NEW NEAR-INFRARED PERIOD–LUMINOSITY–METALLICITY RELATIONS FOR RR LYRAE STARS AND THE OUTLOOK FORGAIA

Abstract

We present results of the analysis of 70 RR Lyrae stars located in the bar of the Large Magellanic Cloud (LMC). Combining spectroscopically determined metallicity of these stars from the literature with precise periods from the OGLE III catalogue and multi-epoch K s photometry from the VISTA survey of the Magellanic Clouds system (VMC), we derive a new near-infrared period-luminosity-metallicity (PL K s Z) relation for RR Lyrae variables. In order to fit the relation we use a fitting method developed specifically for this study. The zero-point of the relation is estimated in two different ways: by assuming the value of the distance to the LMC and by using Hubble Space Telescope (HST) parallaxes of five RR Lyrae stars in the Milky Way (MW). The difference in distance moduli derived by applying these two approaches is ∼ 0.2 mag. To investigate this point further we derive the PL K s Z relation based on 23 MW RR Lyrae stars which had been analysed in Baade-Wesselink studies. We compared the derived PL K s Z relations for RR Lyrae stars in the MW and LMC. Slopes and zero-points are different, but still consistent within the errors. The shallow slope of the metallicity term is confirmed by both LMC and MW variables. The astrometric space mission Gaia is expected to provide a huge contribution to the determination of the RR Lyrae PL K s Z relation, however, calculating an absolute magnitude from the trigonometric parallax of each star and fitting a PL K s Z relation directly to period and absolute magnitude leads to biased results. We present a tool to achieve an unbiased solution by modelling the data and inferring the slope and zero-point of the relation via statistical methods.

Gaia Data Release 1

“…The B-W absolute magnitudes were taken from the compilations in Table 11 of Cacciari et al (1992) and Table 16 of Skillen et al (1993) and revised, first assuming for the p factor used to transform the observed radial velocity to true pulsation velocity the value p = 1.38 proposed by Fernley (1994) 6 , and then averaging multiple determinations of individual stars. We note that the K-band magnitudes of RR Lyrae stars analysed with the B-W method are in the Johnson photometric system; however, the difference between the 2MASS K s and the Johnson K is small, about 0.03 mag on average, for the typical colour of RR Lyrae stars (Muraveva et al 2015) and is always much smaller than the individual errors in the B-W M K magnitudes. We have transformed the B-W absolute magnitudes to photometric parallaxes.…”

“…1, coefficients and zero point of the relation differ significantly; the literature values for the dependence of M K s on period range from −2.101 (Bono et al 2003) to −2.73 (Muraveva et al 2015) and the dependence on metallicity ranges from 0.03 (Muraveva et al 2015) to 0.231 (Bono et al 2003). We used the sample of 200 RR Lyrae stars with TGAS parallaxes along with K s magnitudes, period, and metallicity values from Dambis et al (2013) to fit the PM K s and PM K s Z relations.…”

“…Bono et al (2003) and Catelan et al (2004) analysed the PM K Z from the semi-theoretical and theoretical point of view and found a non-negligible dependence of the RR Lyrae K-band absolute magnitude, M K , on metallicity: b = 0.231 ± 0.012 and b = 0.175, respectively. Conversely, the dependence of the K-band luminosity on metallicity derived in empirical studies is generally much shallower (Del Principe et al 2006) or even negligible (Sollima et al 2006(Sollima et al , 2008Borissova et al 2009;Muraveva et al 2015). The values in the literature for the dependence of M K on period vary from −2.101 (Bono et al 2003) to −2.73 (Muraveva et al 2015).…”

“…Conversely, the dependence of the K-band luminosity on metallicity derived in empirical studies is generally much shallower (Del Principe et al 2006) or even negligible (Sollima et al 2006(Sollima et al , 2008Borissova et al 2009;Muraveva et al 2015). The values in the literature for the dependence of M K on period vary from −2.101 (Bono et al 2003) to −2.73 (Muraveva et al 2015).…”

“…We considered 19 MW RR Lyrae variables with TGAS parallaxes and absolute visual (M V ) and K-band (M K ) magnitudes available in the literature from B-W studies (see Table 2 in Muraveva et al 2015). The B-W absolute magnitudes were taken from the compilations in Table 11 of Cacciari et al (1992) and Table 16 of Skillen et al (1993) and revised, first assuming for the p factor used to transform the observed radial velocity to true pulsation velocity the value p = 1.38 proposed by Fernley (1994) 6 , and then averaging multiple determinations of individual stars.…”