Astrometry

The location of a transient within its host is an important indication of its origin. Finding a strong preference for a particular type of transient to inhabit regions with strong UV emission might indicate an association with star formation, and thus young or massive stars, while a position far from the bulk of the galaxy could indicate the progenitor had received a kick prior to the event, ejecting it from its host. Indeed, in the case of transients considered within this work, one major requirement for inclusion is that they come from the nuclear regions of their hosts. Thus, both initially in order to be included in the study and again later if higher resolution imaging becomes available, the astrometric position of the transient must be determined. This position must also be compared to the morphology of the host and thus to the expected position of the supermassive black hole in the system which is generally assumed to be at the centroid position of the host light (though note that this assumption can fall apart in interacting hosts or on very small scales). In this section I discuss the various techniques which are used within this work to determine these properties.

2.3.1 Astrometric Matching

Several of the techniques discussed below require that the coordinate transformation between two images be known. This is important both in attempting to determine the relative positions of objects within the two images, as well as for cases where the images themselves need to be transformed to identical coordinates, perhaps in preparation for subtraction. While world coordinate system (WCS) information is encoded into many images taken on modern instruments, this is often insufficient for these purposes as it is subject to systematic offsets. Instead, it is preferable to determine the transformation between the two images using objects in the field.

Ideally the astrometric matching is completed using a number of point sources in the field, fitted using a simple Gaussian or Moffat profile, which are typically good fits in seeing-limited observations, or by using a central moment finding routine such as iraf imexam. Identifying point sources is done first by eye and then, having

and small width is identified. This is because ideal point sources represent sources too small to be resolved and thus are merely scaled point spread functions, the narrowest profile a real1 _{source can have. Any extended object, assuming the fitting}

process does not fail, should have a profile which is wider than point sources and so can be excluded. In cases where the point spread function is not an ideal Gaussian or Moffat profile, for example in cases where the pointing of an observation drifts during the exposure, elongating objects in the drift direction, or the observations are diffraction-limited and the optical system is not ideal (e.g. HST point spread functions are non-trivial), any systematics introduced should be equally felt by all point sources in the field so that the net relative systematic is zero.

With a sample of objects for use in the fitting process identified, the posi- tions of each object in both images are used as variables in a fitting routine such as

iraf geomap. This produces a functional form for the coordinate transformation

which can include offsets in pointing, orientation and pixel scale, while the fitting polynomial’s order can also be changed to allow for distortion of the image, as- suming enough point sources have been identified to accommodate fitting all of the required variables. An estimate of the RMS of the fit can also be obtained which is useful for determining the astrometric uncertainty in later analysis. When required, anomalous positions, more often than not the result of misidentifying an extended source as a point source, can be removed from the fit. However on some occasions, as these point sources can be relatively local stars, they can have non-negligible proper motions meaning they can move across the field from one image to the next, requiring that they too be removed from the fitting process.

Most problems associated with astrometric matching can, for the most part, be overcome by having as large a number of well-detected point sources to fit the positions of as possible. However, in sparsely populated fields, with minimal overlap between the images, or with necessarily small fields of view, perhaps due to image buffer constraints on space-based instruments (e.g. HSTsub-arrays), it can difficult to find enough sources for comparison between the two. In cases where an insufficient number of point sources are available, extended sources can be used, though the systematics are more difficult to determine in this case and the fit is generally of poorer quality.

1

i.e. not a CCD defect, such as a hot pixel, or a cosmic ray hit, both of which should have been dramatically reduced in severity and frequency by the reduction process. They are also often identifiable by eye or fail to be fitted with simple profiles

2.3.2 Image Subtraction

While some transient phenomena are, at least for a short time, far more intrinsically luminous than their hosts, in most cases any determination of the position of the transient will necessarily be confused by the underlying host emission. In order to remove this host contribution and leave only the transient emission for modelling, a technique known as image subtraction can be used.

In its simplest and most ideal form, an image taken either before the transient occurred or after the transient has faded below the instrumental sensitivity is aligned and subtracted from an image taken while the transient was bright. As the host contribution is effectively unchanged over the short time between the two images, the subtraction should produce an image that includes only transient light with no appreciable contamination from the host. Ideally the two images should have been taken with the same instrument, in the same configuration and waveband, in identical observing conditions and with the the same pointing and orientation. If this is the case, the reduced images can be simply scaled by exposure time and subtracted from each other.

In reality though, many of the above requirements are not met, requiring a more in depth method of analysis. Typically, even if the observations were taken in near-identical conditions and were designed to have identical pointings and ori- entations, this will usually be confirmed first through astrometric matching (see subsection 2.3.1 above) and any required transformation applied. Large transfor- mations are discouraged, however, as every transformation the data is put through adds systematic distortions and flux losses/inconsistencies that will affect the out- puts. This effect can be minimised in cases where specialised software is available for the individual instrument, designed to deal with these problems, such as as- trodrizzlefor HST (Fruchter and Hook, 2002; Fruchter, 2010). Thus, if both of

the intended images have been taken in identical instrumental configurations with

HST, given the minimal changes in point spread function in this diffraction-limited case, the images can be merely aligned, scaled and subtracted. This method is used extensively in Chapter 5.

However, for most ground-based, seeing limited observations used in this work, changes in observing conditions will lead to an inevitable change in the point spread function, requiring one image be convolved to match the seeing of the other before the images may be subtracted. Within this work, the image subtraction softwareisis (Alard and Lupton, 1998; Alard, 2000) is used for this process. This

software uses a reference image, typically the one with the best seeing, which is then convolved with a spatially variable kernel that allows for changes in the point

spread function across the image. The software is also capable of aligning images that have minor mismatches in pointing or orientation, though, once again, large translations should be avoided. Once complete, the convolved and aligned images can be subtracted from one another and the transient light analysed separately from the host emission. This process is used to subtract ground-based images with quite different seeing within Chapter 3.

2.3.3 Modelling Galaxy Morphology and Determining Centroid Po- sitions

The final stage in determining the position of a transient within its host is to analyse the morphology of the host itself and determining the centroid position of both it and the transient. This can be completed in a number of ways depending on the signal to noise ratio of the detection, the resolution of the imaging, the presence or absence of clear structure within the host and any secondary science goals the study may have.

In the case of a low significance, low resolution (i.e. close to being unresolved) detection of a host galaxy, it is quite possible that no clear structure will be visible in the host, particularly if the host is at high redshift. In this case, there is often little benefit in completing a complicated morphological fit to the data. As such, in order to find the central position of the galaxy, a simple centroiding method, such as that used byiraf imexamcan be used. The central moments of the object is calculated

and returned as an estimate of the central position of the source. The uncertainty on this method can be reasonably approximated as the theoretical uncertainty on the centroid of a Gaussian with the FWHM and signal to noise (S/N) equal to that of the source, given by:

σcen =

FWHM

2.3×S/N (2.4)

This method is also used when determining the position of the centroid of the transient emission following subtraction or in higher signal to noise cases where an otherwise well-resolved galaxy has a clear, relatively narrow central peak that is unlikely to be affected by the more extended parts of the host.

In cases where the extent of the galaxy is larger and the signal to noise allows for it, more complicated methods can be applied and the precise morphology of the host can be determined. In particular, within this thesis, the galaxy morphology modelling code,galfit(Peng et al., 2002, 2010), is used extensively. This program

components that can include, for example, point sources, gaussians, s´ersic profiles and edge-on disks. Each has a set of input variables that are then fitted to the 2- dimensional image. The best fit model is determined to be that with the minimum reduced chi-square when comparing the input model and actual image. The results include the best fit model parameters and estimates of the uncertainties on each, where possible.

However, a number of issues with this method exist. For example, in addition to the usual issues in fitting routines of local minima in the chi-square distribution and determining reasonable “first guesses” for the input values, the number of input components is based on a judgement call by the user. It is therefore difficult to tell when adding a new component to the model is a useful addition or an over- fit. Visual inspection of the residual image is usually the best way to attempt to determine whether another component has actually improved the fit or not. Further, because the sky background is also a fitted variable within the program and the input section of the image can be made arbitrarily large, a particular model’s goodness of fit can be skewed by choosing a larger region of sky. While experience with the program can help determine the “ideal” size of the fitting region to enable the accurate fitting of the sky without arbitrarily adding background pixels that improve the apparent quality of the fit, the uncertainties on the best fit parameters should always be viewed with caution. This method is used briefly in Chapters 3 and 4 and extensively in fitting the galaxies in Chapter 5.