STScI: Hubble Measures White Dwarf's Mass with Relativity Experiment

[bystander]

Hubble Astronomers Develop a New Use for a Century-Old
Relativity Experiment to Measure a White Dwarf’s Mass
NASA | GSFC | STScI | HubbleSite | 2017 Jun 07

[c][attachment=0]STScI-H-p1725a.jpg[/attachment][/c][hr][/hr]

Astronomers have used the sharp vision of NASA’s Hubble Space Telescope to repeat a century-old test of Einstein’s general theory of relativity. The Hubble team measured the mass of a white dwarf, the burned-out remnant of a normal star, by seeing how much it deflects the light from a background star.

This observation represents the first time Hubble has witnessed this type of effect created by a star. The data provide a solid estimate of the white dwarf’s mass and yield insights into theories of the structure and composition of the burned-out star.

First proposed in 1915, Einstein’s general relativity theory describes how massive objects warp space, which we feel as gravity. The theory was experimentally verified four years later when a team led by British astronomer Sir Arthur Eddington measured how much the sun’s gravity deflected the image of a background star as its light grazed the sun during a solar eclipse, an effect called gravitational microlensing.

Astronomers can use this effect to see magnified images of distant galaxies or, at closer range, to measure tiny shifts in a star’s apparent position on the sky. Researchers had to wait a century, however, to build telescopes powerful enough to detect this gravitational warping phenomenon caused by a star outside our solar system. The amount of deflection is so small only the sharpness of Hubble could measure it. ...

Relativistic deflection of background starlight measures the mass of a nearby white dwarf star - Kailash C. Sahu et al

• Science (online 07 Jun 2017) DOI: 10.1126/science.aal2879

New Confirmation of Einstein's General Theory of Relativity
Embry-Riddle Aeronautical University | 2017 Jun 07

A Centennial Gift from Einstein
Science Magazine | 2017 Jun 07

[neufer]

<<Stein 2051 (Gliese 169.1, G 175-034, LHS 26/27) is a nearby binary star system, containing a red dwarf (component A) and a degenerate star (white dwarf) (component B), located in constellation Camelopardalis at about 18.2 ly (5.6 pc) from Earth. The brighter of this two stars is A (a red dwarf), but the more massive is component B (a white dwarf). Stein 2051 is the nearest (red dwarf + white dwarf) separate binary system (40 Eridani BC is located closer (at 16.26 light-years), but it is a part of a triple star system). Stein 2051 B is the 6th nearest white dwarf after Sirius B, Procyon B, van Maanen's star, LP 145-141 and 40 Eridani B.>>

[b][color=#0000FF]Radius–mass relations for a model white dwarf. M[sub]limit[/sub] is denoted as M[sub]Ch[/sub] Stein 2051 B has a measured mass 0.675 ± 0.051 M[sub]☉[/sub][/color][/b]

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<<As we add mass to a white dwarf, its radius will decrease, so, by the uncertainty principle, the momentum, and hence the velocity, of its electrons will increase. As this velocity approaches c, the extreme relativistic analysis becomes more exact, meaning that the mass M of the white dwarf must approach a limiting mass of M_limit. Therefore, no white dwarf can be heavier than the limiting mass M_limit, or 1.4 M_☉.

For a more accurate computation of the mass-radius relationship and limiting mass of a white dwarf, one must compute the equation of state which describes the relationship between density and pressure in the white dwarf material. If the density and pressure are both set equal to functions of the radius from the center of the star, the system of equations consisting of the hydrostatic equation together with the equation of state can then be solved to find the structure of the white dwarf at equilibrium. In the non-relativistic case, we will still find that the radius is inversely proportional to the cube root of the mass. Relativistic corrections will alter the result so that the radius becomes zero at a finite value of the mass. This is the limiting value of the mass—called the Chandrasekhar limit—at which the white dwarf can no longer be supported by electron degeneracy pressure. The graph on the right shows the result of such a computation. It shows how radius varies with mass for non-relativistic (blue curve) and relativistic (green curve) models of a white dwarf. Both models treat the white dwarf as a cold Fermi gas in hydrostatic equilibrium. The average molecular weight per electron, μ_e, has been set equal to 2. Radius is measured in standard solar radii and mass in standard solar masses.

These computations all assume that the white dwarf is non-rotating. If the white dwarf is rotating, the equation of hydrostatic equilibrium must be modified to take into account the centrifugal pseudo-force arising from working in a rotating frame. For a uniformly rotating white dwarf, the limiting mass increases only slightly. If the star is allowed to rotate nonuniformly, and viscosity is neglected, then, as was pointed out by Fred Hoyle in 1947, there is no limit to the mass for which it is possible for a model white dwarf to be in static equilibrium. Not all of these model stars will be dynamically stable.>>

[Ann]

The maximum mass of a white dwarf is 1.4 M_☉.

www.nasa.gov wrote:

Using the deflection measurement, the Hubble astronomers calculated that the white dwarf’s mass is roughly 68 percent of the sun’s mass.

I believe that a mass of 0.68 M_☉ makes Stein 2051B relatively massive. My guess is that the Sun will lose about half its mass on its way to becoming a white dwarf, creating a ~0.5 M_☉ white dwarf. I would think that the relatively high mass of Stein 2051B means that the progenitor star was considerably more massive than the Sun, perhaps some 3 times more massive.

I have read somewhere - and don't ask me where - that most neutron stars contain a mass of 1.4 M_☉. So a star of, say, 30 M_☉, may create a 1.4 M_☉ neutron star. (Okay, I may be wrong here - maybe a star as massive as 30 M_☉ will turn into a neutron star more massive than 1.4 M_☉. Unless such a massive star turns into a black hole, of course.)

The most famous pulsar (pulsating neutron star) is probably the central star of the Crab Nebula.

Wikipedia wrote:
Theoretical models of supernova explosions suggest that the star that exploded to produce the Crab Nebula must have had a mass of between 9 and 11 M_☉.
...
Estimates of the mass of the nebula are made by measuring the total amount of light emitted, and calculating the mass required, given the measured temperature and density of the nebula. Estimates range from about 1–5 M_☉, with 2–3 M_☉ being the generally accepted value. The neutron star mass is estimated to be between 1.4 and 2 M_☉.

The predominant theory to account for the missing mass of the Crab Nebula is that a substantial proportion of the mass of the progenitor was carried away before the supernova explosion in a fast stellar wind, a phenomenon commonly seen in Wolf-Rayet stars. However, this would have created a shell around the nebula. Although attempts have been made at several wavelengths to observe a shell, none has yet been found.

Ann

[neufer]

I believe that a mass of 0.68 M_☉ makes Stein 2051B relatively massive. My guess is that the Sun will lose about half its mass on its way to becoming a white dwarf, creating a ~0.5 M_☉ white dwarf. I would think that the relatively high mass of Stein 2051B means that the progenitor star was considerably more massive than the Sun, perhaps some 3 times more massive.

Astronomers watch as a star’s gravity bends light from another star
Phil Plait, Wed, Jun 07, 2017

Previous measurements had the mass of the white dwarf [Stein 2051B] at [~0.5 M_☉], and that was causing all sorts of problems with theories of how these critters form. If the mass was that low, it would have had to have some weird core of iron to be as small as calculations indicated it being. However, the new, higher mass means everything is in order, and the theories governing white dwarf structure are right on the money as well.

I have read somewhere - and don't ask me where - that most neutron stars contain a mass of 1.4 M_☉. So a star of, say, 30 M_☉, may create a 1.4 M_☉ white dwarf. (Okay, I may be wrong here - maybe a star as massive as 30 M_☉ will turn into a neutron star more massive than 1.4 M_☉. Unless such a massive star turns into a black hole, of course.)

<<When a slowly-rotating carbon-oxygen white dwarf accretes matter from a companion, it can exceed the Chandrasekhar limit of about 1.44 M_☉, beyond which it can no longer support its weight with electron degeneracy pressure. In the absence of a countervailing process, the white dwarf would collapse to form a [~1.44 M_☉] neutron star, in an accretion-induced non-ejective process, as normally occurs in the case of a white dwarf that is primarily composed of magnesium, neon, and oxygen. The current view among astronomers who model Type Ia supernova explosions, however, is that this limit is never actually attained and collapse is never initiated.>>

<<A neutron star has a mass of at least 1.1 and perhaps up to 3 M_☉. The maximum observed mass of neutron stars is about 2.01 M_☉. But in general, compact stars of less than 1.39 M_☉ (the Chandrasekhar limit) are white dwarfs, whereas compact stars with a mass between 1.4 M_☉ and 3 M_☉ (the Tolman–Oppenheimer–Volkoff limit) should be neutron stars (though there is an interval of a few tenths of a solar mass where the masses of low-mass neutron stars and high-mass white dwarfs can overlap). Between 3 M_☉ and 5 M_☉, hypothetical intermediate-mass stars such as quark stars and electroweak stars have been proposed, but none have been shown to exist. Beyond 10 M_☉ the stellar remnant will overcome the neutron degeneracy pressure and gravitational collapse will usually occur to produce a black hole, though the smallest observed mass of a stellar black hole is about 5 M_☉.

The temperature inside a newly formed neutron star is from around 10¹¹ to 10¹² kelvin. However, the huge number of neutrinos it emits carry away so much energy that the temperature of an isolated neutron star falls within a few years to around 10⁶ kelvin. At this lower temperature, most of the light generated by a neutron star is in X-rays.>>