Looking beyond Chandrasekhar

A new finding provides the theoretical basis for the existence of progenitor white dwarfs that can breach the Chandrasekhar limit.

Nobel laureate Dr S Chandrasekhar.

IN 1931, the astrophysicist Subrahmanyan Chandrasekhar theorised that a star would not form a stable white dwarf at the end of its life if its mass was greater than 1.44 times the solar mass (1.44 Ms). This is known as the Chandrasekhar limit, above which the white dwarf will explode as what is called a “Type 1a supernova”. This work fetched Chandrasekhar the Nobel Prize in 1983.

In a recent work published in the latest issue of Physical Review Letters, Banibrata Mukhopadhyay and Upasana Basu, astrophysicists at the Indian Institute of Science (IISc), Bangalore, have shown that white dwarfs with very high magnetic fields (greater than about 2 x 10 ¹³ gauss, or 20 trillion gauss) in their cores can breach this limit and grow into much bigger and brighter white dwarfs.

Significantly, the Nobel laureate had not included the effect of magnetic field in arriving at his result. The new finding leads the authors to postulate the existence of a “Super-Chandrasekhar limit” of 2.58 Ms for such highly magnetised white dwarfs beyond which these too will explode.

The new limit also serves to explain the puzzling observations during the last decade of Type 1a supernovae, which have defied explanation so far. Since 2003, astronomers have observed several bizarre Type 1a supernovae, which do not seem to conform to the conventional theoretical understanding of such objects.

Type 1a supernovae are thought to be formed when a stable white dwarf acquires mass by accreting matter from a (non-white dwarf) companion star and exceeds the Chandrasekhar limit, which sets off a runaway thermonuclear process causing the star to explode.

The mass cut-off (a la Chandrasekhar) makes all conventional Type 1a supernovae explode with about the same intrinsic brightness because they have roughly similar amounts of fuel (in the form of carbon and oxygen) in the progenitor white dwarf, which undergoes nuclear fusion and ends up as nickel-56. They have characteristic spectra, which are devoid of hydrogen lines but have silicon absorption lines. Their light curves —plot of light intensity vs time—are also very similar.

Because of this intrinsically uniform property of Type 1a supernovae, they have been regarded as the best “standard candles” for measuring cosmological distances. By comparing the known intrinsic luminosity of a given Type 1a supernova to its observed brightness, the distance to the object can be computed using the inverse square law.

Expansion of universe

It was, in fact, the observations on Type 1a supernovae in 1998 that led to the surprising discovery that the expansion of the universe is actually accelerating. Astrophysicists have sought to explain this by hypothesising an unknown dark energy that fills the universe and opposes the mutual gravitational attraction of matter.

But these recent dozen or so peculiar Type 1a supernovae are about twice as bright as the normal ones (which are numerous) and their light curves cannot be reconciled with the conventional picture of white dwarfs in the framework of the Chandrasekhar limit with any amount of fine-tuning. Moreover, in a brighter normal Type 1a supernova, matter is ejected from the explosion at a higher velocity because the explosion has more kinetic energy. But in these, even though they are much brighter, ejecta have been found to be unusually slow.

The mass of the progenitor white dwarf required to explain these anomalously bright supernovae is greater than 2.1 Ms. This follows from the following argument. In a normal Type 1a supernova, the amount of nickel is about 2/3 Ms, the rest being other elements. Therefore, a Type 1a supernova twice as bright should have at least twice the amount of nickel. The only way to get that is with a progenitor white dwarf that is at least 50 per cent more massive than the limiting mass. But the physics underlying the Chandrasekhar limit alone cannot give rise to such high-mass white dwarfs.

Some scientists have sought to explain this new class of Type 1a supernovae in terms of two merging white dwarfs, but this, others have argued, will actually lead to a neutron star and not a massive white dwarf. The other favoured explanation is that these white dwarfs are rotating at great speeds and the centrifugal force acts against gravity preventing their collapse even after they exceed the mass limit. Arguing that these explanations lack a foundational physical principle, Mukhopadhyay and Das have provided a theoretical basis for the existence of progenitor white dwarfs with super-Chandrasekhar limit mass by postulating very high intrinsic magnetic fields in them.

The authors have shown that white dwarfs with extremely high magnetic fields can be stabilised at a mass greater than the Chandrasekhar limit. This comes about because of what is known as “Landau quantisation”, a quantum mechanical phenomenon that modifies the energy distribution of electrons in the presence of magnetic fields. This enables a greater electron degeneracy pressure to act against gravity (see box), thus allowing the white dwarf to grow beyond the limiting mass, and the star explodes as an “overluminous supernova”. Das and Mukhopadhyay calculate this new mass limit to be 2.58 Ms, a value that fits with the observed new class of Type 1a supernovae.

Magnetised white dwarfs themselves are not new. Many isolated white dwarfs and about a quarter of accreting white dwarfs are known to have high surface magnetic fields of 100,000 to a billion gauss (the earth’s field is about a gauss). The authors argue that their central magnetic fields could be 100-1,000 times stronger.

The key issue, however, is that the effect of Landau quantisation becomes significant only for central magnetic fields of greater than 1013 G. Below such values of the magnetic field, the Chandrasekhar limit is a good limiting mass even for magnetised white dwarfs. For the high central fields required for Landau quantisation, the surface fields should be of the order of 1011 G and more. But accreting white dwarfs with such high-surface fields have not been seen so far.

Giving justification for considering such high magnetic fields, Mukhopadhyay and Das have argued that an initial non-zero magnetic field is crucial for facilitating mass accretion, and as the star shrinks, both the surface and central magnetic fields, too, continuously increase owing to the conservation of the total magnetic flux. According to Mukhopadhyay, in a yet-to-be-published paper, he and colleagues have apparently argued that about one-tenth of the high-field accreting white dwarfs actually have such extreme high fields but perhaps owing to magnetic shielding by accreting matter, the measured values may be orders of magnitude lower.

Questions raised

Some have raised questions about the work at a fundamental level. “The authors have not taken into account the effect of magnetic pressure [which depends on the gradient of the magnetic field] in their calculations. This could prevent the star’s growth beyond the Chandrasekhar limit,” pointed out Dipankar Bhattacharya of the Inter-University Centre for Astronomy and Astrophysics (IUCAA), Pune.

In their paper, the authors have assumed the magnetic field to be constant in the envisaged scenario of high-density and an extremely compact white dwarf and, therefore, zero field gradient and zero magnetic pressure. “This is a reasonable assumption at least insofar as we are trying to calculate the limiting mass of the white dwarf, which is concentrated in the central matter up to say 60-70 per cent of the star’s radius. There would be a gradient in the surface matter but that would change the result only slightly,” Mukhopadhyay said.

“We have seen thousands of white dwarfs but most of them do not even come close to the Chandrasekhar limit; those we see as Type 1a are already extreme cases,” pointed out Sandip Chakrabarti of the S.N. Bose Centre for Basic Sciences, Kolkata, who had worked with the Nobel laureate in the 1980s. “If there is a higher limiting mass, why have we not seen any stable white dwarf above the Chandrasekhar limit? If the white dwarf has such high magnetic fields, the same field would, in fact, expel accreting matter from the surface along the ‘open bipolar field lines’ and prevent it from growing,” he said. “However, the authors have opened an interesting area of inquiry into white dwarf evolution, which should eventually lead to a better understanding of such objects,” he added.

The authors have, in fact, gone further to speculate that their result could have far-reaching implications for the expansion history of the universe itself, including the question of dark energy, as it could change the very definition of the standard candle that astronomers have been using to measure cosmological expansion. “This [the new limiting mass] might eventually lead these supernovae to be considered as altogether new standard candles. This has many far-reaching implications, including a possible reconsideration of the expansion history of the universe,” they wrote in their paper.

From the theoretical perspective of the authors, these peculiar, highly magnetised white dwarfs constitute the generic case, while the unmagnetised (or even weakly magnetised) white dwarfs form the special case. Phenomenologically, of course, the situation is the opposite because in terms of statistics of white dwarf observations, the number of this new class of objects is very small as compared to the countless normal Type 1a supernovae that have been seen.

However, in a forthcoming paper, Das and Mukhopadhyay, in association with A.R. Rao, an astronomer from the Tata Institute of Fundamental Research (TIFR), consider the more favoured single degenerate progenitor scenario of a binary system—where a single white dwarf (a degenerate state carbon-oxygen compact star) accretes matter from a non-degenerate companion star—and argue that, observationally, such high-magnetic field, high-mass white dwarfs with small radii must exist as progenitors of the peculiar supernovae, provided the single-degenerate accreting scenario is the correct progenitor model for Type Ia supernovae.

“We have begun to see such objects only now and in due course we may see many more such to become statistically significant,” Mukhopadhyay said. He hopes to launch a collaborative experimental search for white dwarfs with extremely high magnetic fields.