Chapter 13 Stars Few thousand stars visible to

Chapter 13: Stars Few thousand stars visible to naked eye Each of them is unique All of them share much in common

13. 1 Snapshot of the Heavens • • We see a brief moment of a star’s life Stars form in great clouds of gas and dust Chemical composition: H, He and Z Most of any star’s life is in gravitational equilibrium • Stars differ in mass, age, chemical composition, rotation, and multiplicity.

13. 2 Stellar Luminosity • Star’s luminosity is total amount of power it radiates. Lsun=3. 8 x 1026 watts • Apparent brightness is the amount of light reaching us per unit area. It obeys an inverse square law with distance.

Luminosity-distance formula • Apparent brightness=luminosity/4 d 2 • Unit of apparent brightness is watts per square meter – Stellar luminosities are usually described in comparison with the Sun. Examples: Proxima Cen has L=0. 00006 Lsun, Betelgeuse has L=52, 000 Lsun.

Stellar Parallax • Small shifts in a star’s apparent position caused by Earth’s motion around the Sun. • Proxima Cen has parallax angle of only 0. 7 degrees. • D(pc)=1/p(arcseconds) • 1 pc=3. 26 light years

The Magnitude System • The ancient (Hipparchus 160 -127 BC) magnitude system classified stars according to how bright they look to the eye. First magnitude=brightest. • Apparent magnitudes describe how bright different stars appear in the sky. • m. A-m. B=-2. 512 log. IA/IB

Magnitude-Distance Relation • Absolute visual magnitude Mv is the apparent visual magnitude a star would have at 10 pc • m. V-MV=-5+5 log 10(d) • Absolute bolometric magnitude. Sun’s Mbol=4. 7, Arcturus Mbol=-0. 3

Stellar Surface Temperature • Stellar surface temperatures are determined from colors or spectra • We do not need to know the distance to the star to calculate the surface temperature • A red star is always cooler than a yellow star

Spectral Type • Spectral types are used to classify stars according to their temperature. • The hottest stars are spectral type O. They are the bluest and display lines of ionized elements. • The coolest (sub)stars are spectral type T. They are reddest and display huge molecular bands. • Time honored mnemonic: Oh Be A Fine Girl/Guy Kiss My Lips Tenderly • Each spectral letter is subdivided into numbered categories (e. g. B 0, B 1, B 2, …, B 9). The larger the number, the cooler the star.

13. 4 Stellar Masses • Most important property of stars, yet hard to measure. Most reliable masses come from binaries and are calculated using Newton’s version of Kepler’s third law. • M=a 3 /P 2 , MA/MB=r. B/r. A • Knowledge of the orbital period and semimajor axis of the orbit are needed. • About half of all stars occur in multiple systems.

Stellar Binaries • Five classes of binaries: visual, eclipsing, spectroscopic, astrometric, and gravitational lenses. • Famous examples: Castor (William Herschel 1782), Sirius (Friedrich Bessel 1844) and Mizar.

Sirius • The brightest star in the sky was discovered to be an astrometric binary in 1844. Its proper motion follows a wavy pattern. • In 1862 Alvan Clark found Sirius B, which is 9 magnitudes fainter than A and is never farther away than 11. 5 arcsec. • MA=2. 35 MSun, MB=1. 17 MSun

Eclipsing Binaries • When the plane of the binary’s orbit is very close to the plane of our light of sight, each star periodically passes in front of the other causing an eclipse. • Light curve: graph of brightness versus time. • Duration of eclipses determines the sizes of stars.

Algol “The Demon’s Head” • Eclipses first reported in 1669 by Geminiano Montanari. • The amount of light lost during eclipses depends only on temperature. • B 8 V+G 0 V. P=68 h, d=10 h

Spectroscopic Binaries • The binary nature of a star can be detected by measuring Doppler shifts in its spectral lines. • Double-line or single-line depends on brightness ratio. • We can get lower limits to the masses but not true masses because of the unknown inclination angle.

The Hertzsprung-Russell Diagram • Ejnar Hertzsprung and Henry Norris Russell made first graphs plotting stellar luminosities versus spectral types. H-R diagram. • Key features: Temperature increases from right to left. Luminosities in solar units and factors of 10. • Each star is represented by a single dot in the graph.

Radii of Stars from the HRD • A star’s luminosity depends on both its surface temperature and surface area. • If two stars have the same surface temperature, the one larger in size is more luminous. • More massive stars are in general larger than less massive stars.

Patterns in the HRD • Stars do not fall randomly in the HRD • Main sequence stars are the most common • Supergiants are the brightest stars • White dwarfs are hot but faint. • Brown dwarfs are cool and faint.

Stellar Luminosity Classes • • • I Supergiants (Betelgeuse M 2 I) II Bright giants III Giants IV Subgiants V Main sequence (Sun G 2 V)

The Mass-Luminosity Relation • Stars spend the majority of their lives fusing H. • On the main-sequence there is tight M-L relation: L=M 3. 5 • Stellar masses range from 100 to 0. 08 Ms • Stellar luminosities range from 10 -6 to 107

Main-Sequence Lifetimes • Stars have a limited supply of core hydrogen. • Massive stars have shorter lifetimes than less massive stars because they consume their hydrogen at a higher rate (M-L relation). • The fact that there are O stars means that they have just formed.

Advanced Stages in Stellar Evolution • Giants and supergiants are stars near the end of their lives. Stars grow more luminous when they are running out of fuel. • A giant with a mass similar to the Sun ultimately loses its outer layers, leaving behind a core that becomes a white dwarf. • Supergiants usually explode as supernovae, leaving behind neutron stars or black holes as corpses.

Pulsating Variable Stars • Variable stars change their brightness significantly with time. • Pulsating stars never achieve a proper balance. Sometimes the photosphere is too opaque making the star expand, then it gets too trasparent making the star contract.

The Instability Strip • The instability is related to a layer of He ionization and thus occurs at roughly constant surface temperature. • Cepheids are pulsating red giants with periods of days. RR Lyraes are pulsating subgiants with periods of order of hours. • White dwarfs also pulsate with periods of order of seconds.

Period-Luminosity Relation • Delta Cephei was discovered to be variable by John Goodricke in 1784. • Henrietta Leavitt discovered the P-L relation in 1912. Larger Cepheids take longer to pulsate in and out. • Cepheids provide a primary means of measuring distances to other galaxies.

13. 6 Star Clusters • Stars almost inevitably form in groups. • Open clusters are always found in the disk of the galaxy. • They contain up to several 1000 s stars and typically span about 10 parsecs. • The most famous OC is the Pleiades or 7 sisters.

Globular Clusters • Contain more than a million stars concentrated in a radius of 20 -50 pc. • They are located in both the halo and the disk of the galaxy.

Star Clusters as Laboratories • All stars in a cluster lie at about the same distance from Earth. • All stars in a cluster are coeval (within a few million years of one another). • All stars where born from the same cloud and share the same chemical composition. • Astronomers use star clusters for comparing the properties of stars.

Pleiades’ H-R Diagram • Pleiades’ stars trail away to the right of the MS at the upper end. O stars are missing. • Main-sequence turnoff is the precise point at which the Pleiades sequence diverges from standard MS. • In the Pleiades, it occurs at spectral type B 6, which has a lifetime of 60 Myr.

Open Cluster Ages • Age of the cluster=lifetime of stars at main-sequence turnoff. • What is the age of a cluster which has the MS turnoff at 1 Msun? • Most open clusters are younger than 5 billion years.

Globular Cluster Ages • Stars at MS turnoff in GCs are less massive than the Sun. • Ages of GCs are 12 -16 billion years. • Lower limit on the possible age of the Universe.

The Big Picture • All stars form with composition dominated by H, He and trace heavier elements. • HRD is one of the most important tools in an astronomer’s kit. • Stars spend most of their lives on the MS. More massive stars have shorter lifetimes. • Stellar clusters are laboratories. They provide much information, for example ages.