The oldest quantitative observations of stars are connected with the determination of the apparent brightness of a star as soon from Earth. AN unfortunate consequence of this is that the subject is even now Union with historical ballast. In particular, the unit given in antiquity, the MAGNITUDE, is still in regular use. Furthermore there is general confusion, even in professional literature over the terms brightness (a physical quantity) and the units in which it is measured (magnitude). Astronomers frequently speak of finding the magnitude of a star or galaxy, when in fact they have measured its brightness, in magnitudes. This section gives a short description of the several magnitude systems used to label stellar brightnesses; each has particular applications.

Apparent brightness or apparent magnitude
The nuclear powerhouse in the interior of a star is continuously sending energy up to the star’s outer layers. Eventually, this energy is radiated into space, much of it in the form of light. The star’s LUMINOSITY is the rate at which it emits radiant energy, and it depends chiefly on the size and surface temperature of the star. How bright a star looks in the sky depends on both its luminosity and its distance. Physicists measure the luminosity of an object in watts, but for historical and other reasons astronomers measure stellar luminosity in magnitudes. This magnitude system arose from the nature of the response of the human eye: what an observer judges to be equal increases in stimulus in the eye (that is equal increases in brightness) turn out to be approximately equal ratios of luminosity. This is because the physiological response to light is proportional to the logarithm of the stimulus. As an example, suppose there are three stars, all at the same distance from the Earth, whose light-energy outputs are in the ratios 1:10: 100. An observer would say that the brightness difference between the first two is about the same as that between the second and third, because the ratios of the luminosities are equal (1/10 and 10/100, i.e. 0.1) in these two cases.

As far back as the second century BO, Hipparchus divided the stars that could be seen with the naked eye into six groups accord¬ing to the sensation registered by the eye. The brightest were designated as first magnitude and the faintest as sixth magnitude. With advances in astronomy in more recent times, it became necessary to define a much more precise system, based on rational physical principles, and this was done by Pogson in 1856. He noted that a first-magnitude star was about one hundred times more luminous than one of the sixth magnitude, so he defined a magni¬tude difference of exactly 1.0 as corresponding to a ratio of luminosities of ^100 = 2.512. A star seen to have magnitude 2 is emitting 2.512 times as much radiant energy as a star of magnitude 3 at the same distance. We use the term APPARENT BRIGHTNESS to refer to the brightness of a celestial object as measured by the observer (generally on Earth!), without regard for the effect of distance on the brightness. The more widely-used term APPARENT MAGNITUDE has the same meaning. Suppose two stars have apparent magnitudes ml and m2 and their apparent luminosities are L1 and L2, (we say apparent because the effect of distance is being ignored for the moment), then the mathematical form of the rela¬tion between these quantities is expressed by the equation

To encompass’ very bright objects, the magnitude scale is extended to negative numbers: For example, the star Sirius has a magnitude of -1.4 and the full Moon -12.5. The faintest stars which can be photographed with the world’s largest telescopes are about twenty-fifth magnitude; they have the same apparent brightness as a candle 300 000 km from an observer.

Brightnesses judged by the response of the human eye are called VISUAL MAGNITUDES, and they were the only magnitudes used prior to photography. However, many stars emit radiation in the ultraviolet and infrared regions of the spectrum. This radiation cannot be detected by the eye, and in fact some of these radiations in certain wavelength ranges never even reach the surface of Earth, as they are absorbed in the terrestrial atmosphere. A smaller magnitude (i.e. a smaller number in the magnitude scale and corresponding to greater brightness) than the visual one would be recorded if this unseen radiation were included, particularly forstars much hotter or cooler than the Sun, whose radiation falls primarily in the ultraviolet or infrared regions respectively. The brightness including radiation at all wavelengths is called the BOLOMETRIC MAGNITUDE. The bolometric correction (B.C.) is the correction which has to be applied to the visual magnitude: B.C. = Mbo— Mv. This correction is defined as zero for the Sun, whose radiation peaks in the visible region, so the bolometric correction is always a negative number. A BOLOMETER is an instrument for detecting electromagnetic radiation at all wavelengths. In practice bolometric magnitudes are difficult to measure directly owing to the atmospheric absorption.

A further complication arises if the brightnesses of stars are compared photographically. Many photographic emulsions are sensitive mainly to blue and violet light (hence the red safe-light used in dark rooms), whereas the eye’s response peaks in the yellow-green spectral region. PHOTOGRAPHIC MAGNITUDES are, therefore, different again to visual or bolometric magnitudes. It is clearly important to specify the type of magnitude, which will depend on the technique used to find it, as well as its value.

Stellar magnitudes are determined by comparison with a few stars whose magnitudes have been measured very accurately by photoelectric techniques. The zero point of the magnitude scale is now fixed by means of frequently-measured standard stars. When the brightnesses of large numbers of stars are required, photo¬graphy is the quickest way of finding the magnitudes. If visual magnitudes are required, it is possible to simulate the response of the eye by using a photographic emulsion that has been treated with a dye sensitive to green and yellow light in conjunction with a yellow filter .Brightnesses measured in this way are described as PHOTOVISUAL MAGNITUDES

The definition of magnitude can be extended to non –stellar and diffuse objects .The INTEGRATED MAGNITUDE is calculated by summing the light output over the entire object .In the case of an object whose luminosity decreases slowly towards the edges ,it may be necessary to specify the area of sky which is included .For a very extended object ,such as a nearby galaxy ,the surface brightness expressed in magnitude per square second of are may also be interest

Multicolour photometry
The values, obtained for photographic and visual magnitude depend on the range of wavelengths to to which the detection equipment in sensitive. For the accurate, reproducible measurements of stellar light output required by modern astrophysics, it is neces¬sary to define precisely the wavelength band used. The measurement of light intensity in particular wavelength regions for a star can be useful in establishing physical facts about the star, such as its temperature. To this end. several standard sets of magnitudes have been devised. The two sets most frequently used are the UBV SYSTEM of Johnson and Morgan and the UBVY SYSTEM of Stromgren. Such sets of magnitudes define what is called a PHOTOMETRIC SYSTEM, photometry meaning simply, the measure¬ment of light . Each system is defined by the colour filters which are used to isolate the wavelength bands.

The UBV system, introduced in the 1950s, is now extensively used The three magnitudes are measured using filters with the following characteristics :
wavelength of peak
magnitude name wavelength range transmission
(nm) (nm)
U'( ultraviolet) 300-400 360
B(blue) 360-550 420
V( visual) 480-680 520

The transmissions of the filters, compared to the response of the human eye. Ordinary visual magnitudes cor¬respond fairly closely with this precisely-defined V magnitude. Of particular use are the so-called COLOUR INDICES, (B–V) and (U-B) which are closely related to the star’s temperature and luminosity. Colour index is defined as the difference between magnitudes measured at two different, wavelengths. The UBV photometric system, based on wide wavelength bands, has been usefully extended by the introduction of two further magnitudes: K (red) and f (infrared), centred at 680 and 825 nm respectively.

The uvby system uses filters of narrower band width as follows:

magnitude name bandwidth central wavelength
(nm) (nm)
u (ultraviolet) 30 350
v (violet) 19 411
b (blue) 18 467
y (yellow) 23 547

Again, colour indices can be formed from combinations of these magnitudes, (b-y) is mainly a function of the star’s temperature, and the index given by (u-v)-(v-b) depends on the star’s lumi¬nosity. A further useful relation (v-b) — (b-y) is a good indicator of the relative proportion of elements heavier than hydrogen in the star’s chemical composition. Multicolour photometry is therefore a very good way of deriving the physical parameters of large numbers of stars relatively quickly.

Absolute brightness or absolute magnitude

The apparent magnitude of a star is governed by the star’s distance as well as its intrinsic luminosity. The apparent brightness of any source of light falls off at the square of the distance from the observer. The ABSOLUTE MAGNITUDE is denned as the brightness (in magnitudes) the star would have if it were at a standard distance from us, and by general agreement the unit distance is taken as 10 pc. Absolute magnitude is therefore a measure of the intrinsic energy output or absolute luminosity of the star.

We can form equations relating the apparent magnitude m and the absolute magnitude M. Suppose that a star is at a distance d parsecs, and denote the luminosity at d parsecs by ld and at 10 parsecs by L10 . By applying the inverse square law we can write l10/ld = d2/102. But we saw above that l2 /l1 = 100-(m2-m1 )/5, so :
Taking logarithms (to base 10) we obtain :
21og10d-2 = 0.4(m-M).
Multiplying by 2.5 and rearranging gives us :
m-M = 5log10d-5 = 51og10(d/10);
the quantity (m-M) is called the DISTANCE MODULUS.

The parallax of a star (measured in seconds of arc), p, is related to its distance in parsecs, d, by the simple expression d = 1/p, so the distance modulus is sometimes expressed in terms of p :
m-M=-(5+5logp).

Comments are closed.