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I know that a white dwarf is mainly balanced by electron degeneracy pressure and that if it gains more than 1.4 solar masses from any source (such as a companion star or a collision), it explodes as a type I supernova. But is there any possibility that a white dwarf can turn into a neutron star (or possibly a black hole)?

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The answer is: to a neutron star - possibly; to a black hole, no.

The process whereby a neutron star is formed is known as an accretion induced collapse and is being seriously debated, especially in the case of white dwarfs that are born at the upper end of the "natural mass range" for white dwarfs and then accrete more mass as part of a binary system. An excellent read are the introductory sections of Taurus et al. (2013), who go through the motivation, process and (limited) observational evidence. See also Schwab et al. (2015); Ruiter et al. (2018).

Explosion vs Collapse

A white dwarf can respond to the accretion of material by exploding or collapsing. It depends on the competition between energy released in fusion reactions and the energy being locked away by endothermic electron capture (also known as neutronisation) reactions.

If thermonuclear reactions are initiated then the likely outcome is a runaway nuclear reaction - the pressure inside the star does not rise rapidly enough to prevent the entire star undergoing fusion. The energy released exceeds the gravitational binding energy and the likely outcome is a type Ia supernova.

On the other hand, the white dwarf is supported by electron degeneracy. If neutronisation begins to occur in the core, then protons (in nuclei) capture electrons to form neutrons. This destabilises the star causing it to collapse. The collapse would proceed (quickly) in a similar way to a core collapse supernova. The nuclei would dissociate, neutronisation would run to near-completion and the collapse would be halted by the formation of a neutron star.

There is little possibility that a black hole could be formed by such a collapse. The collapsing object would be of order 1.4 solar masses and comfortably smaller than the maximum mass of observed neutron stars (at least 2 solar masses). Therefore the collapse will be halted at the neutron star phase.

White dwarfs of moderate mass

Most white dwarfs of moderate mass have a C/O composition. They will need to accrete a lot of mass to get to a density (at about $4\times 10^{13}$ kg/m$^3$, reached at $1.38M_{\odot}$ in a non-rotating WD) where neutronisation becomes energetically feasible. Before this happens, it is probable that fusion reactions are ignited (due to high density, rather than temperature). The threshold density for ignition is *lower * for nuclei with lower atomic number (He < C < O) because of lower Coulomb repulsion, and the ignition threshold densities for He and C are also lower than the neutronisation threshold for C.

This means that in a C/O WD that has accreted a lot of matter, ignition could take place in C at the core, or it could be triggered in He (at even lower densities) at the base of a deep accreted shell of material. The outcome would likely be runaway thermonuclear fusion and the complete destruction of the star.

More massive white dwarfs

O/Ne/Mg WDs are made as the final stages of more massive stars ($8-10M_{\odot}$) and are probably born as remnants with much higher mass $>1.2M_{\odot}$ than typical C/O WDs. More massive WDs are smaller, with higher density. The neutronisation thresholds for O, Ne and Mg are only $1.9\times10^{13}$, $6\times 10^{12}$ and $3\times 10^{12}$ kg/m$^3$ respectively (all lower than for C, especially for Ne and Mg). This means that a O/Ne/Mg WD may have to accrete very little mass to reach this central density, begin neutronisation, which leads to collapse. In addition if such densities are insufficient to trigger C burning in a C/O WD, then they certainly won't be high enough to trigger burning in O/Ne/Mg because of stronger coulomb repulsion. Further, if little mass is accreted, then there won't be a deep envelope of accreted material in which to ignite burning off-centre.

For all these reasons, O/Ne/Mg WDs may be more likely (Liu et al. 2018; but see also Wang 2018) to collapse than explode (the collapse would cause a type of core-collapse supernova though).

Does accretion induced collapse occur?

At present there is only indirect evidence. When we look at recently formed neutron stars - identified as fast-spinning pulsars - we see they generally have very high velocities. These velocities are thought to result from an asymmetric "kick" delivered by a type II core-collapse supernova. This in turn suggests it might be quite difficult to retain a neutron star in a binary system, but many neutron stars are observed to be in binary systems, and many of these, particularly the millisecond pulsars, are thought to have undergone significant mass transfer in the past.

Further evidence comes from the retention of a significant population of neutron stars inside globular clusters. Again, the kicks might have been expected to expel most of these. In addition, there are a number of examples which appear to be "young", in that the ratio of their spin periods to rate of spin decay indicates they were formed recently. Since there are no high mass stars in globular clusters, and so no possible progenitors for these objects via the core-collapse of massive stars, then accretion induced collapse of a high mass white dwarf is a possibility.

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Not for most white dwarfs, because they are usually full of fusionable material (most notably carbon and oxygen). When material like that starts to undergo gravitational collapse, it heats up and fuses, creating the type Ia supernova and leaving nothing behind because of the intensity of the explosion. But some white dwarfs have iron cores, for example, https://arxiv.org/abs/astro-ph/9911371, and it might be expected that the iron core would survive the supernova. Whether it could gain enough material to collapse into a neutron star I couldn't say, it doesn't sound easy but never say never.

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  • $\begingroup$ The 90s evidence for possible iron white dwarfs (based mainly on the Hipparcos results for Procyon B) has subsequently gone away. iopscience.iop.org/article/10.1086/338769/fulltext/… $\endgroup$ – Rob Jeffries Apr 14 '18 at 10:37
  • $\begingroup$ Ah, that's very interesting, thank you-- so now the answer would seem to be an even stronger "no" than before. $\endgroup$ – Ken G Apr 14 '18 at 19:24
  • $\begingroup$ Somehow I only say your comment, but not your full answer. The latter explains in some clarity how neutronization could proceed ignition in some white dwarfs, even without iron. I see your point! So yes, you do seem to have found a path to a neutron star from a white dwarf, well done. $\endgroup$ – Ken G Apr 14 '18 at 22:10
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If your white dwarf has a large Iron core . . . maybe. But probably not. The rapid type 1a collapse at the Chandrasekhar limit, with the radiative pressure pressing into the Iron core . . . just maybe, but even then I want to say no, it's not possible, only that, that scenario just might has a chance.

A black hole is a hard no. A 2.5 (about) solar mass neutron star can turn into a black hole. A 1.4 solar mass white dwarf even if made from Iron, even if it somehow manages to collapse into a neutron star, it would be much too light to collapse into a black hole.

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