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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.

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2 - Stellar Masses & Radii

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2 stellar masses radii

2 - Stellar Masses & Radii

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?

2 stellar masses radii

Diffraction Effects

Because light acts like a wave, it undergoes diffraction when passing through an aperture, whether it is a slit or a circular hole, etc.


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

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Resolving Power

Overlap of the Point Spread Functions (PSFs)

Resolving Power (Rayleigh’s criterion)

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Astronomical “Seeing”

mostly “image motion”


more “image blur”

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High Resolution Imaging from Space

Hubble Space Telescope - 2.4m primary mirror

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Speckle Interferometry

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

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Adaptive Optics

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Here they can use a moon of the planet as a guide star

Hammel et al. 2007, AJ, 134, 637

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Lunar Occultations

Grazing occultation of Aldebaran

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Michelson Interferometry

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IOTA JHK-spectro-interferometry

of the Mira star T Cep

wavelength range:

1.0µm (left) to 2.3µm (right)

G. Weigelt et al., 2003, SPIE 4838, 181

see: http://www.mpifr-bonn.mpg.de/div/ir-interferometry/

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The atmosphere causes the fringes to move around, requiring rapid compensation

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H- and K-band VLTI-AMBER interferograms

(two 1.8 m ATs; HD 48433)

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Model of Altair, based on data from the Navy Prototype Optical Interferometer (Peterson et al. 2006, ApJ, 636, 1087)

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Intensity (Hanbury Brown) Interferometry

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Space Interferometry Mission (SIM)


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Pipe Dream?

Terrestrial Planet Finder (TPF)

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(assuming spherical stars

& uniform temperatures)

Main Sequence

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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)!

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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”

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R. Pogge



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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.


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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”!!

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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:

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L vs M for Main Sequence Stars

The Main Sequence is a sequence of masses

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How Massive Are They?

About 1/12 the Sun (brown dwarf boundary) to ~200 time the Sun

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