Resolved Astrometric Binary Stars Brian D. Mason filemotion affect significant, but companion hard...

9/12/2012 U.S. Naval Observatory 1

Resolved Astrometric Binary Stars

Brian D. Mason

U.S. Naval Observatory

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 (main-sequence 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.

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 (main-sequence 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 Orbit: Sirius AB

• Sirius Period = 50.090y.

• Procyon Period = 40.82y.

• 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.

Current Orbit: Procyon AB

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 semi-major axis of the photocentric orbit.

• If an astrometric pair is subsequently resolved, 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).

U.S. Naval Observatory

MB lB 1

B = ------------- ; β = ---------- = -------------

MA + MB lA + lB 1 + 100.4∆m

ap

B = ------ + βa”

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 Yale-Rochester group with the WIYN telescope.

• The new resolved orbit is similar to astrometric orbit and with the π generates a Σ M of 0.559 +/- 0.370.

• 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 M, MB

= 0.25 M, 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 M and 16 +/- 9.5 M.

as well as individual masses of MA

= 0.50 M, MB

= 0.09 M8 and MA

= 7.1 M, MB

= 8.9 M8.

Combined Solutions

Combined solutions of resolved double-lined spectroscopic binaries allow for direct determination of stellar masses and parallax.

U.S. Naval Observatory

This parallax, called the orbital parallax, is a calculated not an observed parameter and has no distance limit.

a” 3

π3 = ---------Σ M P2

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

• ξ Cep:• M

A= 1.045(0.032) M, M

B=

0.409(0.066) M, 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:• M

A= 0.802(0.055) M, M

B=

0.622(0.053) M, 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.

The New Solutions: ξ Cep