Key Ideas and Terms

10-1 Measuring the distances to nearby stars utilizes an effect called parallax

• Stellar parallax is the apparent change in position of a star due to Earth’s motion around our Sun and is used to measure the distance to nearby stars.
• The parallax angle, p, is equal to half the angle through which a star’s apparent position changes due to the change in position of an observer.
• A star with a parallax angle of 1 second of arc (p = 1 arcsec) is defined to have a distance of 1 parsec (d = 1 pc), which is 3.26 ly.

10-2 A star’s brightness can be described in terms of luminosity or magnitude

• How bright a star appears in the sky for an Earth-based observer is called its apparent magnitude, with the brightest stars having the lowest numbers.
• Without a telescope, the brightest stars are magnitude 1 stars and the dimmest stars are magnitude 6 stars.
• The magnitude of a star if it were at a distance of 10 pc is its absolute magnitude, and it is a quantity that reflects a star’s true energy output so it can be compared to other stars.

10-3 A star’s distance can be determined by comparing its luminosity and brightness

• A star’s luminosity is the total amount of energy a star emits each second.
• The inverse-square law relationship states that the apparent brightness of light that an observer can see or measure is inversely proportional to the square of the observer’s distance (d) from the source.
• For a given distance, the brighter the star, the more luminous that star must be. For a given apparent brightness, the more distant the star, the more luminous it must be to be seen at that distance.

10-4 A star’s color depends on its surface temperature

• The primary wavelength of light emitted by a star is dependent on its temperature, with higher temperature stars emitting relatively greater amounts of short wavelength light.
• Red stars are relatively cold, with low surface temperatures.
• Blue stars are relatively hot, with high surface temperatures.

10-5 The spectra of stars reveal their chemical compositions as well as surface temperatures and sizes

• Stars are categorized into spectral classes, designated by letters, that are organized by details of the stars’ spectra.
• Stars are further subdivided into spectral types and numbered 0–9.
• From hottest to coolest, the sequence of spectral classes is OBAFGKM.
• Substars too small to sustain thermonuclear fusion in their cores are widely known as brown dwarfs.
• By mass, almost all stars (including the Sun) and brown dwarfs are about three-quarters hydrogen, one-quarter helium, and 1% or less metals.

10-6 Stars come in a wide variety of sizes and masses

• The key to finding a star’s radius from its luminosity and surface temperature is the Stefan-Boltzmann law.
• We can determine the radius of a star from its luminosity and surface temperature. For a given luminosity, the greater the surface temperature, the smaller the radius must be. For a given surface temperature, the greater the luminosity, the larger the radius must be.
• Double stars are two stars that lie along nearly the same line of sight but are actually at very different distances from us.
• Some multiple star systems are true binary stars, or binaries, which are pairs of stars that actually orbit each other; the details of their orbits allow us to determine sizes and masses.
• Each of the two stars in a binary system actually moves in an elliptical orbit about the center of mass of the system.

10-7 Hertzsprung-Russell (H-R) diagrams reveal the different kinds of stars

• Graphs of the luminosity/absolute magnitude versus spectral class/surface temperature are today known as Hertzsprung-Russell diagrams or H-R diagrams.
• Main sequence stars are found on the H-R diagram extending from the hot, luminous, blue stars in the upper left corner of the diagram to the cool, dim, red stars in the lower right corner.
• Tremendously luminous and large stars are called giants. Cooler members of the largest stars are often called red giants because they appear reddish.
• A few rare stars are considerably bigger and brighter than typical giants, with radii up to 1000 R_⊙; they are called supergiants.
• White dwarfs are so dim that they can be seen only with a telescope and are approximately the same size as Earth.
• The mass-luminosity relation is that the greater the mass of a main-sequence star, the greater its luminosity, its surface temperature, and its radius.
• Luminosity classes are based upon the subtle differences in spectral lines, which provide a useful subdivision of the star types in the upper right of the diagram for stars of differing radii.
• Spectroscopic parallax is the process of inferring the distance to a main-sequence star based on its apparent magnitude and its spectral classification.