2 - Stellar Masses & Radii. Stellar Radii. “If the stars are so far away, how do we know their names?”. Stars are very far away, so how do we determine their physical sizes?. Diffraction Effects.
2 - Stellar Masses & Radii
“If the stars are so far away, how do we know their names?”
Stars are very far away, so how do we determine their physical sizes?
Because light acts like a wave, it undergoes diffraction when passing through an aperture, whether it is a slit or a circular hole, etc.
A TELESCOPE OBJECTIVE ACTS LIKE A CIRCULAR APERTURE!
So the light of any star produces a diffraction pattern. THIS SETS THE MAXIMUM SPATIAL RESOLUTION THAT A TELESCOPE CAN ACHIEVE.
This is usually referred to as the Point Spread Function. In reality, other effects (aberrations) may contribute to the actual PSF of a star.
The pattern is the Fourier transform of the opening
Overlap of the Point Spread Functions (PSFs)
Resolving Power (Rayleigh’s criterion)
mostly “image motion”
more “image blur”
High Resolution Imaging from Space
Hubble Space Telescope - 2.4m primary mirror
Real-time bispectrum speckle interferometry: 76 mas resolution.
Frame rate of data recording and processing: ~ 2 frames per second.
SAO 6 m telescope, K-band.
G. Weigelt, MPI for Radioastronomy, 1999
Here they can use a moon of the planet as a guide star
Hammel et al. 2007, AJ, 134, 637
Grazing occultation of Aldebaran
of the Mira star T Cep
1.0µm (left) to 2.3µm (right)
G. Weigelt et al., 2003, SPIE 4838, 181
The atmosphere causes the fringes to move around, requiring rapid compensation
H- and K-band VLTI-AMBER interferograms
(two 1.8 m ATs; HD 48433)
Model of Altair, based on data from the Navy Prototype Optical Interferometer (Peterson et al. 2006, ApJ, 636, 1087)
Intensity (Hanbury Brown) Interferometry
Space Interferometry Mission (SIM)
Terrestrial Planet Finder (TPF)
(assuming spherical stars
& uniform temperatures)
How Big Are They?
As small as a city (neutron stars), and as large as the solar system (a few, but not really well-known)!
Stellar Masses from Binary Stars
Optical Doubles – 2 stars in the line of sight with no physical relationship.
Visual Binaries – Two physically related stars orbiting one another that can be resolved independently.
β Cyg = “Albireo”
Astrometric Binaries – Physically the same as a visual binary, except that one member is too faint to be detected.
Eclipsing Binaries – here, the plane of the orbit is so close to the line of sight that the stars pass in front of one another as they orbit their mutual center of mass.
Spectrum Binaries –Unresolved binary where the spectra of both stars are visible, but no orbital motion is detected through the Doppler effect.
Spectroscopic Binaries – Here, the orbital velocity and orbital inclination provide a Doppler shift large enough to be detected.
For a pair of stars with masses m1 and m2, located a1 and a2 from the center of mass:
We don’t measure a’s directly, but the angular separation α in arcsec
Kepler’s 3rd Law:
in “astronomer’s units”:
Remember, if you can, stick with “astronomer’s units”!!
Masses from Spectroscopic Binaries
We see only the radial component of the orbital velocity
So we measure:
But you need to know i pretty well
In many cases you see only the spectrum of star 1 and all you can find is the mass function:
L vs M for Main Sequence Stars
The Main Sequence is a sequence of masses
How Massive Are They?
About 1/12 the Sun (brown dwarf boundary) to ~200 time the Sun