Oliver Thewalt

    Oliver Thewalt

    Theoretical Physics | Quantum Biology | Dark Matter Research | Energy Consulting | Creation of Hydrogen ATOM in the Higgs Field >> Vote for Nobel Prize

    Relativistic deflection of background starlight measures the mass of a nearby white dwarf star

      Oliver Thewalt
      By Oliver Thewalt
      http://science.sciencemag.org/content/early/2017/06/06/science.aal2879.full

      Relativistic deflection of background starlight measures the mass of a nearby white dwarf star

      Abstract
      Gravitational deflection of starlight around the Sun during the 1919 total solar eclipse provided measurements that confirmed Einstein’s general theory of relativity. We have used the Hubble Space Telescope to measure the analogous process of astrometric microlensing caused by a nearby star, the white dwarf Stein 2051 B. As Stein 2051 B passed closely in front of a background star, the background star’s position was deflected. Measurement of this deflection at multiple epochs allowed us to determine the mass of Stein 2051 B —the sixth-nearest white dwarf to the Sun—as 0.675 ± 0.051 solar masses. This mass determination provides confirmation of the physics of degenerate matter and lends support to white dwarf evolutionary theory.

      One of the key predictions of general relativity set forth by Einstein was that the curvature of space near a massive body causes a ray of light passing near it to be deflected by twice the amount expected from classical Newtonian gravity. The subsequent experimental verification of this effect during the 1919 total solar eclipse (2, 3) confirmed Einstein’s theory, which was declared “one of the greatest—perhaps the greatest—of achievements in the history of human thought” .

      In a paper in this journal 80 years ago, Einstein extended the concept to show that the curvature of space near massive objects allows them to act like lenses, with the possibility of substantially increasing the apparent brightness of a background star. Despite Einstein’s pessimistic view that “there is no hope of observing this phenomenon directly” , the prospect of detecting dark matter through this effect, now known as microlensing, revived interest in this subject. Coupled with improvements in instrumentation, this led to the detection of large numbers of microlensing brightening events in the Galactic bulge, the Magellanic Clouds, and the Andromeda Galaxy. Monitoring of these events has led to the discovery of several extrasolar planets. Other forms of gravitational lensing by intervening massive galaxies and dark matter produce multiple or distorted images of background galaxies.

      Within the Milky Way, all microlensing encounters discovered so far have been brightening events. No shift in the apparent position of a background star caused by an intervening massive body has been observed outside the solar system—which is not surprising, because the deflections are tiny. Even for the nearest stars, the angular offset is two to three orders of magnitude smaller than the deflection of 1.75 arcsec measured during the 1919 solar eclipse.

      Relativistic deflections by foreground stars
      When a foreground star (the lens) is perfectly superposed on a background star (the source), the lensed image of the source will form a circle, called the Einstein ring. The angular radius of the Einstein ring is (Image 1), where M is the lens mass and Dr is the reduced distance to the lens, given by 1/Dr = 1/Dl − 1/Ds, Dl and Ds being the distances to the lens and to the source, respectively. For typical cases like the Galactic bulge and Magellanic Clouds brightening events, the radius of the Einstein ring is less than a milliarcsecond (mas). However, for very nearby stellar lenses, it can be as large as tens of mas.

      In the more general case where the lens is not exactly aligned with the source, the source is split into two images, the minor image lying inside and the major image outside the Einstein ring. The major image is always the brighter, with the brightness contrast increasing rapidly as the lens-source separation increases. In practical cases of lensing by stars, the two images either cannot be resolved, or the minor image is too faint to be detected. In both cases, the net effect is an apparent shift in the centroid position of the source. This phenomenon is referred to as astrometric microlensing.

      In cases where the angular separation between the lens and the source is large compared to θE, so that the minor image is well resolved but is too faint and too close to the bright lens to be detected, only the major image can be monitored. In that situation, the change in angular position of the source caused by the deflection of the light rays, δθ, can be expressed as (Image 2) where u = Δθ/θE, and Δθ is the lens-source angular separation. Equations 1 and 2 show that the mass of the lens can be determined by measuring the deflection of the background source’s position at a known angular separation from the lens, provided the reduced distance to the lens is known. Astrometric microlensing thus provides a technique for direct determination of stellar masses, in those favorable cases of a nearby star fortuitously passing closely in front of a distant background source. Unlike classical methods involving binaries, this method can be applied to mass measurements for single stars.

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      http://science.sciencemag.org/content/early/2017/06/06/science.aal2879.full