Photometric Systems

The intensity of the light emitted by stars and other astronomical objects varies strongly with wavelength. Thus, the apparent magnitude, $m$, observed for a given star by a detector depends on the range of wavelengths to which the detector is sensitive; a detector sensitive to red light will usually record a different brightness than one sensitive to blue light.

The first estimates of stellar magnitudes were made either using the unaided eye or later by direct observation through a telescope. Magnitudes estimated in this way are referred to as visual magnitudes, $m_{v}$⁴. The sensitivity of the human eye peaks at a wavelength of around 5500Å.

The bolometric magnitude, $m_{bol}$, is the notional magnitude measured across all wavelengths. Clearly the bolometric magnitude cannot be measured directly, because of absorption in the terrestrial atmosphere (see Section ) and the practical difficulties of constructing a detector which will respond to a sufficiently wide range of wavelengths. The bolometric correction is the difference between $m_{v}$ and $m_{bol}$:

$$m_{bol}=m_v - BC$$ (10)

Note, however, that sometimes the opposite sign is given to $BC$. The concept of a bolometric magnitude is only really applicable to stars, which to a first approximation emit thermal radiation as black bodies. The bolometric correction is used to derive an approximation to the bolometric magnitude from the observed one. It would clearly be absurd to try to apply a bolometric correction to the observed visual magnitude of some exotic object which was emitting most of its energy non-thermally in the X-ray or radio regions of the spectrum. Schmidt-Kaler[65] gives tables of stellar bolometric corrections.

Another type of magnitude which is sometimes encountered is the photographic magnitude, $m_{pg}$. Photographic magnitudes were determined from the brightness of star images recorded on photographic plates and thus are determined by the wavelength sensitivity of the photographic plate. Early photographic plates were relatively more sensitive to blue than to red light and the effective wavelength of photographic magnitudes is about 4200Å. Note that photographic magnitudes refer to early plates exposed without a filter. Using a combination of more modern emulsions and filters it is, of course, possible to expose plates which are sensitive to different wave-bands.

However, modern photometric systems are defined for photoelectric, or latterly, CCD detectors. In modern usage a photometric system comprises a set of discrete wave-bands, each with a known sensitivity to incident radiation. The sensitivity is defined by the detectors and filters used. Additionally a set of primary standard stars are provided for the system which define its magnitude scale. Photometric systems are usually categorised according to the widths of their passbands:

wide band

systems have bands at least 300Å wide,

intermediate band

systems have bands between 300 and 100Å,

narrow band

systems have bands no more than a few tens of Å wide.

The optical region of the spectrum is only wide enough to accommodate three or four non-overlapping wide bands. A plethora of photometric systems have been devised and a large number remain in regular use. The criteria for designing photometric systems and descriptions of the more common systems are given by Sterken and Manfroid[67], Straizys[70], Lamla[49], Golay[32] and Jaschek and Jaschek[40]. Some of the more common ones are summarised below.

Johnson-Morgan UBV System

The Johnson-Morgan UBV wide-band system[43,44] is easily the most widely used photometric system. It was originally introduced in the early 1950s. The longer wavelength R and I bands were added later[42]. Table  includes the basic details of the Johnson-Morgan system and Figure  shows the general form of the filter transmission curves. Tabulations of these curves are given by Jaschek and Jaschek[40].

The Johnson-Morgan $R$ and $I$ bands should not be confused with the similar, and similarly named, bands in the Cousins VRI system[13,14]. The Cousins $V$ band (complemented by $U$ and $B$) is identical to the Johnson-Morgan system. However, the Cousins $R$ and $I$ bands respectively have wavelengths of 6700Å  and 8100Å  and thus both are bluer than the corresponding Johnson-Morgan bands. They are usually indicated by $(RI)_{C}$, where `C' stands for `Cape'. For further details see Straizys[70], pp294-296 and pp309-312.

The zero points of the UBV system are chosen so that for a star of spectral type A0 which is unaffected by interstellar reddening (see Appendix ) $U = B = V$. Despite its ubiquity the UBV system has some disadvantages. In particular, the short wavelength cutoff of the $U$ filter is partly defined by the terrestrial atmosphere rather than the detector or filter. Thus, the cutoff (and hence the observed magnitudes) can vary with altitude, geographic location and atmospheric conditions.

Table: Details of common photometric systems. The values are taken from Astrophysical Quantities[1], except those for the $JHKLM$ system which are taken from Sterken and Manfroid[67] and those for the $L^{\prime}$ band which are from the UKIRT on-line documentation

System	Band	Effective	Bandwidth
		Wavelength	(FWHM)
		Å	Å
visual	$m_{v}$	$\sim5500$	-
photographic	$m_{pg}$	$\sim4250$	-
Johnson-Morgan	$U$	3650	680
	$B$	4400	980
	$V$	5500	890
	$R$	7000	2200
	$I$	9000	2400
Strömgren	$u$	3500	340
	$v$	4100	200
	$b$	4670	160
	$y$	5470	240
		$\mu$m	$\mu$m
$JHKLM$	$J$	1.25	0.38
	$H$	1.65	0.48
	$K$	2.2	0.70
	$L$	3.5	1.20
	$L^{\prime}$	3.8	0.6
	$M$	4.8	5.70

Figure: Relative transmission profiles of the $UBVRI$ filters. The transmission maxima have been normalized

Strömgren System

Another widely used system is the Strömgren intermediate-band uvby system[71,72]. The details of this system are included in Table . Filter transmission curves for the Strömgren system are given by Jaschek and Jaschek[40]. Strömgren $y$ magnitudes are well-correlated with Johnson-Morgan $V$ magnitudes.

$JHKLM$ System

The $JHKLM$ system is an extension of the $UBV$ system to longer wavelengths. It was originally introduced by Johnson and his collaborators though modern versions of it derive from the work of Glass[29]. Details of the system are included in Table . The bands are matched to, and share the same names as, the windows in which the terrestrial atmosphere is transparent at infrared wavelengths (see Section ). The $L^{\prime}$ band is a later addition. It is better matched to the corresponding atmospheric window than the the original $L$ band.

The $JHKLM$ system is less well-standardised than other systems and each observatory will often define its own system which differs slightly from the others. These differences arise because the atmospheric windows which are transparent at infrared wavelengths are themselves different at different observatories and, in particular, vary with altitude. Consequently, great care must be exercised in inter-comparing $JHKLM$ observations made at different observatories. Table  summarises some of the more common $JHKLM$ systems. For further details see Bersanelli et al.[4], Bouchetet al.[5] and Straizys[70], pp292-307. Leggett[54] gives details of the transformations between the various infrared systems. Simons and Tokunaga[66] have recently reported an attempt to standardise infrared photometric systems.

Table: Common JHKLM systems. Adapted from Bersanelli et al.[4]

System	Institute	Bands	Reference
Arizona	Lunar and Planetary Lab.	$JKLM$	Johnson[41]
SAAO	South African Astron. Obs.	$JHKL$	Glass[29]
		$JHKL$	Carter[6,7]
ESO	European Southern Obs.	$JHKLM$	Wamsteker[76]
		$JHKL$	Engels et al.[26]
AAO	Anglo-Australian Obs.	$JHKL^{\prime}$	Allen and Cragg[3]
MSO	Mount Stromlo Obs.	$JHK$	Jones and Hyland[45]
CIT	California Inst. Technol.	$JHK$	Frogel et al.[28]
		$JHKL$	Elias et al.[25,24]
UNAM	Univ. Autonoma de Mexico	$JHKL^{\prime} M$	Tapia et al.[73]
UKIRT	Joint Astron. Centre, Hawaii	$JHK$	Casali and Hawarden[8]

As for the original Johnson-Morgan system, the zero point of the JHKLM system is defined so that an unreddened A0 star has the same magnitude in all colours: $J = H = K = L = M (= U = B = V)$. The standard star used is Vega ($\alpha$ Lyræ).

Observing programmes which use a given photometric system need not necessarily observe in all the bands of that system. Often only some, or perhaps even only one, of the bands will be used. The choice of bands will be dictated by the aims of the programme and the observing time available.