Structural function analysis of luminous blue variables (LBVs) in the Local Group Gantchev, G. Astronomy Department, University of Sofia, bul. J. Bourchier 5, Sofia 1164 (University of Aix-Marseille, France) IX BULGARIAN-SERBIAN ASTRONOMICAL CONFERENCE: ASTROINFORMATICS Institute of Mathematics and Informatics, 1-4 July 2014, Sofia

Summary LBV stars Structure Function Analysis Historical Data Preliminary Results Prospective work Concluding remarks

General Evolutionary Scheme for Massive Stars Massey, arXiv: v1, 2014

The evolutionary connection The full curve is the main sequence. The dashed line is the Humphreys–Davidson limit. Filled and open circles indicate LBVs in our Galaxy and in the Large Magellanic Cloud.

Some Properties of LBVs LBVs are the most luminous stellar objects with luminosities up to 10 6 L  LBVs are poorly observed (sampled) variable stars, small and large scale variations, large outbursts on scales of several decades, poorly determined stellar parameters irregular and unpredictable brightness variations represent a short critical phase in the evolution of very massive stars variations due to changes in the radius and surface temperature of the stars Theoretical LBVs light curves: complicated structures due to shock waves running through the stellar atmosphere during large eruptions (several LBVs): - brightened by as much as a factor ~100 (  m ~ 5m ) - only once every few 100 year -  M~1M  or more very rare: only 5 confirmed LBVs in our Galaxy and a few tens in other galaxies after the short LBV phase evolve directly into very hot helium-rich stars W–R stars

Three types of variations: Short time variations (a) Short time variations t ~ months with  m ~ m magnitudes; (α Cygni variations) Typical LBV variations (b) Typical LBV variations on a t ~ years with  m ~ m radius grow and shrink unknown inside instability r/R~10 times L=const.: visual light  UV radiation Sp. Class: A  early B (S Doradus variations) Large eruptions (c) Large eruptions  t ~ n x 100 yr,  m ~ 5 m (observed in P Cygni & η Carinae, not in S Dor) unknown origin: - outward directed radiation pressure force? - large instability created by minor disturbances?

Basic properties of LBVs The LBV classification is phenomenological, where one of the following properties has to be present. Either the star shows S-Doradus type variability, or giant eruptions of several solar masses must have occurred.... Murdin, P.: 2001, Encyclopedia of Astronomy and Astrophysics, Institute of Physics Publishing, London

The Local Group

red circles: new LBV candidates Lee et al. Apj. 785,11 (2014) blue circles: known LBVs Gil de Paz et al. (2007) - GALEX near UV image

red labels: new LBV candidates from Lee (2014) and Massey (2006)

Historical lightcurves of LBVs AF And, AE And, VA1 and V15 in M31 galaxy

The structure function: log(time-lag) Schematic showing the “ ideal ” structure function for a time series plus measurement noise. Hughes et al, 1992, ApJ, 396, 469 log(time-lag) Structure function for the quasar QSO J

Structure functions for LBVs AF And, AE And, VA1 and V15 in M31 galaxy

Historical lightcurves of LBVs Var2, Var A, Var B and Var C in M33 galaxy

Structure functions for LBVs Var2, Var A, Var B and Var C in M33 galaxy

Historic lightcurve of “supernova impostor” Eta Carinae Visual, photographic, photoelectric and CCD data from Fernández-Lajús et al. (2009)

Parameteric space of slope and log(time scale) Hughes et al. 1992, ApJ, 396, 469

The true “ladder-like” structure function (?) We suppose that this shape (in red) is what the structure function is expected to be Hughes et al, 1992, ApJ, 396, 469 log(time-lag) Structure function for the quasar 3C 120

Future work The candidate star with a constructed structure function IS an LBV or NOT ? Diagnostic on diagram “Slope – Time- scale” Structure functions for equivalent line widths of H-alpha and other spectral features Check of sustainability of the results: Pass-band, metallicity, quiescence vs eruption phase Could LBVs be used as distance indicators ? Ivanov G.R., 1990 “In Physics of LBV”, 1988 Period  Log(time-scale) Example: AF And Log(time-scale) ~ 0.38 = lgP = 2.94 P, days time-scale, yr.7 Ivanov G. AF And lgP= 3.23 Shift ΔlgP=0.29

Благодаря за вниманието We gathered and combined archived observational data (timespan~100 yrs.) for the best studied LBVs in M31 galaxy: AF And, AE And, VA1 and V15. Also we did the same analysis for some LBVs in M33 galaxy, our galaxy and the great Magellanic cloud. For the first time, we constructed their structure functions and for each variable we calculated their characteristic parameters: slope and time scale. The consistency of these parameters has been tested throughout historical photometric data, time coverage and type of variability (quiescence or eruption ) the LBV star was in. Among the four (mostly) studied LBVs in M31, only one (AF And) shows high stability of it’s structure function slope and time scale. The variable AE And has a plateau in the middle part of it’s function. For the other two, only the lower limit of it’s time-scale cannot be estimated. We plan to perform a long term observational campaign of all known and candidate LBVs in M31 and to do the same analysis pipeline for the other known LBVs of the Local Group.

References: Hubble, E., Sandage, A., 1953, ApJ, 118, 353 Rosino, L., Bianchini, A., 1973, A&A 22, 453 Sharov, A.S., 1990, Astron. Zh. 67, 723 Hughes, P. A., Aller, H. H., Aller, M. F.: 1992, ApJ, 396, 469 Ovcharov, E. et al., 2008, MRAS 386, 819 Massey, P., 2013, arXiv: v1 Groh, J. H. et al., 2013, A&A arXiv: v1 Lee, C. H. et al., 2014, arXiv: v1 Thank you for your attention ! To be continued…