2.5 Photometry

Photometry is the measurement of the flux density from an object, which gives the amount of the radiation per unit area. Flux density is a measure of either:

• Flux per unit wavelength range (F)
• Flux per unit frequency (F).

Flux is defined as the integral of flux density, i.e., 

(2.6)

The wavelength range is determined by the filter chosen and ability of the detector to record the energy of the photons incident upon it. Another measure of a star’s brightness is its magnitude. The definition of an apparent magnitude (m) is that magnitude that is received directly above the Earths atmosphere and is defined by

(2.7)

where the subscripts 1 & 2 refer to the two separate stars being compared. The conversion of F to m is therefore a logarithmic and relative one that had its original reference point fixed by the star Lyrae (Vega) which had its all its apparent magnitudes defined as zero, regardless of wavelength. The foundation for this is purely historical and more recently the average of several Vega type stars has been used to redefine the scale, with m_v(Vega)= 0.02 ± 0.01.

The apparent magnitude of a source is related to the flux densities we receive on Earth and so does not take into account distance. It is therefore not a measure of intrinsic luminosity. The absolute magnitude (M) of a star refers to the apparent magnitude a star would have if it were at a distance of 10pc from the Earth and is defined by:

(2.8)

where d is the distance to source in parsecs and A is the interstellar extinction between observer and source. The apparent magnitude of a source refers to the flux as measured from above the Earth’s atmosphere, i.e., after correction for the absorption that occurs during the transmission through it. Rearranging equation 2.7 gives:

(2.9)

Since the LHS of Equation 2.9 is a function of source 1 only and the RHS is a function of source 2 only, if we equate Equation 2.9 to a constant, ZP, we can say that ZP is independent of the source and must therefore be a function of the medium between the top of the atmosphere and the detector. Since the zenith distance, the angular distance of an object from the zenith, of a source is not constant and the more air light passes through to arrive at the detector the greater the diminution of it will be, it can be shown (see Böhm-Vitense, 1989) that:

(2.10)

Where ZP is known as the zero-point, k is an absorption coefficient - dependent upon wavelength and sec(z) is a measure of the air that is between detector and atmospheric penetration - the “airmass”. Regular observations of standards throughout the night, as their airmass changes, makes possible the derivation of k for the night in question. It desirable to use standards of similar colour to the target object due to the weak dependence of k on stellar colour.

2.5.1 Filters, Colours and Passbands

A star’s emitted light intensity is strongly dependent on wavelength. Therefore m is dependent on the range of wavelengths to which the CCD is sensitive. Photometric systems are therefore used to define discrete passbands, each with a known sensitivity to incident radiation. The sensitivity is defined by the detectors and filters used and a set of primary standard stars is provided which define its magnitude scale (Palmer and Davenhall, 1999). When a photometric system is established the detectors and filters used define the passbands. However these passbands can never be precisely reproduced with a new detector and filter set, a new instrument set-up to use a defined photometric system is said to observe in its natural system.

A factor in defining a photometric system is the variable transparency of the Earth’s atmosphere with wavelength, see Figure 2.2. Observations are performed within these passbands or windows of transparency in the Earth’s atmosphere. The original photometric filter system was introduced in 1953 by Johnson & Morgan and covered U, B and V; it was later extended to cover R & I. The Cousins system V band (complemented by U and B) is identical to the Johnson-Morgan. However, the Cousins R and I bands have wavelengths of 6700Å and 8100Å respectively, as such both are bluer than the corresponding Johnson & Morgan bands, and are usually indicated thus: R_c and I_c. The Cousins system remains the standard photometric system. See Table 2.2 for a summary of the filters systems discussed in this section.

Another widely used system is the Strömgren intermediate ubvy system. Strömgren y magnitudes are well correlated with Johnson-Morgan V magnitudes (Palmer and Davenhall, 1999). See Chapters 6 & 8 for discussion of the science that can be carried out using the Strömgren system.

The Sloan filter system comprises five colour bands that divide the entire wavelength range from the atmospheric ultraviolet cutoff at 3000Å to the sensitivity limit of silicon CCDs at 11000Å into five virtually non-overlapping pass bands. These filters ensure high efficiency for faint object detection and essentially cover the entire accessible optical wavelength range (Fukugita et al., 1996). The r' filter has a curtailed red wing compared to the Cousins R filter, which means that fringing with thinned CCDs will be much reduced in r'.

---

---

Above 1m the atmosphere becomes highly variable in its transparency, this is because water vapour and carbon dioxide have a dipole moment similar in size to that of the wavelength of infra-red radiation. This results in the absorption and re-emission of radiation at different wavelengths, effectively blocking observations at some wavelengths and giving the natural J(~ 1.2m) H(~ 1.6m) K(~ 2.2m) and near IR passbands. Infra-red astronomy requires very dry conditions like those of Mauna Kea, Hawaii.

---

---

2.5.2 Colour Indices

A colour index is the difference between the magnitudes of an object in two different bands. The (B-V) index is primarily related to temperature and hence spectral class, while (U-B) is a more complex function of temperature.