In 1919 Arthur Eddington traveled to the island of Principe off the coast of West Africa to photograph a total eclipse. Mission was to observe the apparent shift of nearby stars by the Sun’s gravity. His experiment was a success, and it verified Einstein’s gravitational theory of general relativity. Since then, we have observed the gravitational deflection of starlight by the Sun numerous times. We have also seen the deflection of the light from distant galaxies, but we haven’t seen the deflection of distant starlight by another star. The gravitational effect of a single star is extraordinarily small. But recently a team has observed the deflection of starlight by a single white dwarf star.

The white dwarf is known as Stein 2051 B, and it’s been in the middle of a controversy for nearly a century. White dwarfs are formed with a star such as our Sun runs out of the hydrogen necessary to generate heat and pressure through nuclear fusion. The star collapses under its own weight until it reaches a point where the pressure of electrons keeps it from collapsing any further. White dwarfs have the mass of a star, but are about the size of Earth. This small size makes them difficult to study.

In 1930, a 19-year old named Subrahmanyan Chandrasekhar calculated the theoretical structure of white dwarfs. Similar models were developed by Wilhelm Anderson and E. C. Stoner, but Chandrasekhar’s was more accurate, and included the calculation of an upper limit to the mass of white dwarf, now known as the Chandrasekhar limit. His model was highly controversial, and Eddington was one of the biggest opponents of the model. As astronomers found more examples of white dwarfs, it became clear that Chandrasekhar’s model worked. But Stein 2051 B seemed to be an exception. It has a distant companion star that allowed us to get a rough idea of its mass and it seemed that Stein 2051 B had a mass that is much smaller than most white dwarfs. This would imply it has some strange structure such a s a large iron core.

A schematic of the gravitational lensing effect. Credit: Wikipedia

But then in 2014 the white dwarf happened to pass in front of a more distant star, as seen from Earth. This allowed astronomers to observe the effects of gravitational lensing by the white dwarf. Using data from the Hubble Space Telescope, the team analyzed the gravitational deflection of the distant star. Using general relativity, they then calculated the size and mass of the white dwarf. They found it has a mass of 0.675 solar masses, which is larger than previously thought and well within the typical range of a white dwarf. So Stein 2051 B doesn’t have an exotic composition after all.

Arthur Eddington was an extremely prominent astronomer, and his opposition to the young upstart’s model meant it gained little traction early on. But the good thing about science is that in the end the data rules. It is perhaps poetic justice that Chandrasekhar’s model has been vindicated by the very experiment Eddington so famously first used.

Paper: Kailash C. Sahu, et al. Relativistic deflection of background starlight measures the mass of a nearby white dwarf star. Science
DOI: 10.1126/science.aal2879 (2017)

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While large stars end their lives as brilliant supernovae, our Sun will face a much quieter end. As it runs out of usable hydrogen to sustain it, the Sun will expand into a red giant for a time, and then what matter it has remaining will collapse into a white dwarf. And then what?

When a white dwarf forms it is extremely hot. The initial surface temperature of a white dwarf is about a million Kelvin. This makes them extremely bright for their tiny size. But unlike main sequence stars that maintain their heat through nuclear fusion, white dwarfs rely upon electron pressure to keep themselves from collapsing under their own weight. They have no way to generate heat on their own, and so they simply radiate away heat and light, gradually cooling to become a black dwarf.

It’s estimated that it would take a thousand trillion (10¹⁵) years for a white dwarf to become a black dwarf, which is much longer than the mere billions of years our Sun will shine as a main sequence star. This assumes there is no other mechanism to heat a white dwarf. In models of dark matter, dark matter particles would interact with the regular matter of the white dwarf, keeping it warm, perhaps a trillion times longer. Over that time scale, if protons are unstable their decay could extend the cooling time a bit more.

But all that would simply delay the inevitable. As the universe continues to expand and cool, our Sun and other white dwarfs will be among the last beacons of light before fading into the cold and dark.

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Yesterday I talked about the Higgs, and how its discovery has led to a flurry of articles about how it might apply to astrophysics. So today here’s another example, and this one’s interesting because it’s not simply trying to use the Higgs to explain known phenomena, it’s trying to use astronomical observations to understand things about the Higgs. It comes from a paper recently published in the Astrophysical Journal, and concerns the spectra of white dwarf stars.

As you might recall, a white dwarf is the remnant of a solar-mass star that has exhausted its ability to fuse elements in its core. Without a source of heat, the star is compressed by gravity to the point where only the pressure of electrons in atoms can prevent it from collapsing further. When our own Sun eventually dies, it will become a white dwarf roughly the size of Earth. The nice thing about white dwarfs is they usually still have remaining heat from their formation, so they glow brilliant white. This means we can observe the light emitted by them fairly easily. We can even observe the line spectra of white dwarfs, which we can use for things like testing general relativity.

Typically when we talk about emission lines, we mean the ones caused by electrons shifting their position in an atom or molecule, but there are also emission lines due to protons and neutrons in the nucleus of an atom. These latter lines are similar to the usual emission lines, but they are governed by the strong nuclear force rather than the electromagnetic force. Studying nuclear emission lines lets us understand the behavior of nuclear forces.

That’s where white dwarfs come in. The emission spectra of white dwarfs contain both traditional emission lines due to electrons, and nuclear emission lines due to protons and neutrons. The reason this is important is that protons and neutrons are much more massive than electrons, so the Higgs field interacts with them differently. As a result, any shift in the behavior of the Higgs will affect the nuclear line spectra differently than the regular one.

What the authors are interested in is whether the Higgs interacts with strong gravitational fields. That isn’t something that we can currently test in the lab, but it could be seen in the strong gravity of a white dwarf. In analyzing white dwarf spectra, the authors find no evidence of any Higgs-gravity interactions, but they are able to determine an upper limit on the strength of any such interaction.

Mainly this work is a proof of concept. Given combination of high-density mass and strong gravitational fields seen in objects like white dwarfs and neutron stars, Higgs interactions may play a role in their evolution and behavior. It is something we can at least try to look for, and this is a first step in that direction.

Paper: Roberto Onofrio and Gary A. Wegner. Search for Higgs Shifts in White Dwarfs. ApJ 791 125 (2014)

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Determining the age of galaxies and globular clusters can be a bit of a challenge. There are several ways you can get a handle on galactic age. One of these is by looking at the ratio of red dwarf stars to larger stars. Red dwarf stars burn very slowly, so their lifetimes can be 100 billion years or more. Given that the universe is only about 14 billion years old, this means that red dwarfs haven’t had time to die off. Larger stars die off faster, so the higher the proportion of red dwarf stars, the older the galaxy should be.

Of course this assumes that all the stars in a galaxy formed around the same time. While this is generally true for star clusters, and to a lesser degree for globular clusters, it isn’t very accurate for galaxies. In galaxies, the largest stars will go supernova, scattering gas and dust that mix with other stellar remnants to collapse into new stellar nurseries. Thus galaxies can produce new generations of stars from old ones. You can still use the red dwarf count to estimate age, but this method isn’t as accurate with galaxies as it is with globular clusters.

Another method is to look at what is known as the metallicity of the stars in a galaxy. In astrophysics, we generally refer to any element other than hydrogen and helium as “metals”. The reason for this is that the amount hydrogen and helium in the universe dwarfs all the other elements combined, so we can put them in the “other” category. The metallicity of a star is a measure of the fraction of metal (in the astrophysics sense) a star has compared to hydrogen and helium.

Metals can only be produced in the cores of stars, so if a star has a high metallicity it must have been formed from the remnants of earlier stars. Stars with low metallicity have formed mainly from the original hydrogen and helium of the universe. So high metallicity stars are younger than low metallicity ones. In this way you can distinguish the initial stars in a galaxy from subsequent generations of stars. This gives you another handle on the age of a galaxy or globular cluster.

There is a third way to determine the age of a galaxy, known as the white dwarf luminosity function. White dwarfs are the remnants of stars like our Sun. If a star is too small to become a supernova when it dies, it will swell to a red giant, casting of some of its outer material before collapsing to a white dwarf. White dwarfs have three important properties that make them very useful in determining the age of a galaxy.

The first is that white dwarfs are generally about the mass of the Sun. There’s a limit to how massive a white dwarf can be (known as the Chandrasekhar limit), of about 1.4 solar masses. If a stellar remnant has more mass than that it will collapse to a neutron star. If it has much less mass than that of the Sun, then it is likely a red dwarf that hasn’t had time to die off yet.

The second is that white dwarfs also have the same general size (about that of Earth). Their size is determined by the pressure of free electrons pushing against each other (a quantum effect known as electron degeneracy pressure). This means their size doesn’t vary with the star’s temperature.

The third is that they form at a temperature of about a million Kelvin. Since white dwarfs have no way to generate heat within themselves, this means they cool over time by radiating light. The amount of radiant heat they emit depends on its temperature and its size.

So white dwarfs have roughly the same temperature and size when they are formed, and they cool via radiation at a rate that depends on their temperature and size. This means you can determine the age of a white dwarf by measuring its temperature. Since hotter white dwarfs are brighter than cooler ones, you can determine their temperature by observing their brightness (or luminosity). The white dwarf luminosity function of a galaxy is the distribution of the luminosities of the white dwarfs in the galaxy. By looking at this function, you can determine not only the age of the oldest white dwarfs, but also the rate at which white dwarfs have formed.

White dwarfs cool rather slowly. As a result most of them are still relatively bright, so they can be observed fairly easily despite their small size. You can see an image of these white dwarfs in a globular cluster in the figure above. Even though they are not as bright as most of the other stars, their high temperature gives them a distinctive bluish hue that makes them easy to distinguish.

White dwarfs are like cosmic cooling embers. In their dying glow is the evidence of the fires of stellar formation, and their glow tells us just how long ago those fires burned.

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A recurrent nova is a stellar nova that occurs from the same star more than once.  You’re probably more familiar with a supernova, where a star is ripped apart in a cataclysmic explosion.   Novas occur when a white dwarf orbits with another star and captures some of the star’s outer material. This material forms an accretion disk around the white dwarf, which gradually falls to its surface.  When material accumulates on the surface of the white dwarf, it can trigger a nuclear explosion that causes it to brighten similar to a supernova, but not nearly as intense.  Since the explosion doesn’t destroy the star, it is possible for a nova to occur again after more material has accumulated.

The most famous recurrent nova is RS Ophiuchi, which becomes a nova about every 20 years.  Other recurrent nova occur at different rates.  Recurrent nova caused by more massive white dwarfs tend to have shorter repeat times than those with less mass.  This seems to be due to the fact that stars with more gravity can accumulate matter from the companion star more quickly.  Some recurrent nova have irregular repeat times, or have novae with highly varying brightnesses.  This seems to be due to disruptions in the accretion disk when the star explodes.

It is thought that recurrent novas could be a precursor to the white dwarf becoming a supernova.  If the material cast off by the nova is less than the material accumulated each time, then the white dwarf will gradually increase in mass.  Eventually this bring its mass to the Chandrasekhar limit, which is the upper limit for the mass of a white dwarf.  Beyond that point the star will collapse, which can trigger a supernova explosion.

Background: The star as a Nova.
Inset: Hubble image of the star when inactive.

Recently astronomers have discovered a fast recurrent nova in the Andromeda galaxy.  A paper on the nova was recently published in Astronomy and Astrophysics, and presents some of the initial results.  The star, known as M31N 2008-12a has a nova outburst about once a year.  This is extremely rapid, since the next highest frequency rate is about once a decade.  The star also brightens quickly and dims quickly, on the order of a few days.  When observed in x-rays, it was found the star emits x-rays during the nova period for about 10 days.  Since x-rays are generated by nuclear interactions, this indicates that the nuclear interactions on the surface only last about that long.

All of this points to M31N 2008-12a being a very massive white dwarf star.  Since the novae occur so rapidly, it is clear that material from its companion star continues to accrete at a regular basis.  It would seem that this star is on its way to becoming a supernova.  Just how soon that might be is unknown, but it’s worth keeping an eye on.  It could explode at any time.

Of course on a cosmic scale “any time” could be anywhere from tomorrow to thousands of years.

Paper: M. Henze, et al. A remarkable recurrent nova in M 31: The X-ray observations. Astronomy & Astrophysics, 563, L8 (2014)

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Last time I talked about how black holes can exceed a maximum luminosity known as the Eddington limit.  The Eddington limit is the point where a star is so bright that its light pressure balances out the gravitational pressure of the star.  Today I’ll talk about another limit known as the Chandrasekhar limit.  This one puts a limit on how massive a star can be when it dies, and it relies on a bit of quantum mechanics.

When a typical star is in its active lifetime (main sequence), the gravitational weight of its mass is balanced by the heat and pressure generated by fusion in its core.  This is a stable period for a star, and can last for billions of years (or in the case of red dwarfs, trillions).  But eventually a star runs out of hydrogen to fuse, and it can’t sustain the heat and pressure in its core.  With no more fusing core, the old star is basically just a hydrostatic mass. The key difference is that the density is so high it isn’t a regular ball of gas, but rather a gas of plasma. All the ions and free electrons act somewhat like a regular gas, but with one big exception: the electrons and ions obey the Pauli exclusion principle.

In broad terms the Pauli exclusion principle means that the electrons can’t occupy the same state. It is kind of like musical chairs where everyone jostles each other to find a seat, and two people can’t share the same seat. The exclusion principle also applies to the ions, but it turns out that the electrons need bigger chairs, so it’s the electrons we most have to worry about. As a result of the exclusion principle the electrons exert a degeneracy pressure to keep all the other electrons out of their chair. You can therefore treat the electrons as a simple gas with a pressure due to the exclusion principle.  Such a star is sometimes called a degenerate star, but it is more commonly known as a white dwarf.

A plot of the radius of a white dwarf vs its mass in a simple model.

So to model such a star, we just need gravity and the equation of state (a description of the pressure) for our electron gas.  What we find is that the more mass a white dwarf has, the smaller its radius. This is exactly what we would expect, since more mass means stronger gravity, which means all those degenerate electrons are squeezed harder. But when the mass reaches about 1.4 solar masses, the electrons are squeezed so tightly that the resulting radius is zero. At this limit the electron pressure can’t withstand gravity. This limit is known as the Chandrasekhar limit (named after its discoverer). Above this limit and the electrons are squeezed into the protons in the ions, leaving a massive ball of neutrons known as a neutron star. Actually, it isn’t quite that simple, but you get the idea.

Since a white dwarf can’t produce heat through fusion or anything else, once it forms it gradually cools.  Since white dwarfs are small they don’t have a lot of surface area, so they cool rather slowly, but given enough time such a star would cool to the background temperature of the universe, becoming a cold and dark frozen star.

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