Research Byte
Published in the RSAA Lunations
Vol1 Issue37 1–28 February 2023
What the slow twinkle of quasars reveals about their accretion discs
Almost exactly 60 years ago, Maarten Schmidt sat in his office at Caltech, puzzled by bizarre emission lines in the spectrum of a blue radio-emitting star. He had taken the spectrum at Palomar a few weeks earlier, after the strange object had been identified at the Parkes radio telescope in Australia. On February 5, 1963, he realised that he had been staring all that time at the well-known Balmer line series except it was redshifted a mind-blowing 47,000 km/sec.
This was the beginning of research into quasars, and the rest is history, we might say. These days nobody is shocked to see quasars being discovered out to redshift 7+, knowing they are powered by accretion onto black holes that can be as massive as 20 billion solar masses; we accept that black holes bend space so much it closes in on itself, and from within the event horizon there is no path leading outside. They tear apart stars and hoover up interstellar gas drifting past. The two most voracious cosmic vacuum cleaners, discovered by Stromlo folk in 2022 and 2018, eat an Earth a second and a Sun every couple of days, respectively.
But one thing that kept both observers and theorists busy for decades is understanding the twinkling of their accretion discs. A good way of discovering quasars is from the nature of their UV-optical variability, which follows random-walk patterns unlike the variability of stars. The random walk model was considered a convenient phenomenological analogy without physical meaning. Naturally, it was a challenge to model magnetic discs, rotating differentially under the influence of space-bending gravity and heating from hard X-rays, a lethal place by any standard. But as we know, physicists are good at finding order in the biggest mess.
Already 25 years ago, Balbus & Hawley worked out that magneto-rotational instability should explain the friction, heat, and luminosity of accretion discs. How the instabilities would show in practice would be a little harder to predict, except the build-up of any instability from the magnetic fields being wound up by differential rotation should naturally happen on the orbital timescale. But discs are large and have a wide variety of orbital timescales within them.
A mere 5 years ago, John Tonry from Hawai’i, sat in a visitor office in the DLT working on a new all-sky calibration with Christopher Onken and myself. He needed that for his new NASA ATLAS project, a nightly all-sky survey scanning the sky above Hawai’i for new asteroids that come out of the dark to menace the Earth. As such, ATLAS would also see every quasar in the sky above Hawai’i, every night (weather permitting) for several years. We agreed that one day he’d give us the light curves so we could look for order in the randomness.
With RSAA PhD student Ji-Jia Tang, that’s what we have done. We focussed on the ~5,000 brightest quasars in a redshift range from 0.5 to 3.5, choosing only those that are seen by Gaia as isolated sources without interfering neighbours. Given the 2-arcsecond pixels of the ATLAS sky scans, we would have no chance disentangling mixed signals. We avoided radio-loud quasars, which have a reputation for excess variability and optical light from synchrotron processes in jets adding to the light from the accretion disc. The near-nightly five-year light curves of 5,000 objects provided billions of magnitude pairs for a “structure function analysis” – which means expressing the average change in apparent magnitude from one observation to another as a function of the rest-frame time that has passed between them.
Given the huge data set, we could avoid fitting just a global model to all the data, which was an unavoidable limitation of the past. Instead, we calculated model-free structure functions and were happy to see detail with little noise. There were clearly two regimes in the structure function: at longer time separations the variability followed a random walk while at shorter times it was suppressed, with a break point that related to quasar luminosity. Focussing on the random walk section alone, we then did a parametric model fit and found a best-fit slope of 0.503 +/- 0.001, very close to a textbook random walk that is defined by an exponent of ½. Past results had seen slopes from 0.2 to 0.6. However, accretion discs of different luminosity (we had a factor 100 range in the sample) and observed at different wavelength still showed a spread in amplitude, albeit increasing at the measured neat and sensible slope with time.
As a next step we changed the x-axis of the structure function from a normal rest-frame clock time to a clock ticking on an orbital timescale (see figure). This is possible, because for every quasar we know the luminosity and the observing wavelength, and by blindly trusting the temperature profiles predicted by generic models of thin accretion discs, we can find the mean orbital timescale seen in any passband for any quasar disc. This delivered a nice surprise as the structure functions, previously offset by a variety of amplitude shifts were now moved on top of each other. Hence, we had found the title for our paper: “Universality in the random walk structure function of luminous quasi-stellar objects”.
One benefit of this work is that a previous confusion is cleaned up and we can now predict better how quasars vary their brightness. The other benefit is that seeing such specific order in the randomness of the data suggests a strong physical order. The result is quite consistent with the theory of magneto-rotational instability and suggests that it is the primary origin of quasar variability. Other effects may contribute, including heating from a rapidly fluctuating X-ray corona, but perhaps on other timescales.
Now, by assuming a strong order as manifest in the tight random-walk relation, we can try to attribute meaning to subtle remaining deviations from the main relation. In not yet published follow-up work, we see small but statistically significant amplitude offsets that relate to other quasar properties. This is intriguing and offers new avenues for research. Some of the quasar properties will be correlated with the viewing angle under which we see the disc, while non-isotropic emission from the disc biases our estimate of luminosity and thus orbital timescale. Is the orientation bias the cause of the present residual offsets? And does that open the possibility of measuring orientation of discs from quasar light curves?
We also find that windy discs, as they are most often found in highly accreting systems, appear to sit on a systematically offset relation. Does that mean their accretion discs have a different temperature profile and are thicker as has been suggested by theoretical expectations? There are exciting times ahead, and surely LSST will play a role here.
The work is now published as:
Ji-Jia Tang, Christian Wolf & John Tonry, Nature Astronomy, 2023
“Universality in the random walk structure function of luminous quasi-stellar objects”
https://www.nature.com/articles/s41550-022-01885-8
See also The Conversation, Fri 3 Feb 2023: https://theconversation.com
Christian Wolf
