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Measuring Radii and Temperatures of Stars

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Measuring Radii and Temperatures of Stars. Definitions (again...) Direct measurement of radii ... Angular diameters typically measured in milli-arcseconds (mas) ... – PowerPoint PPT presentation

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Title: Measuring Radii and Temperatures of Stars


1
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

R radius r distance R/rangular diameter
2
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?

3
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

4
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

5
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6
CHARA Interferometer on Mt. Wilson
7
CHARA Delay Compensator
8
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9
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 (i90)

10
Photometric Methods Bolometric Flux
  • Must know bolometric flux of star
  • Distance
  • Temperature
  • Bolometric correction
  • Calibrated with
  • Stellar models
  • Nearby stars with direct measurements

11
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

12
Absolute Flux
  • Determine the apparent monochromatic flux at some
    wavelength, Fn
  • From a model that fits the spectral energy
    distribution, compute the flux at the stars
    surface, Fn
  • From the ratio of Fn/Fn, compute the radius
  • The infrared flux method is just this method
    applied in the infrared.

13
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 2m)
  • USNO CHARA interferometers lt 1 mas
  • Surface structure
  • Pulsations
  • Circumstellar material
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