Solar luminosity

Figure 8.30. Cumulative number distribution for the galaxies in the Universe. Mass is assumed proportional to absolute luminosity (units solar luminosity x 10 ). From Brown et al. (1983).

Abstract. We present the results of an observational campaign undertaken to assess the influence of the iron content on the Cepheid Period-Luminosity relation. Our data indicate that this dependence is not well represented by a simple linear relation. Rather, the behaviour is markedly non monotonic, with the correction peaking at about solar metallicity and declining for higher and lower values of [Fe/H]. 

Fig. 1. N/C and N/O ratios are shown as a function of luminosity relative to the initial solar values. The lower hatched line in each plot is the standard model prediction and the upper hatched line is the predicted value for an initial rotational velocity of 300 km s 1 [6]. Our measurements show that the low ratios seen in aOri are not commonly seen in supergiants. Instead the ratios indicate extensive mixing as predicted by the rotation models.

The chemical analysis has revealed that rather low C/O ratios are found in metal-poor extragalactic carbon stars, as found for galactic carbon stars of the solar vicinity. Furthermore, the three analyzed stars show similar s-elements enhancements [ls/Fe]=0.8-1.3 and [hs/Fe]=l.l-1.7. This leads to new constraints for evolutionary models. For instance, the derived C/O and 13C/12C ratios are lower than model predictions at low metallicity. On the contrary, theoretical predictions of neutrons exposures for the production of the s-elements are compatible with observations (see Fig. 1). Finally, from their known distances, we have estimated the luminosities and masses of the three stars. It results that SMC-B30 and Sgr-C3 are most probably intrinsic carbon stars while Sgr-Cl could be extrinsic. 

The calculation for flux arriving at the Earth requires the Sun s luminosity and the distance from the Sun. The total solar flux (FSun x total area of the Sun) gives solar luminosity LSun = 3.8 x 1026 W and the flux at the Earth, /, is given by ... 

Consider the amount of radiation arriving on the surface of the Earth at a distance of 1 AU or 1.5 x 1011 m. The total flux of the Sun is distributed evenly over a sphere of radius at the distance of the planet, d. From the luminosity calculation of the Sun, F, the solar flux at the surface of Earth, FEarth, is F/47t(1.5 x 1011)2 = 1370 Wm-2 from the least-square law of radiation discussed in Example 2.4 (Equation 2.4). Substituting this into Equation 7.6 with the estimate of the albedo listed in Table 7.2 gives a surface temperature for Earth of 256 K. 

Kuhn, W. R., J. C. G. Walker, and H. G. Marshall. 1989. The effect on Earth s surface temperature from variations in rotation rate, continent formation, solar luminosity, and carbon dioxide. J. Geophys. Res. 94, 11129-36. 

Fig. 3.44. Metallicities in gas-poor galaxies (open symbols) and oxygen abundances at a representative radius in gas-rich disk galaxies (filled symbols), as a function of galaxy luminosity in blue light. The dotted lines in each panel represent identical trends for [Fe/H] and [O/H] and the ordinate 0.0 represents solar composition. Adapted from Zaritsky, Kennicutt and Huchra (1994).

The most metal-deficient stars comprise field stars in the solar neighbourhood (where in some cases distances and luminosities can be found from parallaxes) and stars in globular clusters where the morphology of the HR diagram can be studied (Fig. 4.8). Such stars are of particular interest because their content of heavy elements (synthesized in still earlier generations of stars) is so low that they can... 

Fig. 5.7. Evolutionary tracks for Z = 0.02 (near solar metallicity) stars with different masses in the HR diagram. (Luminosities are in solar units.) Points labelled 1 define the ZAMS and points labelled 2 the terminal main sequence (TAMS), the point where central hydrogen is exhausted. The Schonberg-Chandrasekhar limit may be reached either before or after this (for M > 1.4 Af0). Points marked 3 show the onset of shell hydrogen-burning. Few stars are found in the Hertzsprung gap between point 4 and point 5 , where the surface convection zone has grown deep enough to bring nuclear processed material to the surface in the first dredge-up. Adapted from Iben (1967).

Other representative data for stars with different initial masses are given in Table 7.1. Numbers in brackets refer to Z = 0.001, Y = 0.24, others to Z = 0.02, Y = 0.28, i.e. near solar. The luminosities of the most massive stars are quite insensitive to Z. 

Since L /M — 1 (in cgs units), it follows from a comparison of equations (7.18) and (7.19) that, for exponential decay in bolometric luminosity, v-1 7 Gyr. Thus a single strong initial burst seems to be ruled out as a dominant contributor in the solar neighbourhood. 

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).

Fig. 3.3. Theoretical Hertzsprung-Russell diagram. The right-hand scale shows in absolute bolometric magnitude what the left-hand scale expresses as the logarithm of the intrinsic luminosity in units of the solar intrinsic luminosity (Lq = 4 x 10 erg s ). On the horizontal axis, the logarithm of the effective temperature, i.e. the temperature of the equivalent blackbody, is put into correspondence with the spectral type of the star, as determined by the observer. This temperature-luminosity diagram shows the lifelines of the stars as strands combed out like hair across the graph. With a suitable interpretation, i.e. viewed through the explanatory machinery of nuclear physics, it opens the way to an understanding of stellar evolution and its twin science of nucleosynthesis. (Courtesy of Andre Maeder and co-workers.)...

Five experiments have so far detected solar neutrinos. These are Homestake (USA), GALLEX, SAGE, KAMIOKANDE and SUPERKAMIOKANDE, all set up down mines or tunnels. Detected fluxes agree qualitatively with theoretical predictions, both in numbers and energies. We may say that we have basically understood how the Sun shines. The same set of nuclear reactions invoked to explain the solar luminosity does give rise to neutrinos. 

Ever since the Sun has been the Sun, its size, surface temperature and luminosity have remained practically unchanged. Solar luminosity has increased by about 30% at the very most over the last 4.6 billion years, and feedback mechanisms have endowed the Earth with the priceless gift of liquid water. 

The Earth s climatic system can be thought of as a well-adjusted thermostat. It is quite clear that it will not be insensitive to changes in the luminosity of our star. Solar luminosity is expected to rise linearly by about 10% over the next billion years, whilst the surface temperature will increase by 1 %. Naturally, supernova specialists would be quite unmoved by such a variation. In their field, luminosities rocket to quite unheard-of values in the merest fraction of a second. But to climate specialists back within the confines of the Earth s atmosphere, an increase of 10% in the Sun s brightness is an alarming prospect. 

If the solar luminosity increases by 2%, the climate model produced by the Goddard Institute for Space Studies indicates a corresponding temperature increase of 4 °C. Climatologists do not usually make predictions over billions of years so this model has not been pursued. However, we may consider that a 10% increase in solar luminosity would lead to a temperature rise of around 12 °C. The result would certainly be catastrophic. Sea level would rise by some 40 cm as the ice caps melted. With a temperature increase of 21 °C, the ice caps would vanish completely and the climate would be changed forever. 

The Sun reaches a luminosity 2300 times greater than its current value and a radius 170 times greater. The planet Mercury is swallowed up. The solar wind is now much amplified and our star loses 38% of its mass into space. 

Apart from these three facts, nuclear astrophysicists take pains to point out that the rate at which the luminosities of SNla events decline, once beyond the maximum, is commensurable with the decay of radioactive cobalt-56, son of nickel-56, atomic nucleus of noble lineage as we know. This is a common factor with gravitational collapse supernovas. SNla light curves are explained through the hypothesis that half a solar mass of nickel-56 is produced when one of these white dwarfs explodes. 

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