The case of the missing neutron stars

29 January 1999

Certain heavy stars at the end of their lives collapse in the most violent explosions known in the universe ­ supernovae. What is left after they have blasted most of their bulk into space is a dense ball of neutrons, a neutron star, or occasionally a Black Hole.

Simulations in the 1980s by Gerry Brown at Stony Brook, New York, suggested that neutron stars of up to two solar masses should be found in supernova remnants, but the heaviest seem to be just 1.5 solar masses. According to Brown’s calculations, there should be a two-solar-mass neutron star in the remnants of SN1987A, but so far none has been found. Working with Hans Bethe, Brown has come up with a possible reason why.

Bethe and Brown suggest that in dense nuclear matter, negative kaons could play a similar role to electrons. What would allow them to do this is a curious phenomena whereby the mass of kaons decreases as the density of the surrounding medium increases. But there is a crucial difference between electrons and kaons: electrons are fermions, kaons are bosons. That means that kaons are not limited by Pauli’s exclusion principle and many more of them can pack into a dense star than can electrons.

The negative charge of large numbers of kaons allows many more protons to exist in the star. Bethe and Brown calculate that, unlike the case of pure neutron matter, a large proton-to-neutron ratio can precipitate the collapse of the star into a Black Hole. If they are right, then what is left after SN1987A’s collapse is probably a Black Hole.

Bethe and Brown’s model lends itself well to experimental testing since kaons are easily produced in accelerator laboratories, and the density of neutron stars can be simulated in heavy-ion collisions. And that is exactly what Peter Senger and his colleagues at GSI Darmstadt have done. They studied kaon production in the collisions of high-energy nickel ions with a nickel target. In such collisions nuclear matter is compressed to about three times its normal density.


The GSI team found that the number of positive kaons emerging from collisions was as expected, but the number of negative kaons was far higher. One possible explanation, put forward by Gerry Brown among others, is that the effective mass of negative kaons is strongly reduced in the dense nuclear medium compared to that of positive kaons ­ just the effect needed by Bethe and Brown’s proposal. That means that negative kaons become easier to produce, and more of them emerge from the collision.

According to Bethe and Brown’s calculations, an effective negative kaon mass at three times normal nuclear density, which would account for the GSI result, could also provoke the gravitational collapse of neutron stars of 1.5 to two solar masses. GSI’s result helps turn Bethe and Brown’s idea into a firm prediction. All that remains now is to identify the Black Hole in the middle of SN1987A.

Further reading

H Bethe 1990 Supernova Mechanisms Rev. Mod. Phys. 62 801.
R Barth et al. 1997 Phys. Rev. Lett. 78 4007.


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