psphot Galaxy Parameter Measurements

Bill Sweeney 2014-12-03

For PV3 we plan to add some additional measurements of extended sources in psphotStack. This note describes these measurements and includes some results from a test on the SAS2 region.

Asymmetry Indices

In Section 5.6 of a paper published in 2002 Luc Simard et al. described two measurements for use in the morphological classification of galaxies. See equations 11a and 11b in section 5.6.

The measurements are performed on residual images created by subtracting a galaxy model fits from the input images. The model used was the combination of bulge (de Vaucouleurs) + disk (exponential). These Asymmetry indices "provide an estimate of the overall smoothness of the galaxy image with respect to the fitting model". The program used to make these measurements is called GIM2D. It is performed on the results of processing by SExtractor. Since the indices consist of sums of absolute values of the residuals a positive signal will result even in the prescence of noise. So the algorithm subtracts off randomly selected "background pixels" which in the GIM2D program are chosen from the SExtractor segmentation image.

A later paper published in 2009 defined the parameter S2 = Rt + Ra where Rt and Ra are measured for 2 half light radii. In 2011 Simard, et al. applied these methods to SDSS images.

In the most recent version of psphotStack I have attempted to implement these measurements. Since we do not fit a bulge + disk model we have chosen to use our sersic model fits. The measurements are preformed independently on each filter's sources as follows.

1 At the beginning of the function the input image has all sources subtracted. The first step for each source is to add the subtracted model back in.

2. Next if the source's model is not the Sersic model fit, the model is temporarily changed to make it so. The indices consist of sums over a specific radius. Following Simard 2009 and 2011 the radius chosen is 2 times the half light radius for which the value that we have chosen is the major axes of the Sersic fit.

3 The next step is to determine the background pixels. psphotStack doesn't have a segmentation image so the background pixels are selected using the "footprints" measured during source detection. A pixel that is not part of any footprint is considered a background pixel. The source's pixels are examined and a vector of background and mirror background pixels are saved. During this loop the sum of the source's pixels is made as well.

4. The Sersic model is subtracted from the images.

5. The sums in the formulas for Rt and Ra are performed.

Bumpiness

Blakeslee, et al. 2006 defined another galaxy shape measurment that we are adding to psphotStack. See Equation (1) in section 3.1.3 This parameter was found to be useful for segregating galaxies by morphological type.

In psphotStack we do this measurement is done in the same loops that do the Rt and Ra measurements, skipping the central pixels as specified in the paper. For the sigma squared value in the numerator we take the values from the variance image.

Results

The new code was used in psphotStack for SAS.37. The results are saved in new columns in the XSRC extension of the staticsky and skycal cmf files. G_RT, G_RA, G_S2, G_BUMPY.

The results may be found in the skycal distribution bundles on the ps1-sas-cat product on the data store. The data_group is SAS.20141118.rerun

Using stilts we created a fits table for the r-band skycal distribution bundles and matched these to a SDSS catalog. This table contains one row per object. The extended source fit parameters are saved in columns with a different suffix for each model. These data were imported into topcat for analysis.

The following plot shows the value of G_S2 (red) as compared with the same parameter measured on the SDSS data set in Simard et al 2009 grey. We see that the range of values is significatnly different. Our measurements are centered around zero while the other paper they are mosly positive.

It appears that in our system the residual sums are simply higher. Here is a plot of Ra versus Rt.

A small number of the measurements from the paper overlap with the SAS2. The following plot compares their values with ours. Not much correlation is seen.

Here is a histogram of our values for the bumpiness parameter for all objects, and for brighter objects.

Finally following Blakeslee, et al. we show a plot of bumpiness versus sersic index. (Figures 6 and 7 in the paper).

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