RR Lyrae light curve decomposition and the Oosterhoff dichotomy A. Arellano Ferro Instituto de Astronomía Universidad Nacional Autónoma de México collaborators: Sunetra Giridhar, IIA, India Carlos Lázaro; M.J. Arévalo, IAC, Spain Victoria Rojas, IA-UNAM, México P. Rosenzweig; G. García Lugo, U. Los Andes, Venezuela Daniel Bramich; Cambridge University, UK Indian Institute of Astrophysics may 2006
The Oosterhoff types of clusters Oosterhoff (1930) The Observatory, 62, 104. noticed that periods of RR Lyraes differe and are grouped in two families: Oo I <Pab>=0.55 d <Pc>=0.32d Oo II <Pab>=0.64 d <Pc>=0.36d Oo II's are more metal poor that Oo I's and Oo II's have higher rate of RRc's than Oo I's
Diagramas C-M de NGC 6934 Kaluzny, Olech & Stanek, 2001, ApJ, 121, 1533
Evolution of the Horizontal Branch (Rood 1973, ApJ 184, 815)
M3 Globular Cluster The metallicities and distances of the globular clusters are of relevance in the contexts stellar evolution and galactic dynamics. The structure of the Horizontal Branch (HB) and the role of metallicity can be studied in detail if accurate metallicities, temperatures and luminosities can be determined. PROBLEM: Accurate metallicities from high resolution spectroscopy do exist for stars with V~ 11-12 In the HB V~13.5 for the nearest clusters. Only very recently, with telescope of the 8m 10m-class, good results can be obtained for V~16-17 mag. with good S/N (e.g. James et al. 2004 Astron. Astrophys., 427, 825-838 (2004) for NGC 6752 (others examples see next slide)
Gratton, et al. (2005) Astron. Astrophys., 440, 901-908 NGC High 6752: Resolution FLAMES at VLT2 allowed in Globular to obtain spectra centred Clusters: on Hα at a resolution some of examples R=6000 and 5<S/N<50 for 120 stars near the turn-off with GIRAFFE from a single 1300 seconds exposure. The same exposure provided UVES spectra of seven stars near the red giant branch bump at a resolution of 40000 and 20<S/N<40. Yong et al. (2005) Astron. Astrophys., 438, 875-888 Elemental abundance ratios [X/Fe] for 20 elements in 38 bright giants of NGC 6752 with UVES on the VLT at resolutions 110 000 and 60 000 with S/N = 250-150 Cohen & Melendez, (2005) Astron. J., 129, 303-329 38 stars distributed from the tip to the base of the red giant branch (RGB) in M3 and M13: HIRES at the Keck Observatory, with resolution of 35,000 with S/N > 75 exp times from 200 s for V~12.5 to 7500 s for V ~ 17.5
ALTERNATIVE APPROACH (more efficient, more accessible) Accurate CCD Photometry + Fourier Descomposition of light curves + Semiempirical calibrations
NGC 4147 Μ2 We shall illustrate some results on these two clusters
DANDIA: A differential imaging package Bramich, D. M., et al. 2005, MNRAS, 359, 1096 Procedure involves the matching of a high quality reference image to each image in the time series, by solving for a spatially-varying convolution kernel and differential sky background function. Difference images are constructed via the subtraction of the convolved reference image from the time series images. Photometry on the difference images yields differential fluxes for each star relative to the flux from the reference image. Conversion of the light curves to magnitudes requires an accurate measurement of the reference flux. We measured the stellar fluxes on the reference frame using DAOPhot (Stetson 1987).
Curvas de luz de RR Lyraes en NGC 4147
V6 in NGC4147 V2 in NGC4147 V2 en M2 P= 69.7 d
M2: known variables
New variables in M2
RRab Known RR Lyraes in M2 RRc
Light curves of new variables
Light Curve Fourier decomposition m(t) = A o +Σ Α κ cos (2πk(t-E)/P + φ κ ) The Fourier parameters are defined as: φ ij =j φ i -i φ j R ij = A i / A j The shape of the light curve can be quantified in terms of low order harmonics φ 1j =j φ 1 - φ j R 1j = A 1 / A j (j=1,2,3,4)
Empirical Calibrations of Physical Parameters RRc log M = 0.52 log P -0.11 φ 31 + 0.39 log L = 1.04 log P -0.058 φ 31 + 2.41 Simon & Clement (1993) log T eff = 3.265-0.3026 log P - 0.1777 log M + 0.2402 + log L log Y = -20.26 + 4.935 log T eff -0.2638 log M + 0.3318 + log L Mv = 1.261 0.961 P 0.044 φ 21 4.447 A 4 Kovács (1998) [Fe/H] = 3.702 log P ^2 + 0.124 φ(c)31^2 0.845 φ(c)31 1.023 φ(c)31log P - 2.620 Morgan et al. (2005) RRab [Fe/H] = -5.038-5.394 P 1.345 φ 31 M v = 1.221-1.369 P -0.477 A 1 + 0.103 φ 31 log T eff = 3.9291-0.1112 (V-K) o - 0.0032 [Fe/H] Jurcsik & Kovács (1996), Kovács & Jurcsik (1996; 1997) Jurcsik (1998)
Results for RRc stars in M2
Results for RRab stars in M2
Determination of the radii Given log L/Lo and Teff one can get the redius log R/Ro (LT) Marconi et al. (2005) offer a P-R-Z relationship log Z = [Fe/H] 1.70 + log(0.638 f + 0.362) with f being the α enhacement factor (=1 Salarsis et al. 1993). the one can determin the radius log R/Ro (PRZ) from individual measurements of [Fe/H].
RR Lyraes in M2 on the HR Diagram Instability strips: Bono et al. (1995); models Jurcsic (1998); 272 RRab s Two luminosities for RRc s from two calibrations. ZAHB models are from Lee & Demarque (1990).
Physical parameters of globular clusters from RRc Fourier light curve decomposition
Physical parameters of globular clusters from RRab Fourier light curve decomposition
General trends in globular clusters from RRc stars log M/Mo = -(0.10+/-0.019)[Fe/H] - (0.381+/-0.032) log L/Lo = -(0.111+/-0.009)[Fe/H] + (1.554+/-0.016) log Teff = +(0.013+/-0.001)[Fe/H] + (3.882+/-0.002)
General Trends in Globular Clusters From RRab Stars Log Teff = +(0.032+/-0.005)[Fe/H] + (3.852+/-0.008) Mv = +(0.191+/-0.037)[Fe/H] + (1.032+/-0.054)
Conclusions from Globular Cluster Trends The RR Lyrae stars in Oo II clusters are: more massive more luminous cooler than in OoI clusters Thus OoII s s are more evolved than Oo I si
M V [Fe/H]: the RR Lyrae distance scale This correlation has been broadly studied in the past. Evidences are given that it is not lineal (Caputo 2000) The average relationship as obtained from assorted approaches is M V = (0.23 +/- 0.04) [Fe/H] + (0.93 +/- 0.12) (Chavoyer 1999) Our average for the RRc and RRab in M2 is: M V = (0.22 +/- 0.03) [Fe/H] + (0.86 +/- 0.05) This relation predicts: M V = 0.53 +/- 0.08 for [Fe/H] = -1.5 This is in good agreement with the results: M V = 0.58 +/- 0.04 (Cacciari 2003) obtained from assorted methods M V = 0.61 +/- 0.11 weighted mean of 7 clusters (Chavoyer 1999) (both for [Fe/H] = -1.5)
Conclusions Accurate CCD photometry of globular clusters and Fourier decomposition of the RR Lyrae stars light curves, lead to physical parameters of astrophysical relevance, and to general trends of these key physical parameters. These trends offer insight to the origin of the Oosterhoff groups and the structure of the Horiozontal Branch. This technique offers an independent approach to the determination of the zero point in the RR Lyrae distance scale. It provides the opportunity to discover and parametrize the Blazhko effect in RR Lyrae stars. New image subtraction techniques allow finding new variables, even in very crowded fields like globular clusters core regions.
Ongoing work Presently our team has data, mostly taken in Hanle by Prof. Sunetra Giridhar, on the globular clusters: NGC 5466 [Fe/H] = -2.22: (19): masters thesis of Victoria Rojas, Mexico NGC 1904 [Fe/H] = -1.57: (3): under analysis during my visit to the IIA NGC 2419 [Fe/H] = -2.12: (35): under analysis during my visit to the IIA NGC 5053 [Fe/H] = -2.29: (9): to be reduced NGC 6981 [Fe/H] = -1.40: (28): to be reduced NGC 7492 [Fe/H] = -1.51: (3): to be reduced