Resolved Astrometric
Binary Stars
Brian D. Mason
9/12/2012
U.S. Naval Observatory
1
Background
Astrometric contributions of
Friedrich Bessel (1784-1846)
•Parallax of 61 Cygni (1838)
U.S. Naval Observatory
Background
Astrometric contributions of
Friedrich Bessel (1784-1846)
•Parallax of 61 Cygni (1838)
•Non-linear proper motion of
Sirius and Procyon (1844)
Image: http://vega.lpl.arizona.edu/sirius/A5.html
U.S. Naval Observatory
Background
Astrometric contributions of
Friedrich Bessel (1784-1846)
•Parallax of 61 Cygni (1838)
•Non-linear proper motion of
Sirius and Procyon (1844)
Due to stellar types (mainsequence and white dwarf)
motion affect significant, but
companion hard to detect.
•
Image: http://vega.lpl.arizona.edu/sirius/A5.html
Sirius B first resolved in 1862 by Alvan Graham Clark (right) testing 18.5” Clark refractor.
U.S. Naval Observatory
Background
Astrometric contributions of
Friedrich Bessel (1784-1846)
•Parallax of 61 Cygni (1838)
•Non-linear proper motion of
Sirius and Procyon (1844)
Due to stellar types (mainsequence and white dwarf)
motion affect significant, but
companion hard to detect.
•
•
Sirius B first resolved in 1862 by Alvan Graham Clark (right) testing 18.5” Clark refractor.
Procyon B first resolved in 1896 by John Martin Schaeberle with Lick 36” Clark refractor.
U.S. Naval Observatory
Current
CurrentOrbit:
Orbit:Procyon
Sirius AB
AB
• Broken line is line of nodes.
• Green plus signs and asterisks:
micrometry.
• Pink asterisks: photography
• Blue circles: HST/WFPC2
• Scales on axis are in arcseconds.
• Direction of orbital motion at
lower right.
• Sirius Period = 50.090y.
• Procyon Period = 40.82y.
U.S. Naval Observatory
Orbits
• The 6th Catalog of Orbits of Visual Binary Stars
has 2298 orbits of 2187 systems.
• While most are the best graded orbits of
resolved pairs, 504 are astrometric orbits.
• These orbits have six of the seven usual
Campbell Elements: P, i, Ω, ω, T0, and e; rather
than the semi-major axis of the resolved orbit
(a”), the astrometric orbit has ap, the semimajor axis of the photocentric orbit.
• If an astrometric pair is subsequently resolved,
B=
the photocentric orbit should be similar
(mathematically) to the resolved orbit.
• The mass ratio, B, depends on the ratio of the
semi-major axes and the luminosity ratio (β).
MB
lB
1
------------- ; β = ---------- = ------------MA + MB
lA + lB
1 + 100.4∆m
ap
B = ------ + β
a”
U.S. Naval Observatory
HIP 42220 = YR 13
•
•
•
•
•
•
HIP 42220 listed as “suspected non-single”
in Hipparcos Catalogue
(1997yCat.1239….0E).
Orbital solution by Heintz & Cantor
(1994PASP..106..363H).
First resolved by Elliott Horch &
Collaborators (2002AJ….123.3442H), and
subsequently only resolved by the YaleRochester group with the WIYN telescope.
The new resolved orbit is similar to
astrometric orbit and with the π generates a
Σ M of 0.559Í +/- 0.370Í.
Based on the measured luminosity ratio and
the ratio of the semi-major axes of the two
orbits (aphoto/a”) a mass ratio of 0.454 is
determined.
This results in masses of MA = 0.30 MÍ,
MB = 0.25 MÍ, which is lower than
expected, but the uncertainty is large.
U.S. Naval Observatory
Other New Orbits: AB Dor & 31 Cyg
They generate a Σ M of 0.59 MÍ and 16 +/- 9.5 MÍ.
as well as individual masses of MA = 0.50 MÍ, MB = 0.09 M8 and MA = 7.1 MÍ, MB = 8.9 M8.
U.S. Naval Observatory
Combined Solutions
Combined
solutions of
resolved
double-lined
spectroscopic
binaries allow
for direct
determination of
stellar masses
and parallax.
a”3
π3 = --------Σ M P2
This parallax, called the orbital parallax, is a calculated not an
observed parameter and has no distance limit.
U.S. Naval Observatory
Orbital Parallax
•
Comparison of Orbital Parallax
and Hipparcos Parallax
(2000A&AS..145..215P)
as of 2000.
•
Focusing only on those with π <
100 milliarcseconds (mas).
Assuming equal π.
Recent orbit solutions
(2000A&A…448..703B,
2008AJ….135..766M,
2010AJ….140.1579M,
2010AJ….139.2308F).
•
•
•
In preparation solutions.
U.S. Naval Observatory
The New Solutions: ξ Cep
• New measures to improve
existing orbits.
• Dashed curve is previous orbit.
• Broken line is line of nodes.
• Filled circles = unpublished
CHARA SFP measures
• open circles = published speckle
interferometry measures
• Large shaded circle = Hipparcos
resolution limit
• Small shaded circle = 4m V band
speckle resolution limit
U.S. Naval Observatory
The
New
Solutions:
HD
178911
The
New
Solutions:
ξ Cep
• ξ Cep:
•
•
MA = 1.045(0.032) MÍ, MB =
0.409(0.066) MÍ, π = 38(3) mas.
The Hipparcos parallax, π = 34(1)
mas, while having a smaller formal
error may be more incorrect due to
the unresolved companion not being
considered.
• HD 178911:
•
•
MA = 0.802(0.055) MÍ, MB =
0.622(0.053) MÍ, π = 28(2) mas.
The Hipparcos parallax (π = 19(2)
mas) may have similar uncertainty.
• The biggest problem is that these need
both radial velocity and resolved orbit
solutions of very high quality, and the
observation methods are limited to the
brightest stars.
U.S. Naval Observatory