Reconstruction Progress 2012 04 10
TC, PJM 2012-04-10
We have initial curves of growth and kappa PDFs, using the Keeton approximation. We see a few galaxies dominate the convergence from within 1 arcminute from the line of sight, but also significant contributions from galaxies outside this aperture. The smooth mass component and correct distances are already a concern.
We have written code to drill out a lightcone around any point in one of Stefan's halo catalogs. We can calculate kappakeeton (a crudely approximate scheme for combining the contribution to kappa and gamma from halos at different redshifts) for every halo, assuming an NFW profile, and a concentration-mass relation.
We don't yet include stellar mass. We cannot correctly account for the kappa expected from a smooth component, as we don't know how much of the Millennium Simulation matter is not held in the halos in the catalogs, and we are also worried about the validity of angular diameter distances (that go into the Keeton approximation) in such an inhomogeneous lightcone. Also, note that we are not yet reconstructing mass from the galaxy photometry, but rather just exploring the lightcones' mass distributions, to try and understand the lightcone radii we will likely need, as well as the uncertainty introduced by various inferences (notably z and Mstar) and scaling relations (notably M200-c, Mstar-M200).
Below are two simple plots, showing the contents and lensing effect in a randomly selected line of sight. The kappakeeton = 0.11 in this lightcone is fairly high, but it isn't particularly atypical (as we show in the third plot in this post). We expect these simple kappa estimates to be biased high, since we don't subtract the smooth component implied by our choice of cosmological matter density used in the distance estimates.
Figure 1. Top: A view of all the galaxies in a cone, radius 5 arcseconds. Each yellow circle represents a galaxy, with area proportional to r band flux. Bottom: The same, but now in the y-redshift plane, and with black circles under plotted, area proportional to subhalo mass.
Figure 2. Top: The growth of kappa_keeton as a function of distance from the line of sight, including all the galaxies in the above cone, for a lens at zd =0.6 and source at zs =2.0. Bottom: lightcone contents, plotted in redshift and radial distance from the line of sight. Each galaxy is represented by a yellow circle, with area proportional to r band flux; the red circles represent the contribution to kappakeeton from each galaxy. (The red circles are plotted underneath the yellow circles, so most are too small to see.) The vertical lines show the lens and source plane redshifts used in the convergence calculation.
Notes for Figure 2: The growth curve keeps increasing with radius - this is because we are always adding mass with more halos, without adding more void to balance it. At large radii this curve should be asymptoting.
The kappa contribution is dominated by a few objects, but these are not necessarily within 45" of the LOS - more distant objects do matter. Objects at redshifts near to that of the lens plane are important.
As expected, if a halo isn't close to the line of sight or it isn't close to the lens plane, it needs to be huge to have a significant contribution to the overall kappa estimate.
Finally, a distribution of kappakeetons:
Figure 3. kappa_keeton distribution for 1000 randomly chosen lens galaxies, with zd = 0.6+/-0.02 and zs = 1.4. Halos in lightcones of 5 arcmin radius from the optical axis were included. Because we are overbudgeting the mass, the centroid of our kappa_keeton distribution is too high, but promisingly the shape is similar to the figure in Suyu et al 2010.
Convergence from Stefan:
- The kappa map from Stefan is presumably the convergence acting on a source at zs due to all the mass in the Universe, and so does not have an associated lens redshift. Is this the kappa that appears in D = D'/(1-kappa)?
- Does the histogram of kappa values read off from Stefan's map match the histogram in Suyu et al 2010? To do: get histogram file from Sherry, compare with home-made histogram from Stefan's map.
Convergence calculation:
At the moment we are using kappakeeton, partly as a placeholder for a more accurate kappablandford - but what if kappakeeton could be made sufficiently accurate?
- What are the correct distances to use in this calculation? eg When computing halo angular sizes, or critical densities, or beta factors... Is there a useful approximation to the full Blandford ray-tracing answer? Or should we just wait for the full formalism to be completed?
- What should we do about the smooth component of matter (that is not included in the halos in the catalog, but is related to the matter density needed in the distance calculations)? Can we compute a kappasmooth that we can just subtract from our current kappa estimates that emulates the full treatment? This might involve the "convergence due to a uniform disk" or somesuch...
Convergence estimation:
Regarding the estimation of kappa in real life, there are 2 things we'd like to investigate:
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How good an approximation is kappakeeton to the true kappa?
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How well can we reconstruct the mass in the lightcones given observations of ugriz and position? Or in the short term, z and Mstar?
- Soon we will want to compare reconstructed kappa values with true kappa values from Stefan's ray tracing (or elsewhere). How should this be done? To do: work through probability theory and derive this. Also look at distribution of (kapparec-kappatrue), and (kappakeeton - kappatrue), to start answering Q1.
- How much uncertainty in kappa do zerr, Mstarerr, (Mstar-M200) and (M200-c) introduce into the kappa estimates? To do: implement scatter in scaling relations, and explore distribution (kapparec-kappatrue), where kappa is kappakeeton. Then go on to look at effects of zerr, Mstarerr, as a function of those quantities.