This page discusses fits to radially binned APEX-SZ data. Radially binning the data reduces the size of the covariance matrix, so that it can now be estimated in real space from jackknifed noisemaps. This eliminates the need to fit in the fourier domain, which eliminates the need for uniform weights in the map. With this, we can extend our fitting region to beyond a radius of 5'.

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Pros: We can fit clusters to R_500 and beyond.

Cons:

1. We are restricted to spherically symmetric models.
2. Including X/Y offsets will require a bit more work.

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Method:

The method is the same that Kaustuv has previously used in his non-parametric stacking work. Here, we validate the method and demonstrate using parametric models.

1. Radially bin the filtered rawmap using the inverse-variance pixel weights
2. Create X-number of jackknifed maps from the individual scan maps
3. Radially bin the X-number of jackknifed maps using the inverse-variance pixel weights and calculate the covariance matrix.
4. At each step in the MCMC chain create a simulated cluster and convolve with the PSF
5. Radially bin the result
6. Calculate chi2 using the noise covariance matrix from step 3.

Note: Only steps 1, 3, and 5 are new.

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Testing

First, we see how the radial fitting compares to the Fourier fitting. We set the radial bins to go out to 5.5' to try and match the 10' length box used in the Fourier fitting. Figure 1. compares the results for A2204, and Figure 2 compares the result on a simulated cluster.

Figure 1.

Figure 2.

Then, following the fourier fitting tests on the Berkeley wiki page at 2011-06-10, we've created maps of a simulated cluster with non-uniform noise. We've use the noisemap from either the RXCJ1206 and RXCJ0516 data. Figure 3 shows the noise from the RXCJ1206 data.

Figure 3.

We then fit a beta model to the simulations and see if we can recover the input Y_500 without any bias. Figure 4 shows the distribution of CDF values for 40 simulations using the RXCJ1206 noise. The distribution is consistent with uniform, as expected for unbiased Y_500 measurements.

Figure 4.

-- JamesKennedy - 2013-03-20

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This topic: APEX_SZ > WebHome > RadialFitting Topic revision: r1 - 2013-03-20 - JamesKennedy

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