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Register a new userSuppression of luminosity and mass-radius relation of highly magnetized white dwarfs
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Added by
Banibrata Mukhopadhyay
Publication date
2020
fields
Physics
and research's language is
English
Authors
Abhay Gupta
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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 Kramers opacity, wherever required. We show that the Chandrasekhar-limit is retained, even at high luminosity upto about 10^{-2} solar luminosity but without magnetic field, if the temperature is set constant inside the interface. However there is an increased mass for large-radius white dwarfs, an effect of photon diffusion. Nevertheless, in the presence of strong magnetic fields, with central strength of about 10^{14} G, super-Chandrasekhar white dwarfs, with masses of about 1.9 solar mass, are obtained even when the temperature inside the interface is kept constant. Most interestingly, small-radius magnetic white dwarfs remain super-Chandrasekhar even if their luminosity decreases to as low as about 10^{-20} solar luminosity. However, their large-radius counterparts in the same mass-radius relation merge with Chandrasekhars result at low L. Hence, we argue for the possibility of highly magnetized, low luminous super-Chandrasekhar mass white dwarfs which, owing to their faintness, can be practically hidden.
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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 their ordinary counterparts (with surface fields restricted to about 10^9 G). In this paper we reformulate the virial theorem for non-rotating, highly magnetized white dwarfs (B-WDs) in which, unlike in previous formulations, the contribution of the magnetic pressure to the magnetohydrostatic balance cannot be neglected. Along with the new equation of magnetohydrostatic equilibrium, we approach the problem by invoking magnetic flux conservation and by varying the internal magnetic field with the matter density as a power law. Either of these choices are supported by previous independent work and neither violates any important physics. They are useful while there is no prior knowledge of field profile within a white dwarf. We then compute the modified gravitational, thermal and magnetic energies and examine how the magnetic pressure influences the properties of such white dwarfs. Based on our results we predict important properties of these B-WDs, which turn out to be independent of our chosen field profiles.
We investigate the luminosity suppression and its effect on the mass-radius relation as well as cooling evolution of highly magnetised white dwarfs. Based on the effect of magnetic field relative to gravitational energy, we suitably modify our treatment of the radiative opacity, magnetostatic equilibrium and degenerate core equation of state to obtain the structural properties of these stars. Although the Chandrasekhar mass limit is retained in the absence of magnetic field and irrespective of the luminosity, strong central fields of about $10^{14}, {rm G}$ can yield super-Chandrasekhar white dwarfs with masses up to $1.9, M_{odot}$. Smaller white dwarfs tend to remain super-Chandrasekhar for sufficiently strong central fields even when their luminosity is significantly suppressed to $10^{-16} L_{odot}$. Owing to the cooling evolution and simultaneous field decay over $10 {rm Gyr}$, the limiting masses of small magnetised white dwarfs can fall to $1.5 M_{odot}$ over time. However the majority of these systems still remain practically hidden throughout their cooling evolution because of their high fields and correspondingly low luminosities. Utilising the stellar evolution code $textit{STARS}$, we obtain close agreement with the analytical mass limit estimates and this suggests that our analytical formalism is physically motivated. Our results argue that super-Chandrasekhar white dwarfs born due to strong field effects may not remain so for long. This explains their apparent scarcity in addition to making them hard to detect because of their suppressed luminosities.
The Gaia Data Release 1 (DR1) sample of white dwarf parallaxes is presented, including 6 directly observed degenerates and 46 white dwarfs in wide binaries. This data set is combined with spectroscopic atmospheric parameters to study the white dwarf mass-radius relationship (MRR). Gaia parallaxes and G magnitudes are used to derive model atmosphere dependent white dwarf radii, which can then be compared to the predictions of a theoretical MRR. We find a good agreement between Gaia DR1 parallaxes, published effective temperatures (Teff) and surface gravities (log g), and theoretical MRRs. As it was the case for Hipparcos, the precision of the data does not allow for the characterisation of hydrogen envelope masses. The uncertainties on the spectroscopic atmospheric parameters are found to dominate the error budget and current error estimates for well-known and bright white dwarfs may be slightly optimistic. With the much larger Gaia DR2 white dwarf sample it will be possible to explore the MRR over a much wider range of mass, Teff, and spectral types.
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 current detection limit. The repetition of this cycle can eventually lead to a B-WD, recently postulated to be the reason for over-luminous type Ia supernovae. A spinning B-WD could also be an ideal source for continuous gravitational radiation and soft gamma-ray repeaters (SGRs) and anomalous X-ray pulsars (AXPs). SGRs/AXPs are generally believed to be highly magnetized, but observationally not confirmed yet, neutron stars. Invoking B-WDs does not require the magnetic field to be as high as for neutron star based model, however reproducing other observed properties intact.
The lowest-mass stars, brown dwarfs and giant exoplanets span a minimum in the mass-radius relationship that probes the fundamental physics of extreme states of matter, magnetism, and fusion. This White Paper outlines scientific opportunities and the necessary resources for modeling and measuring the mass-radius relationship in this regime.
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