of massive pulsar-like white dwarfs.
Ever since the observation of peculiar over-luminous type Ia supernovae (SNeIa), exploring possible violations of the canonical Chandrasekhar mass-limit (CML) has become a pressing research area of modern astrophysics. Since its first detection in 2003, more than a dozen of peculiar over-luminous SNeIa has been detected, but the true nature of the underlying progenitors is still under dispute. Furthermore, there are also under-luminous SNeIa whose progenitor masses appear to be well below the CML (sub-Chandrasekhar progenitors). These observations call into question how sacrosanct the CML is. …
This paper aims to provide an introduction to the problem of determining the mass-radius relationship for white dwarfs. Both Newtonian and general relativistic case are examined, electromagnetic interactions are considered and the problem of $β$-decay equilibrium is discussed in particular for Helium WD
The relativistic Feynman-Metropolis-Teller treatment of compressed atoms is extended to treat magnetized matter. Each atomic configuration is confined by a Wigner-Seitz cell and is characterized by a positive electron Fermi energy which varies insignificantly with the magnetic field. In the relativistic treatment the limiting configuration is reached when the Wigner-Seitz cell radius equals the radius of the nucleus with a maximum value of the electron Fermi energy which can not be attained in presence of magnetic field due to the effect of Landau quantization of electrons within the Wigner-Se…
