Louise Breuval
Cepheids are peculiar stars: their luminosity vary in time with a constant period ranging from a few days up to about sixty days. They are particularly useful tools for measuring astronomical distances, thanks to the empirical relation between their pulsation period and intrinsic luminosity, the period-luminosity (PL) relation. Indeed, by observing the apparent luminosity of such stars and by comparing it to the brightness predicted by the PL relation, it is then possible to derive their distance.
However, this law between Cepheids period and brightness is still not known with a sufficient accuracy. Its imprecision currently represents the main source of uncertainty in the determination of the Hubble constant, that describes the expansion rate of the Universe. Measuring the Hubble constant is paramount since its value is at the center of a major controversy, often called crisis: its recent empirical estimate by Riess et al. (2019), 74.0 +/- 1.4 km/s/Mpc, differs by about 4 sigma from the value estimated by Planck Collaboration (2018) based on a Lambda-CDM model and the Planck CMB data, 67.4 +/- 0.5 km/s/Mpc. This discrepancy could possibly provide evidence for a breach in the standard cosmological model that currently describes our Universe.
Calibrating the Cepheid PL relation is therefore of critical importance and requires the prior measurement of a set of precise distances. However, Cepheids distances are difficult to access since they are often affected by systematics and saturation. We present an original and alternative method that aims to calibrate the PL relation, not based on Cepheid distances as commonly done, but on the distances of Cepheids resolved companions and on average distances of star clusters hosting Cepheids. From an initial Hubble constant of 76.2 +/- 2.4 km/s/Mpc, we derive a revised value of 72.8 +/- 1.9 km/s/Mpc.
In 2018, the second data release of the Gaia satellite (Gaia DR2) provided parallaxes for 1.3 billion stars with an unprecedented precision. However, Cepheids are bright stars and are often saturated in detectors. Moreover, their parallaxes can be affected by systematics due to their photometric variability (Breuval et al. 2020). For these reasons, using Gaia DR2 parallaxes of Cepheids may not be the finest method to calibrate the PL relation. We propose an original approach in order to avoid the direct use of potentially unreliable Cepheid parallaxes.
First, we adopt a sample of 22 parallaxes of resolved Cepheids companions (Kervella et al. 2019). Assuming companions are located at the same distance as Cepheids, they provide an indirect measurement for their distance. Unlike Cepheids, companions are not variable and are unsaturated. We complement this sample by searching for Cepheids in open clusters. These objects contain a large number of stars, so the average parallax of their members provides a solid estimate for the distance to the Cepheids they host. We cross-match Gaia DR2 Cepheids with a catalog of open clusters with average Gaia DR2 parallaxes (Cantat-Gaudin et al. 2018). We compared their positions, parallaxes, proper motions and ages and we obtained 14 Cepheids in open clusters. Combining these two samples, we obtain 36 indirect, unbiased and accurate distances for galactic Cepheids.
Before being used, Gaia DR2 parallaxes must be corrected for a zero-point offset: we applied a correction of -0.046 +/- 0.015 mas that accounts for the diverse values found in the literature for this parameter. Moreover, our sample contains some Cepheids pulsating in the first overtone mode: we converted they period into the fundamental mode so they can still be used in the PL calibration. Finally, we retrieved well-sampled light curves of our Cepheids to derive their apparent mean magnitudes and we corrected them for the extinction. We performed a Monte-Carlo algorithm to fit the data and derived the PL relation in the Ks band: Ks = -3.257 (+/- 0.163) (logP-1) -5.844 (+/- 0.037).
The Cepheid PL relation is used to calibrate the cosmic distance ladder, which provides a measurement of the Hubble constant. This parameter is currently at the center of a major controversy: while it is estimated at 67.4 +/- 0.5 km/s/Mpc by the Planck satellite (Planck Collaboration 2018), the local measurement based on Cepheids is larger by 4 sigma, with a value of 74.0 +/- 1.4 km/s/Mpc (Riess et al. 2019). This discrepancy may provide evidence for physics beyond the standard model. Therefore, precise and accurate distance measurements of Cepheids are of paramount importance to solve this crisis.
We revise the 76.18 +/- 2.37 km/s/Mpc Hubble constant by Riess et al. (2016) based on Milky Way Cepheids: adopting our sample, we obtain 72.8 ± 2.7 km/s/Mpc. This result does not solve the tension, mostly because of the uncertainty on the Gaia DR2 offset. However, it allows to bring the Milky Way estimate in excellent agreement with the values based on extragalactic anchors. The next Gaia data releases are expected to provide more precise and accurate parallaxes of Cepheids in the near future, hopefully leading to a sub-percent measurement of the Hubble constant.