8. The Lives of Stars


Fig8_1 Original Hertzsprung-Russell diagram

Fig8_1 Original Hertzsprung-Russell diagram

Fig. 8.1 . The absolute luminosity, in magnitude units (vertical axis) plotted in 1914 by Henry Norris Russell (1877?1957) as a function of spectral class (top horizontal axis) for four moving star clusters: the Hyades (black dots); the Ursa Major group (small crosses), the large group in Scorpius (small open circles), and the 61 Cygni group (triangles). The large circles and crosses represent points calculated from the mean parallaxes and magnitudes of other groups of stars. The two diagonal lines mark the boundaries of Ejnar Hertzsprungís (1873?1967) observations of the Pleiades and Hyades open star clusters in 1911; this is now known as the main sequence along which most stars, including the Sun, are located. The giant stars are located at the upper right. In his publication, Russell included a very similar diagram for individual bright stars whose distances had been established from stellar parallax measurements, it closely resembled the diagram shown here with an exceptional point in the lower left-hand corner, which we included here with an x mark. This star is the faint companion of a double-star system Omicron2 Eridani, or 40 Eridani, now known to be a white dwarf star. [Adapted from Henry Norris Russell, Relations between the spectra and other characteristics of stars, Popular Astronomy 22, 275-294 (1914).]


Fig8_2 Hertzsprung-Russell diagram for nearby stars

Fig8_2 Hertzsprung-Russell diagram for nearby stars

Fig. 8.2 . A plot of the luminosity (left vertical axis), in units of the Sunís absolute luminosity denoted L?, against the effective temperature of the starís disk in degrees kelvin, designated K (bottom horizontal axis) for 22,000 stars in the catalogue of the HIPPARCOS satellite. This plot is known as the Hertzsprung-Russell diagram, abbreviated H-R diagram. The spectral class is also denoted (bottom horizontal axis), as well as the absolute visual magnitude (right vertical axis) and color index, B?V (top horizontal axis). Most stars, including our Sun, lie along the main sequence, which extends from the high temperature, blue-white stars at the top left to the low temperature, red stars at the bottom right. The Sun is a main-sequence star with an absolute visual magnitude MV = 4.8 and color index B?V = 0.68. The radiation from all main-sequence stars is sustained by hydrogen-burning reactions in their cores. Stars of about the Sunís mass evolve into helium-burning red giant stars, located in the upper-right side of the diagram. Very rare, bright giant stars, and extremely scarce and luminous supergiants are found above the giant stars and along the top of the diagram. Faint and initially hot white dwarf stars are located in the lower left side. Owing to their low luminosity, these end points of stellar evolution are relatively difficult to observe. (Data points courtesy of ESA/HIPPARCOS mission.)


Fig8_3 Spectral type and luminosity class in the H-R Diagram

Fig8_3 Spectral type and luminosity class in the H-R Diagram

Fig. 8.3 . When both a starís spectral type (top horizontal axis) and luminosity class (Roman numerals) are known, the starís luminosity (left vertical axis) in units of the Sunís luminosity, denoted L?, and effective disk temperature (bottom horizontal axis) can be obtained. The spectral types are shown at the coolest temperature for each type. A Roman numeral V designates the main sequence stars, subgiants by IV, giants by III, bright giants by II and supergiants by Ia and Ib. VI or SD denotes the subdwarfs, and D or VII designates the white dwarf stars.


Fig8_4 Stellar mass and lifetime on the main sequence

Fig8_4 Stellar mass and lifetime on the main sequence

Fig. 8.4 . The relation between a starís luminosity (left vertical axis), in units of the Sunís luminosity denoted L?, and the starís effective disk temperature (bottom horizontal axis) in degrees kelvin, designated K, for the main-sequence stars in the Hertzsprung-Russell diagram. The stellar masses that are given along the main-sequence curve are in units of the Sunís mass, denoted M?. Stars of higher mass are hotter and more luminous. All of these stars shine by hydrogen burning with a lifetime that is also denoted along the main-sequence curve. More massive stars burn their hydrogen fuel at a faster rate and have shorter lifetimes.


Fig8_5 Giants, Supergiants and white dwarfs

Fig8_5 Giants, Supergiants and white dwarfs

Fig. 8.5 . The vast majority of stars occupy the main sequence in the H-R diagram. Stars with a mass comparable to that of the Sun will evolve into helium-burning giant stars, illustrated by Aldebaran and Arcturus in this diagram. These red giants are a bit cooler than the Sun, but about 100 times more luminous. The luminosity (left vertical axis) is in units of the Sunís luminosity, denoted L?. More massive stars, which have shorter lifetimes on the main sequence, evolve into supergiant stars that are between 10,000 and 1,000,000 times as luminous as the Sun. Antares and Betelgeuse illustrate the supergiant stars on this diagram. After depleting all their helium fuel, the less-luminous giant stars evolve into white dwarf stars of very low luminosity and initially hot disk temperatures. They are illustrated in the bottom left of this diagram by Sirius B, 40 Eridani B and Procyon B.


Fig8_6 Energy generation by two hydrogen burning processes

Fig8_6 Energy generation by two hydrogen burning processes

Fig. 8.6 . The energy output (left vertical axis), in units of power per kilogram or J s-1 kg-1, as a function of core temperature (bottom horizontal axis) in millions, or 106, degrees kelvin, designated K. The proton-proton chain, denoted PP, dominates the hydrogen-burning energy production for the Sun and less massive stars that have lower core temperatures. At the center of the Sun, where the temperature is 15.6 x 106 K, the proton-proton chain is the dominant nuclear reaction chain for converting hydrogen nuclei into helium nuclei, with an energy output 0.016 J s-1 kg-1, or 51 million MeV g-1 s-1 in the units that nuclear astrophysicists employ. In more massive main-sequence stars, the central temperature is higher, and the CNO cycle of hydrogen burning is the most efficient process. Main-sequence stars of mass less than 1.5 solar masses shine by the proton-proton chain of nuclear reactions, while the main sequence stars with mass greater that 1.5 solar masses burn hydrogen by the CNO set of nuclear reactions.


Fig8_7 Convection inside stars of different mass

Fig8_7 Convection inside stars of different mass

Fig. 8.7 . Most stars have convective zones in which energy is transported by the wheeling motion of convection, denoted here by closed curves with arrows for stars of different mass, designated by M and compared to the Sunís mass designated M-. The symbol < means less than, and > denotes greater than. Low-mass stars, with less than half a solar mass, are fully convective from core to visible disk and thus of uniform composition. Their low temperatures result in a high opacity to radiation. In intermediate-mass stars, such as the Sun, radiation transport dominates convection in the hot central regions, which are enveloped by a cooler convective region. The visible disks of these stars do not include the nuclear fusion products from their core, but retain the same composition as the interstellar medium from which these stars formed. High-mass stars, with more than 1.5 times the mass of the Sun, have a large radiative zone that is not enveloped by a convective zone. The temperature-sensitive hydrogen burning reactions of the CNO cycle causes the development of a convective core in these stars.


Fig8_8 Formation of a giant star

Fig8_8 Formation of a giant star

Fig. 8.8 . When a main-sequence star consumes the hydrogen in its core, the inside of the star contracts and heats up, causing the outside to expand and cool down. Hydrogen burning resumes in a shell that envelops the collapsing core. The center of the star eventually heats up to about 100 million K, which is hot enough to burn helium and stop the core collapse. A giant star has then been created with a luminosity of about 100 times that of the Sun and a radius of approximately 50 times the radius of the Sun.


Fig8_9 Open star clusters in the H-R diagram

Fig8_9 Open star clusters in the H-R diagram

Fig. 8.9 . The open star clusters are relatively young, and most of their stars have not yet left the main sequence in the Hertzsprung-Russell, abbreviated H-R, diagram. The youngest clusters, such as the Pleiades, retain all but the topmost part of the main sequence. The turn off point of the Pleiades star cluster from the main sequence indicates an age of roughly 100 million years. The Hyades star cluster, which turns off about halfway down the main sequence, is about 600 million years old. The lowest open cluster in this diagram, M67, is an estimated 5 billion years old, with a main sequence that stops just above the Sun. One globular star cluster, M3, is shown for comparison. Alan Sandage (1926-2010) first published this diagram in 1957 (Astrophysical Journal 126, 326 (1957)).


Fig8_10 How old is a globular star cluster

Fig8_10 How old is a globular star cluster

Fig. 8.10 . A plot of the luminosity (left vertical axis), in units of the Sunís luminosity LĚ, against the color index, B-V (bottom horizontal axis), for the stars in the southern globular star cluster 47 Tucanae, also designated NGC 104. The absolute visual magnitudes, MV, of the stars are also shown (right vertical axis). Although low mass, relatively faint stars are still on the main sequence (diagonal line from middle left to bottom right), the massive, bright stars in the cluster have left the main sequence and are evolving into giant stars (top right). Theoretical tracks, called isochrones, show the evolutionary distributions at different ages of 10, 12, 14 and 16 billion years from top to bottom and left to right. The best fit to the observed data corresponds to an age of between 12 and 14 billion years for this star cluster. (Courtesy of James E. Hesser.)


Fig8_11 Globular star cluster in the H-R diagram

Fig8_11 Globular star cluster in the H-R diagram

Fig. 8.11 . The Hertzsprung-Russell diagram, abbreviated H-R diagram, for the globular star cluster M 5, where the absolute visual magnitude (left vertical axis) is plotted as a function of color index (bottom horizontal axis). It is very different from the H-R diagrams for open star clusters shown in Figure 8.9. The high mass stars in this globular star cluster have left the main sequences at a relatively low turn off point, denoted TO, indicating a greater age than the open star clusters, and it illustrates the evolutionary tracks of these stars into the red giant branch, designated RGB (top right), as well as other evolutionary stages such as the subgiant branch, denoted SGB, the asymptotic giant branch, designated AGB, and the horizontal branch, denoted HB, that extends to the left. The gap of missing stars in the horizontal branch for the globular star cluster M 5 shows the instability strip of pulsating stars, known as RR Lyrae stars. Halton Arp (1927- ) published the data shown in this diagram were in 1962 (Astrophysical Journal 135, 311 (1962).


Fig8_12 Abundance of the elements in the Sun

Fig8_12 Abundance of the elements in the Sun

Fig. 8.12 . The relative abundance of the elements in the solar photosphere, plotted as a function of their atomic number Z, which is the number of protons in the atomís nucleus and roughly half the atomic weight. The abundance is plotted on a logarithmic scale and normalized to a value a million, million, or 1.0 x 1012, for hydrogen. Hydrogen, the lightest and most abundant element in the Sun, was formed about 14 billion years ago in the immediate aftermath of the big bang that led to the expanding universe. Most of the helium now in the Sun was also created then. All the elements heavier than helium were synthesized in the interiors of massive stars that no longer shine, and then wafted or blasted into interstellar space where the Sun subsequently originated. Carbon, nitrogen, oxygen and iron, were created over long time intervals during successive nuclear burning stages in former massive stars, and also during their explosive death. Elements heavier than iron, were produced by neutron capture reactions during the supernova explosions of stars that lived and died before the Sun was born. The light elements boron, beryllium and most of the lithium are believed to originate from heavier cosmic-ray particles that have been stripped of some of their ingredients by collisions, in a process called spallation. The exponential decline of abundance with increasing atomic number and weight can be explained by the rarity of stars that have evolved to later stages of life. (Data courtesy of Nicolas Grevesse.)