Pilar 2: Vías más seguras

Photometry is a fundamental observational technique, used to measure the (total) flux of a specific object over a range of wavelengths. Observations can be performed using a photometric filter, e.g.

observations in the SDSS u-band filter allow the measurement of the flux of an object in the range 3000 ˚A₋4000 ˚A, or without one, usually called filterless or white light photometry. Time-series photometry, i.e. a long series of successive images of a specific target, is used to construct a light

curve, depicting the variation of the target’s luminosity with time. However, before a light curve can

be obtained, the CCD data need to be properly calibrated and reduced. This involves the following steps.

Bias subtraction

The conversion of analog signal to a digital number in a CCD is not a perfectly repeatable process. In the digitisation phase, the ADC will produce a statistical distribution of possible answers, centred on a mean value. Upon read out of an unexposed pixel, the value of zero collected photoelectrons will translate into a mean value with a small distribution around zero. To avoid having to digitise negative numbers (which would require a “sign bit” to be used), CCDs have a built-in positive offset. This offset value, the mean “zero” level of a CCD, is called the bias level. The bias level can be estimated using bias frames, zero exposure-time frames - essentially, a read-out of the unexposed CCD chip. A mean bias frame, constructed from a large number of bias frames taken before (and/or after) the science images, should be subtracted from the science images, to remove the unnecessary extra ADUs.

Dark-current subtraction

Dark current is caused by electrons in the chip having enough thermal energy to make the transition

from the valence to the conductivity band without the intervention of a photon. As the ADC cannot distinguish the source for any electron, these thermal electrons are counted along with the photo- electrons and introduce spurious ADUs in the final image. In practise, the problem is alleviated by cooling the CCD to very low temperatures using liquid nitrogen. However, in CCDs where less efficient cooling methods are used (peltier or water cooled CCDs), the dark current needs to be taken into account. This is achieved with the help of dark frames. Dark frames are long exposures (of the order of several minutes) with the CCD shutter closed. As the dark current is proportional to the exposure time, the dark frame can be scaled to match the exposure time of the science images, thus providing a measurement of the rate of thermal electrons in the science images. The usual practise is to combine a few dark frames in a mean frame, which is then scaled accordingly and subtracted from each science image and flat field (introduced below).

Flat-fielding

Each pixel on the CCD chip does not have the same response to incoming photons, i.e. the prob- ability that a photon will create a photoelectron is different between pixels. In simple terms, some pixels are more sensitive than others. This results in a non-uniform spatial behaviour of the CCD chip, which must be corrected before measurements of any kind are performed on the science im- ages. The correction is achieved through flat fields, exposures of the chip under a uniform source of light. The most common way to obtain flat fields is to take exposures of the twilight sky (sky flats),

Figure 2.3: An example of a CCD image. The field is that of V 455 And (Chapter 7) and

the image was obtained at the 1.20 m Mercator Telescope using the MEROPE CCD. The

straight line to the right-hand side of the image is a defective CCD column.

or use special flat-field screens provided in many observatories (dome flats). Similarly to bias and dark frames, a number of flat fields is used to create a mean image, which is normalised to unity. Any deviations from unity will correspond to different pixel sensitivity. Dividing the science images with the mean flat frame results in “flattened” images.

Aperture photometry

An example of a CCD image of a stellar field is shown in Figure 2.3. The most common way to obtain the desired photometric signal is to employ aperture photometry.

As its name suggests, aperture photometry is the process of placing an aperture, usually circular with a radius rT of a few pixels, around the target and summing all the counts contained

within the aperture. This sum S is the total photometric signal, including the contribution from the target and also from background sources, such as the sky. In order to estimate the contribution of the sky, common practise is to use two more apertures, with radii rS1and rS2, which define a sky annulus

around the target, “sampling” the sky background in the immediate vicinity of the target (obviously

rT<rS1<rS2). The estimated sky background B can then be subtracted from S, yielding the desired

quantity, the photometric signal I of the target, which is usually given in instrumental magnitudes. Care needs to be taken when choosing the size of the apertures. The target aperture needs to

be large enough, so that it encompasses the whole stellar profile, but not too large, so that it doesn’t encompass a large background region. The same applies for the radii defining the sky annulus. They need to be large enough to adequately sample the sky around the target, but not too large, to avoid any potential inclusion of neighbouring stellar profiles, e.g. in crowded regions. Common practice is to employ variable apertures, scaled according to the full width at half maximum (FWHM) of the stellar profile in each image, to minimise aperture losses and maximise the signal-to-noise ratio.

Obtaining a light curve

Performing photometry on a long sequence of images allows us to measure the (instrumental) magnitude of the target, MAGT, with respect to time, i.e. construct the target’s light curve. The

common practise is to also measure the magnitude from a photometrically constant star, MAGC,

called the comparison star, and calculate the light curve in differential magnitude ∆Mag, where

∆Mag=MAGT−MAGC. This process, called differential photometry, preserves any intrinsic vari-

ability of the target but removes spurious/unwanted variations, e.g. drops of signal due to clouds. Another advantage of differential photometry is the ability to calculate the target’s apparent mag- nitude, if the apparent magnitude of the comparison star is known. This can be achieved because CCDs operate in a linear fashion2.