A Binary System on the Edge of Merger

by Paul Gilster on July 14, 2011

A pair of white dwarf stars too close together to distinguish visually may help us in the hunt for gravitational waves, while potentially explaining a whole class of rare, relatively faint supernovae. The system in question — called SDSS J065133.33+284423.3, or J0651 for short — was found during a spectroscopic survey looking for extremely low mass white dwarfs. J0651 includes one white dwarf with about a quarter of the Sun’s mass compacted down to Neptune-size, along with a companion white dwarf that is half the Sun’s mass and about the size of the Earth.

Usefully, this is a system oriented so that we can observe eclipses of each star by the other, which is how we can measure orbital parameters, masses and white dwarf radii. The General Theory of Relativity predicts that close pairs of stars produce gravitational waves that are ripples in the curvature of spacetime, and as the paper on the new work points out, the binary pulsar PSR B1913+16 has already given us indirect evidence for such waves through the gradual decay of the orbit as predicted by Einstein’s theory. J0651 now emerges as an opportunity to study gravitational waves again by measuring small changes in the stars’ orbital periods.

Image: Two white dwarfs have been discovered on the brink of a merger. In just 900,000 years, material will start to stream from one star to the other (as shown in this artist’s conception), beginning the process that may end with a spectacular supernova explosion. Watching these stars fall in will allow astronomers to test Einstein’s general theory of relativity as well as the origin of a special class of supernovae. Credit: David A. Aguilar (CfA)

Thus we have an unusually useful celestial laboratory. Because there seems to be no exchange of mass, the change in separation over time should be easy to measure. From the paper:

We…predict that J0651’s orbital period is shrinking by 2.7 × 10-4 sec per year due to gravitational wave radiation. The expected change in period adds up to a 5.5 sec change in time-of-eclipse in one year. When we measure this change we expect to provide yet another fundamental test of general relativity and the existence of gravitational waves.

It’s a test that could potentially be confirmed by the proposed ESA/NASA Laser Interferometer Space Antenna (LISA) mission, which the authors predict could detect this gravitational wave source within its first week of operation considering its peak sensitivity at frequencies corresponding to orbital periods like those found here. The white dwarfs complete an orbit in just 13 minutes and will merge quickly in astronomical time. On that issue the paper comments:

The absence of mass transfer in J0651 is perhaps surprising given how quickly it will merge. In all known binaries with periods comparable to J0651… one star fills its Roche lobe and transfers mass to its companion. Our data show that the J0651 primary has a Roche lobe radius 1.5 times its current radius. Under the assumption of energy and angular momentum loss due to gravitational wave radiation, the primary WD will reach its Roche lobe radius at an orbital period of 6.5 minutes in 0.9 Myr.

What happens when the stars merge 900,000 years from now is another issue. In some models, merging white dwarf pairs are the source of faint stellar explosions called underluminous supernovae. Such objects are 10 to 100 times less luminous than normal Type Ia supernovae. The supernova SN 2005E, for example, can be explained using parameters similar to the J0651 system, but mass transfer between the two stars could lead to a variety of different outcomes. Thus the need for the ongoing survey of low mass white dwarf systems using the MMT telescope at the Whipple Observatory on Mt. Hopkins, Arizona, from which the current paper draws its data.

The two white dwarfs are circling at a speed of some 600 kilometers per second. “If there were aliens living on a planet around this star system, they would see one of their two suns disappear every 6 minutes – a fantastic light show.” said Smithsonian astronomer and co-author Mukremin Kilic. So strong is the mutual gravitational pull of the white dwarfs here that the lower-mass star is deformed by three percent and, as this Harvard-Smithsonian Center for Astrophysics news release notes, a similar bulge on our own planet would result in tides 190 kilometers high.

The paper is Brown et al., “A 12 minute Orbital Period Detached White Dwarf Eclipsing Binary,” accepted by Astrophysical Journal Letters and available as a preprint.

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kurt9 July 14, 2011 at 14:47

I heard Betelgeuse is supposed to blow sometime soon.

djlactin July 14, 2011 at 19:27

“J0651’s orbital period is shrinking by 2.7 × 10-4 sec per year … adds up to a 5.5 sec change in time-of-eclipse in one year.”

This does not compute. Can somebody explain the math/physics behind this statement? (I am interpreting to mean that this refers to “time aat which we observe the (e.g.) onset of eclipse; might they actually mean “duration of eclipse.”?)

Ron S July 14, 2011 at 20:42

djlactin,

Just going by Paul’s article (that is, without reading the paper) the math does add up. As follows:
- “…they would see one of their two suns disappear every 6 minutes…”: therefore the orbital period is 12 minutes. This is about 43,800 orbits per year (that’s one of our years, not theirs!).
- The orbital decay is roughly linear, so over one year the mean orbital decay is 1.35 x 10^-4 seconds.
- Multiply 43,800 by 1.35 x 10^-4 = 5.9 seconds.

That’s close enough to 5.5 seconds, given that I spent 30 seconds with a calculator.

Rob Henry July 14, 2011 at 22:42

As an ignorant outsider, I would assume that the first 0.25 solar mass white dwarfs formed at least 100 billion years after the big bang. What am I missing here?

David July 15, 2011 at 3:44

djlactin,

Decreasing the orbital period of J0651 will result in J0651 moving faster in its orbit.
Moving faster means that the time of eclipse happens earlier. You are correct that the duration of the eclipse will also be shorter provided there is also no change in the eccentricity of the orbit.
Things get more complicated when there is mass loss and one also has to consider relativistic effects when one wants to calculate the actual timing changes.

Anthony Mugan July 15, 2011 at 4:13

Can I ask if any reader is aware on any work published in relation to gravitational waves in terms of Verlinde’s concept of entropic gravity – in particular if gravitational waves also emerge from that model? (This is in relation to something I’m looking at which is requiring me to get my head around some of the maths of some of this and this struck a chord…)

Freederick July 15, 2011 at 6:53

@djlactin:
“J0651’s orbital period is shrinking by 2.7 × 10-4 sec per year … adds up to a 5.5 sec change in time-of-eclipse in one year.”
The paper is just sloppily written. The first “year” is the rotation period of the star pair, or 13 minutes; the second “year” is our terrestrial year of 365.25 days. If you plug in these values, you will come up with a reduction of orbital period by about 11 seconds per terrestrial year; in one complete rotation there will be 2 “eclipses” (actually, one occultation/eclipse and one transit; sloppy writing yet again), so 5.5 seconds is about right.
This raises the question: when talking about 900 000 years until the big crunch, which years do they mean? I have a hunch they mean “local rotation periods”, so that would be about 22.25 our years.
A clarification by the author would be appreciated :-)

Mike July 15, 2011 at 10:00

To Rob Henry, the .25 solar mass white dwarf was certainly more massive as a main sequence star for most of its life. A .25 solar mass main sequence red dwarf would have a very long life indeed. All red dwarfs that have formed since the big bang are still shining, unless they have been disturbed by something like supernovae, or mass transference from a companion or gobbled up by a black hole etc. So no way could a .25 solar mass red dwarf have evolved off the main sequence yet. I think that’s what you are pointing out by your post.
But the white dwarf is a remnant of an evolved star that would have had a much higher mass initialy, hence a shorter stay on the main sequence. When the star aged and evolved off the main sequence it would have lost most of its’ mass as the swollen up outer layers are pushed away by the hot cores’ radiation pressure and wind likely forming a planetary nebula.
All white dwarfs are considered to be the end product of stars not massive enough to go supernova but massive enough to have aged within the estimated life of the universe. Interactions between binary stars can complicate this picture somewhat but it is generally pretty accurate. We think.

Rob Henry July 15, 2011 at 20:51

Mike, thanks for trying to put me straight, but I fear I’m going to display further ignorance. I thought that, proportionately, mass loss due to the solar wind was only really significant for high mass stars. Also when the first red giant stage star depleted the outer layers of the other I would have thought the mass of the ‘absorbing’ star would have ended up higher than it did. I am puzzling as to what is the minimum developmental timespan that would allow the above situation as its result, and still can’t believe that it is less than the age of our universe.

djlactin July 15, 2011 at 21:12

Thanks to David and Freederick.

andy July 16, 2011 at 8:14

0.25 solar masses is quite low for a white dwarf star: the typical mass of such objects is around 0.6 solar masses. The universe is not old enough to produce such low-mass white dwarf stars except via mass transfer in binary systems.

coolstar July 19, 2011 at 12:17

@Freederick I agree the paper is sloppily written, surprising given that the first author and that at least two of the other authors (the well known and respected Kenyon and Winget) are native English speakers. It’s actually somewhat worse than you noted though: the decrease in orbital period per “ORBIT” (hard to see how that mistake was allowed to reach the preprint stage) will indeed lead to a decrease in orbital period of about 11.1 seconds per YEAR. But that means that each eclipse will come 11.1 seconds earlier than predicted by a linear ephemeris, not HALF that value. What is close to 5.5 seconds is the decrease of half the period, the time between the primary and secondary minimums, since the orbit is circular. Give the short period of the system of about 765 seconds, that difference is probably going to turn out to be easier to measure than the time of either minimum independently. Looking at their binned light curve, neither eclipse is well sampled. This is not surprising given that the eclipses each last about 20% of the orbital period or about 150 seconds and that the faintness of the system (and the short orbital period) required exposures of 10 and 15 seconds on a 2.1 meter telescope. But if the period is decreasing at about 11 seconds a year (and that number will increase as the stars get closer together and more gravitational radiation is emitted) then it will take less than 35 years for the period to decrease by half and mass transfer to start, not 0.9 Myr (the authors HAD to mean YEAR here). Even if one randomly adds “per century” at various places, I still can’t make any sense out of the numbers quoted. Even the title is silly, as the 12.75 min period rounds to 13 minutes, not 12! Ok, I’ve made silly calculator errors in papers myself (caught by other readers, praise be….), but there seems to be multiple errors here and
they really impact any understanding of the basic facts meant to be communicated.

fishin July 19, 2011 at 17:06

I feel the need to comment quickly on this system given the immense confusion in the above posts. It seems that people are confused by the use of time here. A “year” ALWAYS refers to our “Earth year”, 31,556,926 seconds, a constant, well-defined unit. First, “J0651′s orbit is shrinking by 2.7×10^-4 sec per year”. @freederick, this “year” is one of our Earth years. When you integrate the differential equations involved, you find that it will take ~900,000 yrs for the binary to coalesce.

As the binary spirals in, the two white dwarfs speed up ever so slightly, so that over the course of a year the change between when the eclipses occur, due to orbital period decay is ~5.5 seconds. This is not 11.1 seconds as people above have said because there is a factor of two from taking the integrated change in when the eclipses occur.

White dwarfs should not exist below ~0.45 solar masses, because they have not had time to evolve through the main sequence, yet astronomers observe “low-mass white dwarfs” with masses much less. The explanation that seems to work is that earlier in their lifetimes, a companion star “stole” the outer envelope of the precursors to these stars, speeding up their evolution and changing their mass. @andy is completely correct in his comment that these low-mass white dwarfs only exist in binary systems.

coolstar July 21, 2011 at 13:47

@fishin A period decrease of 2.7E-4 sec per year IS consistent with a time to reaching mass exchange of around 0.9 Myr (assuming an acceleration in that rate). If the period changed instantaneously by that value, then over the 41 thousand plus orbits in a year, then the time of either primary or secondary eclipse would change by 11.1 seconds. One doesn’t have to do an integral to find that the average value (of the period over that year) is just half of that (well, I suppose, one is doing an integral in their head, but no one would call it that), which is the correct value for a linear rate of period change. Binary stars are my field, and I still think it’s a sloppily written paper, though I should have figured this out sooner. I also still think they’re really underestimating how difficult it’s going to be to measure that change as you cannot do it (accurately) from a binned light curve (since the phase change of the minimum is only 0.007 and is lost in the noise, at the one year point, at least) , but need to fit individual times of minimum, none of which they’ve yet resolved (but probably could with a 4 meter class telescope; good luck in getting that time, if you’re an American!).

Rob Henry July 21, 2011 at 20:57

Isn’t it frustrating how changing English language into the language of maths creates so many ambiguities. I’m sure that I’m not the only one that notes that the disagreement between the 5.5 or 11.1 second delay is due to two different translations of the above. Clue: think of a falling rock on Earth. It accelerates at 10m/s/s, yet if we take its current frame of reference as stationary we find that in the next second it has fallen only 5m.

Getting back to the problem that is tearing me apart, I understand that one star must reach red dwarf stage before the other, and mass transfers can alter the final mass of the other, but then the pair must have always been so close that little mass was ever lost from the combined system. The fastest evolution would happen if one stars’ initial mass was negligible, but then two relatively low mass stars have to come to their red giant stage from effectively two successive stellar lifespans (I understand that the outer layer of a red giant are not so massively enriched in helium as its core so the second evolving star would not be excessively pre-aged and the end of the firsts red giant stage). Can anyone estimate how long all this would take, because it all seems so wrong to me!

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