Photometry

Photometry throughout this thesis was performed using one of two di↵erent meth-

ods, dependant upon the appearance of the host galaxy within the observations. Where possible (i.e. for galaxies which are clearly detected within their images) I

Figure 2.1: Adapted from Fruchter and et al. [2009], a representation of an input

pixel being dropped into the output pixel frame. The regionsa,b,cand drepresent

the overlapping regions of the input pixel with pixels in the output frame. This overlap causes an underestimation of the error associated with any one pixel, as the cross terms caused by the division of flux with neighbouring pixels cannot be incorporated.

used the automatic detection and extraction package, Source Extractor [here after SExtractor; Bertin and Arnouts, 1996]. The key advantage of using SExtractor for

photometry is the ultimate production of a ‘segmentation map’, in which di↵erent

groups of pixels are identified as belonging to di↵erent astronomical objects within

the image. This is a particular bonus when considering di↵use objects, or to ensure

the incorporation of low surface brightness features when performing photometric analysis.

The SExtractor process (outlined briefly here, for a more complete overview, see Bertin and Arnouts [1996]) first creates a background map from the input image, using iterative sigma clipping to estimate it’s level and applying a median filter to account for any potential overestimations from bright sources in the field. Once background subtracted, the image is then convolved with an input PSF profile before object identification begins. A user-specified detection threshold (typically number

of above the background) and limits on the number of adjoining pixels an object

should have before triggering a detection are applied before object extraction. For each object extracted from the image, the pixel group is passed through a deblending filter which attempts to separate any overlapping objects contained within it. It does so by creating a 2-dimensional brightness profile for the extracted object then, working from the brightest points downward, searches for ‘saddles’ be- tween peaks in the brightness profile. At each saddle point the program determines whether the intensity contained within the peak above the saddle point is greater than a user-specified fraction of the total intensity of the composite object. If this is so, the peaks (and their surrounding pixels) are identified as two separate ob- jects. The algorithm continues to move downwards through the brightness profile, searching for new saddle points (treating any identified objects individually). This is schematically represented within Figure 2.2.

Once de-blending has commenced, SExtractor will then determine the po- sitional parameters (location of the peak, isophotal centre, barycentre, size, ellip- ticity etc.) of each of the identified objects before photometric measurements are performed. The user may specify whether they require isophotal magnitudes or aperture magnitudes, with the option for corrections to be applied if attempting to account for additional light which may be outside of the notional aperture.

Thus for each host galaxy the program parameters were adjusted accordingly to optimise its detection and extraction within the image, and since I was concerned with individual galaxies this means that blending decisions were made manually. For

theHSTdata set I applied a surface brightness signal to noise cut of two per pixel

Figure 2.2: Figure taken from Bertin and Arnouts [1996]; a schematic representa- tion of the method used to identify separate objects during the deblending process. The 2D brightness profile of the pixel group (smooth line) is analysed - the program works in a top-down fashion, searching for saddles in the brightness profile. If the integrated brightness of the peak above the saddle point in found to exceed a spec- ified fraction of the total brightness of the input pixels, the peak (and neighbouring pixels) are regarded as separate from the rest of the profile. Here the input object has been broken into two separate objects, A and B.

features, measuring the host galaxy magnitudes using theMAG AUTO feature, which provides are the most precise estimate an objects total magnitude using a flexible elliptical aperture around the object and measuring the flux contained within it

[Kron, 1980]. For theseHST images, zeropoints for each filter were taken from the

STScI WFC3 handbook [Dressel, 2012].

It should be noted that some of the photometry produced within SExtractor

provides extremely small photometric errors, occasionally as low as _⇠1/1000 of a

magnitude. Such unrealistic errors are a result of using “weight maps” for the ex- traction of sources from the science frame. A weight map is a combination of weight images from the individual dithered inputs containing information on the location of bad pixels within the image produced during the drizzle process, [Gonzaga and et al., 2012]. Whilst the use of weight maps for object extraction is beneficial for better photometric detection of faint sources, they produce problems with the way in which SExtractor computes photometric errors.

SExtractor takes the inverse of the drizzled weight map (which thus creates a lower significance for highly weighted pixels and vice versa) and then uses this map to scale the variance that the program itself measures within the science frame [Bertin and Arnouts, 1996]. Thus the resulting noise associated with most pixels is lower than it should be (as pixels of a high weighting become low in variance within SExtractor’s error algorithm). This underestimation becomes more apparent

in sources which have an intrinsically higher S/N. Whilst the side-e↵ects of using a

weight map for object extraction a↵ects the photometric uncertainties of all SLSN

within our sample, this should not significantly impact upon the conclusions drawn from the results presented within this thesis.

Several galaxies showed a light distribution dominated by individual bright knots in UV imaging, and the deblending parameters were adjusted for each host to ensure it was not broken into multiple components. Where possible, the nIR images were used to determine which UV components should be included in the analysis, as these bands are dominated by a smoother light profile arising from an older stellar population.

I also utilised straightforward aperture photometry, particularly for cases in which the host galaxy was either undetected within the image, or for cases in which

the SExtractor deblending was insufficient to reconcile to the various components

of a particularly di↵use host. When doing this, I typically set large apertures (>1.4

FWHM) to encompass the majority of the light of the galaxy, and determine the

background via the use of a large number (>20) of sky apertures. This technique

3 limits where necessary. In cases in which I employ aperture photometry, I apply aperture corrections determined by the estimated encircled energy curves of WFC3

detectors [Dressel, 2012]. In the event of a host detection in oneHST band but no

detection in another, the size of the aperture used to determine the upper limit was set equal to that used to measure the magnitude in the band where the source was detected.

Additional photometry of hosts imaged using the WHT and VLT in r’ and Johnson-Morgan R bands respectively was carried out in a like manner to the

HSTimages, applying a surface signal to noise cut o↵of one per pixel before extrac-

tion with SExtractor. Photometry of galaxies on ground based images was carried out relative to SDSS observations of the same field, and is given in the r’ band.

For all photometric results here I perform a K-correction. This allows for the

photometric comparison of objects at di↵erent redshifts which have been observed

within a single bandpass (which will only cover a fraction of the total light emitted by the object). As objects move to higher redshifts, their spectral energy distribution

becomes stretched by a factor of 1 +z, such that as an object moves to higher

redshifts, observations within the same photometric band will sample progressively bluer parts of the spectrum. A K-correction corrects for this by converting the flux measurement in the observer frame into an equivalent measurement of that flux in the rest frame of the object.

Normally filter-matching must also be performed, where a redder filter is selected which corresponds to the approximate wavelength coverage and sensitivity of the filter the observations were taken with, but in the rest frame wavelength of the observed object. If the Spectral Energy Distribution (SED) of the object is known (for instance, a blackbody spectrum), then a K-correction is determined in two stages: by integrating the redshifted SED over the redder bandpass and then by integrating the same SED as seen at zero redshift over the band passes of interest to the observer to produced two expected fluxes. The K-correction is thus computed as:

K= 2.5 logFz=0

Fz

WhereFz=0 and Fz are the expected fluxes at zero redshift and at the red-

shift of the object. If multi-wavelength photometry of the object exists, then the observer fits this photometry to a model SED of choice, before following the above steps. However, if observations are obtained in the observer frame within a filter corresponding the the rest frame wavelength of interest, as there is no energy loss

due to redshifting then the K-correction simply becomes:

K = 2.5 log (1 +z)

as the di↵erence between the expected fluxes is diluted by a factor of 1 +z.

All photometry within this thesis was also corrected for Galactic extinc- tion using the Milky Way dust maps of Schlafly and Finkbeiner [2011] (via the

NASA/IPAC Infrared Science Archive4_{) for the appropriate image filter and ad-}

heres to the AB magnitude system.