dark matter halos

The only research I did on my week-long vacation off the grid was to draft a section for Peebles's and my synthesis of galaxy evolution in the cold-dark-matter paradigm. The section I drafted was on the predictions and observations of the dark-matter halos (or concentrations, virialized or otherwise) around galaxies and groups of galaxies. I think that weak and strong lensing, along with sensitive measurements of intragroup light, might put serious constraints on the cold dark matter model at small scales, because, depending on some issues of how baryons populate the halos, each of these provides some handle on the distribution of dark matter—radial distribution, large-scale anisotropy, and small-scale substructure—which is (apparently) a robust prediction of the model.

psf, M/L

I spent time yesterday (traveling for family reasons) and today working on incorporating non-trivial point-spread-function estimates into the proper-motion measurement code. I fear that the gaussian approximation to the point-spread function is affecting my results, at least slightly.

I also spent some time reading and commenting on a very nice draft paper by Sheldon on the mass-to-light ratios (as a function of scale) of virialized structures in the Universe, based on a comparison of cluster–galaxy cross-correlations and cluster–mass cross-correlations (based on statistical weak lensing).

My loyal readers will both be sad to learn that I go out of all internet contact for a week starting Monday, so there may not be much here.

merger rates

I spent the morning re-reading papers about merger rates, to improve the discussion in our merger-rate estimate paper. I was reminded of how stark the difference is between studies that estimate the merger rate morphologically (ie, by identifying probable merging galaxies by tidal features or asymmetries in their appearances) and studes that estimate it by close pairs. The morphological studies all get much higher rates, which says to me that either morphological asymmetries are raised by very small accretion events, or else that they last many dynamical times. The close-pair rates have the virtue that—if done correctly—they can provide a strict upper limit on the merger rate, so the fact that the close-pair studies come in lower means that the morphological studies are biased high.

constrained realizations, confirming the known

In among many non-research activities today, I managed to have a long and useful argument with Blanton and visiting student Abate (UCL) about constrained realizations, the local velocity field, and velocity correlation functions. I also spent some time measuring the proper motions of objects in the SDSS Southern Stripe with known proper motions.

brown dwarfs have higher proper motions than quasars!

Stop the presses! No, seriously, I showed today that I can measure the faint, very red sources in the SDSS Southern Stripe—sources so red that they must either be brown dwarfs or high-redshift quasars—with enough accuracy that I can separate them with some reliability on the basis of proper motion alone. The separation is not perfect, because there are some faint brown dwarfs with very small proper motions. However, the most widely separated brown dwarfs are also the most interesting, because they have the highest probabilities of being very low luminosity and therefore old and cold.

In other news, Lang, Mierle, and Roweis worked all night and got the first astrometry.net paper submitted.

debugging and tweaking

I spent most of my time yesterday (forgot to post!) and today continuing to add functionality to and debug the proper motion code. I decided that debugging requires that I have code to visually compare the stack of a set of epochs at zero proper motion and at some candidate non-zero proper motion, to understand, functionally, why I get some (clearly wrong) proper motions for some sources in real data, while not in the artificial data. I expect neighboring objects and noise issues (eg, underestimated noise) are affecting me. On the former (neighbors), the right thing to do is to simultaneously fit for all sources in the field!

The time not spent debugging was spent helping Lang, Mierle, Blanton, and Roweis finish the astrometry.net submission to Science. They are intent on submitting today. It is a lofty goal, and perhaps an achievable one.

refactoring

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.

astrometry.net first paper

I worked on the text of astrometry.net's first paper, to be submitted to Science as soon as we can get it finished. This week, Lang, Mierle, and Roweis converge on Mountain View to get it as close as possible.

quasar proper motions

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.

real data

I started the process of getting the proper-motion measurement code to run on real SDSS data on the Southern Stripe (where there are 20-30 epochs).

the power of statistics

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.

theoretical limits on proper motion measurements

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!

growth by merging

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.

one trivial faint-source proper motion

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!

robust astrometric tweak

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.