This quasi-stellar object (QSO) is so bright that (with some mild assumptions, including that it's a single supermassive black hole and that its angular momentum is not super-extremal) its outgoing high-energy photons should collide with the electrons in star-forming gas and dust anywhere near it, pushing the electrons outwards from the QSO. In (quasi-)neutral gas, where the electrons are pushed, they drag their protons with them. If all the electron-containing matter is pushed away, how do we reconcile that this QSO [a] grew at all and [b] shines so brightly?

QSOs like this one appear to crash into the Eddington limit, which depends almost entirely on mass (more below). If we assume a "bottom-up" formation for this QSO, with early stellar-collapse black holes merging into this supermassive giant, the problem is that its observed mass is so high that it and its many smaller progenitor BHs should have blasted away all the star-forming dust and gas from their neighbourhood. You need a lot of stellar black holes to merge into this giant, so suppressing star-formation at all is a problem. Moreover, removing much of the matter from neighbourhood then mechanisms like dynamic friction fall off, making the black hole merging process too slow for the relatively short duration (locally to the QSO) between the epoch early star formation and the QSO as we observe it.

A reasonably accessible 40-slide tutorial on the Eddington limit:

http://www-astro.physics.ox.ac.uk/~garret/teaching/lecture7-...

Note, however, slide 33, which offers up a couple of hints about how the Eddington limit can be evaded: thick low-density accretion clouds. These are expected in the "dark ages" of the early universe before there are many stars, under the standard structure formation model [1].

If we do the hard computing that slide alludes to and consider a "direct collapse" black hole as the progenitor of this QSO, rather than building it out of smaller stellar black holes, we can explore a class of such "evasions". In essence we need a starless pocket of gas to become dense enough to collapse while relatively cold into a black hole of perhaps a million solar masses. Alternatively we could get perhaps ~10 such pockets to collapse into BHs of a hundred thousand solar masses each, and then rapidly merge. The first approach tends to create a later Eddington problem: such a BH will generically interfere with star formation within kiloparsecs, so its subsequent growth is checked. The second seems to require scenarios like early galaxy-galaxy mergers, where several smaller galaxies with a direct-collapse BH collide in such a way that the BHs rapidly merge. This is even harder to model, but has the advantage of bringing already-formed stars into the neighbourhood of the SMBH, so it can continue growing.

Lastly, I've found a quick non-technical overview of the problem and the direct-collapse idea in the context of the CR7 galaxy: https://www.ras.org.uk/news-and-press/2887-astronomers-find-... (and a further quick article with a pointer to work on the galaxy-galaxy merger idea https://www.simonsfoundation.org/2017/03/17/how-supermassive... )

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[1] http://sci.esa.int/planck/51561-the-history-of-structure-for...