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
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 The metallicities and distances of the globular clusters are of Globular Cluster 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
NGCHigh 6752: ResolutionFLAMES at VLT2 allowe ind Globularto obtain spectra centred Clusters: on Hα at a resolutionsome of examplesR=6000 and 5
The same exposure provided UVES spectra of seven stars near the red giant branch bump at a resolution
of 40000 and 20
• 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)
AccurateAccurate CCDCCD PhotometryPhotometry ++ FourierFourier DescompositionDescomposition ofof lightlight curvescurves ++ SemiempiricalSemiempirical calibrationscalibrations 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) = Ao +Σ Ακ cos (2πk(t-E)/P + φκ)
●The Fourier parameters are defined as:
φij=j φi-i φj Rij = Ai / Aj
•The shape of the light curve can be quantified in terms of low order harmonics
φ1j=j φ1 - φj R1j = A1 / Aj (j=1,2,3,4) Empirical Calibrations of Physical Parameters
RRc
• log M = 0.52 log P -0.11 φ31 + 0.39
• log L = 1.04 log P -0.058 φ31 + 2.41 Simon & Clement (1993)
• log Teff = 3.265 -0.3026 log P - 0.1777 log M + 0.2402 + log L
• log Y = -20.26 + 4.935 log Teff -0.2638 log M + 0.3318 + log L
•Mv= 1.261 –0.961 P –0.044 φ21 – 4.447 A4 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 φ31 Jurcsik & Kovács (1996), •Mv = 1.221 -1.369 P -0.477 A1 + 0.103 φ31 Kovács & Jurcsik (1996; 1997) Jurcsik (1998) • log Teff = 3.9291 -0.1112 (V-K)o - 0.0032 [Fe/H] 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 are more evolved than Oo I’s MMV –– [Fe/H]:[Fe/H thethe RRRR LyraeLyrae distancedistance scalescale
• 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
MV = (0.23 +/- 0.04) [Fe/H] + (0.93 +/- 0.12) (Chavoyer 1999) • Our average for the RRc and RRab in M2 is:
MV = (0.22 +/- 0.03) [Fe/H] + (0.86 +/- 0.05) This relation predicts:
MV = 0.53 +/- 0.08 for [Fe/H] = -1.5 • This is in good agreement with the results:
MV = 0.58 +/- 0.04 (Cacciari 2003) obtained from assorted methods
MV = 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. OngoingOngoing workwork
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