Simulated data

Our first test is a Monte Carlo simulation of BOSS galaxies. This was achieved by simu- lating 10,000 galaxy images each with parameter values drawn at random from distribu- tions similar to those observed for real BOSS galaxies. For each galaxy in our simulation, we assumed a de Vaucouleurs profile (Eisenstein et al, 2001), as BOSS galaxies are pre- dominately massive early–type galaxies (Masters et al. 2011), and selected at random the de Vaucouleurs scale radius, central surface brightness, and axial ratio from fits (shown in red) to the observed distributions of these parameters as shown in Figure2.4. The fits to these observeddistributionswere obtained empirically as there are several data artefacts that we wish to avoid. For example, the observed distribution of de Vaucouleurs scale radii has noticeable peaks at zero and other integer values. The source of these artefacts is unknown but are clearly data errors and not a true reflection of the underlying galaxies; therefore we ignore them in our simulations.

We next create a 2-D image (pixel scale 0.4 arcseconds) from each of the randomly constructed de Vaucouleurs profiles with the correct axial ratio. These galaxy images are thenconvolvewith aGaussianwhose width is drawn at random from the distribution of typical BOSS galaxy seeing values also shown in Figure2.4. These simulated galaxy

CHAPTER 2. A FAST METHOD FOR PRODUCING MATCHED PHOTOMETRY...36 images are only created for the SDSS component of our match photometry, as we only wish to demonstrate our interpolation technique works, and were done separately for each of the SDSS passbands; for illustration purposes, we only show in Figure2.4the param- eter distributions for the SDSS r-band as these typically have the highest signal–to–noise. The next stage of our simulation is to create the Photoprofile table for each galaxy. This was achieved by using the IDL routine APER(from the IDLASTRO library of routines)on the 2-D images for all 15 apertures described in Table 1. This provides a noiseless measurement of Photoprofile for each simulated galaxy but with the correct pixellation of a typical BOSS galaxy. We then added noise to each bin of the sim- ulated Photoprofile using the error distribution shown in red in Figure 2.4, which has a zero mean but a variance that is typical for the underlying distribution of observed errors for our BOSS galaxies (black histogram). These observed errors were estimated from the repeated photometric observations of Stripe82, which were part of the recent SDSS DR8, i.e., each galaxy inStripe82has multiple independent observations (up to 40 in some cases) over a range of different observing conditions.

In the lower left panel Figure 2.4, we show the difference in the repeat photometry compared to the coadded flux for each object, matching each repeat observation to the coadded object within one arcsecond. We use the coadded flux as a reference as this measurement should have significantly higher signal-to-noise than any single-epoch de- tection of the galaxies and therefore, the observed variance in the flux is primarily due to the individual detections rather than the reference flux. We do see an offset of ∼ 0.1 magnitudes in the relative uncertainties (see Figure2.4) which we ignore in the simu- lated error distribution (red histogram) and is probably due to differences in the reference flux. We note that the standard deviation of the fluxes in each bin of Photoprofile (from the repeat observations) is significantly larger than the reported errors in the SDSS Skyserver of up to ∼0.1nanomaggies, which is probably due to the larger variations in observing conditions experienced during the repeat observations.

Comparison of input photometry with that produced

These data were then used according to the method outlined in Section 2.2, i.e. The profile was pixellated, convolved to 2” seeing and aperture photometry measured. The flux within this aperture could then be compared to that of the original noiseless De Vaucouleurs profile when convolved to the same seeing when the same aperture was used. The results from this can be seen in Figure2.5, where the free parameters of the simulated data were all drawn from an SDSS-like distribution (see Figure 2.4) and the

CHAPTER 2. A FAST METHOD FOR PRODUCING MATCHED PHOTOMETRY...37

0 1 2 3 4 5 6 7 8 9 10

De Vaucouleurs scale radius /arcsec 0.0 0.2 0.4 0.6 0.8 1.0 0.5 1.0 1.5 2.0 2.5 Seeing FWHM /arcsec 0.0 0.2 0.4 0.6 0.8 1.0 -0.6 -0.3 0.0 0.3 0.6

(flux_coadd - flux_individual)/flux_coadd 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Axis Ratio 0.0 0.2 0.4 0.6 0.8 1.0

Figure 2.4: The distributions of each free parameter in the simulation code. Within each panel, the solid black filled histogram shows the observed distribution from SDSS DR8 data of BOSS galaxies, and the red hatch filled histogram is the distribution of the random numbers for this parameter in the simulation. The upper left panel is the best fit De Vaucouleurs scale radius, the upper right panel is the seeing FWHM, the lower left panel is the fractional error in photoprofile bin flux values and the lower right is the axis ratio.

resulting magnitudes from a fixed radius aperture were compared to those from the pure De Vaucouleurs profile convolved with a Gaussian of 2” FWHM and integrated within the same aperture. The recovered values have no systematic deviation from the input values, and a standard deviation of 0.1 magnitudes,which demonstrates that the method introduces no systematic error and a small random error.