How do we know that supermassive black holes can gain mass by means other than merging with other supermassive black holes? I just stumbled across the following answer &quot;update&quot; from 2013:

This just in, recent observations have ruled out the possibility that SMBHs gain mass only through merging with other black holes. For more, see this Astronomy.com article.

Question: How do we know that supermassive black holes can gain mass by means other than merging with other supermassive black holes? I can't figure it out from the linked Astronomy.com article. In fact I can barely read it behind all the blinking advertisements that it now displays (and probably didn't back in 2013)

Potentially related:

Why can&#39;t supermassive black holes merge? (or can they?)
How do two supermassive black holes reach &quot;the last parsec&quot; in merging galaxies?
Why do we believe that the super massive black holes at the centers of two merging galaxies would themselves merge?
What enhances the capture and merge rates of pairs of small black holes orbiting around supermassive black holes?
Why would the merger of spinning black holes within the accretion disk of a supermassive black hole cause them to &quot;shoot straight up&quot; out of the disk?
The idea behind the paper (Shannon et al. 2013) that article is based on is to measure the gravitational wave background (GWB) produced by mergers of supermassive black holes, and determine which models of SMBH merger histories can replicate the SMBH population and the corresponding gravitational wave background. In this paper, measuring the GWB is done using pulsar timing - in particular, using the Parkes Pulsar Timing Array and some supplementary data from Arecibo. A pulsar timing array (PTA) detects (or attempts to detect - we have nothing definite yet) gravitational waves by measuring when individual pulses from pulsars arrive at radio telescopes. Gravitational waves should change the times of arrival (TOAs), so if you have enough TOAs from a selection of millisecond pulsars, you can constrain the GWB spectrum's amplitude $A$ and its associated energy density $\Omega_{\text{GW}}$.
The authors applied the aforementioned methodology and then considered four different models of SMBH population synthesis to try and replicate the observational results. The one which involved mass growth entirely through black hole-black hole mergers at low redshifts was ruled out at the 91% confidence level by the pulsar timing array measurements, while the others were more favored. These other models generally included SMBHs growing by accreting gas. No single one is a clear favorite, but the authors were able to rule out substantial regions of parameter space, and these three models were certainly favored more than the pure black hole-black hole merger model.
I want to emphasize something here that wasn't emphasized in the article: That merger model is focused on SMBH growth at low redshifts, and in particular on the SMBH population evolution at $z&lt;1$. Why? It's because this is where the dominant component of the GWB we detect today is expected to come from (see e.g. McWilliams et al. 2013), so it's much easier to say something about low-redshift populations based on PTA data. This is also why the group is interested in how the other models fare at low redshifts for doing things like replicating the quasar luminosity function at $z&lt;1$.
I feel like saying that the pure merger model has been entirely &quot;ruled out&quot; is maybe a bit strong; fortunately, pulsar timing arrays have made major advances since 2013, and we have stricter limits on $A$ and a better understanding of SMBH populations. The 2013 paper used only 20 pulsars, but PTAs have easily more than doubled that number in the interim, and that's only going to increase in the years to come. At the same time, the other models are certainly strongly preferred. I can look into whether this particular analysis has been replicated with newer data.