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AY202a Galaxies & Dynamics Lecture 24: Cosmological Distance Ladder

Explore the cosmological distance ladder and the Hubble Constant, which determines the current expansion rate of the universe. Learn about various distance indicators and calibration methods used in measuring distances to galaxies.

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AY202a Galaxies & Dynamics Lecture 24: Cosmological Distance Ladder

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  1. AY202a Galaxies & DynamicsLecture 24:Cosmological Distance Ladder

  2. The Hubble Constant: H0 = *current* expansion rate = (velocity) / (distance) = (km/s) / (Megaparsecs) named after Edwin Hubble who discovered the relation in 1929.

  3. The story of the Hubble Constant (never called that by Hubble!) is the “Cosmological Distance Ladder” or the “Extragalactic Distance Scale” Basically, we need distances & velocities to galaxies and other things. Velocities are easy --- pick a galaxy, any galaxy, get spectrum with moderate resolution, R ~ 1000 (i.e λ/R ~ 5Å) N.B. R = Linear Reciprocal Dispersion, get line centroids to ~ 1/10 R ~ 0.5Å/5000Å ~ 1 part in 104 ~ 30 km/s

  4. Distances are Hard! Hubble’s original estimates of galaxy distances were based on brightest stars which were based on Cepheid Variables • Distances to the LMC, SMC, NGC6822 & eventually M31 from Cepheids. • Find the brightest stars and assume they’re the same (independent of galaxy type, etc.)

  5. Lemaitre 1927 Hubble 1929 Oort 1932 Baade 1952

  6. Lemaitre 1927 Hubble 1929 Oort 1932 Baade 1952

  7. DV++ 102 +/- 5 S&T 52 +/- 2 !!! deVaucouleurs ‘76 Cosmological Distance Ladder Une construction solide et durable pour atteindre H0

  8. Fukugita, Hogan & Peebles 1993

  9. Cosmological Distance Ladder Find things that work as distance indicators (standard candles, standard yardsticks) to greater and greater distances. Locally: Primary Indicators Cepheids MB ~ -2 to -6 RR Lyrae Stars MB ~ 0 Novae MB ~ -6 to -9

  10. RR Lyraes

  11. Cepheids Pretty Good Distance Indicators --- Standard Candles from the Leavitt Law (PL) relation: L ≈ P3/2 PLC relation • MV = -2.61 - 3.76 log P +2.60 (B-V) • but ya gotta find them! H0 circa 1929 ~ 600 km/s/Mpc Wrong! 1. Hubble’s galactic calibrators not classical Cepheids. 2. At large distances, brightest stars confused with star clusters. 3. Hubble’s magnitude scale was off.

  12. Galactic/LMC Calibration of Leavitt Law

  13. H-band version Welch et al P-L Relation, LMC

  14. Calibrate Cepheids via parallax, moving cluster = convergent point method, expansion parallax Baade-Wesselink, main sequence (HR diagram) fitting. Secondary Distance Indicators Brightest Stars (XX??) Tully-Fisher (+ IRTF) Planetary Nebulae LF Globular Cluster LF

  15. Supernovae of type Ia Supernovae of type II (EPM) Fundamental Plane (Dn-σ) Faber-Jackson Surface Brightness Fluctuations Red Giant Branch Tip Luminosity Classes (XXX) HII Region Diameters (XXX) HII Region Luminosities (???)

  16. Tully-Fisher

  17. Basis for TF = L vs Vrot Law The Back-of-the-Envelope (BOTE) approach: ½ mv2 = GMm/r (A ha!) Assume M/L ~ constant  M ~ L  v2≈ 2GLC/r (where C = M/L) but we also have L = <μ> π r2 mean surface brightness

  18. For Spiral Galaxies, empirically <μ>B ~ constant ~ 21.65 mag/sq-arcsec = Freeman’s Law thus r = (L/π<μ>) ½ v2 = 2GC(π<μ>)1/2 L/L1/2 = 2GC (π<μ>)1/2 L1/2 so L ~ v4 (4G2C2) π <μ>

  19. A more complete and general derivation of the L ~ v4 law involves assuming self-similarity among most spiral galaxies. You can find the derivation in AHM (1979)

  20. Surface Brightness Fluctuations Tonry & Schneider Image by J. Tonry

  21. SBF in practice Tonry & Schneider ’88 M32 vs NGC3379

  22. Baade-Wesselink --- EPM EPM = Expanding Photospheres Method Basically observe and expanding/contracting object at two (multiple) times. Get redshift and get SED. Then L1 = 4πR12σT14 &L2 = 4πR22σT24 and R2 = R1 + v δt (or better ∫ vdt)

  23. Dn-σ

  24. PNLF

  25. GCLF MV ~ -7.3 σ ~ 1.4 magnitudes From MW + M31 M31 IR Nantais

  26. TRGB = Tip of the Red Giant Branch M31 TRGB in LMC Sharp cut-off at the bright end of the RGB Luminosity Function measured using an “edge” detector MI(TRGB) = -3.63 + 0.68[Fe/H] + 0.26[Fe/H]2 (Bellazzini et al ’04)

  27. Jj Jjj Jjjj Jjj Jjj Jjj Jjj jjj

  28. HST H0 Key Project Team

  29. Aaronson et al. 1985 Mould et al. 1989…..

  30. HST Servicing Mission STS61 December 1993

  31. Cepheid Light Curves N1326a

  32. Matching P-L RelationsIC4182 (HST) MW (Ground)

  33. ITF Calibration

  34. SBF Calibration

  35. SN Ia Calibration

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