Stellar Properties Relativity and Astrophysics Lecture 15 Terry Herter Outline Spectroscopic Parallax Masses of Stars Periodic Variable Stars RR Lyrae Variables Cepheids Variables Period-Luminosity Relation Discovering Galaxies A2290-15 Stellar Properties 2 A2290-15 1
Sun s radius is about 1/200 of an AU. So largest stars would extend beyond the orbit of the earth!! L 2 4 4 R T A2290-15 Stellar Properties 3 Spectroscopic Parallax From a star s spectrum, we can determine its spectral and luminosity class. Given the star s apparent brightness (observed flux), we can then estimate its distance. This distance determination technique is called spectroscopic parallax Example: Observe a G2 Ia star (supergiant) with apparent magnitude m v = 10. The absolute magnitude (from the H-R diagram) is M v = -5. but m v - M v = - 5 + 5 log 10 ( d ) => log 10 ( d ) = 20/5 = 4 => d = 10,000 pc A2290-15 Stellar Properties 4 A2290-15 2
Stellar Masses We know many properties of stars now: Temperature, radius, luminosity, surface composition But the most important determining characteristic of a star is its mass. How do we weigh a star? Binary stars (75% of all stars are binary stars ) pairs of stars that orbit each other used to determine masses of stars Visual Binary Type of Binaries Stars are separated in a telescope Spectroscopic Binary See two sets of spectral lines Doppler shifted due to orbital motion Eclipsing Binary (rare) Stars cross in front of one another A2290-15 Stellar Properties 5 Spectroscopic Binary Simulation The Doppler shift shows the velocity changing periodically. The system is probably not a visual binary and you may only be able to detect one star. A2290-15 Stellar Properties 6 A2290-15 3
Binary simulation Cross indicates the center of mass of the system. The stars orbit about this point. A2290-15 Stellar Properties 7 Masses of Binary Stars Newton s laws allow us to determine the total mass in a binary system. Send end of Lecture 14 for a derivation of the equation below For star of mass M A and M B (in solar masses), the total mass is related to the period, P, in years and the average distance between the stars, a (in AU). 3 a M A M B 2 P Example: If a visual binary has a period of 32 years and an average separation of 16 AU then M A M B 16 32 3 2 161616 16 4 M 3232 4 Now with stellar masses in hand we can compile table with properties of stars sun A2290-15 Stellar Properties 8 A2290-15 4
Summary of Main-Sequence Stellar Properties Class O5 B0 A0 F0 G0 K0 M0 Mass (M sun ) 40 15 3.5 1.7 1.1 0.8 0.5 L (L sun ) 400,000 13,000 80 6.4 1.4 0.46 0.08 Temp. (K) 40,000 28,000 10,000 7,500 6,000 5,000 3,500 Radius (R sun ) 13 4.9 3.0 1.5 1.1 0.9 0.8 Lifetime (10 6 yrs) 1 12 440 2,700 7,900 17,000 57,000 The luminosity of stars on the main-sequence varies approximately as L M 3.5 with mass. Since the fuel in stars is proportional to the mass, M, the lifetime of a star is roughly fuel M 2.5 Where M is in solar masses and t life M 3.5 t burn rate M life is in solar lifetimes (~ 10 10 yrs). A2290-15 Stellar Properties 9 Periodic Variable Stars A small fraction of stars have brightness variations that are periodic. Due to radial oscillations (pulsation which causes expansion and contraction) Partial ionization zone of HeII (HeII -> HeIII -> HeII transition) acts as a valve to dam and un-dam energy flow toward the surface of the star. These are stars which have evolved off the mainsequence (post main-sequence stars). Two types: RR Lyrae Variables Cepheid Variables And there are two types of Cepheid variable stars A2290-15 Stellar Properties 10 A2290-15 5
Periodic Variable Stars Although the periods from 0.5 to 100 days. Any given star has a constant period. Brightness 1.5.75 Period 1 2 3 4 5 6 Time (Days) 7 A2290-15 Stellar Properties 11 H-R Instability Strip Cepheids RR Lyrae Variables Instability strip due to partial ionization zone of HeII (HeII -> HeIII) within the star. At higher temperatures this zone is too near the surface while at lower temperatures convection damps out the oscillations. A2290-15 Stellar Properties 12 A2290-15 6
Period-Luminosity Relations Luminosity (L sun ) 10 4 10 3 10 2 Cephei Type I (Classical) Cepheids RR Lyrae Stars Type II (W Virginis) Cepheids 0.3 1 3 10 30 100 Period (days) A2290-15 Stellar Properties 13 Cepheids Variables Named after Cephei (first discovered) Red Giants and Supergiants There are two types (labeled Type I and II Cepheids) Periods: ~ 1 to 100 days Luminosity is a function of period Period-Luminosity relation discovered by Henrietta Leavitt in 1908. Type I Cepheids (Classical Cepheids) Luminosity: 400 to 20,000 L sun Found in Open clusters and the galactic disk (Pop I stars) Type II Cepheids (W Virginis Stars) Luminosity: 100 to 5,000 L sun Found in Globular clusters (Pop II stars) A2290-15 Stellar Properties 14 A2290-15 7
RR Lyrae Variables Horizontal branch stars (because of where they appear in the H-R diagram). Periods: ~ 12 to 24 hours Luminosity: ~ 50 L sun Found in Globular clusters (Pop II stars) Luminosity is independent of period A2290-15 Stellar Properties 15 Distances with P-L relation Measure Period Luminosity M v (absolute magnitude) Measure m v (apparent magnitude) M v and m v distance from distance modulus m v - M v = - 5 + 5 log 10 ( d ) A Hubble key project was to determine the distances to galaxies w/ Cepheids. A2290-15 Stellar Properties 16 A2290-15 8
Discovering Galaxies From the late 1700 s to the 1920 astronomers had noticed may spiral nebulae. It was not known whether these nebula were far away or nearby Various arguments were put forward in support of each distance Edwin Hubble (1924) Discovered Cepheid variables in M31 (Andromeda Galaxy) also in NGC 6822 and M33 Using the Period-Luminosity Relation for Cepheids Determined that M31 is a galaxy, an Island Universe Galaxy derives from the Greek word galaktikos which means milky white. Note Galaxy is only capitalized (a proper noun) when it refers to our Galaxy, the Milky Way. A2290-15 Stellar Properties 17 M31 (Andromeda Galaxy) A2290-15 9
M100 Cepheid Variation A2290-15 10