Hello all! My name is Dusty Madison. I do research on pulsars, specifically how they can be used to detect extremely low-frequency gravitational waves from things like supermassive black hole binaries. I hope to use this space to talk about neat new work on pulsars, gravitational waves, and any other astronomical topic I can trick enough people into thinking I'm marginally qualified to discuss.
In this first post of mine, I want to talk about a paper that's a few years old now that many of you are possibly already familiar with: A two-solar-mass neutron star measured using Shapiro delay, or Demorest et al. (2010). This paper came out just after I started working on pulsar timing. I have always found it to be a crazy beautiful paper with profound scientific implications that really deftly shows how damn cool pulsar science can be. It's a modern classic in my field (as evidenced by the 1000+ citations). I think discussing it will be a good warm up for me. Full disclosure: I know most of the authors of this paper personally through my work in NANOGrav and the IPTA, but I didn't know them when I first read this paper and realized how cool it was.
So the reason this paper is awesome is because the subject is a truly remarkable millisecond pulsar/white dwarf binary system. The pulsar has a rotational period of 3.1508076534271(6) milliseconds. The orbital period of the system is 8.6866194196(2) days. Pulsar papers are neat places where you'll see this many significant digits and you can take them seriously. The eccentricity of the orbit is 0.00000130(4)---a nearly perfect circle. What really enables the extra-special science you can do with this system though is the inclination angle is 89.17(2) degrees. This system is almost perfectly edge-on to the line of sight making it ideal for measuring the Shapiro delay.
The Shapiro delay is a general relativistic delay that the clock-like pulsations of radio waves from the pulsar experience as they traverse the gravitational potential of the white dwarf companion. Schematically, the pulses have to fall into the gravitational well and climb back out before getting to Earth and this takes a little bit of time. How big the delay is depends on the geometrical configuration of the orbit (it's biggest when the white dwarf lies between the pulsar and the Earth) and the mass of the companion (bigger mass, bigger delay).
With this nearly edge-on binary, if you carefully monitor the Shapiro delay throughout the orbital period, you can very precisely measure the white dwarf mass. Once you know the companion mass to high precision, you can directly infer the neutron star mass. Demorest et al. did this. The figure above shows the Shapiro delay they measured (in microseconds) as a function of orbital phase. The white dwarf mass they infer from the shape of this Shapiro delay curve is 0.500(6) solar masses. This yields a neutron star mass of 1.97(4) solar masses.
This was the largest high-precision mass of a neutron star ever measured and it was a big deal. It was a big deal because general relativity dictates that neutron stars have an absolute maximum mass (see TOV limit) and what that maximum mass is depends on the equation of state of nuclear matter at super-nuclear densities. Now, it's nearly impossible to learn anything in a laboratory about the behavior of matter at super-nuclear densities, especially in the degenerate conditions of a neutron star, so measurements of the sort done by Demorest et al. are essentially the only way to gain insight into the nuclear physics in these regimes of parameter space.
In the figure on the left, Demorest et al. depict the mass-radius relations anticipated for a wide variety of theoretical equations of state. The red horizontal bar represents the new lower-bound on the maximum neutron star mass that this neutron star (code name J1614-2230) yielded. Many of the proposed equations of state say you can have a neutron star even heavier than 2 solar masses. They are safe. However, many of the curves predict maximum neutron star masses well below 2 solar masses. This single mass measurement basically kills those theories. I love it.
Sadly, many of those equations of state that can't support a 2 solar mass neutron star predict really cool exotic phases of matter in neutron star interiors--things like pion condensates, equilibrium populations of hyperons, or deconfined quark matter. Now, these things can't be completely ruled out. Equations of state have tunable parameters that can be tweaked a bit so that they yield maximum neutron star masses compatible with the 2 solar mass neutron star. But the fact is, the 2 solar mass neutron star painted some of these equations of state into a corner and spurred a lot of activity in nuclear theory circles. I think that's awesome.
In this first post of mine, I want to talk about a paper that's a few years old now that many of you are possibly already familiar with: A two-solar-mass neutron star measured using Shapiro delay, or Demorest et al. (2010). This paper came out just after I started working on pulsar timing. I have always found it to be a crazy beautiful paper with profound scientific implications that really deftly shows how damn cool pulsar science can be. It's a modern classic in my field (as evidenced by the 1000+ citations). I think discussing it will be a good warm up for me. Full disclosure: I know most of the authors of this paper personally through my work in NANOGrav and the IPTA, but I didn't know them when I first read this paper and realized how cool it was.
So the reason this paper is awesome is because the subject is a truly remarkable millisecond pulsar/white dwarf binary system. The pulsar has a rotational period of 3.1508076534271(6) milliseconds. The orbital period of the system is 8.6866194196(2) days. Pulsar papers are neat places where you'll see this many significant digits and you can take them seriously. The eccentricity of the orbit is 0.00000130(4)---a nearly perfect circle. What really enables the extra-special science you can do with this system though is the inclination angle is 89.17(2) degrees. This system is almost perfectly edge-on to the line of sight making it ideal for measuring the Shapiro delay.
 |
| From Figure 1 in Demorest et al. (2010) |
The Shapiro delay is a general relativistic delay that the clock-like pulsations of radio waves from the pulsar experience as they traverse the gravitational potential of the white dwarf companion. Schematically, the pulses have to fall into the gravitational well and climb back out before getting to Earth and this takes a little bit of time. How big the delay is depends on the geometrical configuration of the orbit (it's biggest when the white dwarf lies between the pulsar and the Earth) and the mass of the companion (bigger mass, bigger delay).
With this nearly edge-on binary, if you carefully monitor the Shapiro delay throughout the orbital period, you can very precisely measure the white dwarf mass. Once you know the companion mass to high precision, you can directly infer the neutron star mass. Demorest et al. did this. The figure above shows the Shapiro delay they measured (in microseconds) as a function of orbital phase. The white dwarf mass they infer from the shape of this Shapiro delay curve is 0.500(6) solar masses. This yields a neutron star mass of 1.97(4) solar masses.
This was the largest high-precision mass of a neutron star ever measured and it was a big deal. It was a big deal because general relativity dictates that neutron stars have an absolute maximum mass (see TOV limit) and what that maximum mass is depends on the equation of state of nuclear matter at super-nuclear densities. Now, it's nearly impossible to learn anything in a laboratory about the behavior of matter at super-nuclear densities, especially in the degenerate conditions of a neutron star, so measurements of the sort done by Demorest et al. are essentially the only way to gain insight into the nuclear physics in these regimes of parameter space.
 |
| Figure 3 from Demorest et al. (2010) |
Sadly, many of those equations of state that can't support a 2 solar mass neutron star predict really cool exotic phases of matter in neutron star interiors--things like pion condensates, equilibrium populations of hyperons, or deconfined quark matter. Now, these things can't be completely ruled out. Equations of state have tunable parameters that can be tweaked a bit so that they yield maximum neutron star masses compatible with the 2 solar mass neutron star. But the fact is, the 2 solar mass neutron star painted some of these equations of state into a corner and spurred a lot of activity in nuclear theory circles. I think that's awesome.
Hi Dusty and welcome.
ReplyDeleteI have a question inspired by your post, but first let me mention something interesting regarding the maximum neutron star mass.
There was a very nice paper a couple of years back (it's been already two years...) by Martinon et al. (Martinon G., Maselli A., Gualtieri L., Ferrari V., 2014, Phys. Rev. D, 90, 064026) that showed that due to the properties of hot equations of state (EoSs) of proto-neutron stars, the resulting cool neutron star can't be close to the maximum TOV mass of the corresponding zero temperature EoS. So, the interesting implication is that, since a new-born neutron star should be under the TOV limit, a $2M_{\odot}$ measurement is a stronger constrain in the end. Of course for pulsars there is the issue of accreting matter that should also be factored in.
Anyway, regarding my question, since you mention hyperons, I've heard of some proposals for hybrid strange/neutron star models that could save hyperons. But I was under the impression (and I could be wrong on this) that strange star models don't go above the $2M_{\odot}$ limit, so my question is, how could a hybrid save the day for hyperons? Maybe this is not your area of expertise, but any insight on this would be nice.
Cheers.
Your comment was probably more informative to me than my answer to your question will be to you. This is definitely not my field of expertise. I would guess that hyperons in the hybrid models have higher effective masses because of some stronger interaction and thus higher Fermi levels. I think this would tend to stiffen the EoS and thus allow for bigger maximum masses.
Delete