163 The H–R Diagram and the Study of Stellar Evolution (98/81) -- Astronomy

163 The H–R Diagram and the Study of Stellar Evolution Learning Objectives By the end of this section, you will be able to: - Determine the age of a protostar using an H–R diagram and the protostar’s luminosity and temperature - Explain the interplay between gravity and pressure, and how the contracting protostar changes its position in the H–R diagram as a result One of the best ways to summarize all of these details about how a star or protostar changes with time is to use a Hertzsprung-Russell (H–R) diagram. Recall from The Stars: A Celestial Census that, when looking at an H–R diagram, the temperature (the horizontal axis) is plotted increasing toward the left. As a star goes through the stages of its life, its luminosity and temperature change. Thus, its position on the H–R diagram, in which luminosity is plotted against temperature, also changes. As a star ages, we must replot it in different places on the diagram. Therefore, astronomers often speak of a star moving on the H–R diagram, or of its evolution tracing out a path on the diagram. In this context, “tracing out a path” has nothing to do with the star’s motion through space; this is just a shorthand way of saying that its temperature and luminosity change as it evolves. To estimate just how much the luminosity and temperature of a star change as it ages, we must resort to calculations. Theorists compute a series of models for a star, with each successive model representing a later point in time. Stars may change for a variety of reasons. Protostars, for example, change in size because they are contracting, and their temperature and luminosity change as they do so. After nuclear fusion begins in the star’s core (see Stars from Adolescence to Old Age), main-sequence stars change because they are using up their nuclear fuel. Given a model that represents a star at one stage of its evolution, we can calculate what it will be like at a slightly later time. At each step, the model predicts the luminosity and size of the star, and from these values, we can figure out its surface temperature. A series of points on an H–R diagram, calculated in this way, allows us to follow the life changes of a star and hence is called its evolutionary track. Evolutionary Tracks Let’s now use these ideas to follow the evolution of protostars that are on their way to becoming main-sequence stars. The evolutionary tracks of newly forming stars with a range of stellar masses are shown in Figure 1. These young stellar objects are not yet producing energy by nuclear reactions, but they derive energy from gravitational contraction—through the sort of process proposed for the Sun by Helmhotz and Kelvin in this last century (see the chapter on The Sun: A Nuclear Powerhouse). Initially, a protostar remains fairly cool with a very large radius and a very low density. It is transparent to infrared radiation, and the heat generated by gravitational contraction can be radiated away freely into space. Because heat builds