Very precise pulsar measurements

A neutron star is made of neutrons, right? Astrophysicists ponder this question and forge theory after theory, but the only thing they conclude with certainty is that a neutron star by any other name would still be made of the densest form of matter know to exist in our Universe. Under certain conditions a star which has exhausted all of its fuel and is sufficiently massive will not be able to support its own weight with pressure support (as in a regular star) or with electron degeneracy support (as in a white dwarf) such that electrons and protons merge to form neutrons because it is a more energetically favorable arrangement of the matter. A neutron star is a sort of massive atomic nucleus, but without charge. The actual composition and detailed properties of neutron star are still theoretically uncertain.
New measurements of the pulsating neutron star and helium-oxygen-carbon white dwarf binary system J1614-2230 reported in a Nature letter are the highest precision determinations of a neutron star's mass to date. The data comes from the massive Green Bank Telescope using the new Green Bank Ultimate Pulsar Processing instrument which accurately records the time of arrival of each radio pulse sent out by the rapidly rotating neutron star (which is a pulsar). The quality of this instrument, having over a tera op of computing power, and the size of the telescope, 100 meters, made this measurement possible. For a quick rundown of this result you can watch these quick movies on the scientific implications and the technology behind the discovery which were created by the NRAO.

The analysis uses a general relativistic effect involving the time delay of light known as the Shapiro delay effect. When a light ray passes a massive object it follows a curved path. General relativity says that curvature of light rays can only take place when the velocity of the propagation of the light rays also varies with position. The Shapiro delay increases the light travel time through the curved space-time near a massive body. The equation to determine the time delay effect is delightfully simple.

The delay depends on the mass, M, of the time delaying body between the source and the observer, the gravitational constant G, the speed of light, c, and the geometry of the system. The geometry is that light has to be passing near the gravitating body before it gets to the observer for the effect to occur at all so the vector that points from the observer to the source, R, and the vector that points from the observer to the gravitating mass are vital. Pulsar J1614-2230 is a nearly edge on, 89 degrees, system meaning that when the white dwarf passes in front of the pulsar during the binary orbit the Shapiro effect will be very strong. I ran a quick calculation of the time delay and found it to be exactly on the order of a few microseconds. The first figure in the paper shows the geometry and the measured effect.

With this data in hand the standard Keplerian orbital parameters are calculated for this clean binary system and the masses of the objects are calculated. The mass of the neutron star was found to be 1.97 +/- 0.04 solar masses which is the most precise measurement of neutron star mass to date. Unfortunately this measurement technique does not provide any information about the radius of the neutron star, but because the mass was so high it already set a limit on the equation of state of the neutron star matter. This means that we can begin to answer what a neutron star is really made of. Different kinds of matter have a different behavior as you add more mass to them which is intuitive if you thought how discrepant with respect to size a planet made out of cotton candy versus rock would be. This result indicates that exotic models of hadronic matter including hyperons, kaon condensates are ruled out. Condensed quark matter is not ruled out, but highly constrained with this data. This is a big deal for particle physicists because this kind of system is an experiment that could never be carried out in a lab, but is necessary to probe fundamental physics.

This cool result on neutron stars glosses over another application of precise pulsar measurements that the authors of this Nature paper regarded as noise. The plot above is very neat and clean, but before the data looks like that a timing analysis must take into account the time delays associated with many more mundane effects. Effects that change the time of arrival of the pulsar include the variations in the Euclidean distance between the Earth and the pulsar resulting from Earth’s orbital motion, the proper motion of the pulsar, and its binary motion, dispersive delays in the interstellar medium, and time dilation of clocks in the observatory and pulsar frames and along the propagation path. The Earth's orbital motion about the solar system barycenter (known as the Roemer delay) is up to 500 seconds and so must be removed from the data. The powerful thing is that the Earth's orbital motion tells us about the mass and orbits of all the bodies in our solar system. A paper published in the Astrophysical Journal states that with ten years of careful observation of 20 pulsars the masses and orbits of solar system bodies could be determined better than with any other method and even undiscovered trans-Neptunian objects could be found.

Precise pulsar measurements are powerful. The first extrasolar planet ever discovered was actually made with pulsar measurements. Pulsars can tell us about the nature of neutron stars, the properties of own solar system, oh and even gravitational waves. If only astronomers had the money to build a pulsar timing array...

References

Demorest PB, Pennucci T, Ransom SM, Roberts MS, & Hessels JW (2010). A two-solar-mass neutron star measured using Shapiro delay. Nature, 467 (7319), 1081-3 PMID: 20981094

D. J. Champion, G. B. Hobbs, R. N. Manchester, R. T. Edwards, D. C. Backer, M. Bailes, N. D. R. Bhat, S. Burke-Spolaor, W. Coles, P. B. Demorest, R. D. Ferdman, W. M. Folkner, A. W. Hotan, M. Kramer, A. N. Lommen, D. J. Nice, M. B. Purver, J. M. Sarkissian, I. H. Stairs, W. van Straten, J. P. W. Verbiest, & D. R. B. Yardley (2010). Measuring the mass of solar system planets using pulsar timing ApJ arXiv: 1008.3607v1

White Cosmonaut, Red Cosmonaut

Check out this lovely art by Jeremy Geddes. He is a Melbourne artist who works with mostly oil paints. His paintings have glowing colors and he has this recurrent cosmonaut theme that vaguely makes them seem relevant. Below are three of my favorite images that I have seen: The White Cosmonaut, The Red Cosmonaut, and Heat Death. Of his cosmonaut series he himself is vague,

I wanted to construct my own reality through my paintings, a quiet melancholic space that operates by it’s own set of underlying rules and runs it’s own oblique narrative. With each successive painting, I try to build the world and uncover it’s form. The cosmonaut paintings are the first step in this.

And on his piece Heat Death he again lets your mind linger on meaning and reasoning,

Hopefully, I communicate everything I want to say through the painting itself. I’m not interested in giving it a didactic final meaning. I just want to spark questions in the viewer.

Artists have the luxury of letting their art speak so that they don't have to. Scientists don't have this luxury and generally must have a didactic (although, not intending to imply moral) explanation of nature; an explanation which may or may not be close to the truth. Science ultimately doesn't self explain its emphases on truth seeking. Truth is like art, sought for its own sake. Oh and please, if someone wants to buy me the Red/White Cosmonaut diptych print feel free.

The Goldilocks Planet

Once upon a time there was a planet named Earth. It orbited exactly one astronomical unity away from a G2V type star. Billions of years went by and Earth found that it lived right in the habitable zone where liquid water was maintained on it surface and life spontaneously arose. Pretty soon life on Earth became restless, questioned its own existence, and looked for life on Gliese 581. Earthlings found many planets and exclaimed, 'Gliese 581 b is too hot, Gilese 581 c is slightly too hot, Gliese 581 d is slightly too cold, Gliese 581 e is way too hot, Gliese 581 f is too cold, but Gliese 581 g is just right!' so the story goes.

Gliese 581 is an unassuming star: it is relativity close at 20 light years away (the 87^th closest cataloged star to earth), it is only a third the mass of the sun, and it is relativity quiet in terms of stellar activity (which is beneficial for life because flares scorch planets). It is the sixth planet from Gliese 581 denoted merely as g that harbors so much potential. It is not to hot, not too cold, it is just right. It is the Goldilocks planet. Vogt et al. 2010 recently reported on the discovery of this planet which is a 3.1 Earth mass (or larger) planet orbiting in the habitable zone of the M3V type star Gliese 581. The problem is that this planet may not exist.

The Media

I did not immediately discuss Gliese 581 here at The Astronomist because I wanted to read the paper before weighing in. However the authors were compelled to issue a press release about their findings before making their peer reviewed paper available. After I finally looked at the paper I was somewhat disappointed. The whole thing was a science journalism media circus. A selection of some of my favorite excerpts:

• “Found: An Earth like Planet, at Last” Time magazine
• “The chances of life on this planet are 100 percent,” Steven Vogt
• “Could contain more gold than we could ever imagine” PR Fire
• "Are the Gliesans going to Hell?" Huffington Post
• "An Alderaan Moment: Earth-Like planet disappears" Death+Taxes

Media coverage is a double edged sword for science. Scientists strive to come up with compelling results that often fall flat when presented to the media or public, but other stories make waves disproportionately large relative to their scientific impact. Arguably the discovery of an earth like planet should have been accompanied by a much larger amount of media attention. The misinformation spread about Gliese 581 g is a symptom of the real problem which is the science. This is not a confirmed planet detection, there is no evidence this planet has a hospitable atmosphere anything like Earth, and there is certainly no evidence of life. This wont stop the media from speculating or spreading dangerous misinformation (like the idea we could travel there if we trash Earth). The quote from Steven Vogt is an example of poor journalism where he prefaced the statement by saying, 'my own personal feeling is that the chances of life on this planet are 100 percent,' but the crucial context was thrown away for headlines.

The Science

All the planets around Gliese 581 were discovered using the radial velocity technique. In any gravitationally bound system the bodies orbit their common center of mass. It is a subtle effect in a star-planet system where the central star dominates the mass. The central star will move at a characteristic speed depending on the orbits of the planets around it. The movement of the star is measured through the Doppler shift of the light emitted by the star. Modern instruments are super sensitive to even the smallest movements of stars down to as little as 1 m/s. Observations of the radial velocity of the star over a period of time (usually several years) is analyzed using Fourier analysis. The Fourier analysis identifies periodic signals in the data corresponding to the orbital period of the planet or planets.

The researchers used two data sets spanning almost two decades. Most of the data came from the researcher's own instrument HIRES, and additional data came from a Swiss group with the HARPS instrument. The HIRES data spans a larger time range, but the HARPS data is more precise. This combined data set is how the researchers identified two new planets f and g.

The Problems

A little after this new Goldilocks planet was announced the Swiss group announced that they could find no evidence of Gliese 581 g in their data. Does this mean it doesn't exist? Well this is tricky. A planetary researcher in my department, Rory Barnes, spoke to the New York times before the Swiss group had spoke up and said that the planet looked like the 'real deal'. After the announcement was made I spoke to Barnes again and he said that he would have to hold off further judgment until more information was available.

The onus of proof in science is upon those who make extraordinary claims. Vogt et al. were only able to find this planet by combing the available data sets; they actually state in their paper that they did not detect the planet in either of the data sets independently, only in combination. The damning part of the Swiss groups statement is that they say they have much more data available at this point that Vogt et al. did no have access to during their analysis. When the Swiss team forces planet g to fit their complete data they actually get a negative fit indicating that planet g really isn't there. The thing about this paper that I am least happy with is the quoted false alarm probability. The false alarm probability appears to be 1% based on the figures in the paper (see figure 3 specifically), but in the text it is quoted as ~10^-5. I don't know what is going on.

Then there is their error analysis (warning this is about to get technical feel free to skip this paragraph). Vogt et al. used the peaks in the power spectrum to identify the planets in the system then subtracted off the highest power modes corresponding to the planets they had found. The power spectrum for each planet carried with it a false alarm probability, but once the planet had been subtracted out of the power spectrum its false alarm probability was washed away (you can see this happening in figure 3). They compound their errors after the 1st, 2nd, 3rd, 4th, and 5th planets which have varying false alarm rates. The proper way to do this is a joint fit model to all planets in the system using Bayesian analysis.

The strangest thing about all this is that when this paper was first submitted to The Astrophysical Journal the Swiss group was reviewing the paper and it was rejected. This Vogt paper meta chronicles its own history and discusses why it was retracted previously over concern of systematics. Unfortunatly the quality of the paper may not have improved. The Swiss group has actually leveled one specific concern, Vogt used perfectly circular orbits to find planet g, but the evidence shows the orbits are probably slightly elliptical. In fact in 2009 Vogt used elliptical orbits, but in this new paper circular orbits have been adopted. The image above illustrates this and makes a pictorial argument as to how circular vs elliptical orbits could introduce errors.

The discovery of an Earth-like planet seems imminent. I do not know if this is it.  I will hold off further judgment until more information was available.

References:

Steven S. Vogt, R. Paul Butler, Eugenio J. Rivera, Nader Haghighipour, Gregory W. Henry, & Michael H. Williamson (2010). The Lick-Carnegie Exoplanet Survey: A 3.1 M_Earth Planet in the
Habitable Zone of the Nearby M3V Star Gliese 581 ApJ accepted : arXiv: 1009.5733v1

Also thanks to Amit and Rory for discussion and figures.