Characterizing Stars part 3: The Hertzsprung-Russell Diagram Luminosity Classes Spectral Types

The Hertzsprung-Russell Diagram We will plot stars on a chart which has temperature on the horizontal axis and the luminosity on the vertical axis. Named after two astronomers who made this type of plot in the 1920’s. Use units of solar luminosity and Kelvin

H–R Diagram of Well-Known Stars Notice the luminosity is a special kind of scale called a logarithmic scale, in powers of ten. The temperature is plotted in reverse: hot on the left, cooler on the right.

H–R Diagram of Nearby Stars Now this shows the Main Sequence of stars that are in the shaded region. Stellar size is indicated by the diagonal lines. (These dotted lines are a result of the luminosity-radius- temperature equation).

H–R Diagram of the 100 Brightest Stars This is biased in favor of giants, which are very luminous, so we see all the giants in a large volume of space, and don’t see the smaller stars in such a large volume. As a result, very few smaller stars show up on this plot.

Hipparcos H–R Diagram This is a more representative set of stars for a plot like this.

FIGURE 11-7 A Hertzsprung-Russell Diagram On an H-R diagram, the luminosities of stars are plotted against their spectral types. Each dot on this graph represents a star whose luminosity and spectral type have been determined. Some well-known stars are identified. The data points are grouped in just a few regions of the diagram, revealing that luminosity and spectral type are correlated: Main-sequence stars fall along the red curve, giants are to the right, supergiants are on the top, and white dwarfs are below the main sequence. The absolute magnitudes and surface temperatures are listed at the right and top of the graph, respectively. These are sometimes used on H-R diagrams instead of luminosities and spectral types. (Answer to text question: An M0 star is the next coolest after a K9.)

FIGURE 11-8 The Types of Stars and Their Sizes On this H-R diagram, stellar luminosities are plotted against the surface temperatures of stars. The dashed diagonal lines indicate stellar radii. For stars of the same radius, hotter stars (corresponding to moving from right to left on the H-R diagram) glow more intensely and are more luminous (corresponding to moving upward on the diagram) than cooler stars. While individual stars are not plotted, we show the regions of the diagram in which main-sequence, giant, supergiant, and white dwarf stars are found. Note that the Sun is intermediate in luminosity, surface temperature, and radius; it is very much a middle of- the-road star.

Determination of Stellar Distances by different methods:

Spectroscopic parallax is really a misnomer, it is not a direct measurement, but empirical, based on a statistical estimate, the most likely distance for a star based on luminosity and color. Variable stars have characteristics which allow us to estimate their distance. Luminosity class is an additional criterion, based on spectral line width and its correlation to gas pressure in the star’s photosphere. We get several types of stars, listed in the Table on Stellar Luminosity Classes.

Spectra vary according to temperature. FIGURE 11-5 The spectra of stars with different surface temperatures. The corresponding spectral types are indicated on the right side of each spectrum. (Note that stars of each spectral type have a range of temperature.) The hydrogen Balmer lines are strongest in stars with surface temperatures of about 10,000 K (called A-type stars). Cooler stars (G- and K-type stars) exhibit numerous atomic lines caused by various elements, indicating temperatures from 4000 to 6000 K. Several of the broad, dark bands in the spectrum of the coolest stars (M-type stars) are caused by titanium oxide (TiO) molecules, which can exist only if the temperature is below about 3500 K. Recall from Section 4-5 that the Roman numeral I after a chemical symbol means that the absorption line is caused by a neutral atom; a numeral II means that the absorption is caused by atoms that have each lost one electron. (R. Bell, University of Maryland, and M. Briley, University of Wisconsin at Oshkosh)

Stellar luminosity and spectral type can be used to characterize stars rather than use the luminosity and temperature.

FIGURE 11-10 Luminosity Classes Dividing the H-R diagram into regions, called luminosity classes, permits finer distinctions between giants and supergiants. Luminosity classes Ia and Ib encompass the supergiants. Luminosity classes II, III, and IV indicate giants of different brightness. Luminosity class V indicates main-sequence stars. White dwarfs do not have their own luminosity class.

Visual binary stars

Stellar masses can be determined most easily in Binary Stars. Kruger 60

FIGURE 11-11 A Binary Star System About one-third of the visible “stars” are actually double stars. Mizar in Ursa Major is a binary system with stars separated by only about 0.01 arcsec. The images that surround this diagram show the relative positions of the two stars over nearly half of their orbital period. The orbital motion of the two binary stars around each other is evident. Either star can be considered fixed in making such plots. (Navy Prototype Optical Interferometer, Flagstaff, AZ. Courtesy of Dr. Christian A. Hummel)

FIGURE 11-12 Center of Mass of a Binary Star System (a) Two stars move in elliptical orbits around a common center of mass. Although the orbits cross each other, the two stars are always on opposite sides of the center of mass and thus never collide. (b) A seesaw balances if the center of mass of the two children is at the fulcrum. When balanced, the heavier child is always closer to the fulcrum, just as the more massive star is closer to the center of mass of a binary star system.

Spectroscopic binary stars

Binary Spectra have line shifts due to the Doppler effect.

FIGURE 11-15 Spectral Line Motion in Binary Star Systems (a) The diagrams at the top indicate the positions and motions of the stars, labeled A and B, relative to Earth (below the diagram), and their spectra at the four selected moments (Stages 1, 2, 3, and 4) during an orbital period. The changes in colors (wavelengths) of the spectral lines are due to changes in the stars’ Doppler shifts, as seen from Earth. (b) This graph displays the radial velocity curves of the binary HD 171978. (The HD means that this is a star from the Henry Draper Catalogue of stars.) The entire binary is moving away from us at 12 km/s, which is why the pattern of radial velocity curves is displaced upward from the zero-velocity line.

Orbital periods and the velocities can be plotted vs. time. FIGURE 11-15 Spectral Line Motion in Binary Star Systems (a) The diagrams at the top indicate the positions and motions of the stars, labeled A and B, relative to Earth (below the diagram), and their spectra at the four selected moments (Stages 1, 2, 3, and 4) during an orbital period. The changes in colors (wavelengths) of the spectral lines are due to changes in the stars’ Doppler shifts, as seen from Earth. (b) This graph displays the radial velocity curves of the binary HD 171978. (The HD means that this is a star from the Henry Draper Catalogue of stars.) The entire binary is moving away from us at 12 km/s, which is why the pattern of radial velocity curves is displaced upward from the zero-velocity line.

FIGURE 11-16 A Double-Line Spectroscopic Binary The spectrum of the double-line spectroscopic binary (kappa) Arietis has spectral lines that shift back and forth as the two stars revolve around each other. (a) The stars are moving parallel to the line of sight, with one star approaching Earth, the other star receding, as in Stage 1 or 3 of Figure 11-15a. These motions produce two sets of shifted spectral lines. (b) Both stars are moving perpendicular to our line of sight, as in Stage 2 or 4 of Figure 11-15a. As a result, the spectral lines of the two stars have merged. (Lick Observatory)

Eclipsing binary stars

Binary Light Curves sometimes indicate a transiting companion.

Stellar masses determine a star’s position along the main sequence, more than other properties do.

Stellar Mass Distribution for some nearby stars. Giants are rare.

Stellar Radii and Luminosities: Radius is proportional to mass Luminosity is proportional to (mass)4

FIGURE 11-14 The Mass-Luminosity Relation (a) For main-sequence stars, mass and luminosity are directly correlated—the more massive a star, the more luminous it is. A main-sequence star of mass 10 M has roughly 3000 times the Sun’s luminosity (3000 L); one with 0.1 M has a luminosity of only about 0.001 L. To fit them on the page, the luminosities and masses are plotted using logarithmic scales. (b) On this H-R diagram, each dot represents a main-sequence star. The number next to each dot is the mass of that star in solar masses (M). As you move up the main sequence from the lower right to the upper left, the mass, luminosity, and surface temperature of main-sequence stars all increase.

FIGURE 11-14 The Mass-Luminosity Relation (a) For main-sequence stars, mass and luminosity are directly correlated—the more massive a star, the more luminous it is. A main-sequence star of mass 10 M has roughly 3000 times the Sun’s luminosity (3000 L); one with 0.1 M has a luminosity of only about 0.001 L. To fit them on the page, the luminosities and masses are plotted using logarithmic scales. (b) On this H-R diagram, each dot represents a main-sequence star. The number next to each dot is the mass of that star in solar masses (M). As you move up the main sequence from the lower right to the upper left, the mass, luminosity, and surface temperature of main-sequence stars all increase.

Main sequence stars show some trends: The small mass stars tend to be cooler and so they burn hydrogen more slowly in their core. Hence they have longer lives, in some cases, lives that will be much longer than the present age of the Universe (trillions of years).