Lone white dwarf star's mass measured - using gravitational lensing

[lpetrich]

For the First Time Hubble Directly Measures Mass of a Lone White Dwarf | NASA
noting
First semi-empirical test of the white dwarf mass–radius relationship using a single white dwarf via astrometric microlensing | Monthly Notices of the Royal Astronomical Society | Oxford Academic

In November 2019, the nearby single, isolated DQ-type white dwarf LAWD 37 (WD 1142-645) aligned closely with a distant background source and caused an astrometric microlensing event. Leveraging astrometry from Gaia and followup data from the Hubble Space Telescope, we measure the astrometric deflection of the background source and obtain a gravitational mass for LAWD 37.

White dwarf LAWD 37 passed in front of another star, doing gravitational lensing on that star's light. That lensing was difficult to observe, because it was very close in line of sight to LAWD 37, close enough to be obscured by that WD's light.

The selection of a star to observe for lensing was made possible by the GAIA satellite, from its doing very high-precision astrometry on a very large number of stars.

They find a mass of 0.56 +- 0.08 solar masses, stating

This mass is in agreement with the theoretical mass–radius relationship and cooling tracks expected for CO core white dwarfs. Furthermore, the mass is consistent with no or trace amounts of hydrogen that is expected for objects with helium-rich atmospheres like LAWD 37.

Back to the NASA article.

Kailash Sahu of the Space Telescope Science Institute in Baltimore, Maryland, the principal Hubble investigator on this latest observation, first used microlensing in 2017 to measure the mass of another white dwarf, Stein 2051 B. But that dwarf is in a widely separated binary system. "Our latest observation provides a new benchmark because LAWD 37 is all by itself," Sahu said.

The collapsed remains of a star that burned out 1 billion years ago, LAWD 37 has been extensively studied because it is only 15 light-years away in the constellation Musca. "Because this white dwarf is relatively close to us, we’ve got lots of data on it – we've got information about its spectrum of light, but the missing piece of the puzzle has been a measurement of its mass," said McGill.

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Hubble Astronomers Develop a New Use for a Century-Old Relativity Experiment to Measure a White Dwarf's Mass

 

[Loren Pechtel]

Wow! I wouldn't have thought they could measure the radius well enough to do this.

That being said--racist! Where are the black dwarfs???

 

[bilby]

Where are the black dwarfs?

Inside their Schwarzschild radii.

 

[lpetrich]

A black dwarf is a white dwarf that has cooled down enough to not be luminous in visible light.

This white dwarf is  LP 145-141 with a radius of about 7000 km, a bit bigger than the Earth.

Its luminosity is 0.0005 times that of the Sun and its temperature 8500 K, a little bit hotter than the Sun. Its estimated white-dwarf age is 1.44 Gyr.

Updated Evolutionary Sequences for Hydrogen-deficient White Dwarfs - IOPscience

From that paper's calculations, a white dwarf's luminosity declines exponentially, by a factor of 10 for each 3.6 billion years for this star. This is because most of the interior heat is in extreme ultrasound, as it is in condensed nonmetals and in condensed metals that are not too cold, the  Debye model. That gives interior heat energy ~ T⁴ for temperature T. But it is radiated outward in accordance that law (Stefan-Boltzmann), so one solves d(T⁴)/dt = - (constant)*T⁴, giving an exponential decline.

To get the lowest temperature where it can be observed to glow in visible light, I used the  Draper point - 798 K. From LAWD 37's present temperature, that's a decline of nearly 13,000 in luminosity, requiring a time of 15 billion years.

So 15 billion years from now, LAWD 37 will become a black dwarf.

I've also found NEW COOLING SEQUENCES FOR OLD WHITE DWARFS - IOPscience

 

[Jarhyn]

A black dwarf is a white dwarf that has cooled down enough to not be luminous in visible light.

This white dwarf is  LP 145-141 with a radius of about 7000 km, a bit bigger than the Earth.

Its luminosity is 0.0005 times that of the Sun and its temperature 8500 K, a little bit hotter than the Sun. Its estimated white-dwarf age is 1.44 Gyr.

Updated Evolutionary Sequences for Hydrogen-deficient White Dwarfs - IOPscience

From that paper's calculations, a white dwarf's luminosity declines exponentially, by a factor of 10 for each 3.6 billion years for this star. This is because most of the interior heat is in extreme ultrasound, as it is in condensed nonmetals and in condensed metals that are not too cold, the  Debye model. That gives interior heat energy ~ T⁴ for temperature T. But it is radiated outward in accordance that law (Stefan-Boltzmann), so one solves d(T⁴)/dt = - (constant)*T⁴, giving an exponential decline.

To get the lowest temperature where it can be observed to glow in visible light, I used the  Draper point - 798 K. From LAWD 37's present temperature, that's a decline of nearly 13,000 in luminosity, requiring a time of 15 billion years.

So 15 billion years from now, LAWD 37 will become a black dwarf.

I've also found NEW COOLING SEQUENCES FOR OLD WHITE DWARFS - IOPscience

In other words the black dwarves are invisible due to systemic factors keeping their energy hidden.

This is mostly a joke. Please interpret it that way.

 

[Loren Pechtel]

To get the lowest temperature where it can be observed to glow in visible light, I used the  Draper point - 798 K. From LAWD 37's present temperature, that's a decline of nearly 13,000 in luminosity, requiring a time of 15 billion years.

So 15 billion years from now, LAWD 37 will become a black dwarf.

I've also found NEW COOLING SEQUENCES FOR OLD WHITE DWARFS - IOPscience

Yeah, I knew the real answer. There's just so many stupid claims of racism that I decided to poke some fun at it.

 

[Loren Pechtel]

Where are the black dwarfs?

Inside their Schwarzschild radii.

Those are black holes, not black dwarfs. Black dwarfs take longer to form than there has been time.

 

[bilby]

Where are the black dwarfs?

Inside their Schwarzschild radii.

Those are black holes, not black dwarfs. Black dwarfs take longer to form than there has been time.

Meh. They are both smaller, and blacker; And they actually exist right now.

Anyway, a joke response to a joke question doesn't need to be exactly technically correct, it just needs to be funnier than the question to which it is responding. Check, and mate.

 

[lpetrich]

 Sirius and  Procyon - two nearby stars with white-dwarf companions. Sirius B was the first WD ever discovered.

White Dwarf	Mass	Radius	Lum	Temp	Atmo	Grav	Age
LAWD 37	0.56 Ms	0.01 Rs	0.0005 Ls	8.500 K	H-poor	1.5*106 m/s^2	1.44 Gyr
Sirius B	1.018 Ms	0.0084 Rs	0.056 Ls	25,000 K	H-rich	4.0*105 m/s^2	228 Myr
Procyon B	0.602 Ms	0.01234 Rs	0.00049 Ls	7,740 K	H-poor	1.1*106 m/s^2	1.37 Gyr

Earth surface gravity: 9.81 m/s^2, Sun: 274 m/s^2.

Let's now try to estimate how high the highest mountain would be on a solidified white dwarf.

Pressure at base due to gravity ~ (density) * (acceleration of gravity) * (height)

 List of tallest mountains in the Solar System - the champions in (gravity) * (height) are Mauna Kea and Mauna Loa at 1.00*10⁵ (m/s)^2, Haleakala at 8.9*10⁴ (m/s)^2, and Olympus Mons on Mars at 8.1*10⁴ (m/s)^2.

That makes the tallest possible mountain of ordinary material on a white dwarf something like 10 centimeters high.

 

[Shadowy Man]

Where are the black dwarfs?

Inside their Schwarzschild radii.

Those are black holes, not black dwarfs. Black dwarfs take longer to form than there has been time.

“Black dwarf” is a phrase I have never heard a professional astronomer utter.

 

[bilby]

Where are the black dwarfs?

Inside their Schwarzschild radii.

Those are black holes, not black dwarfs. Black dwarfs take longer to form than there has been time.

“Black dwarf” is a phrase I have never heard a professional astronomer utter.

...nineteenth century carnival barkers, though...

 

[thebeave]

Wow! I wouldn't have thought they could measure the radius well enough to do this.

That being said--racist! Where are the black dwarfs???

Here they are. And they have a message for you regarding your racist "joke":

Spoiler: Black Dwarfs

 

[lpetrich]

Besides extreme ultrasound (lattice vibrations), white dwarfs have an additional reservoir of thermal energy: electron excitation. This is from nearly all of their bulk being "degenerate matter", essentially a high-pressure metallic state. Metal atoms' outermost electrons are not bound to individual ones or small sets of them, but instead wander freely, as a "Fermi liquid". This wandering makes metals electrical conductors, strong thermal conductors, and good reflectors of light. It also means that there is no "band gap" of disallowed energies for excited electrons just above their ground-state maximum energy, unlike for nonmetals. That means that electrons can be excited even at low energies, also unlike for nonmetals.

E. S. R. Gopal (auth.) - Specific Heats at Low Temperatures-Springer US (1966).pdf

At low temperatures, lattice energy (that ultrasound) goes at T⁴ from quantization of lattice vibrations as "phonons", quantized sound waves. Yes, quantum mechanics works for sound also. At high temperatures, it goes as T, the "Dulong-Petit law", from the lattice vibrations' wavelengths being at most twice the separation of atoms. One can find this result by modeling each atom as a separate oscillator. The transition temperatures for most zero-pressure materials are near room temperature or below it, but there are exceptions, like diamond.  Debye model - lists some "Debye temperatures", roughly that transition temperature. Also Debye Model For Specific Heat - Engineering LibreTexts and Debye Theory of Specific Heat[/url

From [url=https://www.astro.umontreal.ca/~bergeron/CoolingModels/FBB_2001.pdf]The Potential of White Dwarf Cosmochronology and An overview of white dwarf stars -- for a 0.6 solar-mass DA white dwarf with a surface temperature of 7,500 K, its central temperature is about 1000 times greater, or 7.5 million K, and its central density 4*10⁶ g/cm^3. I've also found The age and colors of massive white dwarf stars - aa6059-06.pdf

For degenerate matter, the Debye temperature varies roughly as (density)^2/3, and scaling upward from 1000 K gives roughly 10⁷ K for a 0.6-solar-mass white-dwarf center.

 

[lpetrich]

 Fermi liquid theory and  Fermi gas and  Fermi energy and Fermi Energies, Solid Properties and  Degenerate matter

Lattice vibration: heat = T⁴/Td³ - Td is the Debye temperature

Electron excitation: heat = T²/Tf - Tf is the Fermi temperature, from the Fermi energy (energy of electrons at the top of ground-state energy levels)

Typical Fermi energies for metals translate into a temperature of 10⁵ K, and for white-dwarf center densities, 10⁹ K.

So lattice vibrations dominate for most white dwarfs, but when their surfaces get down to the Draper point, their interior temperatures go down to 1 million K or less, and electron excitation starts to dominate. So my previous calculation was approximately correct. Let's look at what happens afterward.

In general: for a heat capacity approximately T⁴ + Te²*T² and with radiative cooling rate r*T⁴ (Stefan-Boltzmann), the numbers work out to be:

T ~ T0 * exp(-(r/4)*t) for high temperatures,
T ~ Te / sqrt(r*t)

t ~ (4/r)*log(T0/T)
t ~ (1/r)*(Te/T)²

For r ~ 1/(0.9 billion years) and Te ~ 1000 K (lattice-electronic transition temperature scaled to surface temperature)

For the surface cooling down to 300 K, it's an additional 10 billion years, and down to 3 K, it's 100 trillion years.

 

[Loren Pechtel]

 Sirius and  Procyon - two nearby stars with white-dwarf companions. Sirius B was the first WD ever discovered.

White Dwarf	Mass	Radius	Lum	Temp	Atmo	Grav	Age
LAWD 37	0.56 Ms	0.01 Rs	0.0005 Ls	8.500 K	H-poor	1.5*106 m/s^2	1.44 Gyr
Sirius B	1.018 Ms	0.0084 Rs	0.056 Ls	25,000 K	H-rich	4.0*105 m/s^2	228 Myr
Procyon B	0.602 Ms	0.01234 Rs	0.00049 Ls	7,740 K	H-poor	1.1*106 m/s^2	1.37 Gyr

Earth surface gravity: 9.81 m/s^2, Sun: 274 m/s^2.

Let's now try to estimate how high the highest mountain would be on a solidified white dwarf.

Pressure at base due to gravity ~ (density) * (acceleration of gravity) * (height)

 List of tallest mountains in the Solar System - the champions in (gravity) * (height) are Mauna Kea and Mauna Loa at 1.00*10⁵ (m/s)^2, Haleakala at 8.9*10⁴ (m/s)^2, and Olympus Mons on Mars at 8.1*10⁴ (m/s)^2.

That makes the tallest possible mountain of ordinary material on a white dwarf something like 10 centimeters high.

But do they have any form of plate tectonics to build mountains? Infalling matter should be pretty erosive (impact velocity will be in megameters/second), I would think they would be polished flat.

 

[lpetrich]

But do they have any form of plate tectonics to build mountains? Infalling matter should be pretty erosive (impact velocity will be in megameters/second), I would think they would be polished flat.

I didn't address the question of the geology of white dwarfs that have cooled enough to have solid crusts. I was considering this as something purely hypothetical. Also, my examples are all volcanoes, and volcanoes likely produced by mantle plumes.

Celestial objects known to have had geological activity:

Mercury, Venus, (*Earth*, Moon), Mars, Vesta, (Jupiter's moons, *Io*, Europa, Ganymede), (Saturn's moons *Enceladus*, Titan), (Uranus's moon Miranda), (Neptune's moon *Triton*), Pluto?

The * * means present-day volcanism or similar geological activity.

 

[lpetrich]

So a mountain's height on a white dwarf would at most be about 10 cm. Turning to biological entities,  List of tallest trees notes that the tallest known tree has a height of about 116 meters. That scales down to 1 millimeter on a white dwarf. So the highest that anything can grow is moss-sized.

Turning to condensed material, in the ocean, pressure increased by 1 bar (~ 1 atmosphere) every 10 meters. On a white dwarf, it would be 10^-4 meters, 0.1 mm. For 1 megabar, around when metallic transitions start, that's 100 meters.

 

[lpetrich]

Metallic transitions are transitions to metallic states. Metallic hydrogen is the most-discussed metallic state of a zero-pressure nonmetal, and I've found Everything you always wanted to know about metallic hydrogen but were afraid to ask: Matter and Radiation at Extremes: Vol 5, No 3

It is clear that we are tantalizingly close to reaching the solid metallic state of hydrogen, but the reproducibility of results will require high-pressure techniques to develop to the point where we can convincingly reach pressures above 400 GPa, while still allowing a suite of diagnostics. Only when we have conclusively reached the solid metallic state of hydrogen can Ginzburg’s third “especially important and interesting” problem in physics be struck off the list.

Referring to Vitaly Ginzburg's list of important and interesting problems: ginzburg.pdf (1999), in turn referring to his original list in Physics and Astrophysics: A Selection of Key Problems: Ginzburg, V. L.: 9780080264998: Amazon.com: Books (translated: 1985)

Wikipedia's  Metallic hydrogen gives an impression of being almost there about that phase.

 Metallization pressure - has references for nearly every nonmetallic element. I'll be going into detail in my next post.

 

[lpetrich]

 Metallization pressure

• Hydrogen: lists a metallization pressure of 3.9 megabars (MBar), at the borderline of experimental accessibility.
• Boron group: boron: 1.6 MBar (observed)
• Carbon group: carbon: 11 MBar (calculated), silicon: 0.12 MBar (observed), germanium: 0.12 MBar (observed)
• Nitrogen group (pnictongens): nitrogen: 20 MBar (calculated), phosphorus: 0.042 MBar (observed), arsenic: 0.022 MBar (calculated)
• Oxygen group (chalcogens): oxygen: 1.2 MBar (observed), sulfur: 0.83 (observed), selenium: 0.23 MBar (observed), tellurium: 0.04 MBar (calculated)
• Halogens: fluorine: 25 MBar (calculated), chlorine: 2.0 MBar (observed), bromine: 0.25 MBar (observed), iodine: 0.16 MBar (observed)
• Noble gases: helium: 329 MBar (calculated), neon: 2084 MBar (calculated), argon: 5.1 MBar (calculated), krypton: 3.1 MBar (calculated), xenon: 1.3 MBar (observed), radon: ?

References:

• Boron group: Pressure-induced metallization in solid boron - NASA/ADS
• Carbon group: Carbon under extreme conditions: Phase boundaries and electronic properties from first-principles theory - PMC and Pressure induced phase transitions in silicon, germanium and some IIIV compounds - ScienceDirect and Crystal data for high-pressure phases of silicon - NASA/ADS and Phase transition studies of germanium to 1.25 Mbar - NASA/ADS
• Nitrogen group: Phys. Rev. Lett. 111, 175502 (2013) - Stable All-Nitrogen Metallic Salt at Terapascal Pressures and Electrical Investigation of Phase Transition in Black Phosphorus under High Pressure - IOPscience and Pressure-induced metallization of black arsenic - NASA/ADS
• Oxygen group: Phys. Rev. Lett. 86, 3108 (2001) - High Pressure Insulator-Metal Transition in Molecular Fluid Oxygen and Phys. Rev. B 48, 6862 (1993) - Pressure-induced structural phase transition in sulfur at 83 GPa and Structural studies of pressure-induced phase transitions in selenium up to 150 GPa - NASA/ADS and High-pressure phases of crystalline tellurium: A combined Raman and ab initio study - NASA/ADS
• Halogens: Prediction of chlorine and fluorine crystal structures at high pressure using symmetry driven structure search with geometric constraints: The Journal of Chemical Physics: Vol 153, No 9 and Band gap closure, incommensurability and molecular dissociation of dense chlorine - PMC and Bromine metallization studied by X-ray absorption spectroscopy - NASA/ADS and Metallization and structural transformation of iodine under pressure: A microscopic view - NASA/ADS
• Noble gases: Electron-Phonon Coupling and the Metallization of Solid Helium at Terapascal Pressures - NASA/ADS and Metallization and positive pressure dependency of bandgap in solid neon: The Journal of Chemical Physics: Vol 150, No 11 and First-principles study of solid Ar and Kr under high compression - NASA/ADS and Equation of state and metallization in compressed solid krypton - NASA/ADS and Electrical Conductivity of Xenon at Megabar Pressures - NASA/ADS

 

[lpetrich]

 Degenerate matter
Metals are metals because their atoms' outermost electrons form a sort of electron fluid, a "Fermi liquid", that surrounds the rest of those atoms, their ion cores. That makes metals semi-degenerate. Nonmetals are non-degenerate, of course. More and more pressure causes more of their electrons to join that electron fluid, until all that is left of the ion cores is the nuclei. Thus making complete degeneracy. Metallic hydrogen is completely degenerate, since hydrogen atoms have only one electron each.

White dwarfs often have strong magnetic fields, like 10⁶ gauss (100 tesla), stronger than any lab magnetic field. The Mystery of White Dwarfs With Intense Magnetic Fields Could Finally Be Solved : ScienceAlert - likely due to a dynamo effect, what makes magnetic fields of planets and big moons.


As white dwarfs cool, their interiors freeze and crystallize, making them last longer than what one would otherwise expect.

GAIA Reveals For the First Time Crystallization in White Dwarfs

The cooling of white dwarfs lasts billions of years. Once they reach a certain temperature, the originally hot matter inside the star’s core starts crystallizing, becoming solid. The process is similar to liquid water turning into ice on Earth at zero degrees Celsius, except that the temperature at which this solidification happens in white dwarfs is extremely high – about 10 million degrees Celsius.

...
The heat released during this crystallization process, which lasts several billion years, seemingly slows down the evolution of the white dwarfs: the dead stars stop dimming and, as a result, appear up to two billion years younger than they actually are. That, in turn, has an impact on our understanding of the stellar groupings these white dwarfs are a part of.

...
Not all white dwarfs crystallize at the same pace. More massive stars cool down more rapidly and will reach the temperature at which crystallization happens in about one billion years. White dwarfs with lower masses, closer to the expected end-stage of the Sun, cool in a slower fashion, requiring up to six billion years to turn into dead solid spheres.

The Sun still has about five billion years before it becomes a white dwarf, and the astronomers estimate that it will take another five billion years after that to eventually cool down to a crystal sphere.

noting
Core crystallization and pile-up in the cooling sequence of evolving white dwarfs | Nature