HST MEASURES THE MASS OF THE NEARBY WHITE DWARF STEIN 2051B THROUGH RELATIVISTIC DEFLECTION OF BACKGROUND STARLIGHT

Kailash C. Sahu1, Jay Anderson1, Stefano Casertano1, Howard E. Bond1,2, Pierre Bergeron3, Ed Nelan1, L. Pueyo1, T. M. Brown1, A. Bellini1, Z. G. Levay1, J. Sokol1, M. Dominik4, A. Calamida1, N. Kains1, M. Livio5

1Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, 2Dep. Astron. & Astrophys. Penn State University, Univ. Park, PA 168023Dép. de Phys., Univ. Montréal, Montreal, Canada, 4U. St Andrews, St. Andrews, UK, 5Dep. Phys.& Astron., U. Nevada, Las Vegas, NV 89154

More details, see

Sahu, K.C. et al. “Relativistic deflection of background starlight measures the mass of a nearby white dwarf star” June 9, 2017 issue of Science (in press).

The Stein 2051B Event• We projected the positions of all ∼5,000 stars in the Luyten Half

Second catalog forward over the next 40 years and searched for close passages near background stars contained in the GSC 2.3 catalog.

• One of the most interesting is the close passage of Stein 2051B in front of a 18th magnitude star, with an impact parameter on ~0.1 arcsec.

• Expected deflection is >2 mas which is ~10 times larger than typical HST accuracy, but the presence of the much brighter WD makes this measurement harder.

Acknowledgements: Data are obtained with the NASA/ESA Hubble Space Telescope, operated by AURA for NASA.

ABSTRACTIn a reprise of the famous 1919 solar eclipse experiment that confirmed Einstein’s general theory of relativity, the nearby white dwarf (WD) Stein 2051B passed very close to a 18th magnitude background star in March 2014, with an impact parameter of ~0.1 arcsec. As Stein 2051 B passed by, the background star’s position was deflected. Since the background star is fainter than the WD by a factor of 400, it was a challenge to measure the astrometric deflection. But thanks to the high angular resolution and stable image quality of HST, we were able to measure the deflection at multiple epochs. The gravitational deflection depends only on the distances and relative positions of the stars, and on the mass of the WD. Since the parallax distance and the positions of the WD could be determined precisely from the HST observations, the astrometric measurement offers a unique and direct method to measure the mass of the WD. The resulting mass of Stein 2051 B —the sixth nearest white dwarf to the Sun—is 0.675±0.051 solar masses. One key astrophysical prediction for WDs is the existence of a mass-radius relation (MRR). Since the radius of Stein 2051B is known from its distance, luminosity, and effectivetemperature, our mass measurement provides an important addition to the small number of WDs with well-determined radii and masses. Our measured mass is in excellent agreement with the MRR, and lends support to white dwarf evolutionary theory. Measurements of Deflection

Summary• Stein 2051B passed very close to a 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 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 mass of Stein 2051 B, as measured from its relativistic deflections, is 0.675±0.051 solar mass.

• This provides a stringent confirmation of the mass-radius relation for white dwarfs.

• The results are in excellent agreement with the physics of electron-degenerate matter.

Source

B A

POSS2-Red (1992) POSS2-IR (1995)

Mass measurement through astrometric microlensing

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. Within our Galaxy, no deflection caused by a star outside the solar system had been observed until now.

The astrometric shift: δ= ϴE2/Δϴ

Where Δϴ is the ang. separation between lens and sourceThus δ is a direct measure of ϴEϴE = RE/DL=[(4GM/C2) DLS/(DL DS)]0.5

~ [(4GM/C2) /DL]0.5 (for nearby lenses)

•Astrometric shift, combined with the distance, provides a direct measure of the mass of the lens. • For Stein 2051B, ϴE ~ 25 mas. Expected deflection >2 mas which should be measurable, but the presence of the much brighter WD makes this measurement challenging.

HST ObservationsObservations were taken at 8 epochs as shown below.

Mass of Stein 2051B and ImplicationsMost stars end their lives as WDs—as will the Sun—and then slowly cool. Composed of degenerate matter, WDs are expected to obey a mass-radius relation (MRR). However, the number of WDs whose masses and radii have been directly measured with sufficient precision to test theoretical MRRs is very small. Our measurement provides an additional data point, and is in excellent agreement with the theoretical MRR. Our measured mass for Stein 2051 B is consistent with the CO core expected from normal stellar evolution.

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HST image showing the close passage of the nearby white dwarf Stein 2051 B in front of a distant source star. The path of Stein 2051 B across the field due to its proper motion combined with its parallax motion, is shown by the wavy cyan line. The small blue squares mark the position of Stein 2051 B at each of our eight observing epochs. Its proper motion in one year is shown by an arrow. The source is also labeled.

Schematic view of relativistic deflection by the white dwarf.

Hubble Space Telescope measurements of the background star’s positions at various epochs.

Measured and model undeflected RA and Dec positions of the background source as a function of time. Our model fit, with an Einstein ring radius of 31.53 mas, is shown as a solid purple curve.

Determination of the mass of Stein 2051B• We measured the parallax and the radius of the angular Einstein radius using the

HST observations. Using these measurements, we estimate the mass of Stein 2051B to be 0.675±0.051 solar masses.

This figure shows the Mass-radius diagram for Stein 2051 B and three nearby white dwarfs in visual binaries. Data points with error bars show the masses and radii for Stein 2051 B (this paper; black), 40 Eridani B (dark brown, Sirius B (blue), and Procyon B (orange). The black curve plots a theoretical mass-radius relation for carbon-oxygen core white dwarfs with the parameters of Stein 2051 B. The blue curve shows the relation for thick hydrogen-layer CO white dwarfs with the effective temperature of Sirius B, and the dark brown curves plot the relations for thick and thin hydrogen-layer CO white dwarfs with the temperature of 40 Eri B. The green curve shows the theoretical relation for zero-temperature white dwarfs with iron cores. The mass of Stein 2051 B inferred from the astrometric microlensing, 0.675±0.051 M⊙, is consistent with the CO core expected from normal stellar evolution.

Theoretical WD cooling tracks. Cooling tracks are shown for four masses (solid lines), along with isochrones showing the WD cooling ages (dashed lines). The position of Stein 2051 B agrees within the uncertainties with that expected for our measured mass.

Stein 2051B and Importance of Its Mass Determination•Stein 2051B is the 6th nearest WD (D=5.58 pc), and the nearest of the DC type.•Proper motion 2.37 arcsec/yr. •Stein 2051B (V=13) is the faint companion of Stein 2051A, which is a V=11.08 dM4 star, ∼ 7 sec away. •Existence of a WD mass-radius relation (MRR) is a key prediction based on the physics on electron- degenerate matter; however, this lacks firm observational support. Mass determination is essential to test the MRR. •Until now, only ~3 mass measurements are available, all in binaries and from the orbital motions. •Stein 2051B is a binary, but the companion is >55 AU away, so the binary is unlikely to have affected the evolution. •Stein 2051B’s model-independent mass determination through microlensing can provide a crucial test for the MRR.