Stellar PropertiesA2290-15 1Stellar PropertiesRelativity and AstrophysicsLecture 15Terry HerterA2290-15 Stellar Properties 2Outline Spectroscopic Parallax Masses of Stars Periodic Variable Stars RR Lyrae Variables Cepheids Variables Period-Luminosity Relation Discovering GalaxiesStellar PropertiesA2290-15 2A2290-15 Stellar Properties 3Sun’s radius is about 1/200 of an AU. So largest stars would extend beyond the orbit of the earth!!424 TRLA2290-15 Stellar Properties 4Spectroscopic 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 parallaxExample: Observe a G2 Ia star (supergiant) with apparent magnitude mv= 10. The absolute magnitude (from the H-R diagram) is Mv= -5.but mv- Mv= - 5 + 5 log10( d )=> log10( d ) = 20/5 = 4=> d = 10,000 pcStellar PropertiesA2290-15 3A2290-15 Stellar Properties 5Stellar 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 starsType of Binaries Visual Binary 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 anotherA2290-15 Stellar Properties 6Spectroscopic Binary SimulationThe 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.Stellar PropertiesA2290-15 4A2290-15 Stellar Properties 7Binary simulationCross indicates the “center of mass” of the system. The stars orbit about this point.A2290-15 Stellar Properties 8Masses 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 MAand MB(in solar masses), the total mass is related to the period, P, in years and the average distance between the stars, a (in AU). Example:  If a visual binary has a period of 32 years and an average separation of 16 AU then Now with stellar masses in hand we can compile table with properties of stars23PaMMBAsunBAMMM 44163232161616321623Stellar PropertiesA2290-15 5A2290-15 Stellar Properties 9Summary of Main-Sequence Stellar Properties The luminosity of stars on the main-sequence varies approximately as L  M3.5with mass.  Since the fuel in stars is proportional to the mass, M, the lifetime of a star is roughly57,00017,0007,9002,700440121Lifetime(106yrs)0.83,5000.080.5M00.95,0000.460.8K01.16,0001.41.1G01.57,5006.41.7F03.010,000803.5A04.928,00013,00015B01340,000400,00040O5Radius(Rsun)Temp.(K)L(Lsun)Mass(Msun)Class5.25.3rateburn fuel MMMtlifeWhere M is in solar masses and tlifeis in solar lifetimes (~ 1010yrs).A2290-15 Stellar Properties 10Periodic 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 -> HeIItransition) 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 main-sequence (post main-sequence stars). Two types: RR Lyrae Variables Cepheid Variables And there are two types of Cepheid variable starsStellar PropertiesA2290-15 6A2290-15 Stellar Properties 11Periodic Variable Stars Although the periods from 0.5 to 100 days. Any given star has a constant period.PeriodBrightnessTime (Days)1463251.5.757A2290-15 Stellar Properties 12H-R Instability StripCepheidsRR LyraeVariablesInstability 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.Stellar PropertiesA2290-15 7A2290-15 Stellar Properties 13Type I (Classical)CepheidsPeriod-Luminosity Relations102103104Luminosity (Lsun)0.3131030100Period (days)Type II (W Virginis)Cepheids CepheiRR Lyrae StarsA2290-15 Stellar Properties 14Cepheids 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 Lsun Found in Open clusters and the galactic disk (Pop I stars) Type II Cepheids (W Virginis Stars) Luminosity: 100 to 5,000 Lsun Found in Globular clusters (Pop II stars)Stellar PropertiesA2290-15 8A2290-15 Stellar Properties 15RR Lyrae Variables Horizontal branch stars (because of where they appear in the H-R diagram). Periods: ~ 12 to 24 hours Luminosity: ~ 50 Lsun Found in Globular clusters (Pop II stars) Luminosity is independent of periodA2290-15 Stellar Properties 16Distances with P-L relation Measure Period Luminosity Mv(absolute magnitude) Measure mv(apparent magnitude) Mvand mv distance from distance modulusmv- Mv= - 5 + 5 log10( d ) A Hubble “key project” was to determine the distances to galaxies w/ Cepheids.Stellar PropertiesA2290-15 9A2290-15 Stellar Properties 17Discovering 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.M31 (Andromeda Galaxy)Stellar PropertiesA2290-15 10M100 Cepheid