How far away is this galaxy? Arp 299 is in the news, with most sources reporting it as 140 or 150 million light-years away. But what kind of distance is this?

The paper which is trhe source for the news item has Supplementary Materials which mention the distance but don't appear to say what kind or give details:


  The merging pair of galaxies Arp 299 (Fig. 1) at a 44.8 Mpc distance (33; corrected to the cosmic microwave background reference frame; H0 = 73 km s^-1 Mpc^-1) is one of the brightest nearby LIRGs with an IR luminosity LIR ~ 7x10^11 L_⊙ (34; L_⊙ = 3.833×10^26 W).


Is it obvious what method is used (and thus what type of distance this is) to measure the distance to this galaxy? Is there a standard reference/database/etc. giving basic information like distances of astronomical objects like galaxies? I'd like to know the answer for this galaxy, but answers that generalize will naturally be more interesting.



Edward L. Wright has a cosmology calculator that is useful in converting between different types of distances. His page on distances gives many methods for measuring distances; I feel that if I knew which type (if any) of these methods was used to find the distance I'd have a decent chance of figuring out what kind of distance it was (and could find the other distances by bisection).
The article references a paper by Huo et al. (2004; that's the reference number "33" in your quoted text). Huo et al. merely list a redshift of "0.0103" for Arp 299 in their Table 1 (without any apparent sources); combined with the fact that the authors of the Science paper say what Hubble constant they assumed (73 km/s/Mpc), this tells us that the distance is redshift-based. That is, they used the redshift plus the Hubble constant to derive the (comoving) distance.

If you look up Arp 299 in the NASA Extragalactic Database and scroll down the resulting page, you can see a list of possible redshifts ("Calculated and Corrected Velocities") for this galaxy, ranging from 3088 km/s (which is in fact $z = 0.0103$) to 3511 km/s. Immediately below that, you can see the derived distances ("Hubble Flow Distance"), assuming $H_0 = 73$, the same value the authors say they used. The closest number to their value is the 44.4 Mpc, assuming "3K CMB" correction (which seems to match the authors' description). Why this isn't exactly the same as the authors' value of 44.8 Mpc I don't know; possible a slightly different value of the redshift was used.

At this relatively small redshift, the differences between the different distances that pela mentions are pretty minor. E.g., plugging $z = 0.0108$ (NED's "3K CMB" corrected redshift) and $H_0 = 73$ into Ned Wright's cosmology calculator gives you a comoving distance of 44.2 Mpc, a luminosity distance of 44.7 Mpc, and an angular-diamter distance of 43.8 Mpc. The differences between these are all smaller than any plausible uncertainty based on using the redshift.[*]

So, to summarize, the distance in the paper is (as pela says) the comoving distance; the method used to derive it was the redshift of the galaxy (corrected to a CMB-relative value) plus a Hubble constant of 73 km/s/kpc.

[*] E.g., if we assume a redshift uncertainty of 300 km/s, based on possible peculiar motion of Arp 299, then the distances are uncertain by +/- 4 Mpc.