Colour luminosity

Optional experiment. When all the air has been displaced, collect a test-tube of the gas over water (by appropriate inclination of the end of the delivery tube beneath the mouth of a test-tube filled with water and supported in a beaker of water). Observe the colour and odour of the gas. Ignite the test-tube of gas, and note the luminosity of the flame and the amount of carbon deposited. Pure acetylene is almost odourless the characteristic odour observed is due to traces of hydrides of phosphorus, arsenic and sulphur. 

Now that we have a simple model for the continuum spectrum of the stars based around the Planck curve, the temperature and the luminosity, we can make some observations and classifications of the stars. There are some constellations that dominate the night sky in both the northern and southern hemispheres and even a casual look should inspire wonder. Star hopping in the night sky should lead to the simplest observation not all stars have the same colour. A high-quality photograph of the constellation of Orion (see page 2 of the colour plate section) shows stars... 

Stellar evolution has consequences in the development of luminosity and colours of stellar populations, as well as chemical enrichment. Boissier and Prantzos (1999) have produced a more-or-less classical model of the evolution of the Milky Way, making a detailed study of this aspect, known as chemo-photometric evolution , using an IMF similar to the Kroupa-Scalo function in Chapter 7 this detail is significant because the Salpeter(O.l) function often used has a smaller contribution from stars of around solar mass which dominate the light at late times. The chemical evolution results are combined with metallicity-dependent stellar isochrones, synthetic stellar spectra by Lejeune et al. (1997) and a detailed treatment of extinction by dust. Some of their results are shown in Fig. 8.39. 

Fig. 8.39. Chemo-spectrophotometric evolution of the solar neighbourhood (left) and the whole Milky Way (right) as a function of time. Panels aA show the oxygen and iron abundances, bB the mass of stars and gas and the star formation rate, cC the extinction in B, V and K bands along a line of sight normal to the plane, dD the luminosity in solar units (taking extinction into account), eE the colour indices and fF the supernova rates. Note that panels aA are in linear units (see Fig. 8.16), while the others are all logarithmic. After Boissier and Prantzos (1999).

Multiplying the apparent luminosity of a heavenly body by the square of its distance, the astronomer calculates its true brightness. The stars can then be sorted, separating out remote bright stars from nearby faint ones which might otherwise appear to be on a par. Colour, on the other hand, does not depend on distance, once corrections have been made for reddening due to interstellar dust. 

Many connections have been found between the luminosity peak, the shape of the light curve, evolution in the colour, spectral appearance, and membership of a galaxy of given morphology. However, after the first 150 days, uniformity takes over and all these objects fade in the same way and with the same spectrum. 

The compact initial state of the supernova ensured that the initial colour evolution is about five times faster than a normal Type IL At five to seven days the (B - V) colour evolution accelerated as line blanketing, initially from higher members of the Balmer series, but later from metal lines, mainly from the iron group, becomes important The climb towards maximum was accomplished at an almost constant temperature as measured by the (V - I) colour, but a further decline in temperature was seen in the post-maximum phase as the luminosity collapsed towards the radioactive tail. An increse in (U - B) occurred at 40 - 50 days, but this does not correspond to any change in photospheric temperature. This is presumably the result of a composition change working its way out to the photosphere. 

The reduction of these colours and the V magnitude to physical quantities is of necessity rather approximate and has been described in detail elsewhere (Dopita et al.). Suffice it to say that the Bolometric luminosities are obtained on the assumption that the apparent distance modulus of the supernova is 18.8, corresponding to a visual absorption Av = 0.44, and using the Bolometric Corrections of Carney (1980). The derived Bolometric luminosity is given in Figure 1. 

The crystals deposited last were reddish in colour, and brightly luminous at first, but the intensity of their luminosity gradually diminished, and the reddish tint deepened in colour. No doubt this is attributable to alteration of the barium platinocyanide in the complex, since the free salt upon exposure to radium radiations undergoes some change, resulting in a weakening of the fluorescence as has already been pointed out (see p. 321). 

Hue and purity alone are not enough to describe the subjective sensation of colour. The element of luminosity must also be taken into account. I hus the difference between the orange represented by = 0-56 and y = 0-41 on the chromaticity chart, and a dark brown with the same co-ordinates, is that one might have a luminosity of 25 per cent and the other 8 per cent. The complete specification of a colour, therefore, requires a third dimension and, in the C.I.E. system it is a mathematical conception that the X and Z stimuli have hue but no luminosity, and the whole of the latter attribute is contained in the Y component. Thus when the whole of the incident light is reflected, the value of T is 1 and the colour is white. For lesser degrees of luminosity the values of F are fractions of unity, until at zero the colour is black because there is no reflection or transmission of light. A three-dimensional colour solid is illustrated in Fig. 26.17 in which the base is black, the apex white, and in any horizontal plane saturation decreases as the location of the colour becomes nearer to the Y axis. 

The Lovibond-Schofield Tintpmeter is a modification of the simpler form of tintometer in which the readings can be converted into the x, y, and Y co-ordinates of the C.I.E. system. Fhe instrument is based on the fact that hue and saturation can be matched with two primaries, but the third only affects the luminosity of the colour. Thus in the case of the brown shade described above, which was matched with ... 

Fig. 1. Hertzsprung-Russell diagram a plot of luminosity (absolute magnitude) against the colours of the brightest stars ranging from the high-temperature blue-white stars on the left side of the diagram to the low temperature red stars on the right side. Original image by Richard Powell licensed for derivative works and redistribution under the Creative Commons Attribution Share Alike 2.5 License...

We have seen that the luminosity of a star depends on its mass. Since the luminosity L determines the rate at which a star uses up its available fuel, and L goes as M 3 > 1, it is evident that stars of different mass effectively age at different rates. The cluster colour-magnitude diagrams are essentially snapshots of stellar evolution in which all the stars have the same age, but cover a wide range of mass. 

For instrument codes see Table 5.6 °For colour scales see Chapter 3 Luminosity value for some older instruments. Rd = Y NM not mentioned in die reference. 

---