H0 and Cepheid variables

Joseph Lorenzo Hall
Abstract
Cepheid variable stars have proven to be some of the most useful distance indicators currently available. There exists a strong correlation between the period of a Cepheid's pulsation and it's luminosity (maximum or minimum) with small scatter (±0.1 mag in the I band). By calibrating this Period- Luminosity relation to variables with known distances, we can get the absolute luminosities-- and accordingly distances-- of Cepheid variables in other galaxies. Cepheids are what much of the cosmological distance scale is bootstrapped to and a more precise measurement of cepheid distances means a more precise measurement of the local value of the Hubble constant, H0. In this web-paper, I will talk about why Cepheids are well suited for measuring H0, what secondary distance indicators are tied to Cepheids, the results of current observational campaigns using Cepheids to measure H0 and the dominant errors in Cepheid distances.
  1. What is a Cepheid?
    1. Cepheids are variable stars.
    2. They obey a period-luminosity relationship (correlation).
  2. Why are they particularly good for measuring H0?
    1. Well-defined P-L relationship with small scatter.
    2. Easy to identify.
    3. Very bright.
    4. Numerous and common in spirals.
  3. Cepheids as a rung on the distance ladder.
    1. Galactic and S/LMC Cepheids.
    2. Secondary distance indicators that depend on Cepheid calibration.
      1. SN Ia
      2. Tully-Fisher
      3. Fundamental plane for elliptical galaxies
      4. Surface Brightness Fluctuations
  4. Cepheid observational campaigns.
    1. Microlensing searches; Calibrating the S/LMC P-L relation (OGLE-II, MACHO, EROS)
    2. HST Key Project
    3. Sandage and Saha et al.
  5. Dominant errors in Cepheid distances.
    1. Zero point of the P-L relation.
      1. NGC 4258 and it's H2O masers
    2. Reddening.
    3. Metallicity effects.
    4. Completeness and bias effects.
    5. Crowding effects.
    6. Local velocities and the Hubble flow.
  6. The future of Cepheid distances.
    There now exists a large and accurate sample of Cepheid variable stars who's properties are well known. The biggest advances in the calibration of the Cepheid scale will be in improving the zero point of the P-L relation and the study of metallicity effects on the P-L relation. Astrometric spacecraft like GAIA and the (apparently now defunct) FAME mission will be able to measure parallaxes to variable stars with much higher accuracy than in the past. Better distances to these, close Cepheids will improve the accuracy of the P-L relation by improving the accuracy of their absolute luminosities.
    1. GAIA (microarcsecond astrometry)
    2. FAME (50 milliarcsecond astrometry)
      "FAME will not be proceeding into the Implementation Phase due to withdrawal of NASA sponsorship."
  7. Conclusion:
    The HST key project seems to have the most comprehensive and detailed analysis of H0 using Cepheid distances. They reach a value of H0 = 72 ±3 (random) ±7 (systematic) km/s/Mpc. A compelling study by Gott, J.R. et al. uses median statistics with 331 values for H0 reported in the literature starting back in 1926 and reaches a value of H0 = 67 km/s/Mpc (95% confidence over 0.65 < h < 0.69). I, for one, plan on using h = 0.65 because, it's inverse, h-1 = 1.5, which is a great thing to know for on-the-fly calculations of cosmological distances (for example, 10 h-1 Mpc = 10*1.5 Mpc = 15 Mpc (h = 0.65) or 10 h-2 kpc2 = 10*1.25 kpc2 = 12.5 kpc2.). If you want to go with the HST Key Project to the digit, use h = 0.71 so that h-1 = 1.4.
Copyright © 2002 Joseph Lorenzo Hall.
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License".