The Alternate View

A Black Hole in Our Sun?
John G. Cramer

Could there be an asteroid-mass black hole, a Big Bang leftover, eating away at the heart of our Sun? David Brin, in his 1990 hard SF novel Earth, considered a scenario in which a scientist created a small black hole in his laboratory and accidentally allowed it to fall to the center of our planet. However, I am not aware of any SF involving a black hole within our Sun. In this AV column, I want to consider that situation, based on a recent paper by astrophysicists M. E. Caplan, E. P. Bellinger, and A. D. Santarelli (CBS).

Our current Standard Model of Cosmology tells us that about 85% of all matter in the universe is Dark Matter, a mysterious and unidentified form of mass that interacts with other matter only through gravity. A leading candidate for explaining this Dark Matter is the hypothetical population of primordial black holes that may have been created in the early so-called QCD stage of the Big Bang.

This primordial black hole scenario would require that matter-density fluctuations in the early Big Bang were large enough to trigger the direct formation of black holes over a range of masses from zero to many solar masses, with a peak at about the mass of our Sun. Thus there may be two black hole productions mechanisms: (1) production in the gravitational collapse of massive stars (which must be preceded by the rather slow process of star formation and burn out), and (2) very rapid direct production during the early Big Bang. The James Webb Space Telescope has recently provided evidence that extremely massive black holes were present very early in the universe, supporting the hypothesis of direct black hole production from density fluctuations during the initial expansion of the universe.

If black holes with a broad range of masses were indeed produced by mechanism (2), not all of them would still be present in today’s universe, because the lightest ones should already have evaporated by Hawking radiation and vanished. In 1974 Steven Hawking showed that black holes should emit radiation, and that the larger the surface curvature of a black hole (i.e., the smaller its mass and radius), the more rapidly it will radiate away all of its mass-energy and vanish. This leads to the conclusion that the lifetime of a black hole, i.e., the time it exists before it evaporates and disappears, is proportional to its mass cubed. Therefore, the smaller black holes with masses less than about 10¹² kilograms should have already evaporated, but those of roughly an asteroid mass or larger (10⁻¹⁶ solar masses or 10¹⁴ kilograms) should have survived, perhaps accounting for the current presence of Dark Matter in the universe.

The existence of primordial black holes remains an unproven hypothesis. While there have been searches for the expected bursts of radiation and particles produced by decaying black holes in their violent final stages of evaporation, none has been conclusively observed. Thus, there is no direct evidence that the Big Bang actually left behind any primordial black holes. Their existence, however, cannot be ruled out, and they could be the mysterious Dark Matter that is required by the Standard Model of Cosmology.

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Can stars contain a black hole? A free primordial black hole could not be captured by a passing star, because its energy loss during passage through the star would be too small for capture. (We note that one could be captured by a white dwarf or a neutron star.) On the other hand, a forming star, as it condensed out of the local gas cloud, could include a primordial black hole and form around it. Such a star, partially powered by the accretion energy released by the black hole at its core, has been called a “Hawking star.” This raises the important questions of whether Hawking stars actually exist and whether they can be distinguished from stars that do not contain a black hole.

Obtaining to the answer to this question is complicated, because the evolution of a Hawking star is difficult to calculate. It depending on the details of the accretion physics and requires assumptions that may be a bit shaky. The CBS work has taken on this problem and has provided reasonable answers.

One might naively expect that a star that captures a black hole will be eaten internally, have a short, violent life, and look nothing like a similar-mass main-sequence star during that lifetime. Such expectations arise from astrophysical images of black-hole-driven quasars sending out galaxy-length jets in the early universe and releasing huge quantities of energy.

We have recently learned that our galaxy’s central black hole has a mass about four million times that of the Sun and a Schwarzschild radius of about 12 million kilometers. On the other hand, a primordial black hole with an asteroid mass (say 10^-12 of a solar mass) could capture surrounding matter within a sphere only about a millimeter in radius. Further, thermal gradients and convection within that sphere would reduce the actual rate of capture. Thus, accretion of a star by an internal asteroid-mass black hole would be rather slow.

For this reason, Hawking stars may not be very different from ordinary ones. Stars like our Sun evolve on the main sequence for about 10 billion years. CBS finds that a Sun-like Hawking star containing a black hole with 10^-12 of a solar mass should have an expected lifetime due to black hole accretion of around 36 billion years. Therefore, it should live through the entire main sequence phase with minimal changes to the appearance of the star. The black hole accretion lifetime depends on the reciprocal of the black hole mass, so Sun-like Hawking stars containing a black hole with about 4 x 10^-12 of a solar mass or more should be consumed earlier and should fall off the main sequence.

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What is the evidence for primordial black holes? Carr, et al (referenced below) have done a comprehensive study of this issue and have assembled an impressive body of evidence supporting primordial black hole existence. In particular, they have identified a number of problems in contemporary astrophysics that can be solved or eased by assuming that primordial black holes play a role. We will consider some of these.

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The gravitational wave detector LIGO has been operating in Washington State and Louisiana since 2015, and it has recently been joined by detectors VIRGO in Italy, KAGRA in Japan, and GEO600 in Germany, forming a sensitive worldwide gravitational wave detector network. So far, this growing network has detected about 90 black-hole merger events and has been able to provide good estimates of the masses of the merger participants. Because of formation details, there should be no black holes produced by stellar collapse in the mass region between 150 and 60 solar masses and none below about 25 solar masses. Below that, neutron stars form but there should be none below 10 solar masses. White dwarfs form below that, but there should be none between 5 and 2.5 solar masses. However, the LIGO merger data shows nine participants with masses within the 150-60 mass gap and 6 participants within the 5-2.5 mass gap. In addition, there is some evidence within the data of five possible merger events in which one of the participants has a mass of less than one solar mass. Stellar collapse models have great difficulty in explaining these observations, while they are easily explained if the participants are primordial black holes.

In addition, the LIGO black hole merger data provides information about the effective spin of emerging binary systems. For the merger events so far detected, an effective spin that has been measured is so low that it is compatible with zero for the majority of the events. Most stars have angular momentum and rotate, and if they collapse to a black hole this angular momentum is preserved. Like a spinning ballerina who pulls in her arms, this gives the resulting black hole a rather high spin. On the other hand, a primordial black hole that was formed from a density fluctuation in the early Big Bang would be expected to have a very small or zero spin.

In a black hole binary merger, if the participants have high spins and are parallel, this should give the merging system a very large effective spin. If the spins are anti-parallel, the effective spin could be small, but that should occur at most half the time. Thus, the small observed effective spin of the detected merging systems provides evidence that many of the participants may be primordial black holes rather than those formed by stellar collapse.

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Carr, et al, provide a number of other astrophysical observations and puzzles that individually can be taken as supporting evidence for the existence of primordial black holes. These include the recent detection of high-redshift dwarf galaxies that formed very early, the puzzling correlations of source-subtracted infrared and X-ray cosmic backgrounds, the size and the mass-to-light ratios of ultra-faint-dwarf galaxies, and the dynamical heating of the galactic disk. While none of these observations in itself provides a “smoking gun” requiring the existence of primordial black holes, taken together they constitute a body of evidence that is difficult to ignore.

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Returning to the question of whether our Sun might have coalesced around an asteroid-mass primary black hole, that is possible but probably unlikely. Our Sun is what astronomers call a “Population I” star. Population I stars are young second generation stars mainly in the galactic disk that contain lots of atoms heavier than helium, produced by earlier supernovas from older Population II stars. The Population II stars are older, metal-poor stars located mainly in the galaxy’s nuclear bulge, halo, and globular clusters.

If primordial black holes were produced in the initial QCD phase of the Big Bang, their density was larger when our galaxy was initially forming than at the later time when our Sun coalesced out of galactic gas and supernova remnants, reducing the chances that a primordial black hole may have participated in its formation. Further, black hole accretion produces energy but no solar neutrinos, while solar fusion in the Sun, after neutrino oscillations are taken into account, is predicted to produce just the quantity of neutrinos that are observed by the Homestake, SNO, and Super K solar neutrino detectors. If any significant fraction of the Sun’s energy output came from black hole accretion, this should not be the case.

Thus, we can probably relax: our Sun is not in the early stages of being eaten by a black hole at its core. However, there are probably many stars in our galaxy, particularly Population I stars near the galactic center, that are being slowly consumed by internal black holes. Astronomers are looking for them. 

References:

2312. E. Caplan, E. P. Bellinger, and A. D. Santarelli, “Is there a black hole in the center of the Sun?”, arXiv: 2312.07647v1 [astro-ph.SR], (2023).
2313. Carr, S. Clesse, J. Garcia-Bellido, et al., “Observational evidence for primordial black holes: A positivist perspective,” arXiv: 2306.03903 [astro-ph.SR], (2023).

Hard SF Novels: John’s new third hard SF novel, Fermi’s Question, and its prequel, his second hard SF novel Einstein’s Bridge, are available as eBooks from Baen Books at: https://www.baen.com/fermi-s-question.html and https://www.baen.com/einstein-s-bridge.html.

His first hard SF novel Twistor is available online at: https://www.amazon.com/Twistor-John-Cramer/dp/048680450X

Nonfiction: John’s 2016 nonfiction book  The Quantum Handshake—Entanglement, Nonlocality, and Transactions, (Springer, January 2016) is available online: https://www.amazon.com/dp/3319246402

Alternate View Columns Online: Electronic reprints of 229 or more of “The Alternate View” columns written by John G. Cramer and previously published in Analog are currently available online at: https://www.npl.washington.edu/av/.

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