From Douglas Rudd

Introduction

This page describes the mock SZ lightcones I've created to explore effects of projection on SZ mass-observable relations and to provide to collaborators.

Method

Simulation

The lightcones are constructed using a single 240h ^{− 1}Mpc box simulated in the non-radiative (or adiabatic) regime and using the WMAP3 cosmology (Ω_m = 0.25, Ω_Λ = 0.75, Ω_b = 0.042, σ₈ = 0.8, h = 0.73, n = 0.95). The resolution is course (30h ^{− 1}kpc comoving), however without cooling the baryon distribution is insensitive to resolution.

I make use of 15 outputs spaced equally in Δa = 0.05 from to construct the lightcones.

Lightcone construction

For computational efficiency I pre-project each output in 60h ^{− 1}Mpc slices along each axis x, y, and z, resulting in 12 two-dimensional projected images. Each lightcone is constructed by stepping back in redshift by steps of comoving distance Δχ = 60h ^{− 1}Mpc, and coadding slices properly scaled by the angular diameter distance at that redshift. Every box length (4 steps, or 240h ^{− 1}Mpc) a new orientation, rotation and translation is selected in order to randomize structure on scales larger than a box-length. Except at very low redshift (where the volume in each lightcone projection is small) the geometric error caused by flattening into slices is negligible (~ 1% or less).

Example lightcone

Tests

Comparison with White et al (2002)

Martin White has kindly made the mock lightcones generated from his non-radiative simuation G4a and used in White et al (2002) [ADS] available to the community. I've used 15 1x1 degree fields, each with 512 (7" pixels). The upper line in the plot below is the log-mean and log-variance of the individual image spectra, and the lower converts cosmologies using the scaling advocated by Komatsu & Seljak (2002) [ADS]. The agreement in amplitude is good at , and I suspect the disagreement at larger scales is due to the small scale images (see next section). The power in modes is highly correlated (Zhang & Sheth (2008) [ADS]), so the disagreement is probably not statistically significant.

Image size/resolution

Here I've generated 15 mock images varying the angular resolution and image size. The fiducial parameters for my images are 5x5 degrees with 1024 (or ~18") pixels. Smaller images limit the power at large scales, while resolution suppresses the power at small scales. I haven't demonstrated convergence in image size here, however with the limited volume I use to construct these images I don't dare generate larger images, due to the size of the box used to construct the images.

Results

Thermal & Kinetic Spectra

Here I've plotted the thermal and kinetic SZ 2-d spectra measured from 100 realizations of the 5x5 degree lightcones (1024/18" pixels). Since the distribution of from lightcone to lightcone is (very) roughly lognormal, I plot the log mean () and log-scatter in bins of . The flattening in the kinetic SZ signal at large scales is also seen in White et al (2002) [ADS], however I'm concerned that the bump at is consistently seen in the individual map spectra.

Projected Quantities

The following plots are used by examining clusters at z = 1 in one realization of the lightcone. Approximately 1000 objects above lie at this redshift in the lightcone, however no effort has been made to remove duplicates or subhalos.

This image compares the intrinsic Y-M relation, which has very little scatter, to the Y_proj-M relation, which more closely represents what observers will measure. Clearly the scatter goes up, and the overall relation is shifted, both due to additional signal along the line of sight, and due to the cluster itself (Y_int is limited to a smaller volume than the projected quantity). As Holder et al (2007) [ADS] showed, at the high-mass end projections are less dominant, however the number of large-mass objects in this volume is limited to a few dozen.

This plot compares the two SZ quantities directly. The line shows the lower-limit where Y_proj = Y_int. Clearly the projected SZ fluxes are properly recovered (in no case does a cluster have less projected SZ than its intrinsic). The increasing disagreement at lower masses may be real (a background which is a larger fraction of the signal at low masses) or may be due to noise when clusters are only a few pixels in size.

Sample Data

Here are 10 mock lighcones which I'm making semi-publicly available. Feel free to download and use them, however if you use them in a publication please contact me and acknowledge their use.

The fits files have 4 images, thermal and kinetic sz, projected gas mass and projected total mass () to z = 4. The halo catalogs include all halos that have projected radii entirely within the image, and whose extent along the line of sight lie entirely within the redshift slice used to create the lightcone. This prevents any clusters from being cut-off in projection, however there may be clusters in the image that are not included in the catalog (don't use the catalog to test blind cluster detection without some thought).

The output aexp = 1/(1+z) and halo id uniquely identify individual outputs. The same cluster may appear multiple times in the same image, but this should be rare.

• lightcone_0000.fits lightcone_0000_catalog.dat
• lightcone_0001.fits lightcone_0001_catalog.dat
• lightcone_0002.fits lightcone_0002_catalog.dat
• lightcone_0003.fits lightcone_0003_catalog.dat
• lightcone_0004.fits lightcone_0004_catalog.dat
• lightcone_0005.fits lightcone_0005_catalog.dat
• lightcone_0006.fits lightcone_0006_catalog.dat
• lightcone_0007.fits lightcone_0007_catalog.dat
• lightcone_0008.fits lightcone_0008_catalog.dat
• lightcone_0009.fits lightcone_0009_catalog.dat