Following directly the from the previous chapter, we see that in addition to a shift toward shorter peak wavelength, a higher temperature also increases the overall brightness of blackbody emission at all wavelengths. This suggests that the total energy emitted over all wavelengths should increase quite sharply with temperature. We introduce the Stefan–Boltzmann law, one of the linchpins of stellar astronomy.

Our initial introduction of surface brightness characterized it as a flux confined within an observed solid angle. But actually the surface brightness is directly related to a more general and fundamental quantity known as the “specific intensity.” The light we see from a star is the result of competition between thermal emission and absorption by material within the star.

Compared with stars, the region between them, called the interstellar medium or “ISM,” is very low density; but it is not a completely empty vacuum. A key theme in this chapter is that stars are themselves formed out of this ISM material through gravitational contraction, making for a star–gas–star cycle. We explore the characteristics of cold and warm regions of the ISM and their roles in star formation.

We now consider why stars shine with such extreme brightness. Over the long-term (i.e., millions of years), the enormous energy emitted comes from the energy generated (by nuclear fusion) in the stellar core, as discussed further in Chapter 18. But the more immediate reason stars shine is more direct, namely because their surfaces are so very hot. We explore the key physical laws governing such thermal radiation and how it depends on temperature.

This chapter explores what is known as the Cosmic Microwave Background (CMB), what it is, how it was discovered and our recent efforts to measure and map it. In general, the analysis finds remarkably good overall agreement with predictions of the now-standard “lambda CDM” model of a universe, in which there is both cold dark matter (CDM) to spur structure formation, as well as dark-energy acceleration that is well-represented by a cosmological constant, lambda. From this we can infer 13.8 Gyr for the age of the universe.

The timescale analyses in Chapter 8 show that nuclear fusion provides a long-lasting energy source that we can associate with main-sequence stars in the H–R diagram. This chapter addresses the following questions: What are the requirements for H to He fusion to occur in the stellar core? And how is this to be related to the luminosity versus surface temperature scaling for main-sequence stars? In particular, how might this determine the relation between mass and radius? What does it imply about the lower mass limit for stars to undergo hydrogen fusion?

We walk through the different epochs and eras of the universe, going forward in time from the Hot Big Bang. In the earliest universe, radiation (photons) dominated over matter. As the universe cools, electrons are able to recombine with protons, then helium and other light elements were formed in the first few minutes. Cosmic inflation is posited to overcome several problems, but investigations to probe and perhaps confirm inflation are ongoing.

This chapter gives a brief overview of observational astronomy, using optical instruments and other wavelengths. We present a general formula for the increase in the limiting magnitude resulting from an increased telescope aperture. For light of particular wavelength, the diffraction from a telescope with a specific diameter sets a fundamental limit to the smallest possible angular separation that can be resolved.

Observations of binary systems indicate that main sequence stars follow an empirical mass–luminosity relation L ~ M 3. The physical basis for this can be understood by considering the two basic relations of stellar structure, namely hydrostatic equilibrium and radiative diffusion. In practice, the transport of energy from the stellar interior toward the surface sometimes occurs through convection instead of radiative diffusion; this has important consequence for stellar structure and thus for the scaling of luminosity.