Photometry

Where possible our images were taken under photometric conditions, with no cloud cover and stable seeing. In addition, it is also preferable to take observations at low zenith angle,z, to reduce the atmospheric extinction (airmass).

Aperture Photometry

For measurement of the source magnitudes the main method applied in this thesis is aperture photometry. Here, a suitable aperture is chosen based on the point spread function (PSF) of unsaturated point sources in the field.

The main quantifiable sources of noise will be the read noise, sky background shot noise and source shot noise. Both the noise on the sky and on the source will be Poisson distributed. In units of detected electrons the Poisson noise is given by

√

nsky and

√

nsourcewherensky andnsourceare the number of detected events for the

sky and source respectively. For counts (ADUs) this noise must be divided by the gain (i.e. pn/G). The gain, as discussed in section 2.1.1, provides the conversion between the measured counts (ADUs) in the image and the number of electrons (primarily photoelectrons) detected.

In our observations we are typically background limited, meaning the sky noise dominates. The noise, a combination of the sky and read noise, is well approx- imated by placing multiple apertures, with the same area as the source aperture, on the sky and measuring the variance between these apertures. Alternatively, an annulus around the source can be used to measure the variance of the sky pixel values. Combining this measured variance with the noise of the source will give us the overall error for the detection.

1_{Original interpolation details from Bertin and Arnouts 1996 have been updated in Bertin,}

In addition to these noise sources there are also many sources of systematic errors which could contribute. This includes mis-calculation of the bias level, bias structure or flat field, non-linearity near the point of saturation and interpolation er- rors introduced from placing a circular aperture on a grid of square pixels. However, most of these additional errors will be small with only the flat field error potentially adding any significant contribution to the noise already accounted for.

Zeropoint calibration

To produce absolute rather than relative photometry, the source magnitude can be calibrated from sources with known magnitude. One method of calibration is from the observation of a standard field containing bright primary standard stars. This can be done if the observations were taken under photometric conditions. Calibrat- ing from a separate image in this way means any differences in exposure time and airmass must be taken into account. At angles from zenith less than z < 60◦ the airmass is well approximated byX= sec(z) (at z= 0◦,X= 1 andz= 60◦,X ∼2) with second order terms becoming increasingly important at higher angles (Birney et al., 2006, pgs. 125-132). The extinction correction is dependant on wavelength with typical corrections in the range 0.02−0.16 magnitudes per unit airmass for the wavelength range 7800−4700 ˚A2. The difference between the standard and science frame airmass values is often minimised and so this correction, especially for longer wavelength observations, is not normally significant.

If no standard calibration frames are available, or if the observations could not be taken under photometric conditions, secondary standard stars within the science images can be selected. These stars have been calibrated from the primary standard stars and are fainter with less accurate photometry. The calibrators chosen must be non-saturated, isolated point sources with magnitudes available in the ap- propriate filter within a photometry catalogue. Using secondary calibrators avoids any complications with different exposure times or airmass since they are within the same frame as the source. For optical observations the point sources selected were normally from the USNO or SDSS catalogues (Monet et al., 2003; Abazajian et al., 2009), where available in the field. For the near-infrared band observations the 2MASS catalogue was most often used (Skrutskie et al., 2006).

2

Extinction values measured using the 0.6 m Bochum telescope at the La Silla site in Chile. Values available online at https://www.eso.org/sci/observing/tools/Extinction.html

Filter and magnitude systems

For calculation of fluxes as well as magnitudes we must also consider both the filter and the magnitude system being used to calibrate the standard stars. One con- sideration is whether the filter transmission as a function of wavelength between the observation and the standard stars differ, though this source of error is usu- ally small. The standard broadband optical filters for the FORS instrument are based on the Johnson-CousinsU BV RIsystem (Johnson and Morgan, 1953; Cousins, 1978) whereas the the Gemini telescopes follow the Sloan system with filtersg0r0i0z0

(Fukugita et al., 1996). For calibration, when the magnitude of the standard stars is only known in the alternative filter set (e.g. g0r0i0z0 rather than U BV RI) a correction can be estimated using standard stellar conversions (e.g. Lupton et al. 2005).

The most frequently used magnitude systems are either based on the stellar spectrum of α-Lyrae (Vega) or on a constant flux per unit Hertz standard (AB). Conversion between these magnitude systems requires knowledge of the spectrum of Vega, sometimes causing a discrepancy if different spectra have been used or different interpolations of the spectrum used to calculate the conversion. In this thesis we try to achieve consistency through use of the astSED python code as part of the astLib package which bases its conversions on the Vega spectrum available from Bohlin and Gilliland (2004).