PHY 521: StarsProf. Stanimir MetchevTopics•Stellar interiors•equations of state•energy transport: radiation, convection, conduction•nucleosynthesis•Stellar photospheres•radiative transfer•opacities•formation of spectral linesTopics (cont.)•Compact objects•white dwarfs, neutron stars, brown dwarfs•Binary stars•evolution, significance•Formation and evolution of stars•determination of stellar ages•Formation and evolution of planetary systemsPrerequisites•Advanced undergraduate-level:•classical mechanics•quantum mechanics•electrodynamics•thermodynamics•No prior knowledge of astronomy expectedTexts•required recommendedCourse Organization•semi-weekly lectures: TuTh 2:20–3:40pm•weekly readings•textbooks + select articles•lecture notes available on website after lecture•bi-weekly homework assignments•some programming will be necessary•co-operation encouraged•submit your own work•office hours: Wed 1–2pm, ESS 452Course Organization•Need to re-schedule following lectures:•Sep 6, 8 (Tue, Thu)•Oct 13 (Thu)•Oct 18, 20 (Tue, Thu)•Possible alternate class meeting times:•Mondays: decided on Mondays, 4–5:20pm•Tue between 5–8pm•Wednesdays between 10am–1pmGrading•40% homework assignments•20% midterm (take-home)•40% final exam (take-home)Astronomical and Stellar PhenomenologyPhenomenology•Radiation, magnitudes•Distances•Detection of light, photometric system•Stellar spectral classification•Planck’s law– specific intensity– [erg s–1 cm–2 Hz–1 sterad–1] or [Jy sterad–1]– 1 Jy = 10–23 erg s–1 cm–2 Hz–1•Wien displacement law! T λmax= 0.29 K cm•Stefan-Boltzmann law! F = σ T 4 – energy flux density – [erg s–1 cm–2]•Stellar luminosity– [erg s–1]–RSun = 6.96×1010 cm–LSun = 3.9×1033 erg cm–1!!Blackbody Radiation€ σ=2π5k415c2h3= 5.67 ×10−5erg cm–2s–1K–4€ L*= 4πR*2σTeff4Blackbody RadiationTeff, Sun = 5777 KColor of Blackbody RadiationAstronomical Magnitudes•Stefan-Boltzmann Law: F = σ T 4 [erg s–1 cm–2]•apparent magnitude: m = –2.5 log F/F0– m increases for fainter objects!– m = 0 for Vega; m ~ 6 mag for faintest naked-eye stars– faintest galaxies seen with Hubble: m ≈ 30 mag• 109.5 times fainter than faintest naked-eye stars– dependent on observing wavelength•mV, mB, mJ, or simply V (550 nm), B (445 nm), J (1220 nm), etc•bolometric magnitude (or luminosity): mbol (or Lbol)– integrated over all wavelengths– Mbol, Sun = +4.75 mag (absolute bolometric magnitude of the Sun)Magnitudes and Colors• bolometric correction:• Mbol = MV + BC• MV,Sun = +4.82 mag, so BCSun = –0.07 mag • magnitude differences:– relative brightness of two objects at the same wavelength V1 – V2 = –2.5 log FV1/FV2•∆m = 5 mag approx. equivalent to F1/F2 = 100 – relative brightness of the same object at different wavelengths (color) B – V = –2.5 (log FB/FV – log FB,Vega/FV,Vega)– by definition Vega has a color of 0 mag at all wavelengths, i.e. (B – V)Vega = 0 magExtinction and Optical Depth• Light passing through a medium can be:– transmitted, absorbed, scattered•dIν(s) = –κν ρ Iν ds = –Iν dτν–medium opacity κν [cm2 g–1]–optical depth τν = κν ρs [unitless]•Iν = Iν,0e–τ = Iν,0e–κρs =Iν,0e–s/l–photon mean free path: lν = (κν ρ)–1 = s/τν [cm]•Extinction along the line of sight: apparent magnitude mν is attenuated by Aν = 2.5 log (Fν,0/Fν) = 2.5 log(e)τν = 0.43τν mag–reddening between two frequencies (ν1, ν2) or wavelengths is defined asEν1,ν2 = mν1 – mν2 – (mν1 – mν2)0 [mag]–(mν1 – mν2)0 is the intrinsic color of the starAV / E(B–V) ≈ 3.0Interstellar Extinction Lawextinction is highest at ~100 nm = 0.1 µmunimportant for >10 µmInterstellar Extinction: Dustvisible(0.5 micron)mid-infrared (~20 micron)Atmospheric TransmissionAbsolute Magnitude and Distance Modulus• The apparent magnitude of a star at 10 pc– used to compare absolute brightnesses of different stars M = m + 2.5 log F(r) / F(10 pc)• Distance modulus (DM)– a proxy for distance m – M = 5 log (r / 10 pc)– DM = 0 mag for object at 10 pc– DM = –4.4 mag for Proxima Cen– DM = 14.5 mag to Galactic centerMeasuring Distance:Trigonometric Parallax•distance d to nearby star is 1 parsec (pc) when angle p = 1 arc sec (1”)•d = 1 AU / p•1 pc = 3.26 ly = 2.06 AU = 3.09e18 cm•Proxima Cen is at 1.3 pc ~ 4.3 lyAtmospheric TransmissionPhotometric Bands: Near-InfraredPhotometric Bands: Visible25Photometric Systems• UBVRI(ZY) (visible)– Johnson, Bessel, Cousins, Kron, etc• ugriz (visible)– Thuan-Gunn, Strömgren, Sloan Digital Sky Survey (SDSS), etc• JHKLM(NQ) (infrared)– Johnson, 2-micron All-Sky Survey (2MASS), Mauna Kea Observatory (MKO), etcDetection of LightQuantum efficiencies of the 4 CCD chipson the Hubble WFPC2 cameraA charge-coupled device (CCD) converts photons to electronsDetection of Light: The Sloan Digital Sky Survey (SDSS)SDSS 2.5 m telescope at Apache Point, NMRitchey-Chretien design(Cassegrain-like)Detection of Light: The Sloan Digital Sky Survey (SDSS)Detection of Light: The Sloan Digital Sky Survey (SDSS)(ansgtroms)ug r i z30Proxima CenPhenomenology•Radiation, magnitudes•Distances•Detection of light, photometric system•Stellar spectral classificationA Spectrographtelescope focusOBAFGKM + LTY•species with higher ionization potentials34Spectral Classification: Temperatureinfrared spectravisible spectraSpectral Classification: TemperatureT1,400–2,500 K noneMolecules: H2O, hydridesreddest star-like objects~ 0.1 10–5–10–3>100 Gyr400–1,400 KnoneMolecules: H2O, CH4~ 0.1 10–6–10–5N/A<0.08Weak Ca+Y<400 KnoneMolecules: H2O, CH4, NH3~ 0.1 <10–6N/A<0.0836Stellar Classification: TemperatureSunM dwarf T dwarfL dwarf Jupiterbrown dwarfs planetsstars5700 K ~3500 K~2000 K ~1000 K 160 K(G dwarf)Spectral Classification: Luminosity• luminosity, radius, surface gravity, and surface pressure are mutually related–L = 4πR2σTeff4, g = GM/R2, P = ρgl (l is photon m.f.p.)• define “luminosity spectral class”V: dwarfs, log g ~ 4.5 [cgs units]IV: subgiants, log g ~ 3 (approximately as on Earth)III: giants, log g ~ 1.5II: (bright) giants, log g ~ 0.5I: supergiants, log g ~ –0.5• Sun: G2 V star (Teff = 5777K, log g = 4.43)(figure from D.