I performed a massive re-organization of the faint-source proper-motion code, to make it less redundant and easier to test and analyze. I improved the use of the SDSS data, though I have yet to build in good estimates of the individual-field point-spread functions. Once that is done, I can try to reproduce some known proper motions in the SDSS data and write it up.
Yesterday the high-z quasar team on SDSS released to the collaboration six new quasars in the SDSS Southern Stripe. I completed my proper-motion code and used it to measure their proper motions. I find that the quasars have no proper motions at my precision! It remains to be seen if I have the precision to separate them from brown dwarfs at the same magnitude.
I pushed my faint-source proper motion measurement experiments to the signal-to-noise limits. Indeed, the system breaks down not when the signal-to-noise per epoch is low, but when the combined signal-to-noise in the data from all epochs is low. It works all the way down to a signal-to-noise around 4 in the combined data set, even when the per-image signal-to-noise is much less than 1.
I tried to figure out how accurately one can possibly measure a proper motion, given a heterogeneous data set. I have an approximate expression, and it seems to agree with my code (ie, my code seems to hew close to the best possible errors), but I don't yet have a proof. One interesting consequence of this exercise is that the proper motion accuracy does not depend explicitly on the number of images you take, only their time span (measured appropriately) and the total signal-to-noise with which you have detected the source. For this reason, if you are concerned to beat down systematics with redundancy, go to town: Take many short exposures at many epochs rather than a few long ones. Of course this is all provided that you are gutsy enough to measure the proper motions below the individual-epoch detection limits!
Eric Bell (MPIA) and I spent some time talking about making precise measures of the merger rate. This was inspired by my finishing up the Masjedi et al paper on the growth of LRGs from accretion of satellites. The main uncertainty, of course, is the merging time-scale. We use a time-scale based on dynamical friction, but that is only good to factor-of-two at best. Will we ever have a reliable statistical measure of the growth of galaxies by merging? Perhaps if we have models that build realistic galaxies in a cosmological context.
Bell and I also discussed the project I was discussing a while back with Darren Croton (Berkeley): If galaxies at the massive, red end of the red sequence grow by merging, then the color-magnitude relation should flatten out there. That is, you can't maintain a linear relationship between color and luminosity if galaxies are merging prodigiously. This project requires good photometry at the bright end. Right now, Blanton and I are among the few on SDSS who can provide.
On Friday I measured the proper motion of a high-redshift quasar, one that is not visible in any individual SDSS epoch, but visible in the stacked image, by fitting simultaneously all the pixels in all the individual images, and then marginalizing over the unknowns (flux and position). I got zero, to within the errors. Woo-hoo!
Continued work on my RANSAC and EM-based astrometry tweak code. It is proceeding by
test-driven development techniques, so what I did today was define the calling sequence and unit tests for the part that does the fitting of positions in the image to positions in the catalog.
In between work supporting our alpha testers and writing other people's papers, I thought a bit more about detecting faint source proper motions. There are really four regimes: slow, in which stars move less than the PSF over the duration of the survey (total epoch range); medium, in which stars move substantially more than the PSF, but less than the size of individual images; fast, in which the sources move a distance comparable to the size of any individual epoch image between epochs, and many times this over the duration of the survey; and streaked, in which the sources make trails even in individual images, and probably have orbits that are non-trivially curved over the duration of the survey. Each of these regimes requires different statistical equipment and techniques for optimal detection and measurement. I realized I need to re-read papers by Lepine.
In the role of Rix and Jestser's graduate student, which I have taken on for the summer, Jester assigned me the project of obtaining the proper motion of UKIDSS z=5.86 QSO ULAS J020332.38+001229.2, which is not visible in any individual SDSS epoch, but is visible as a z-band-only object in the combined image from many epochs, as it is in the SDSS Southern Stripe.
Today was the first day of Galaxy Growth in a Dark Universe here in Heidelberg. I could only go to part of the day, but I did see convincing evidence from Kriek and Kodama that there is some kind of
red sequence in place at redshifts 2<z<3. Of course the
old galaxies at these epochs in fact look like K+A or post-starburst galaxies!
Our web service astrometry.net works by rapidly generating large numbers of hypotheses and then attempting to verify them using a statistical test; as soon as one generated hypothesis verifies, its job is done. I spent the day working on a similar methodology for detecting—and measuring the proper motions of—extremely faint sources in multi-epoch astronomical imaging.
Wu and I had a long chat today with Frank van den Bosch (MPIA), who is working on galaxy environments with his high-test group catalog constructed from the SDSS data. His results are all in general agreement with ours, including especially that all environment effects come in at the group scale or smaller, and that a lot of what is happening is driven by the differences between
satellite galaxies in the groups (where by these terms we usually mean
highest stellar mass and
lower stellar mass, observationally, since group centers are notoriously hard to determine).
What is new about van den Bosch's work is that he finds that almost all of the information in the environment relations—once you make the central–satellite split—comes from mass segregation among the satellites! The higher mass satellites are more concentrated towards the centers of the groups, and the more massive groups have more massive satellites. Since star-formation rate and everything else is strongly related to galaxy mass, these mass effects drive most of the action. This is remarkable, but not in conflict with our results, and the starting point for some new observational experiments.
Of course, like with our work, the van den Bosch results are easy to misinterpret, because they involve controlling for multiple variables and looking at dependences on remaining variables, which is a subtle business. Also, vdB showed that some of the environment effect conflicts in the literature come from the use of different simple scalar statistics to describe the complex variation of distribution functions.
This is all further motivation for writing a review of galaxy environments that assembles and synthesizes this!
I had a vision this morning, and followed that by figuring out a strategy for detecting, in multi-epoch imaging, sources that are below the detection limit at any individual epoch, and which are moving too fast to be detected in the stacked image, where all epochs have been combined. Jester describes this as
detecting and measuring objects that are not detectable.
This problem is harder than the problem of just measuring the proper motion of a source you already know to be there (mentioned in earlier posts), as when the proper motion is small (so the source is visible in the stacked image). Indeed, even the PanSTARRS people (to my knowledge) have no strategy for this hard (but important, given local brown dwarfs) problem. Most methods you can imagine involve testing enormous numbers of hypotheses, which clearly costs you signal-to-noise. My method—a variant on RANSAC—limits these combinatoric costs. Now to see if it works?
Discussed with Jester the issues of measuring and detecting faint sources in multi-epoch imaging, especially sources too faint to be detected well at any individual epoch. It seems that these problems are not currently solved, although they are relatively simple statistics problems.
Discussed with Romeel Davé (Arizona) some issues of stellar baryons and dark matter in massive collapsed objects. If massive objects (like clusters and groups of galaxies) have formed through many mergers, and if some of the major mergers follow star formation (as we think they do), then in general it is hard to avoid having the sum total stellar mass distribution (including galaxies and intragroup light) trace the dark matter (in azimuthal average). That's a serious prediction! Testing it may require sharpening some blunt tools. But Sheldon, Blanton, and I have started down this path for other reasons.
I spent time working out how we might challenge galaxy formation in CDM by considering normal galaxy halos. The simulations make several non-trivial predictions, although all are hard to test: They predict non-spherical halos, with substantial triaxiality. They predict small-scale structure including concentrated substructure in real space and also velocity space. They predict that central galaxies at the centers of halos have different formation histories and properties than satellites. Each of these predictions has different kinds of uncertainty associated with it, and relates to other predictions, so directly getting at fundamental CDM properties is challenging. But I think it may be possible with a combination of Milky Way and Milky Way halo kinematics and structure, weak lensing on distant galaxies, clustering studies and studies of groups, and models of galaxy merger and accretion events.
I also continued work on the Masjedi paper.
For Masjedi's paper I worked on the text on K-correcting the imaging subsamples. My loyal reader will recall that Masjedi's project involves cross-correlating the imaging galaxies fainter than LRGs with spectroscopic LRGs. In general, we don't know the redshifts of the imaging galaxies, but we do want a real-space correlation function. His K-correction method is very clever: We K-correct each imaging galaxy in each imaging–spectroscopic pair of galaxies using the spectroscopic galaxy's redshift. Then we K-correct differently when that same imaging galaxy appears in a pair with a different spectroscopic galaxy. It all comes out in the wash, because the excess pairs at small scales that survive the correlation analysis are all true pairs (statistically) and so we subtract away all the wrong K-corrections and are left with only the correct ones (statistically).
Did that make sense?
There are now several diffuse stellar overdensities (and at least one reported underdensity) in the stellar halo. By consensus, these provide evidence for the build-up of the halo by accretion of smaller objects. I am skeptical, but Rix and I discussed a possible project to analyze the kinematics of one of them—the Hercules-Aquila cloud, which does seem to have a small velocity dispersion.
I continued working on text in the Masjedi paper
Wrote figure captions in the Barron & Stumm paper, and annotated equations in the Masjedi paper.
Jester and I discussed the problem of the determination of proper motions of sources in multi-epoch imaging, even when the sources are too faint to be detected at any single epoch. It is a beautiful statistics problem, and highly relevant to the SDSS Southern Stripe (where there are many epochs), PanSTARRS, and LSST.
I spent today writing papers for others. Blanton and I have a strict rule for the group that no-one ever writes text for a paper on which he or she will not be first author. But I am violating this rule all summer, as I finish up the paper with Barron and Stumm on cleaning USNO-B and the paper by Masjedi et al on the accretion rate onto LRG primaries. Barron, Stumm, and Masjedi are all now working at Novartis, Microsoft, and Goldman Sachs, so writing astronomy papers is below their respective pay grades. I spent much of today working on the Masjedi paper, particularly the data section.
There was a lively discussion over lunch with Bell about by-eye morphologies, with me arguing that by-eye results are (a) not repeatable and not objective, and (b) in this day and age, rarely useful for physics. Astronomy maybe, but not physics!
I worked on the USNO-B Catalog cleaning paper this morning, mainly shortening it.
discovered halo subdwarfs via a reduced proper motion diagram this afternoon. I (embarrassed) got a lesson on the subject from Wikipedia.
Rix and I had the terrible realization that most of the 9 epochs of SDSS data that overlap Milky Way globular cluster Palomar 5 are in fact
Apache Wheel data taken at low angular resolution for calibration purposes. So we will have to go to historical or HST data to perform the proper motion measurement. We made some inquiries about both.
We had some conversations with Sebastian Jester (MPIA) about finding quasars and halo giants by their low proper motions. He obtained the proper motion catalog developed in the SDSS multiply-imaged
southern equatorial stripe and is looking at that now.