Dynamite Diameters Observations of main sequence stars with long baseline optical/infrared interferometry Tabetha Boyajian (Georgia State University / CHARA) Hubble Fellow Symposium March 8-11, 2010

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Big Picture: Empirically determined H-R diagram from interferometric measurements An interferometer measure the angular diameter (θ) of a star. (yields the effective temperature and L with distance and flux) An interferometer measure the angular diameter (θ) of a star. (yields the effective temperature and L with distance and flux) Important issues at hand: Important issues at hand: Calibration of temperature scales established through less direct methods Calibration of temperature scales established through less direct methods Discrepancies between theory and observations Discrepancies between theory and observations 4 Sun α Cen A,B Vega Hyades Giants Altair Regulus Spica 61 Cyg A,B Procyon

Interferometers today Direct methods to measure stellar sizes: Direct methods to measure stellar sizes: Long baseline optical interferometry Long baseline optical interferometry Eclipsing binaries Eclipsing binaries Occultation (Planetary and Lunar) Occultation (Planetary and Lunar) Speckle interferometry Speckle interferometry Current and Future Optical / Infrared Interferometers a) Closed 2006, b) closed 2009, c) under construction 5

The CHARA Array Six 1 meter telescopes with maximum baseline of 330 meters Six 1 meter telescopes with maximum baseline of 330 meters Longest optical interferometer in the world Longest optical interferometer in the world Five beam combiners available (2,3, and 4 telescope modes) Five beam combiners available (2,3, and 4 telescope modes) Accommodates remote and parallel observing modes Accommodates remote and parallel observing modes 6

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The First Diameters Michelson and Pease measure the diameter of Betelgeuse Michelson and Pease measure the diameter of Betelgeuse 20-foot interferometer mounted on the 100- inch Hooker telescope 20-foot interferometer mounted on the 100- inch Hooker telescope Narrabri Stellar Intensity Interferometer Narrabri Stellar Intensity Interferometer 32 diameters of stars measured in the visible 32 diameters of stars measured in the visible Empirical temperature scale for stars hotter than our Sun is based upon this data Empirical temperature scale for stars hotter than our Sun is based upon this data 8 Code et al. 1976

Progress Source: Davis 1997 Source: Richichi et al (CHARM2 Catalogue) Total # of stars with angular diameter measurement Stars with σθ < 5% Stars with σθ < 5% and on main-sequence (~3) (~5.5) (4) 9

Census 2009 *Measurements outlined in black are from the CHARA Array. Does not include new results presented here on K-M dwarfs. 10

How do direct measurements compare to semi-empirical values? APL99=Allende Prieto and Lambert 1999; GCS07=Holmberg 2007; Tak07=Takeda Boyajian et al. 2009, 2010, in prep

Inconsistencies and their implications Y 2 isochrones fit to empirically determined T and L to determine M and age Y 2 isochrones fit to empirically determined T and L to determine M and age Results agree well will eclipsing binaries Results agree well will eclipsing binaries If temperature is over-estimated: If temperature is over-estimated: Gravity (log g) is over-estimated Gravity (log g) is over-estimated e.g.: if you use spectroscopic log g and interferometric radius to derive a mass, then the star appears too massive e.g.: if you use spectroscopic log g and interferometric radius to derive a mass, then the star appears too massive Radius is under-estimated Radius is under-estimated Age is under-estimated Age is under-estimated 12 Boyajian et al. 2009, 2010, in prep

Metallicity effects on temperature K0 A0 K0 13 Effective temperature calibrations Calibrations used for transforming observed colors and metallicity to temperatures Calibrations used for transforming observed colors and metallicity to temperatures Solution finds coefficients to polynomial where θ=5040/T, X is color index and [Fe/H] is metallicity of object (Alonso et al. 1996) Solution finds coefficients to polynomial where θ=5040/T, X is color index and [Fe/H] is metallicity of object (Alonso et al. 1996) Spread in temperatures of different scales is up to 300K Spread in temperatures of different scales is up to 300K At [Fe/H]=-1.5, the empirical scale is ~200K cooler for all stars in other relations compared here At [Fe/H]=-1.5, the empirical scale is ~200K cooler for all stars in other relations compared here

Observations of late-type dwarfs K-M stars with diameters measured to better than 5% K-M stars with diameters measured to better than 5% 14

Theory versus observation: I Masses for single stars are derived from the K-band mass-luminosity relationship from Delfosse et al. 2000, and assume a 10% error. Masses for single stars are derived from the K-band mass-luminosity relationship from Delfosse et al. 2000, and assume a 10% error. (TOP) The solid black line is a 5 Gyr isochrone from the BCAH98 models (Baraffe et al. 1998) for L mix =H p, the dotted and dashed lines are L mix =1.5 and 1.9 H p, respectively. (TOP) The solid black line is a 5 Gyr isochrone from the BCAH98 models (Baraffe et al. 1998) for L mix =H p, the dotted and dashed lines are L mix =1.5 and 1.9 H p, respectively. (BOTTOM) dotted line signifies zero deviation between observation and model. (BOTTOM) dotted line signifies zero deviation between observation and model. 15

Theory versus observation: II More data makes these plots look a little different More data makes these plots look a little different A new explanation is needed to explain offset in single stars A new explanation is needed to explain offset in single stars Berger et al López-Morales 2007 Demory et al (Includes Mass<.9 M  ) 16

Theory versus observation: III ll ll The KINK and The GAP 17

Interferometry allows us to empirically determine fundamental properties of stars in order to provide the foundation for calibrating the effective temperature scales and testing model atmosphere and evolution calculations Interferometry allows us to empirically determine fundamental properties of stars in order to provide the foundation for calibrating the effective temperature scales and testing model atmosphere and evolution calculations For main sequence stars, the temperature is often overestimated while the radius is underestimated compared to observations For main sequence stars, the temperature is often overestimated while the radius is underestimated compared to observations Thank you for your interference! Thank you for your interference! 18