|Annu. Rev. Astron. Astrophys. 2010. 48:
Copyright © 2010 by Annual Reviews. All rights reserved
We briefly summarize below the results from the HST Key Project, and provide an updated calibration for these data. The primary goals of the HST Key Project were to discover and measure the distances to nearby galaxies containing Cepheid variables, calibrate a range of methods for measuring distances beyond the reach of Cepheids to test for and minimize sources of systematic uncertainty, and ultimately to measure Ho to an accuracy of ± 10%. HST provided the opportunity to measure Cepheid distances a factor of 10 more distant than could be routinely obtained on the ground. It also presented a practical advantage in that, for the first time, observations could be scheduled in a way that optimized the discovery of Cepheids with a range of periods independent of phase of the moon or weather (Madore & Freedman 2005).
Cepheid distances to 18 galaxies with distances in the range of 3 to 25 Mpc were measured using WF/PC and (primarily) WFPC2 on HST. Observations at two wavelengths (V- and I-band) were made, chosen to allow corrections for dust. The spacing of observations was optimized to allow for the discovery of Cepheids with periods in the range of 10 to 50 days. In addition, 13 additional galaxies with published Cepheid photometry were analyzed for a total of 31 galaxies.
These Cepheid distances were then used to calibrate the Tully-Fisher relation for spiral galaxies, the peak brightness of Type Ia SNe, the Dn- relation for elliptical galaxies, the Surface Brightness Fluctuation (SBF) method, and Type II supernovae (Freedman 2001 and references therein). These methods allowed a calibration of distances spanning the range of about 70 Mpc (for SBF) out to about 400 Mpc for Type Ia SNe. These results are summarized in Figure 10. Combining these results using both Bayesian and frequentist methods yielded a consistent value of Ho = 72 ± 3 (statistical) ± 7 (systematic) km s-1 Mpc-1.
Figure 10. Graphical results of the HST Key Project (Freedman et al. 2001). Top Panel: The Hubble diagram of distance vs. velocity for secondary distance indicators calibrated by Cepheids. Velocities are corrected using the nearby flow model of Mould et al. (2000). Squares: Type Ia supernovae; filled circles: Tully-Fisher clusters (I-band observations); triangles: fundamental plane clusters; diamonds: surface brightness fluctuation galaxies; open squares: Type II supernovae. A slope of Ho = 72 ± 7 km s-1 Mpc-1 is shown. Beyond 5000 km/s (vertical line), both numerical simulations and observations suggest that the effects of peculiar motions are small. The Type Ia supernovae extend to about 30,000 km/s, and the Tully-Fisher and fundamental plane clusters extend to velocities of about 9,000 and 15,000 km/s, respectively. However, the current limit for surface brightness fluctuations is about 5,000 km/s. Bottom Panel: The galaxy-by-galaxy values of Ho as a function of distance.
We update this analysis using the new HST-parallax Galactic calibration of the Cepheid zero point (Benedict et al. 2007), and the new supernova data from Hicken et al. (2009). We find a similar value of Ho, but with reduced systematic uncertainty, of Ho = 73 ± 2 (random) ± 4 (systematic) km s-1 Mpc-1. The reduced systematic uncertainty, discussed further in Section 4.1 below, results from having a more robust zero-point calibration based on the Milky Way galaxy with comparable metallicity to the spiral galaxies in the HST Key Project sample. Although, the new parallax calibration results in a shorter distance to the LMC (which is no longer used here as a calibrator), the difference in Ho is nearly offset by the fact that no metallicity correction is needed to offset the difference in metallicity between the LMC and calibrating galaxies.
4.1. Systematics on Ho at the End of the Key Project and a Decade Later
A primary goal of the HST Key Project was the explicit propagation of statistical errors, combined with the detailed enumeration of and accounting for known and potential systematic errors. In Table 2 we recall the systematics error budget given in Freedman et al. (2001). The purpose of the original tabulation was to clearly identify the most influential paths to greater accuracy in future efforts to refine Ho. Here we now discuss what progress has been made, and what we can expect in the very near future using primarily space-based facilities, utilizing instruments operating mainly at mid-infrared and near-infrared wavelengths.
|(1) Cepheid Zero Point||± 0.12 mag||± 0.06 mag||± 0.03 mag||Galactic Parallaxes|
|(2) Metallicity||± 0.10 mag||± 0.05 mag||± 0.02 mag||IR + Models|
|(3) Reddening||± 0.05 mag||± 0.03 mag||± 0.01 mag||IR 20-30x Reduced|
|(4) Transformations||± 0.05 mag||± 0.03 mag||± 0.02 mag||Flight Magnitudes|
|Final Uncertainty||± 0.20 mag||± 0.09 mag||± 0.04 mag||Added in Quadrature|
|Percentage Error on Ho||± 10%||± 5%||± 2%||Distances|
|Revisions (Column 2) incorporating the recent work of Benedict et al. (2007) and Riess et al. (2009a).|
Identified systematic uncertainties in the HST Key Project determination of the extragalactic distance scale limited its stated accuracy to ± 10%. The dominant systematics were: (a) the zero point of the Cepheid PL relation, which was tied directly to the (independently adopted) distance to the LMC; (b) the differential metallicity corrections to the PL zero point in going from the relatively low-metallicity (LMC) calibration to target galaxies of different (and often larger) metallicities; (c) reddening corrections that required adopting a wavelength dependence of the extinction curve that is assumed to be universal; and (d) zero-point drift, offsets, and transformation uncertainties between various cameras on HST and on the ground. Table 2 compares these uncertainties to what is now being achieved with HST parallaxes and new HST SNe Ia distances (Table 2, Column 3 "Revisions"), and then what is expected to be realized by extending to a largely space-based near and mid-infrared Cepheid calibration using the combined power of HST, Spitzer and eventually the James Webb Space Telescope (JWST) and GAIA. (Column 4, "Anticipated").
In 2001 the uncertainty on the zero point of the Leavitt Law was the largest on the list of known systematic uncertainties. Recall that the Key Project zero point was tied directly to an LMC true distance modulus of 18.50 mag. As we have seen in Section 3.1.4 improvement to the zero point has come from new HST parallax measurements of Galactic Cepheids, improved distance measurements to the LMC from near-infrared photometry, and measurement of a maser distance to NGC 4258. We adopt a current zero-point uncertainty of 3%.
We next turn to the issue of metallicity. As discussed in Section 3.1.3, in the optical, metallicity corrections remain controversial. However, by shifting the calibration from the low-metallicity Cepheids in the LMC to the more representative and high-metallicity Milky Way (or alternatively to) the NGC 4258 Cepheids, the character of the metallicity uncertainty has changed from being a systematic to a random uncertainty. We conservatively estimate that the systematic component of the uncertainty on the metallicity calibration should now drop to ± 0.05 mag. Including the recent results from Benedict et al. (2007) and Riess et al. (2009a, b), our estimate for the current total uncertainty on Ho is ± 5%.
In terms of future improvements, as discussed further in Section 7, with the Global Astrometric Interferometer for Astrophysics (GAIA), and possibly the Space Interferometry Mission (SIM), the sample of Cepheids with high precision trignometric parallaxes will be increased, and as more long-period Cepheids enter the calibration both the slope and the zero point of the high-metallicity Galactic Leavitt Law will be improved. By extending both the calibration of the Leavitt Law and its application to increasingly longer wavelengths the effects of metallicity and the impact of total line-of-sight reddening, each drop below the statistical significance threshold. At mid-infrared wavelengths the extinction is a factor of ~ 20 reduced compared to optical wavelengths. And line blanketting in the mid and near infrared is predicted theoretically to be small compared to the blue portion of the spectrum. Direct tests are now being undertaken to establish whether this is indeed the case and/or calibrate out any residual impact (Section 7.3).
In principle, a value of Ho having a well determined systematic error budget of only 2-3% is within reach over the next decade. It is the goal of the new Carnegie Hubble Program, described briefly in Section 7.3, based on a mid-infrared calibration of the extragalactic distance scale using the Spitzer satellite, GAIA and JWST.