Measuring Radii and Temperatures of Stars Definitions (again…)



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tarix30.12.2017
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#18525


Measuring Radii and Temperatures of Stars

  • Definitions (again…)

  • Direct measurement of radii

    • Speckle
    • Interferometry
    • Occultations
    • Eclipsing binaries
  • Photometric determinations of radii

    • Bolometric flux
    • Surface brightness
    • Absolute flux
  • Determining temperatures

    • Absolute flux
    • Model photospheres
    • Colors
    • Balmer jump
    • Hydrogen lines
    • Metal lines

Stellar Diameters

  • Angular diameters typically measured in milli-arcseconds (mas)

  • Angular diameter (in radians) given by physical diameter divided by distance

  • The diameter of Aldebaran is ~40 RSUN. Its distance is about 19 pc. The angular diameter of Aldebaran is …

  • (work in cgs or MKS units or work in AU and use the definition of a parsec)

  • What would the angular diameter of the Sun be at 10 pc?



Speckle Diameters

  • The diffraction limit of 4-m class telescopes is ~0.02” at 4000A, comparable to the diameter of some stars

  • The seeing disk of a large telescope is made up of the rapid combination of multiple, diffraction-limited images

  • 2-d Fourier transform of short exposures will recover the intrinsic image diameter

  • Only a few stars have large enough angular diameters.

  • Speckle mostly used for binary separations



Interferometry

  • 7.3-m interferometer originally developed by Michelson

  • Measured diameters for only 7 K & M giants

  • Until recently, only a few dozen stars had interferometric diameters





CHARA Interferometer on Mt. Wilson



CHARA Delay Compensator





Other Methods

  • Occultations

    • Moon used as knife-edge
    • Diffraction pattern recorded as flux vs. time
    • Precision ~ 0.5 mas
    • A few hundred determined
  • Eclipsing binaries

    • Photometry gives ratio of radii to semi-major axes
    • Velocities give semi-major axes (i=90)


Photometric Methods – Bolometric Flux

  • Must know bolometric flux of star

    • Distance
    • Temperature
    • Bolometric correction
  • Calibrated with

    • Stellar models
    • Nearby stars with direct measurements


Surface Brightness

  • To avoid uncertainties in Teff and BC

  • Determine PV as a function of B-V

  • PV(B-V)=logTeff – 0.1BC

  • PV(B-V) is known as the “surface brightness function”

  • Calibrate with directly measured diameters



Absolute Flux

  • Determine the apparent monochromatic flux at some wavelength, F

  • From a model that fits the spectral energy distribution, compute the flux at the star’s surface, F

  • From the ratio of F/F, compute the radius

  • The infrared flux method is just this method applied in the infrared.



Hipparcos!

  • The European Hipparcos satellite determined milli-arcsec parallaxes for more than 100,000 stars.

  • Distances are no longer the major source of uncertainty in radius determinations for many stars

  • Zillions of stars within range of the Keck interferometer (3 mas at 2)

  • USNO & CHARA interferometers < 1 mas

    • Surface structure
    • Pulsations
    • Circumstellar material


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