# Why does the Chandrasekhar limit affect white dwarfs differently?

The Chandrasekhar limit is the maximum mass of a stable white dwarf star. Beyond this, a carbon-oxygen white dwarf will typically explode in a type 1a supernova, due to the nuclear reactions at those temperatures.

I've heard that oxygen-neon-magnesium white dwarfs, on the other hand, will not ignite. Rather, electron capture becomes energetically favorable and they become neutron stars. If I understand correctly, this also happens for carbon-oxygen white dwarfs in binaries, if the white dwarf has most of the mass in the system.

Why is this? Can anyone walk me through, step by step, what happens if a white dwarf (of both compositions) exceeds the Chandrasekhar limit, and how each differs?

Whether a white dwarf responds to the accretion of material by exploding or collapsing depends on the competition between energy being released in fusion reactions and energy being locked away by endothermic electron capture (neutronisation) reactions.

It is thought that 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. It is possible, that before this happens, 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) and the ignition threshold densities for He and C are probably lower than the neutronisation threshold for C.

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 electron degenerate matter has a pressure that is independent of temperature, leading to runaway fusion and the complete destruction of the star.

O/Ne/Mg WDs are made as the final stages of more massive stars ($8-10M_{\odot}$) and are 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, 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). 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 to collapse than explode (the collapse would cause a type of core-collapse supernova though).

EDIT: Actually looking at the paper you reference (which is a bit dated), although some of the numbers have changed slightly, the semi-quantitative argument I give above is exactly how it is explained there. So I'm not sure whether my answer helps you.

• You just said the collapse of wouldn't trigger burning in an O/Ne/Mg neutron star, and then said the collapse would cause a type of core-collapse supernova. Could you elaborate? Wouldn't the supernova be caused by oxygen fusion? Why would it leave a remnant behind? May 12 '16 at 23:35
• @SirCumference Type II supernovae are powered by gravitational potential energy, not fusion. The GPE released when a WD collapses to neutron star size in less than a second is greater than can be generated by oxygen fusion (the oxygen is in any case removed by electron capture). Most of the energy is lost as neutrinos. Why wouldn't it leave a remnant? May 13 '16 at 5:28

There are a variety of white dwarfs with various compositions, and analysing how they detonate in a supernova (or not) is an topic under investigation. A simple model, described in "How is the first detonation in Supernove type Ia triggered?" is of a helium shell initially igniting and that setting off the carbon in the core.

In this type of Type 1a supernova there is no neutron star formed, as the star is completely destroyed. The mass at which a white dwarf will undergo a type 1a supernova is just below the chandrasekhar limit, so neutronisation won't occur.

However in some white dwarfs with an atypical composition (as you note a Mg-Ne-O white dwarf) it is possible for the star to avoid detonation, and reach the chandrasekhar limit, and so for electron capture to occur, and a neutron star to form. It is worth noting that there is not definite observation of a white dwarf collapsing to a neutron star (where as there a lots of observations of type 1a supernovae) however these "accretion induced collapse" scenarios may explain some magnetars and short gamma ray burst

Progenitors of the Accretion-Induced Collapse

So the two scenarios are,

1. Accretion occurs onto a Carbon-oxygen WD. The pressure and temperature in the core of a white dwarf increases until thermonuclear reactions begin (at about 1.38 solar masses). Since the white dwarf is degenerate it can't expand to reduce the rate of thermonuclear reactions, and the entire star detonates and is destroyed.
2. Accretion occurs onto a ONeMg WD. The star reaches 1.44 solar masses, electron degeneracy is no longer sufficient to prevent collapse. Electron capture occurs and the star collapses to neutron star.
• The link I added also mentions neutronization in binaries. Why does that happen? May 2 '16 at 11:41
• The "vanilla" Chandrasekhar mass is not 1.44 solar masses for any kind of white dwarf. It is set by GR at between 1,38 and 1,39 solar masses for (non-rotating) C/O and O/Ne/Mg white dwarfs, if you define it as the maximum possible mass supportable and ignore the possibility of electron capture (which can lead to instability at marginally lower masses in the case of O/Ne/Mg WDs). May 2 '16 at 12:48
• @RobJeffries So what happens if it's rotating? Why would it be different? May 2 '16 at 12:49
• If a WD is rotating at an appreciable fraction of its Keplerian breakup speed, then the Chandrasekhar mass can be increased by a few percent, and have lower densities at the same mass. arxiv.org/abs/1204.2070 May 2 '16 at 13:17