Carnegie Hubble Program: A Mid-Infrared Calibration of the Hubble Constant

Abstract

Using a mid-infrared calibration of the Cepheid distance scale based on recent observations at 3.6 um with the Spitzer Space Telescope, we have obtained a new, high-accuracy calibration of the Hubble constant. We have established the mid-IR zero point of the Leavitt Law (the Cepheid Period-Luminosity relation) using time-averaged 3.6 um data for ten high-metallicity, Milky Way Cepheids having independently-measured trigonometric parallaxes. We have adopted the slope of the PL relation using time-averaged 3.6 um data for 80 long-period Large Magellanic Cloud (LMC) Cepheids falling in the period range 0.8 < log(P) < 1.8. We find a new reddening-corrected distance to the LMC of 18.477 +/- 0.033 (systematic) mag. We re-examine the systematic uncertainties in H0, also taking into account new data over the past decade. In combination with the new Spitzer calibration, the systematic uncertainty in H0 over that obtained by the Hubble Space Telescope (HST) Key Project has decreased by over a factor of three. Applying the Spitzer calibration to the Key Project sample, we find a value of H0 = 74.3 with a systematic uncertainty of +/-2.1 (systematic) km/s/Mpc, corresponding to a 2.8% systematic uncertainty in the Hubble constant. This result, in combination with WMAP7 measurements of the cosmic microwave background anisotropies and assuming a flat universe, yields a value of the equation of state for dark energy, w0 = -1.09 +/- 0.10. Alternatively, relaxing the constraints on flatness and the numbers of relativistic species, and combining our results with those of WMAP7, Type Ia supernovae and baryon acoustic oscillations yields w0 = -1.08 +/- 0.10 and a value of N_eff = 4.13 +/- 0.67, mildly consistent with the existence of a fourth neutrino species.

Figures (7)

• Figure 1: The Leavitt law at 3.6 $\mu$m for 80 LMC Cepheids and ten Milky Way Cepheids with HST trigonometric parallaxes.The Milky Way data are from Monson et al. (2012) and the LMC sample is from Scowcroft et al. (2012). The data have been corrected for extinction. Small circled points are LMC Cepheids; large filled circles, individually named, are Galactic Cepheids with trigonometric parallax measurements. The slope of the Leavitt relation is set by the LMC sample. Applying this slope to the Milky Way sample yields a reddening-corrected distance modulus of 18.477 mag to the LMC. The five LMC points with periods less than 6 days are from the sample of Meixner et al. (2006). They are shown for illustration only, and are not included in the fit to determine the slope. The dashed slope is defined by the sample of 80 LMC stars; the solid lines are 2-$\sigma$ ridge lines.
• Figure 2: Sensitivity of mid-infrared Cepheid magnitudes to metallicity. The (lower-metallicity) Large Magellanic Cloud Cepheids are shown as open circles; the (higher-metallicity) Milky Way Cepheids are plotted as filled squares. The PL residuals are measured in the sense of observed magnitudes minus the mean PL relation. The highly correlated nature of the vertical scatter in these plots is a reflection of the scatter due to temperature and radius variations across the instability strip and to correlated back-to-front geometric effects. Neither of these effects are expected to correlate with metallicity. No statistically significant correlation of the Cepheid magnitudes with atmospheric [Fe/H] metallicity can be seen in these plots. The 4.5 $\mu$m residuals are plotted in the upper panel; the 3.6 $\mu$m residuals are shown in the middle panel. The lower panel shows the remarkably small scatter in the color residuals as a function of metallicity where the correlated scatter due to instability strip position and back-to-front geometry is cancelled.
• Figure 3: Comparison of the seven dominant sources of systematic error in determining the Hubble constant. The left-hand panel shows the individual errors given for the HSTKey Project by Freedman et al. (2001) (filled circles), followed by the total systematic error formed from the quadrature sum of the six preceding values (circled dots). The right-hand portion of the panel shows the current errors for the same terms for the CHP determination of the Hubble constant. Open circles represent systematic terms that have estimated errors less than or equal to 1%. As discussed in § \ref{['sec:systematics']}, the sharp drop in the crowding error on the right-hand side is based on both the new simulations described in Appendix A, as well as the original analysis by Ferrarese et al. 2000. The lower error for the tie-in error results from correcting an error in Table 14 of Freedman et al. (2001), which reported the magnitude of a photometric zero-point correction and not its uncertainty. The decrease in the zero-point and metallicity uncertainties result from the new Spitzer data.
• Figure 4: 2D confidence plots of the equation of state parameter $w_{0}$ and the Hubble constant $H_{0}$ using (a) the WMAP7 data alone and (b) WMAP7 and BAO data combined, and assuming $\Omega_{k}=0$, $w_{a}=0$, and $N_{eff}=3.046$. The red contours show the results using the prior from F01, while the blue contours show the results using the prior from this paper (labeled CHP). The right and bottom panels show the 1D marginalized posterior probability distributions (PPD) for $w_{0}$ and $H_{0}$, respectively. The F01 PPD is plotted as red dashed lines, the CHP PPD is plotted as blue solid lines.
• Figure 5: 2D confidence plot of the effective number of neutrinos $N_{eff}$ and the Hubble constant $H_{0}$ using the WMAP7 data and BAO data combined and assuming $\Omega_{k}=0$, $w_{a}=0$. The red contours show the results using the prior from F01, the blue contours show the results using the prior from this paper (labeled CHP), and the green contours show the results using the CHP prior and assuming $w_{0}=-1$ . The right and bottom panels show the 1D marginalized posterior probability distributions (PPD) for $N_{eff}$ and $H_{0}$, respectively. The F01 ppd is plotted as red dashed lines, the CHP PPD is plotted as blue solid lines and the CHP+$w_{0}=1$ PPD is plotted as a green dash-dotted line.