1. Jay Anderson, Stefano Casertano, Howard Bond,
Relativistic Deflection of Background Starlight by a Nearby White Dwarf
[iPoster: ]
Kailash C. Sahu
Jay Anderson, Stefano Casertano, Howard Bond,
Pierre Bergeron, Ed Nelan, Laurent Pueyo, Tom Brown, Joshua Sokol, Martin Dominik, Annalisa Calamida, Noé Kains, Mario Livio

2. A century after Einstein postulated general theory ofrelativity, we have used the Hubble Space Telescope to measure the relativistic deflection by a nearby star, the white dwarf Stein 2051 B.
Stein 2051 B passed closely in front of a background star, which caused a small deflection of the background star’s position. We determined the mass of the white dwarf by measuring this deflection.

3. Tests of General Theory of Relativity
(Einstein 1916)
One of the crucial tests was the curvature test: Bending of Light-rays.
A ray of light going past the sun will be deflected by 1.75 arcsec.
1919 Solar Eclipse:
First measurement of the deflection of a background star by Dyson/Eddington et al. 1920: 1.98+/—0.18 arcsec.
First clear confirmation of the general theory of relativity.

4. Gravitational Bending of Light
Measurement of such deflection by a star outside the solar system would provide a direct method to measure the mass of the star.
However, the expected deflections are tiny, about 1000 times smaller than what Eddington measured.
So no such deflection caused by a star outside the solar system (astrometric microlensing) had been observed until now.
Hubble’s high angular resolution capability allows us to observe such a phenomenon.

5. Search for Microlensing Events by Stars
Nearby and higher proper-motion stars are the most interesting because the expected deflection is large, and measurable with HST.
Input catalog: ~5000 high-proper motion stars from Luyten’s Catalog, with improved coordinates from Lepine and Shara (2005) and Bakos, Sahu and Nemeth (2002).
Projected the positions forward taking proper motion and parallax into account, and searched for encounters within 2 arcsec with stars in the GSC-II catalog.
One particularly interesting event: Stein 2051B (impact parameter 0.1”)
1992
1995

6. Importance of White Dwarf Mass Determination
All stars with mass less than 8 solar mass end their lives as white dwarfs.
Existence of a mass-radius relation is a key prediction of the white dwarf theory; however, this lacks firm observational support.
Until now, all (~3) masses for white dwarfs have come from binaries.
Stein 2051B is a binary, but the companion is >55 AU away, so the binary is unlikely to have affected the evolution.
So Stein 2051B’s mass determined through microlensing will provide a crucial test for the theory of white dwarfs, and can also be used to determine its age.

7. Nearby Old White Dwarf Stein 2051B
Stein 2051B is the 6th nearest white dwarf (D~ 17 light yr).
Proper motion 2.37 arcsec/yr.
Stein 2051B (V = 13) is the faint companion of Stein 2051A, which is about 5 times brighter M star, ∼ 7 sec away.
Mass of Stein 2051B has been a matter of debate.
Its mass as estimated from old astrometry suggested that it may be a Fe core WD, which is physically unrealistic, and would suggest that the white dwarf is as old as the Universe.

8. Motion of STEIN 2051B

9. Motion of STEIN 2051B

10. Observational Challenges
The source is ~400 times
fainter than Stein 2051B
The red dwarf (LHS27) is
~10 times brighter than
Stein 2051B, and saturates
even in the shortest exposure
in F814W.
We need to measure the position
of the source at the presence
of the much brighter WD, a
few pixels away.

11. Observed deflections by STEIN 2051B
Time-evolution of the
deflection is consistent
with the model.
All other 25 stars in the
image show no such motion.
This suggests that
the mass of the
White dwarf is
0.675 solar mass.

12. Results Mass-Radius Relation ϴE = 31.3 mas Mass = 0.675 solar mass.
This provides a confirmation
of the WD evolutionary theory.
WD cooling age: 1.9 Gyr.
Progenitor mass: 2.6 solar mass Pre-WD evolutionary lifetime: 0.4 to 1.3 Gyr .
Total age : 1.9 to 3.6 Gyr.
So there is no conflict with the age of the Universe.

13. Conclusions
Stein 2051B passed very close to an 18th mag background star in 2014 causing astrometric microlensing.
The event was observed with HST at 8 epochs to measure the astrometric deflections.
This is the very first astrometric deflection measurement of a Milky Way source beyond solar system.
This is the first mass measurement through astrometric microlensing, of an effectively-isolated white dwarf.
The results are in excellent agreement with the physics of electron-degenerate matter.
This study opens up a new method of determining stellar masses, and this method works for isolated stars.
TWITTER VERSION (131 characters):
A century after Einstein postulated general theory of relativity, bending of light by a white dwarf is used to determine its mass.