A quarter of a century ago, near the end of 1996 — just before I received tenure at Harvard, a Princeton graduate student named Andrew Ulmer, gave a seminar at Harvard about his PhD thesis concerning the disruption of stars by massive black holes.
If a star like the Sun arrives within a distance comparable to the Earth-Sun separation (the so-called astronomical unit, abbreviated as `au’) from a massive black hole like Sgr A* at the center of the Milky-Way galaxy, the gravitational tide induced by Sgr A* which is four-million times more massive, will rip the star apart and morph it into a spaghetti-like stream of gas, wrapped around the black hole. Back then, it was common practice to associate the radiation flare from the disruption event with the emission from an accretion disk of gas near the black hole. The disk forms as the spaghettified gas intersects itself, like a stream of water looping around the sink and ending in a drain. However, the feeding rate of the gas is so high that the radiation pressure emanating from the disruption event could easily overcome the inward gravitational pull and disperse much of the gas around the black hole. Given these complex circumstances, it was unclear what to expect.
While Andrew was speaking, it occurred to me that this complicated situation might resemble a star. Instead of the central engine being powered by nuclear fusion, the power supply here is provided by viscous accretion of some gas onto the mouth of the black hole. Given the power input from the central engine, one could derive the surface temperature and luminosity of the opaque envelope that obscures it. I was inspired to follow this path of reasoning from my knowledge of the history of astronomy.
In 1916, before nuclear fusion was discovered as the source of energy in stars, the distinguished English astronomer, Arthur Eddington, wrote a paper titled “On the Radiative Equilibrium of the Stars”, in which he derived the structure of stellar envelopes. Eddington was able to explain observed luminosities and surface temperatures of stellar photospheres as a function of the star’s mass. He did it by balancing the inward pull of gravity with the outward push of pressure from gas and radiation, and by following radiation transport within these opaque envelopes out to the photosphere, from where the radiation escapes to the outside world.
Eddington also realized that if the star’s luminosity reaches some limit, then radiation pressure balances gravity. This limit is realized for very massive stars and equals 35,000 times the luminosity of the Sun times the mass of the object in units of solar masses. If the luminosity of the central engine exceeds this limit, the envelope cannot remain gravitationally bound to the star and so the star expands, its central temperature and fusion output go down, and its luminosity returns to stay below the limit.
This so-called Eddington luminosity limit, also applies to the central engines of black holes which are powered by accretion, because they lose their fuel supply once they shine above this limit. Indeed, the Eddington limit describes the brightest black holes at the centers of galaxies, also called quasars, all the way back to the infant universe, less than a billion years after the big Bang.
After the seminar, I approached Andrew and said: “Thank you for the inspiring talk; I think we can derive the characteristics of flares from tidal disruption events based on simple considerations, just as Eddington did for stars.” Within a few hours, I wrote down the underlying equations, assuming that at peak brightness — the central engine shines near the Eddington luminosity and its output is processed by a nearly spherical envelope of debris that is heated by this radiation. For a Sun-like star disrupted by a Sgr A*-like black hole, the photosphere of this envelope was calculated to be about 100 au, with a surface temperature of 10–20 thousand degrees, resulting in optical-UV emission. I reasoned that the opacity of the ionized gas to the radiation would be dominated by electron scattering, but Andrew refined this simplistic assumption with detailed opacity data. A few months later, we submitted a paper titled: “Optical Appearance of the Debris of a Star Disrupted by a Massive Black Hole”. When Andrew presented the results in his thesis defense at Princeton, he confronted heavy criticism and pushback from senior faculty who argued that “this model is too simple to be right”.
Over the decades since then, numerous researchers developed detailed models that are far more sophisticated than ours, commonly arguing that observations could reveal the central engine of the accretion disk through openings in the tidal debris stream. Many PhD theses predicted the appearance of tidal disruption events based on computer simulations of stream intersections, accretion and winds. These theses were mentored by some of the brightest minds in theoretical astrophysics.
By now, observers are collecting detailed data on tidal disruption events. A new observational paper that just appeared last month, authored by a UC Berkeley graduate student Kishore C. Patra and collaborators, was titled: ”Spectro-Polarimetry of the Tidal Disruption Event AT 2019qiz: a Quasi-Spherical Reprocessing Layer”. The paper’s abstract reads: “… These findings are incompatible with a naked eccentric disk that lacks significant mass outflow. Instead, the spectro-polarimetry paints a picture wherein, at maximum brightness, high-frequency emission from the accretion disk is reprocessed into the optical band by a nearly spherical, optically thick, electron scattering photosphere located far away from the black hole. We estimate the radius of the scattering photosphere to be ∼ 100 au at maximum brightness — significantly larger than the tidal radius (~ 1 au) …”
I rest my case. Nature is sometimes simpler than we might imagine it to be. Another way to put it is: “nature is under no obligation to challenge us intellectually.” In another context, an interstellar object of artificial origin might be a highly consequential discovery, even if its interpretation does not require advanced mathematics in extra dimensions.
ABOUT THE AUTHOR
Avi Loeb is the head of the Galileo Project, founding director of Harvard University’s — Black Hole Initiative, director of the Institute for Theory and Computation at the Harvard-Smithsonian Center for Astrophysics, and the former chair of the astronomy department at Harvard University (2011–2020). He chairs the advisory board for the Breakthrough Starshot project, and is a former member of the President’s Council of Advisors on Science and Technology and a former chair of the Board on Physics and Astronomy of the National Academies. He is the bestselling author of “Extraterrestrial: The First Sign of Intelligent Life Beyond Earth” and a co-author of the textbook “Life in the Cosmos”, both published in 2021.
