Photographic photometry of RR Lyrae variables in the globular cluster M15

Light curves in B and V are presented for 56 RR Lyrae variables in the Oosterhoff Group II globular cluster M15. Our measures are combined with original measures published by Sandage, Katem & Sandage (SKS) to yield data of improved precision for a total of 62 RR Lyraes. Correlations between the various light curve parameters are obtained, and their significance is discussed. In particular, the new period–colour relation shows less scatter than that published by SKS, and less overlap in colour between c- and ab-types. The multimode variables now occur close to the (ab/c) transition colour, as expected from their periods. An accurate assessment of the sources of error in the period-colour relation enables the prediction of a range in mass amongst the variables, with a (1 σ) dispersion of $$\sim 0.025 \enspace M_\odot$$. The theoretical period–colour relation is used to derive a mass-to-light ratio (solar units), log $$(M^{0.81}/L) = -1.92\pm 0.03$$ which, with a mean mass of $$0.65 \pm 0.05\enspace M_\odot$$ obtained by Cox, Hodson & Clancy for the multimode variables gives log $$L = 1.77 \pm 0.06 \enspace L_\odot\enspace \text {or}\enspace M_\text {bol} = + 0.34 \pm 0.15$$. This luminosity implies an age a few billion years less than current estimates, but there are still many uncertainties attached to such a derivation. From a number of independent estimates of the helium abundance (see Section 3.2) a value of Y = 0.25±0.03 seems to be the most appropriate for M15. The observed distribution of stars in the log L/log T_e diagram of M15 agrees satisfactorily with what could be expected from the appropriate evolutionary tracks of Sweigart & Gross (SG). However, the mass-to-light ratios of these ‘standard’ models can only be reconciled with those derived pulsationally, within the quoted uncertainties, if the helium abundance, $$Y, \gtrsim 0.30$$. If $$Y, \lesssim 0.25$$ as also might be expected from external evidence, the evolutionary models predict a lower luminosity ($$\Delta \text {log} \enspace L \sim 0.1$$) than obtained from pulsation theory. This discrepancy can be removed on the basis of the expected behaviour of non-standard models, as shown by Caputo, Castellani & Gregorio. The observations are compared in detail with those of RR Lyraes in the Oosterhoff I cluster M3 in a discussion of the Oosterhoff problem. It is shown that the Oosterhoff effect, as manifest between M15 and M3 cannot be simply described in terms of a period shift, since the distribution of amplitude and number with period and temperature differ in detail, in particular a unique amplitude–temperature relation over both pulsation modes is not possible. We confirm Sandage's result, though with somewhat different arguments, that the correlation of period shift with heavy element abundance [Fe/H] over many clusters requires an anticorrelation of [Fe/H] with Y within the standard frame of evolution models. Finally, the morphology of the SG tracks appropriate to account for the difference in overall horizontal branch morphology between M15 and M3 leads to a natural explanation of the great excess of c-type variables in the neighbourhood of the transition temperature found in Oosterhoff II clusters like M15 (an effect which contributes significantly to the difference in mean period between the Oosterhoff groups). The tracks indicate that many of the RR Lyraes in M15 begin their horizontal branch evolution within the instability strip, spending much longer in the centre of the strip than variables in M3-like clusters which evolve more rapidly bluewards across the strip. The distribution in M15 peaks just bluewards of the transition temperature giving rise to the many c-type variables found there. The multimode variables occur precisely at the transition temperature (the same in M15 and M3) and appear to be a ‘stable’ mode of pulsation. However, further work is still needed to determine precisely the luminosity and/or mass differences that produce the observed period shift between the Oosterhoff groups.