## Magnitude Systems

The apparent magnitude m, which we have just defined, depends on the instrument we use to measure it. The sensitivity of the detector is different at different wavelengths. Also, different instruments detect different wavelength ranges. Thus the flux measured by the instrument equals not the total flux, but only a fraction of it. Depending on the method of observation, we can define various magnitude systems. Different magnitudes have different zero points, i. e. they have different flux densities F0 corresponding to the magnitude 0. The zero points are usually defined by a few selected standard stars.

In daylight the human eye is most sensitive to radiation with a wavelength of about 550 nm, the sensitivity decreasing towards red (longer wavelengths) and violet (shorter wavelengths). The magnitude corresponding to the sensitivity of the eye is called the visual magnitude mv.

Photographic plates are usually most sensitive at blue and violet wavelengths, but they are also able to register radiation not visible to the human eye. Thus the photographic magnitude mpg usually differs from the visual magnitude. The sensitivity of the eye can be simulated by using a yellow filter and plates sensitised to yellow and green light. Magnitudes thus observed are called photovisual magnitudes mpv.

If, in ideal case, we were able to measure the radiation at all wavelengths, we would get the bolometric magnitude mbol. In practice this is very difficult, since part of the radiation is absorbed by the atmosphere; also, different wavelengths require different detectors. (In fact there is a gadget called the bolometer, which, however, is not a real bolometer but an infrared detector.) The bolometric magnitude can be derived from the visual magnitude if we know the bolometric correction BC:

By definition, the bolometric correction is zero for radiation of solar type stars (or, more precisely, stars of the spectral class F5). Although the visual and bolometric

magnitudes can be equal, the flux density corresponding to the bolometric magnitude must always be higher. The reason of this apparent contradiction is in the different values of F0.

The more the radiation distribution differs from that of the Sun, the higher the bolometric correction is. The correction is positive for stars both cooler or hotter than the Sun. Sometimes the correction is defined as mboi = mv + BC in which case BC < 0 always. The chance for errors is, however, very small, since we must have mbol < mv.

The most accurate magnitude measurements are made using photoelectric photometers. Usually filters are used to allow only a certain wavelength band to enter the detector. One of the multicolour magnitude systems used widely in photoeletric photometry is the UBV system developed in the early 1950's by Harold L. Johnson and William W. Morgan. Magnitudes are measured through three filters, U = ultraviolet, B = blue and V = visual. Figure 4.6 and Table 4.1 give the wavelength bands of these filters. The magnitudes observed through these filters are called U, B and V magnitudes, respectively.

The UBV system was later augmented by adding more bands. One commonly used system is the five colour UBVRI system, which includes R = red and I = infrared filters.

There are also other broad band systems, but they are not as well standardised as the UBV, which has been defined moderately well using a great number of

1.0 0.8 0.6 0.4 0.2

L

B

V

R

I

: I

\ \

A

1

Fig. 4.6. Relative transmission profiles of filters used in the UBVRI magnitude system. The maxima of the bands are normalized to unity. The R and I bands are based on the system of Johnson, Cousins and Glass, which includes also infrared bands J, H, K, L and M. Previously used R and I bands differ considerably from these

200 400 600 800

Fig. 4.6. Relative transmission profiles of filters used in the UBVRI magnitude system. The maxima of the bands are normalized to unity. The R and I bands are based on the system of Johnson, Cousins and Glass, which includes also infrared bands J, H, K, L and M. Previously used R and I bands differ considerably from these

 Magnitude Band width Effective [nm] wavelength [nm] U ultraviolet 66 367 B blue 94 436 V visual 88 545 R red 138 638 I infrared 149 797 u ultraviolet 30 349 v violet 19 411 b blue 18 467 y yellow 23 547

standard stars all over the sky. The magnitude of an object is obtained by comparing it to the magnitudes of standard stars.

In Stromgren's four-colour or uvby system, the bands passed by the filters are much narrower than in the UBV system. The uvby system is also well standardized, but it is not quite as common as the UBV. Other narrow band systems exist as well. By adding more filters, more information on the radiation distribution can be obtained.

In any multicolour system, we can define colour indices; a colour index is the difference of two magnitudes. By subtracting the B magnitude from U we get the colour index U — B, and so on. If the UBV system is used, it is common to give only the V magnitude and the colour indices U — B and B — V.

The constants F0 in (4.8) for U, B and V magnitudes have been selected in such a way that the colour indices B — V and U — B are zero for stars of spectral type AO (for spectral types, see Chap. 8). The surface temperature of such a star is about 10,000 K. For example, Vega (a Lyr, spectral class A0V) has V = 0.03, B — V = U — B = 0.00. The Sun has V =— 26.8, B — V = 0.62 and U — B = 0.10.

Before the UBV system was developed, a colour index C.I., defined as

C.I. = mpg — mv , was used. Since mpg gives the magnitude in blue and mv in visual, this index is related to B — V. In fact,

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