The mass limit of white dwarfs with strong magnetic fields in general relativity

Recently, U. Das and B. Mukhopadhyay proposed that the Chandrasekhar limit of a white dwarf could reach a new high level （2.58M） if a superstrong magnetic field were considered （Das U and Mukhopadhyay B 2013 Phys. Rev. Lett. 110 071102）, where the structure of the strongly magnetized white dwarf （SMWD） is calculated in the framework of Newtonian theory （NT）. As the SMWD has a far smaller size, in contrast with the usual expectation, we found that there is an obvious general relativistic effect （GRE） in the SMWD. For example, for the SMWD with a one Landau level system, the super-Chandrasekhar mass limit in general relativity （GR） is approximately 16.5% lower than that in NT. More interestingly, the maximal mass of the white dwarf will be first increased when the magnetic field strength keeps on increasing and reaches the maximal value M = 2.48MQ with BD = 391.5. Then if we further increase the magnetic fields, surprisingly, the maximal mass of the white dwarf will decrease when one takes the GRE into account.

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.

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.

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.

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.

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.

Maximum mass of magnetic white dwarfs

We revisit the problem of the maximum masses of magnetized white dwarfs （WDs）. The impact of a strong magnetic field on the structure equations is addressed. The pressures become anisotropic due to the presence of the magnetic field and split into parallel and perpendicular components. We first construct stable solutions of the Tolman-Oppenheimer-Volkoff equations for parallel pressures and find that physical solutions vanish for the perpendicular pressure whenB ≥ 10^13 G. This fact estab- lishes an upper bound for a magnetic field and the stability of the configurations in the （quasi） spherical approximation. Our findings also indicate that it is not possible to obtain stable magnetized WDs with super-Chandrasekhar masses because the val- ues of the magnetic field needed for them are higher than this bound. To proceed into the anisotropic regime, we can apply results for structure equations appropriate for a cylindrical metric with anisotropic pressures that were derived in our previous work. From the solutions of the structure equations in cylindrical symmetry we have con- firmed the same bound for B- 10^13 G, since beyond this value no physical solutions are possible. Our tentative conclusion is that massive WDs with masses well beyond the Chandrasekhar limit do not constitute stable solutions and should not exist.

The gravitational wave emission of double white dwarf coalescences

Type Ia Supernovae(SNe Ia)are widely used as standard candles to probe the Universe.However,how these fierce explosions are produced itself is still a highly debated issue.There are mainly two popular models for SNe Ia:the double-degenerate scenario and the single-degenerate scenario.The doubledegenerate scenario suggests that SNe Ia are produced by the coalescence of two degenerate white dwarfs,while the single-degenerate scenario suggests that the continuous accretion of a single degenerate white dwarf from its normal stellar companion will finally lead to a disastrous explosion when it is over-massive,resulting in an SN Ia.The rapid development of the gravitational wave astronomy sheds new light on the nature of SNe Ia.In this study,we calculate the gravitational wave emissions of double white dwarf coalescences and compare them with the sensitivities of several upcoming detectors.It is found that the gravitational wave emissions from double white dwarf mergers in the local universe are strong enough to be detected by LISA.We argue that LISA-like gravitational wave detectors sensitive in the frequency range of 0.01—0.1 Hz will be a powerful tool to test the double-degenerate model of SNe Ia,and also to probe the Universe.

The formation of neutron star systems through accretion-induced collapse in white-dwarf binaries

The accretion-induced collapse(AIC)scenario was proposed 40 years ago as an evolutionary end state of oxygen-neon white dwarfs(ONe WDs),linking them to the formation of neutron star(NS)systems.However,there has been no direct detection of any AIC event so far,even though there exists a lot of indirect observational evidence.Meanwhile,the evolutionary pathways resulting in NS formation through AIC are still not thoroughly investigated.In this article,we review recent studies on the two classic progenitor models of AIC events,i.e.,the single-degenerate model(including the ONe WD+MS/RG/He star channels and the CO WD+He star channel)and the double-degenerate model(including the double CO WD channel,the double ONe WD channel and the ONe WD+CO WD channel).Recent progress on these progenitor models is reviewed,including the evolutionary scenarios leading to AIC events,the initial parameter space for producing AIC events and the related objects(e.g.,the pre-AIC systems and the post-AIC systems).For the single-degenerate model,the pre-AIC systems(i.e.,the progenitor systems of AIC events)could potentially be identified as supersoft X-ray sources,symbiotics and cataclysmic variables(such as classical novae,recurrent novae,Ne novae and He novae)in the observations,whereas the post-AIC systems(i.e.,NS systems)could potentially be identified as low-/intermediate-mass X-ray binaries,and the resulting low-/intermediate-mass binary pulsars,most notably millisecond pulsars.For the double-degenerate model,the pre-AIC systems are close double WDs with short orbital periods,whereas the post-AIC systems are single isolated NSs that may correspond to a specific kind of NS with peculiar properties.We also review the predicted rates of AIC events,the mass distribution of NSs produced via AIC and the gravitational wave(GW)signals from double WDs that are potential GW sources in the Galaxy in the context of future spacebased GW detectors,such as LISA,TianQin,Taiji,etc.Recent theoretical and observational constraints on the detection of AIC events are summarized.In order to confirm the existence of the AIC process,and resolve this long-term issue presented by current stellar evolution theories,more numerical simulations and observational identifications are required.

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.

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.

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.

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 likely candidate of type Ia supernova progenitors: the X-ray pulsating companion of the hot subdwarf HD 49798

HD 49798 is a hydrogen depleted subdwarf 06 star and has an X-ray pulsating companion （RX J0648.0-4418）. The X-ray pulsating companion is a massive white dwarf. Employing Eggleton＇s stellar evolution code with the optically thick wind assumption, we find that the hot subdwarf HD 49798 and its X-ray pulsating companion could produce a type Ia supernova （SN Ia） in future evolution. This implies that the binary system is a likely candidate of an SN Ia progenitor. We also discuss the possibilities of some other WD ＋ He star systems （e.g. V445 Pup and KPD 1930＋2752） for producing SNe Ia.

The Progenitors of Type Ia Supernovae with Asymptotic Giant Branch Donors

TypeⅠa supernovae(SNe Ia)are among the most energetic events in the universe.They are excellent cosmological distance indicators due to the remarkable homogeneity of their light curves.However,the nature of the progenitors of SNeⅠa is still not well understood.In the single-degenerate model,a carbon-oxygen white dwarf(CO WD)could grow its mass by accreting material from an asymptotic giant branch(AGB)star,leading to the formation of SNe Ia when the mass of the WD approaches to the Chandrasekhar-mass limit,known as the AGB donor channel.In this channel,previous studies mainly concentrate on the wind-accretion pathway for the mass-increase of the WDs.In the present work,we employed an integrated mass-transfer prescription for the semidetached WD+AGB systems,and evolved a number of WD+AGB systems for the formation of SNe Ia through the Roche-lobe overflow process or the wind-accretion process.We provided the initial and final parameter spaces of WD+AGB systems for producing SNe Ia.We also obtained the density distribution of circumstellar matter at the moment when the WD mass reaches the Chandrasekhar-mass limit.Moreover,we found that the massive WD+AGB sample AT 2019qyl can be covered by the final parameter space for producing SNe Ia,indicating that AT 2019qyl is a strong progenitor candidate of SNe Ia with AGB donors.

Double-detonation model of type Ia supernovae with a variable helium layer ignition mass

Although Type Ia supernovae （SNe Ia） play an important role in the study of cosmology, their progenitors are still poorly understood. Thermonuclear explosions from the helium double-detonation sub-Chandrasekhar mass model have been considered as an alternative method for producing SNe Ia. By adopting the assumption that a double detonation occurs when a He layer with a critical ignition mass accumulates on the surface of a carbon-oxygen white dwarf （CO WD）, we perform detailed binary evolution calculations for the He double-detonation model, in which a He layer from a He star accumulates on a CO WD. According to these calculations, we obtain the initial parameter spaces for SNe Ia in the orbital period and secondary mass plane for various initial WD masses. We implement these results into a detailed binary population synthesis approach to calculate SN Ia birthrates and delay times. From this model, the SN Ia birthrate in our Galaxy is ～0.4 - 1.6 × 10^-3 yr^-1. This indicates that the double-detonation model only produces part of the SNe la. The delay times from this model are ～ 70 - 710 Myr, which contribute to the young population of SNe Ia in the observations. We found that the CO WD ＋ sdB star system CD-30 11223 could produce an SN Ia via the double-detonation model in its future evolution.

Color excesses of type Ia supernovae from the single-degenerate channel model

The single degenerate model is the most widely accepted progenitor model of type Ia supernovae （SNe Ia）, in which a carbon-oxygen white dwarf （CO WD） accretes hydrogen-rich material from a main sequence or a slightly evolved star （WD＋MS） to increase its mass, and explodes when its mass approaches the Chandrasekhar mass limit. During the mass transfer phase between the two components, an optically thick wind may occur and the material lost as wind may exist as circumstellar material （CSM）. Searching for the CSM around a progenitor star is helpful for discriminating different progenitor models of SNe Ia. In addition, the CSM is a source of color excess. The purpose of this paper is to study the color excess produced from the single-degenerate progenitor model with an optically thick wind, and reproduce the distribution of color excesses of SNe Ia. Meng et al. systemically carded out binary evolution calculations of the WD ＋MS systems for various metallicities and showed the parameters of the systems before Roche lobe overflow and at the moment of supernova explosion in Meng ＆ Yang. With the results of Meng et al., we calculate the color excesses of SNe Ia at maximum light via a simple analytic method. We reproduce the distribution of color excesses of SNe Ia by our binary population synthesis approach if the velocity of the optically thick wind is taken to be an order of magnitude of 10km s^-1. However, if the wind velocity is larger than 100km s^-1, the reproduction is bad.

GalevNB:a conversion from N-body simulations to observations

We present GalevNB （Galev for N-body simulations）, a utility that converts fundamental stellar properties of N-body simulations into observational properties using the GALEV （GAlaxy EVolutionary synthesis models） package, and allowing direct comparisons between observations and N-body simulations. It works by converting fundamental stellar properties, such as stellar mass, temperature, luminosity and metallicity into observational magnitudes for a variety of filters used by mainstream instruments/telescopes, such as HST, ESO, SDSS, 2MASS, etc., and into spectra that span the range from far-UV （90 A） to near-IR （160 ~tm）. As an application, we use Ga 1 evNB to investigate the secular evolution of the spectral energy distribution （SED） and color magnitude diagram （CMD） of a simulated star cluster over a few hundred million years. With the results given by GalevNB we discover a UV-excess in the SED of the cluster over the whole simulation time. We also identify four candidates that contribute to the FUV peak： core helium burning stars, second asymptotic giant branch （AGB） stars, white dwarfs and naked helium stars.

Distribution of ^(56)Ni Yields of Type Ia Supernovae and its Implication for Progenitors

The amount of 56↑Ni produced in Type Ia supernova （SN Ia） explosion is probably the most important physical parameter underlying the observed correlation of SN Ia luminosities with their light curves. Based on an empirical relation between the 56↑Ni mass and the light curve parameter △m15, we obtained rough estimates of the 56↑Ni mass for a large sample of nearby SNe Ia with the aim of exploring the diversity in SN Ia. We found that the derived 56↑Ni masses for different SNe Ia could vary by a factor of ten （e.g., MNi = 0.1 - 1.3 M⊙）, which cannot be explained in terms of the standard Chandrasekhar-mass model （with a 56↑Ni mass production of 0.4 - 0.8 M⊙）. Different explosion and/or progenitor models are clearly required for various SNe Ia, in particular, for those extremely nickel-poor and nickel-rich producers. The nickel-rich （with MNi 〉 0.8 M⊙） SNe Ia are very luminous and may have massive progenitors exceeding the Chandrasekhar-mass limit since extra progenitor fuel is required to produce more 56↑Ni to power the light curve. This is also consistent with the finding that the intrinsically bright SNe Ia prefer to occur in stellar environments of young and massive stars. For example, 75% SNe Ia in spirals have △ml5 〈 1.2 while this ratio is only 18% in E/S0 galaxies. The nickel-poor SNe Ia （with MNi 〈 0.2 M⊙） may invoke the sub- Chandrasekhar model, as most of them were found in early-type E/S0 galaxies dominated by the older and low-mass stellar populations. This indicates that SNe Ia in spiral and E/S0 galaxies have progenitors of different properties.

Stellar structure model in hydrostatic equilibrium in the context of f(R)-gravity

In this work we present a stellar structure model from the f（R）-gravity point of view capable of describing some classes of stars（white dwarfs, brown dwarfs, neutron stars, red giants and the Sun）. This model is based on f（R）-gravity field equations for f（R） = R ＋ f2R2, hydrostatic equilibrium equation and a polytropic equation of state. We compare the results obtained with those found by Newtonian theory. It has been observed that in these systems, where high curvature regimes emerge,stellar structure equations undergo modifications. Despite the simplicity of this model, the results are satisfactory. The estimated values of pressure, density and temperature of the stars are within those determined by observations. This f（R）-gravity model has proved to be necessary to describe stars with strong fields such as white dwarfs, neutron stars and brown dwarfs, while stars with weaker fields, such as red giants and the Sun, are best described by Newtonian theory.