Theoretical Models of Highly Magnetic White Dwarf Stars with Non-Polytropic Equation of State

Super-massive white dwarf (WD) stars in the mass range 2.4 - 2.8 solar masses are believed to be the progenitors of “super-luminous” Type Ia supernovae according to a hypothesis proposed by some researchers. They theorize such a higher mass of the WD due to the presence of a very strong magnetic field inside it. We revisit their first work on magnetic WDs (MWDs) and present our theoretical results that are very different from theirs. The main reason for this difference is in the use of the equation of state (EoS) to make stellar models of MWDs. An electron gas in a magnetic field is Landau quantized and hence, the resulting EoS becomes non-polytropic. By constructing models of MWDs using such an EoS, we highlight that a strong magnetic field inside a WD would make the star super-massive. We have found that our stellar models do indeed fall in the mass range given above. Moreover, we are also able to address an observational finding that the mean mass of MWDs are almost double that of non-magnetic WDs. Magnetic field changes the momentum-space of the electrons which in turn changes their density of states (DOS), and that in turn changes the EoS of matter inside the star. By correlating the magnetic DOS with the non-polytropic EoS, we were also able to find a physical reason behind our theoretical result of super-massive WDs with strong magnetic fields. In order to construct these models, we have considered different equations of state with at most three Landau levels occupied and have plotted our results as mass-radius relations for a particular chosen value of maximum Fermi energy. Our results also show that a multiple Landau-level system of electrons leads to such an EoS that gives multiple branches in the mass-radius relations, and that the super-massive MWDs are obtained when the Landau-level occupancy is limited to just one level. Finally, our theoretical results can be explained solely on the basis of quantum and statistical mechanics that warrant no assumptions regarding stars.

Asteroseismology of DAV white dwarf stars and G29–38

Asteroseismology is a powerful tool used for detecting the inner structure of stars, which is also widely used to study white dwarfs. We discuss the asteroseismology of DAV stars. The period-to-period fitting method is discussed in detail, including its reliability in detecting the inner structure of DAV stars. If we assume that all observed modes of some DAV stars are the l = I cases, the errors associated with model fitting will be always large. If we assume that the observed modes are com- posed of I = 1 and 2 modes, the errors associated with model fitting in this case will be small. However, there will be modes identified as l = 2 that do not have ob- served quintuplets. G29-38 has been observed spectroscopically and photometrically for many years. Thompson et al. made 1 modes identifications in the star through the limb darkening effect. With 11 known I modes, we also study the asteroseismology of G29-38, which reduces the blind l fittings and is a fair choice. Unfortunately, our two best-fitting models are not in line with the previous atmospheric results. Based on factors like only a few observed modes, stability and identification of eigenmodes, identification of spherical degrees, construction of physical and realistic models and so on, detecting the inner structure of DAV stars by asteroseismology needs further development.

Formation and Destiny of White Dwarf and Be Star Binaries

The binary systems consisting of a Be star and a white dwarf(Be WDs) are very interesting.They can originate from the binaries composed of a Be star and a subdwarf O or B star(Besd OBs),and they can merge into red giants via luminous red nova or can evolve into double WD potentially detected by the LISA mission.Using the method of population synthesis,we investigate the formation and the destiny of Be WDs,and discuss the effects of the metallicity(Z) and the common envelope evolution parameters.We find that Besd OBs are significant progenitors of Be WDs.About 30%(Z = 0.0001)-50%(Z = 0.02) of Be WDs come from Besd OBs.About 60%(Z = 0.0001)-70%(Z = 0.02) of Be WDs turn into red giants via a merger between a WD and a non-degenerated star.About 30%(Z = 0.0001)-40%(Z = 0.02) of Be WDs evolve into double WDs which are potential gravitational waves of the LISA mission at a frequency band between about 3 × 10^(-3)and 3 × 10^(-2)Hz.The common envelope evolution parameter introduces an uncertainty with a factor of about 1.3 on Be WD populations in our simulations.

Quark-novae in neutron star - white dwarf binaries: a model for luminous (spin-down powered) sub-Chandrasekhar-mass Type Ia supernovae?

We show that, by appealing to a Quark-Nova （QN） in a tight binary system containing a massive neutron star and a CO white dwarf （WD）, a Type Ia explosion could occur. The QN ejecta collides with the WD, driving a shock that triggers carbon burning under degenerate conditions （the QN-Ia）. The conditions in the compressed low-mass WD （MwD 〈 0.9 M） in our model mimic those of a Chandrasekhar mass WD. The spin-down luminosity from the QN compact remnant （the quark star） pro- vides additional power that makes the QN-Ia light-curve brighter and broader than a standard SN-Ia with similar 56Ni yield. In QNe-Ia, photometry and spectroscopy are not necessarily linked since the kinetic energy of the ejecta has a contribution from spin-down power and nuclear decay. Although QNe-Ia may not obey the Phillips relationship, their brightness and their relatively ＂normal looking＂ light-curves mean they could be included in the cosmological sample. Light-curve fitters would be con- fused by the discrepancy between spectroscopy at peak and photometry and would correct for it by effectively brightening or dimming the QNe-Ia apparent magnitudes, thus over- or under-estimating the true magnitude of these spin-down powered SNe-Ia. Contamination of QNe-Ia in samples of SNe-Ia used for cosmological analyses could systematically bias measurements of cosmological parameters if QNe-Ia are numerous enough at high-redshift. The strong mixing induced by spin-down wind combined with the low 56Ni yields in QNe-Ia means that these would lack a secondary maximum in the/-band despite their luminous nature. We discuss possible QNe-Ia progenitors.

A Study of Magnetized White Dwarf+Helium Star Binary Evolution to Type Ia Supernovae

The white dwarf(WD)+helium(He)star binary channel plays an important role in the single degenerate scenario for the progenitors of type Ia supernovae(SNe Ia).Previous studies on the WD+main sequence star evolution have shown that the magnetic fields of WDs may significantly influence their accretion and nuclear burning processes.In this work we focus on the evolution of magnetized WD+He star binaries with detailed stellar evolution and binary population synthesis(BPS)calculations.In the case of magnetized WDs,the magnetic fields may disrupt the inner regions of the accretion disk,funnel the accretion flow onto the polar caps and even confine helium burning within the caps.We find that,for WDs with sufficiently strong magnetic fields,the parameter space of the potential SN Ia progenitor systems shrinks toward shorter orbital periods and lower donor masses compared with that in the non-magnetized WD case.The reason is that the magnetic confinement usually works with relatively high mass transfer rates,which can trigger strong wind mass loss from the WD,thus limiting the He-rich mass accumulation efficiency.The surviving companion stars are likely of low-mass at the moment of the SN explosions,which can be regarded as a possible explanation for the non-detection of surviving companions after the SNe or inside the SN remnants.However,the corresponding birthrate of Galactic SNe Ia in our high-magnetic models is estimated to be~(0.08–0.13)×10^(-3)yr^(-1)(~0.17–0.28×10^(-3)yr^(-1)for the non-magnetic models),significantly lower than the observed Galactic SN Ia birthrate.

The Remnant of Neutron Star-White Dwarf Merger and the Repeating Fast Radio Bursts

Fast radio bursts (FRBs) at cosmological distances still hold concealed physical origins. Previously Liu (2018) proposes a scenario that the collision between a neutron star (NS) and a white dwarf (WD) can be one of the progenitors of non-repeating FRBs and notices that the repeating FRBs can also be explained if a magnetar formed after such NS-WD merger. In this paper, we investigate this channel of magnetar formation in more detail. We propose that the NS-WD post-merger, after cooling and angular momentum redistribution, may collapse to either a black hole or a new NS or even remains as a hybrid WDNS, depending on the total mass of the NS and WD. In particular, the newly formed NS can be a magnetar if the core of the WD collapsed into the NS while large quantities of degenerate electrons of the WD compressed to the outer layers of the new NS. A strong magnetic field can be formed by the electrons and positive charges with different angular velocities induced by the differential rotation of the newborn magnetar. Such a magnetar can power the repeating FRBs by the magnetic reconnections due to the crustal movements or starquakes.

Possibility of Searching for Accreting White Dwarfs with the Chinese Space Station Telescope

Accreting WDs are very important for the studies of binary evolution,binary population synthesis and accretion physics.So far,there are a lot of accreting WD binaries with low accretion rates,such as cataclysmic variables,detected by different surveys.However,few accreting WD binaries with high accretion rates have been detected.In this paper,we studied the spectrum properties of accreting WD binaries and investigated whether accreting WD binaries with high accretion rates can be detected by the Chinese Space Station Telescope(CSST).We found that some accreting WD binaries with high accretion rates can be distinguishable from other types of stars with(NUV-y,u-y),(NUV-r,u-g),(NUV-i,u-g),(NUV-z,u-g)and(NUV-y,u-g)color-color diagrams.Therefore,some accreting WD binaries with high accretion rates can be detected by the CSST.

A catalog of DB white dwarfs from the LAMOST DR5 and construction of templates

In this study, we employ machine learning to build a catalog of DB white dwarfs(DBWDs) from the LAMOST Data Release(DR) 5. Using known DBs from SDSS DR14, we selected samples of highquality DB spectra from the LAMOST database and applied them to train the machine learning process.Following the recognition procedure, we chose 351 DB spectra of 287 objects, 53 of which were new identifications. We then utilized all the DBWD spectra from both SDSS DR14 and LAMOST DR5 to construct DB templates for LAMOST 1 D pipeline reductions. Finally, by applying DB parameter models provided by D. Koester and the distance from Gaia DR2, we calculated the effective temperatures, surface gravities and distributions of the 3 D locations and velocities of all DBWDs.

The double helium-white dwarf channel for the formation of AM CVn binaries

Most close double helium white dwarfs will merge within a Hubble time due to orbital decay by gravitational wave radiation.However,a significant fraction with low mass ratios will survive for a long time as a consequence of stable mass transfer.Such stable mass transfer between two helium white dwarfs（He WDs） provides one channel for the production of AM CVn binary stars.In previous calculations of double He WD progenitors,the accreting He WD was treated as a point mass.We have computed the evolution of 16 double He WD models in order to investigate the consequences of treating the evolution of both components in detail.We find that the boundary between binaries having stable and unstable mass transfer is slightly modified by this approach.By comparing with observed periods and mass ratios,we redetermine masses of eight known AM CVn stars by our double He WDs channel,i.e.HM Cnc,AM CVn,V406 Hya,J0926,J1240,GP Com,Gaia14 aae and V396 Hya.We propose that central spikes in the triple-peaked emission spectra of J1240,GP Com and V396 Hya and the surface abundance ratios of N/C/O in GP Com can be explained by the stable double He WD channel.The mass estimates derived from our calculations are used to discuss the predicted gravitational wave signal in the context of the Laser Interferometer Space Antenna（LISA） project.

The cooling time of white dwarfs produced from type Iasupernovae

Type Ia supernovae （SNe Ia） play a key role in measuring cosmological parameters, in which the Phillips relation is adopted. However, the origin of the relation is still unclear. Several parameters are suggested, e.g. the relative content of carbon to oxygen （C/O） and the central density of the white dwarf （WD） at ignition. These parameters are mainly determined by the WD＇s initial mass and its cooling time, respectively. Using the progenitor model developed by Meng ＆ Yang, we present the distributions of the initial WD mass and the cooling time. We do not find any correlation between these parameters. However, we notice that as the range of the WD＇s mass decreases, its average value increases with the cooling time. These results could provide a constraint when simulating the SN Ia explosion, i.e. the WDs with a high C/O ratio usually have a lower central density at ignition, while those having the highest central density at ignition generally have a lower C/O ratio. The cooling time is mainly determined by the evolutionary age of secondaries, and the scatter of the cooling time decreases with the evolutionary age. Our results may indicate that WDs with a long cooling time have more uniform properties than those with a short cooling time, which may be helpful to explain why SNe Ia in elliptical galaxies have a more uniform maximum luminosity than those in spiral galaxies.

Measuring the Fundamental Parameters of Hot Hydrogen- Rich White Dwarfs

This review considers the observations of hot, hydrogen-rich white dwarfstars, with particular reference to measurements of temperature, surface gravity and composition.Spectroscopic data from a variety of wavelength ranges are required for this work and, inparticular, the important contributions from optical, ultraviolet and extreme ultraviolet studiesare discussed. Using the values of T_(eff) and log g determined for an individual white dwarf,estimates of mass and radius might be derived from the theoretical mass-radius relation. The issueof the accuracy of the theoretical mass-radius calculations and the prospects for making empiricaltests using observational data are outlined.

Noncommutative dispersion relation and mass-radius relation of white dwarfs

The equation of state of the electron degenerate gas in a white dwarf is usually treated by employing the ideal dispersion relation.However, the effect of quantum gravity is expected to be inevitably present and when this effect is considered through a non-commutative formulation, the dispersion relation undergoes a substantial modification.In this paper, we take such a modified dispersion relation and find the corresponding equation of state for the degenerate electron gas in white dwarfs.Hence we solve the equation of hydrostatic equilibrium and find that this leads to the possibility of the existence of excessively high values of masses exceeding the Chandrasekhar limit, although the quantum gravity effect is taken to be very small.It is only when we impose the additional effect of neutronization that we obtain white dwarfs with masses close to the Chandrasekhar limit with nonzero radii at the neutronization threshold.We demonstrate these results by giving numerical estimates for the masses and radii of helium, carbon and oxygen white dwarfs.

Iron group nuclei electron capture in super-Chandrasekhar superstrong magnetic white dwarfs

Using the theory of relativistic mean-field effective interactions,the influences of superstrong magnetic fields(SMFs)on electron Fermi energy,binding energy per nucleus and single-particle level structure are discussed in super-Chandrasekhar magnetic white dwarfs.Based on the relativistical SMFs theory model of Potekhin et al.,the electron chemical potential is corrected in SMFs,and the electron capture(EC)of iron group nuclei is investigated by using the Shell-Model Monte Carlo method and Random Phase Approximation theory.The EC rates can increase by more than three orders of magnitude due to the increase of the electron Fermi energy and the change of single-particle level structure by SMFs.However,the EC rates can decrease by more than four orders of magnitude due to increase of the nuclei binding energy by SMFs.We compare our results with those of FFNs(Fuller et al.),AUFDs(Aufderheide et al.)and Nabi(Nabi et al.).Our rates are higher by about four orders of magnitude than those of FFN,AUFD and Nabi due to SMFs.Our study may have important reference value for subsequent studies of the instability,mass radius relationship,and thermal and magnetic evolution of super-Chandrasekhar magnetic white dwarfs.

On the DB gap of white dwarf evolution: effects of hydrogen mass fraction and convective overshooting

We investigate the spectral evolution of white dwarfs by considering the effects of hydrogen mass in the atmosphere and convective overshooting above the convection zone. Our numerical results show that white dwarfs with MH- 10^-16 MG show the DA spectral type between 46 000 ≤ Teff≤ 26 000 K and the DO or DB spectral type may appear on either side of this temperature range. White dwarfs with MH - 10^-15 M⊙ appear as DA stars until they cool to Teff - 31 000 K; from then on they will evolve into DB white dwarfs as a result of convective mixing. If MH in the white dwarfs is more than 10-14 M⊙, the convective mixing will not occur when Teff 〉 20 000 K, thus these white dwarfs always appear as DA stars. White dwarfs within the temperature range 46 000 ≤ Teff ≤ 31 000 K always show the DA spectral type, which coincides with the DB gap. We notice the importance of the convective overshooting and suggest that the overshooting length should be proportional to the thickness of the convection zone to better fit the observations.

Mass-accreting white dwarfs and type Ia supernovae

Type Ia supernovae（SNe Ia） play a prominent role in understanding the evolution of the Universe. They are thought to be thermonuclear explosions of mass-accreting carbon-oxygen white dwarfs（CO WDs） in binaries, although the mass donors of the accreting WDs are still not well determined. In this article, I review recent studies on mass-accreting WDs, including H-and He-accreting WDs. I also review currently most studied progenitor models of SNe Ia, i.e., the single-degenerate model（including the WD＋MS channel, the WD＋RG channel and the WD＋He star channel）, the doubledegenerate model（including the violent merger scenario） and the sub-Chandrasekhar mass model.Recent progress on these progenitor models is discussed, including the initial parameter space for producing SNe Ia, the binary evolutionary paths to SNe Ia, the progenitor candidates for SNe Ia, the possible surviving companion stars of SNe Ia, some observational constraints, etc. Some other potential progenitor models of SNe Ia are also summarized, including the hybrid CONe WD model, the core-degenerate model, the double WD collision model, the spin-up/spin-down model and the model of WDs near black holes. To date, it seems that two or more progenitor models are needed to explain the observed diversity among SNe Ia.

Hydrogen and helium shell burning during white dwarf accretion

Type Ia supernovae（SNe Ia） are believed to be thermonuclear explosions of carbon oxygen（CO） white dwarfs（WDs） with masses close to the Chandrasekhar mass limit. How a CO WD accretes matter and grows in mass to this limit is not well understood, hindering our understanding of SN Ia explosions and the reliability of using SNe Ia as a cosmological distance indicator. In this work, we employed the stellar evolution code MESA to simulate the accretion process of hydrogen-rich material onto a 1.0 M⊙CO WD at a high rate（over the Eddington limit） of 4.3 × 10^-7 M⊙yr^-1. The simulation demonstrates the characteristics of the double shell burning on top of the WD, with a hydrogen shell burning on top of a helium burning shell. The results show that helium shell burning is not steady（i.e.it flashes）. Flashes from the helium shell are weaker than those in the case of accretion of helium-rich material onto a CO WD. The carbon to oxygen mass ratio resulting from the helium shell burning is higher than what was previously thought. Interestingly, the CO WD growing due to accretion has an outer part containing a small fraction of helium in addition to carbon and oxygen. The flashes become weaker and weaker as the accretion continues.

The C/O ratio of He-accreting carbon-oxygen white dwarfs and type Ia supernovae

Type Ia supernovae(SNe Ia)are thermonuclear explosions of carbon-oxygen white dwarfs(CO WDs),and are believed to be excellent cosmological distance indicators due to their high luminosity and remarkable uniformity.However,there exists a diversity among SNe Ia,and a poor understanding of the diversity hampers the improvement of the accuracy of cosmological distance measurements.The variations of the ratios of carbon to oxygen(C/O)of WDs at explosion are suggested to contribute to the diversity.In the canonical model of SNe Ia,a CO WD accretes matter from its companion and increases its mass till the Chandrasekhar mass limit when the WD explodes.In this work,we studied the C/O ratio for accreting CO WDs.Employing the stellar evolution code MESA,we simulated the accretion of He-rich material onto CO WDs with different initial WD masses and different mass accretion rates.We found that the C/O ratio varies for different cases.The C/O ratio of He-accreting CO WDs at explosion increases with a decreasing initial WD mass or a decreasing accretion rate.The various C/O ratios may,therefore,contribute to the diversity of SNe Ia.

Accreting CO material onto ONe white dwarfs towards accretion-induced collapse

The final outcomes of accreting ONe white dwarfs（ONe WDs） have been studied for several decades,but there are still some issues that are not resolved. Recently,some studies suggested that the deflagration of oxygen would occur for accreting ONe WDs with Chandrasekhar masses. In this paper,we aim to investigate whether ONe WDs can experience accretion-induced collapse（AIC） or explosions when their masses approach the Chandrasekhar limit. Employing the stellar evolution code Modules for Experiments in Stellar Astrophysics（MESA）,we simulate the longterm evolution of ONe WDs with accreting CO material. The ONe WDs undergo weak multicycle carbon flashes during the mass-accretion process,leading to mass increase of the WDs. We found that different initial WD masses and mass-accretion rates influence the evolution of central density and temperature. However,the central temperature cannot reach the explosive oxygen ignition temperature due to neutrino cooling. This work implies that the final outcome of accreting ONe WDs is electroncapture induced collapse rather than thermonuclear explosion.

Accreting He-rich material onto carbon-oxygen white dwarfs until explosive carbon ignition

Type Ia supernovae （SNe Ia） play an important role in studies of cosmology and galactic chemi- cal evolution. They are believed to be thermonuclear explosions of carbon-oxygen white dwarfs （CO WDs） when their masses approach the Chandrasekar （Ch） mass limit. However, it is still not completely under- stood how a CO WD increases its mass to the Ch-mass limit in the classical single-degenerate （SD） model. In this paper, we studied the mass accretion process in the SD model to examine whether the WD can explode as an SN Ia. Employing the stellar evolution code called modules for experiments in stellar as- trophysics （MESA）, we simulated the He accretion process onto CO WDs. We found that the WD can increase its mass to the Ch-mass limit through the SD model and explosive carbon ignition finally occurs in its center, which will lead to an SN Ia explosion. Our results imply that SNe Ia can be produced from the SD model through steady helium accretion. Moreover, this work can provide initial input parameters for explosion models of SNe Ia.

周期性重复快速射电暴双星模型再研究

在椭圆轨道的致密双星模型作为周期性重复快速射电暴(Fast Radio Bursts,FRBs)起源的基础上,考虑引力辐射对快速射电暴周期性行为的影响。这个双星系统包含一个具有强偶极磁场的中子星和一个磁化的白矮星。当白矮星充满它的洛希瓣时,物质将通过内拉格朗日点转移到中子星表面。由于角动量守恒,白矮星可能在一次爆发之后被踢开,接着在演化过程中由于引力辐射再次充满洛希瓣,实现再次爆发。这种情况下,快速射电暴的周期对应于双星轨道周期P_(orb),而它与两次质量转移时间间隔Δt之间的关系是能否显现周期性行为的关键因素。很明显,Δt≈P_(orb)或者Δt<P_(orb)是周期性行为显现的必要条件。反之,如果Δt>>P_(orb),周期性将很难观测到。结果表明,只有相对较长周期的快速射电暴才能显示周期性行为,这表明目前仅有的两个周期性快速射电暴都对应于较长的周期是合理的。