### 7 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 8) 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], Straižys[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[4344] 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 1 includes the basic details of the Johnson-Morgan system and Figure 2 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[1314]. 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 ${\left(RI\right)}_{C}$, where ‘C’ stands for ‘Cape’. For further details see Straižys[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 A) $U=B=V$. 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.

 System Band Effective Bandwidth Wavelength (FWHM) Å Å visual ${m}_{v}$ $\sim 5500$ - photographic ${m}_{pg}$ $\sim 4250$ - 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

Table 1: 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

Strömgren System
Another widely used system is the Strömgren intermediate-band uvby system[7172]. The details of this system are included in Table 1. 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 1. 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 8.1). 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 2 summarises some of the more common $JHKLM$ systems. For further details see Bersanelli et al.[4], Bouchetet al.[5] and Straižys[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.

 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. $JHK{L}^{\prime }$ 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 $JHK{L}^{\prime }M$ Tapia et al.[73] UKIRT Joint Astron. Centre, Hawaii $JHK$ Casali and Hawarden[8]

Table 2: Common JHKLM systems. Adapted from Bersanelli et al.[4]

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: $J=H=K=L=M\left(=U=B=V\right)$. 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.

#### 7.1 Colour indices

A photometric system with more than one band is formally called a multi-colour system (though in practice most photometric systems are multi-colour). For any multi-colour system a series of colour indices, or colloquially colours, can be defined. A colour index is simply the difference between the magnitude of a given object in any two bands. For example, in the UBV system the $B-V$ index is simply the $V$ magnitude subtracted from the $B$ magnitude5. Multi-colour photometry is usually published as a single magnitude and a set of colours rather than a set of magnitudes.

#### 7.2 Standard and instrumental systems

When a standard photometric system is first set up the detectors and filters used define its passbands. Also the originators of the system will typically observe and publish a set of standard stars which define the magnitude scale for the system.

Subsequently, instrumentation for observing in the system will be built at other observatories. There are, for example, many observatories with photometers and CCDs capable of observing in the Johnson-Morgan system. However, the original passbands can never be reproduced precisely, even if the original instrumentation is simply copied and similar filters are purchased from the same manufacturers. The system in which the new instrumentation actually observes is called its natural or instrumental system. In this cookbook the standard system to which a given instrumental system approximates is called the target standard system. Usually considerable effort is expended to make the instrumental system match the target standard system as closely as possible6.

However, in order to make reproducible observations one of the calibrations which must be done is to convert instrumental to standard magnitudes. Conceptually this calibration is done be re-observing the standard stars for the system and comparing the instrumental and standard magnitudes. If the instrumental system is a good match to the standard system then it may be possible to compare just the corresponding bands in the two systems. Conversely, if the two systems are less well-matched or high precision is required then the standard magnitude may have to be computed from the corresponding band in the instrumental system with corrections using the colour indices.

#### 7.3 Catalogues of standard stars

There are many catalogues of photometric standard stars. A catalogue of primary standards for a given photometric system is usually published when the system is defined. For widely used systems further catalogues of ‘secondary’ standards will often be compiled by making observations calibrated with the original primary standards. Recent catalogues of standards are usually available in a computer-readable form.

Johnson-Morgan system
The primary standards for the Johnson-Morgan system are listed in various places, including the original publications. See, for example, Zombeck[81], p101. These standards are often too bright (and too few in number) for modern instrumentation and programmes, and catalogues of fainter (and more numerous) secondary standards are often more useful.

Some suitable catalogues of secondary standards are: Johnson and Morgan[44], Landolt[50515253], Christian et al.[9], Graham[30] and Menzies et al.[5758]. Landolt’s catalogues are, perhaps, the most useful.

Strömgren system
For catalogues of standards in the Strömgren system see Grønbech and Olsen[34], Grønbech, Olsen and Strömgren[33] and references therein.
$JHKLM$ system
For catalogues of standards in the $JHKLM$ system see Straižys[70], pp305-307 and also the references in Table 2.
##### 7.3.1 Computer-readable catalogues

Some of the recipes in Part II of this cookbook use the CURSA package (see SUN/190[16]) for manipulating catalogues of standards. A small collection of photometric standard catalogues in a format accessible to CURSA is available by anonymous ftp. This collection includes most of Landolt’s catalogues. The details are:

 Anonymous ftp to: ftp.roe.ac.uk Directory: /pub/acd/catalogues File: photostandards.tar.Z

Remember to reply anonymous when prompted for a username and to give your e-mail address as the password. You should use ftp in binary mode. photostandards.tar.Z is a compressed tar file and should be de-compressed with uncompress (sic). See Section 13 for more details.

Other sources of computer-readable versions of catalogues of photometric standards are the Centre de Données astronomiques de Strasbourg (CDS) and the US Astronomical Data Center (ADC). These institutions now keep many of the catalogues in their collections permanently on-line and you can retrieve copies via anonymous ftp or the World Wide Web. Briefly, the CDS and ADC may be contacted as follows.

CDS
URL: http://cdsweb.u-strasbg.fr/CDS.html

Electronic mail: question@simbad.u-strasbg.fr

Postal address: Centre de Données astronomiques de Strasbourg, Observatoire de Strasbourg, 11, rue de l’Université, 67000 Strasbourg, France.

ADC
URL: http://adc.gsfc.nasa.gov/

Electronic mail: request@nssdca.gsfc.nasa.gov

Postal address: World Data Center A for Rockets and Satellites, NASA, Goddard Space Flight Center, Code 633, Greenbelt, Maryland 20771, USA.

4The last major catalogues compiled using magnitudes estimated by direct observation are the great Durchmusterungen produced in the late nineteenth and early twentieth centuries: the Bonner Durchmusterung, the Bonner Südliche Durchmusterung and the Cordoba Durchmusterung. However, the visual system is still in use, particularly for variable-star work. The various extensive archives of variable-star data consist largely of visual observations, mostly contributed by amateurs.

5En passant, for stars $B-V$ is primarily related to temperature (and hence spectral class) while $U-B$ is a more complex function of both luminosity and temperature.

6Clearly, instrumentation will be designed so that the combination of detector and filters matches the target system as closely as possible. However, there are a number of potential pitfalls. One is that most of the older photometric systems were originally set up using photoelectric detectors. Modern CCDs are usually relatively more sensitive in the red and less in the blue than photoelectric detectors (see Figure 3). Thus, a CCD detector will usually use a different or additional set of filters to match a given system than a photoelectric detector. Another potential problem is that some filters are prone to ‘leakage’. Here the filter correctly blocks light at wavelengths surrounding the required passband but becomes transparent again at very different wavelengths (so, for example, a filter which correctly defined the $R$ band might also leak light at much shorter wavelengths, perhaps corresponding to the $U$ or $B$ bands). If leakage occurs it is necessary to use an additional filter, a so-called blocking filter, to remove the extraneous light. The choice of filters to match photometric systems is far beyond the scope of this cookbook and as an observer using CCD detectors neither will it normally concern you. However, it is useful to be aware of some of the potential problems.