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2.3 Problems and comments

2.3.1 Distance to the LMC

The LMC distance is probably the best-known, and least controversial, part of the distance ladder. Some methods of determination are summarised in [40Jump To The Next Citation Point] and little has changed since then. Independent calibrations using RR Lyrae variables, Cepheids and open clusters, are consistent with a distance of ∼ 50 kpc. While all individual methods have possible systematics (see in particular the next Section 2.3.2 in the case of Cepheids), their agreement within the errors leaves little doubt that the measurement is correct. Moreover, an independent measurement was made in [108] using the type II supernova 1987A in the LMC. This supernova produced an expanding ring whose angular diameter could be measured using the HST. An absolute size for the ring could also be deduced by monitoring ultraviolet emission lines in the ring and using light travel time arguments, and the distance of 51.2 ± 3.1 kpc followed from comparison of the two. An extension to this light-echo method was proposed in [144] which exploits the fact that the maximum in polarization in scattered light is obtained when the scattering angle is ∘ 90. Hence, if a supernova light echo were observed in polarized light, its distance would be unambiguously calculated by comparing the light-echo time and the angular radius of the polarized ring.

The distance to the LMC adopted by most researchers in the field is between μ0 = 18.50 and 18.54, in the units of “distance modulus” (defined as 5 log d – 5, where d is the distance in parsecs) corresponding to a distance of 50 – 51 kpc. The likely error in H0 of ∼ 2% is well below the level of systematic errors in other parts of the distance ladder; recent developments in the use of standard-candle stars, main sequence fitting and the details of SN 1987A are reviewed in [2] where it is concluded that μ0 = 18.50 ± 0.02.

2.3.2 Cepheids

If the Cepheid period-luminosity relation were perfectly linear and perfectly universal (that is, if we could be sure that it applied in all galaxies and all environments) the problem of transferring the LMC distance outwards to external galaxies would be simple. Unfortunately, to very high accuracy it may be neither. Although there are other systematic difficulties in the distance ladder determinations, problems involving the physics and phenomenology of Cepheids are currently the most controversial part of the error budget, and are the primary source of differences in the derived values of H0.

The largest samples of Cepheids outside our own Galaxy come from microlensing surveys of the LMC, reported in [164Jump To The Next Citation Point]. Sandage et al. [133Jump To The Next Citation Point] reanalyse those data for LMC Cepheids and claim that the best fit involves a break in the P-L relation at P ≃ 10 days. In all three HST colours (B, V, I) the resulting slopes are different from the Galactic slopes, in the sense that at long periods, Galactic Cepheids are brighter than LMC Cepheids and are fainter at short periods. The period at which LMC and Galactic Cepheids have equal luminosities is approximately 30 days in B, but is a little more than 10 days in I6. Sandage et al. [133Jump To The Next Citation Point] therefore claim a colour-dependent difference in the P-L relation which points to an underlying physical explanation. The problem is potentially serious in that the difference between Galactic and LMC Cepheid brightness can reach 0.3 magnitudes, corresponding to a 15% difference in inferred distance.

At least part of this difference is almost certainly due to metallicity effects7. Groenewegen et al. [51Jump To The Next Citation Point] assemble earlier spectroscopic estimates of metallicity in Cepheids both from the Galaxy and the LMC and compare them with their independently derived distances, obtaining a marginally significant (–0.8 ± 0.3 mag dex–1) correlation of brightness with increasing metallicity by using only Galactic Cepheids. Using also the LMC cepheids gives –0.27 ± 0.08 mag dex–1.

In some cases, independent distances to galaxies are available in the form of studies of the tip of the red giant branch. This phenomenon refers to the fact that metal-poor, population II red giant stars have a well-defined cutoff in luminosity which, in the I-band, does not vary much with nuisance parameters such as stellar population age. Deep imaging can therefore provide an independent standard candle which can be compared with that of the Cepheids, and in particular with the metallicity of the Cepheids in different galaxies. The result [130Jump To The Next Citation Point] is again that metal-rich Cepheids are brighter, with a quoted slope of –0.24 ± 0.05 mag dex–1. This agrees with earlier determinations [7572] and is usually adopted when a global correction is applied.

The LMC is relatively metal-poor compared to the Galaxy, and the same appears to be true of its Cepheids. On average, the Galactic Cepheids tabulated in [51] are approximately of solar metallicity, whereas those of the LMC are approximately –0.6 dex less metallic, corresponding to an 8% distance error if no correction is applied in the bootstrapping of Galactic to LMC distance. Hence, a metallicity correction must be applied when using the highest quality P-L relations from the OGLE observations of LMC Cepheids to the typically more metallic Cepheids in galaxies with SNe Ia observations.

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