false positives, galaxy merging

[Just back from travel, hence intermittent posting. The following was composed on an airplane.]

I spent this morning (Thursday) in San Francisco (thank you, delayed flight) working with Roweis on what we call the verify step in astrometry.net. This is the step where we decide, for a given hypothesis about an image's pointing, rotation, or scale, whether that hypothesis is correct (or very close to correct). Roweis and I are proposing that we base this decision on an approximate but conservative estimate of the false-positive probability; that is, we consider a hypothesis correct if the match we observe between the image stars and the catalog stars is extremely unlikely to have occurred by chance. One interesting aspect of this is that we have to track all hypotheses we have tested so far: Your false positive rate goes up the more you look.

Philosophically, the reason that astrometry.net's internals work is that the verify step is very simple and fast. Our quad matching system is very unreliable; it generates thousands of hypotheses, only one of which is correct. But because the verify step is fast, we don't mind having many hypotheses to check. The least flattering description of our system is that it does brute-force search of every conceivable hypothesis (of which there are many billions), but with the quad system ordering the hypotheses so that we are very likely to hit the correct one in the first few thousand!

I spent yesterday (Wednesday) battling it out with Santa Cruzians about the red sequence of early-type galaxies and constraints on any processes of galaxy–galaxy merging that can cause it to evolve. That was lively! Also Croton (Berkeley) and Wechsler (Stanford) came to UCSC to join the battle.

It is hard to summarize the discussion here, but points that came up include: If you want to look at the stellar populations of a galaxy that is post-merger, you have to consider that some of the stars may have been thrown to large radius and are now part of the intragroup stellar population. In thinking about the evolution of the tilt of the red sequence, you have to correctly treat the differential evolution that comes from blue galaxies fading more into the L-star part of the sequence, percentage-wise, than into the high-mass part. There might be massive, star-forming progenitors of the massive red galaxies hiding among ULIRGs and luminous AGN. The observed evolution of the total mass on the red sequence does not require a lot of evolution at the most massive end, though that is in large part because the signal-to-noise of the observations is limited. And etc. Interestingly, I think we all agreed that merging ought to make the massive end of the red sequence become broader (in some metric) with cosmic time.


  1. Bummer I missed this session, though I enjoyed your talk.

    First, a question. Garth and I came away with the impression that Erik Bell got a similar answer to you with regard to the number of mergers among massive galaxies. Instead, according to him, a huge fraction of z~0.7 galaxies will merge. Apparently this all happens between z~0.7 and z~0.3? Do you have any other thoughts?

    Second, I wonder how much ICL/IGL is made as a function of halo mass. Clusters have large amount of light, but they are big. It seems like that the theorists are never going to tell us an answer and that measuring this could make a big impact. So, is there enough uncertainty in the ICL computation to explain away your result? Could one sweep under the ICL all of your missing second galaxies?

  2. In answer to your first question, a lot of the difference between how Bell's paper reads and how I describe it comes from the fact that Bell and I have measured different rates: I measure the rate at which LRGs will merge, so I divide the density of LRG–LRG pairs by the density of LRGs. Bell measures the rate at which LRGs have merged, so he divides the density of sub-LRG–sub-LRG pairs by the density of LRGs. Because the luminosity function is steep, Bell gets a much higher rate. But the evolution in the observable is not as strong.