List of Footnotes

1 This is known in the literature as the “instability strip” and is almost, but not quite, parallel to the luminosity axis on the H-R diagram; brighter Cepheids have slightly lower temperatures. The instability strip has a finite width, which causes a small degree of dispersion in period–luminosity correlations among Cepheids.
2 There are numerous subtle and less-subtle biases in distance measurement; see [151] for a blow-by-blow account. The simplest bias, the “classical” Malmquist bias, arises because, in any population of objects with a distribution in intrinsic luminosity, only the brighter members of the population will be seen at large distances. The result is that the inferred average luminosity is greater than the true luminosity, biasing distance measurements towards the systematically short. The Behr bias [8Jump To The Next Citation Point] from 1951 is a distance-dependent version of the Malmquist bias, namely that at higher distances, increasingly bright galaxies will be missing from samples. This leads to an overestimate of the average brightness of the standard candle which becomes worse at higher distance.
3 Cepheids come in two flavours: type I and type II, corresponding to population I and II stars. Population II stars are the first generation of stars, which formed before the enrichment of the ISM by detritus from earlier stars, and Population I stars like the Sun are the later generation which contain significant amounts of elements other than hydrogen and helium. The name “Cepheid” derives from the fact that the star δ Cephei was the first to be identified (by Goodricke in 1784). Population II Cepheids are sometimes known as W Virginis stars, after their prototype, W Vir, and a W Vir star is typically a factor of 3 fainter than a classical Cepheid of the same period.
4 Because of the expansion of the Universe, there is a time dilation of a factor (1 + z)–1 which must be applied to timescales measured at cosmological distances before these are used for such comparisons.
5 The effective radius is the radius from within which half the galaxy’s light is emitted.
6 Nearly all Cepheids measured in galaxies containing a SN Ia have periods > 20 days, so the usual sense of the effect is that Galactic Cepheids of a given period are brighter than LMC Cepheids.
7 Here, as elsewhere in astronomy, the term “metals” is used to refer to any element heavier than helium. Metallicity is usually quoted as 12 + log(O/H), where O and H are the abundances of oxygen and hydrogen.
8 Indeed, R05 calculate the value of H0 for SN 1994ae together with SN 1998aq according to the prescription of the Sandage et al. group as at 2005, and find 69 km s–1 Mpc–1.
9 There are two effects here. The first is the “long versus short” effect, which causes a decrease of recorded flux of a few percent in short exposures compared to long ones. The second is the effect of radiation damage, which affected later WFPC2 observations more than earlier ones and resulted in a uniform decrease of charge transfer efficiency and observed flux. This is again an effect at the few percent level.
10 See External Link for a much longer exposition and tutorial on all these areas.
11 Beware plausible assumptions, however; fifteen years ago Ω Λ = 0 was a highly plausible assumption.
12 An isothermal model is one in which the projected surface mass density decreases as 1/r. An isothermal galaxy will have a flat rotation curve, as is observed in many galaxies.
13 Essentially all radio time delays have come from the VLA, although monitoring programmes with MERLIN have also been attempted.
14 As discussed extensively in [77Jump To The Next Citation Point, 80Jump To The Next Citation Point], this is not a global degeneracy, but arises because the lensed images tell you about the mass distribution in the annulus centred on the galaxy and with inner and outer radii defined by the inner and outer images. Kochanek [77Jump To The Next Citation Point] derives detailed expressions for the time delay in terms of the central underlying and controlling parameter, the surface density in this annulus [49Jump To The Next Citation Point].
15 The aspiring measurer of time delays is faced with a dilemma, in terms of whether to justify the proposal in terms of measuring H0, given the previously mentioned problems with mass modelling, or in terms of determining mass models by assuming H0 = 71 km s–1 Mpc–1 (or whatever).
16 This term, “golden lens”, was coined over ten years ago to describe the perfect time-delay lens. Since none have been found, it is probably time to abandon it and metallic derivatives thereof, perhaps in return for vanilla CMB models and their associated error ellipses, vanilla bananas.
17 Full details are in Appendix A.