measuring radii and temperatures of stars
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
Measuring Radii Measuring Radii and and
Temperatures Temperatures of Starsof 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
Fr 22 44 RF
42
0)/( effTrRd
F
R = radius r = distanceR/r=angular diameter
4
0 effTdF
Stellar DiametersStellar 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 DiametersSpeckle 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
InterferometryInterferometry
• 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. CHARA Interferometer on Mt. WilsonWilson
CHARA Delay CompensatorCHARA Delay Compensator
Other MethodsOther 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 Photometric Methods – Bolometric FluxFlux
• Must know bolometric flux of star– Distance– Temperature– Bolometric correction
• Calibrated with– Stellar models– Nearby stars with direct measurements
42
SunSunSun T
T
R
R
L
L
460.72.02.0log2loglog Veff mBCTrR
Surface BrightnessSurface 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
32 )()()()( VBdVBcVBbaVBPV
460.72.0)(2loglog VV mVBPrR
Absolute FluxAbsolute 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.
2
1
F
FrR
Hipparcos!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