Final Report Summary - AMXP DYNAMICS (Accreting millisecond X-ray pulsar dynamics)
The aim of this project was to evaluate, for the first time, the impact that the interior dynamics of accreting neutrons stars can have on their gravitational wave emission. We found that, as expected, the signals are predicted to be weak, making accreting neutron stars a target for next generation gravitational wave detectors, such as the proposed European Einstein Telescope.
The main achievement of the project was, however, that we were able, for the first time, to use available X-ray data on accreting systems to constrain gravitational wave emission mechanisms and the interior composition of the neutron star in the system.
First of all we analysed two particular systems, SAX J1808 and XTE 1814, whose unusual timing behaviour had led to the conjecture that they may be emitting gravitational waves. We found that most gravitational wave emission mechanisms that had been proposed can be excluded by the data, leading to the conclusion that interaction between the accretion disc and the magnetic field of the star must be leading to the observed behaviour (Haskell & Patruno, 2011). This led us to analyse the population of accreting systems as a whole. It had been suggested that the fact that no accreting neutron stars are observed to be spinning faster than approximately 700 Hz (which is well below the limit at which the star would be torn apart by rotation), is due to gravitational waves being emitted at a rate that is sufficient to halt the accretion induced spin up.
We found that by taking the most up to date observational constraints and accretion disc models, such behaviour can be explained by the disc / magnetic field interaction, without invoking gravitational wave emission (Patruno, Haskell & D'Angelo, 2011).
Although such a conclusion may seem discouraging for gravitational wave detection at first, we did in fact find that hotter, faster systems, are more likely to be active as gravitational wave sources. This conclusion was also verified by a bachelor student, supervised by myself, Manuel Oppenoorth. His work focused on the 'mountain' mechanisms, in which thermal fluctuations give rise to small mountains on neutron stars, which lead to gravitational wave emission. Manuel found that for systems that are close enough even temperature asymmetries of a few percent will lead to signals that could be detected by the Einstein Telescope (Oppenoorth, UvA bachelor thesis, 2012).
We also analysed in detail the r-mode mechanism for gravitational wave emission. In this case it is a fluid mode of oscillation that becomes large and provides the necessary perturbation that leads to gravitational wave emission. In particular one of the best candidates is the so-called r-mode, a fluid mode that exists in a rotating star for which the restoring force is the Coriolis force (analogous to Rossby waves on Earth).
We found that the standard neutrons star model of a star composed of neutrons, protons and electrons that does not account for other components or strong superfluidity / superconductivity in the core, is not consistent with observations (Ho, Andersson & Haskell 2011, Haskell, Degenaar & Ho, 2012). In fact, the standard models would predict that nearly all the observed systems should be emitting gravitational waves and not only be spinning down much faster than observed, but also be much hotter. This is perhaps a surprising result, as it already allows us to place some constrains on the interior physics of neutron stars, and to suggest possible mechanisms that could be consistent with the data.
Let us note that also for the r-mode mechanism we find that a few of the faster, hotter, systems may still be consistent with spin equilibrium due to gravitational wave emission. During the whole project we also continued to develop the theoretical framework that is needed to model the interior dynamics of superfluid neutron stars (Haskell 2011, Andersson, Haskell & Samuelsson 2011, Haskell, Andersson & Comer 2012).
In conclusion we have found that available X-ray data can strongly constrain gravitational wave emission mechanisms for accreting systems. In most cases the data indicates that gravitational waves do not play an important role in the evolution of the system and allow to constrain both the interior composition of the neutron star and the nature of the interaction between the accretion disc and the magnetic field of the star. Our results do, however, point to faster and hotter systems as the best targets for gravitational wave detection. This is a very important point when evaluating detection strategies for future gravitational wave observatories such as the Einstein Telescopes and suggests that even persistently accreting systems for which the spin is not known may be emitting gravitational waves. If such a signal were detected, and allowed us to measure the spin of the star, it would, for the first time, provides us with information that electromagnetic waves cannot provide.
The main achievement of the project was, however, that we were able, for the first time, to use available X-ray data on accreting systems to constrain gravitational wave emission mechanisms and the interior composition of the neutron star in the system.
First of all we analysed two particular systems, SAX J1808 and XTE 1814, whose unusual timing behaviour had led to the conjecture that they may be emitting gravitational waves. We found that most gravitational wave emission mechanisms that had been proposed can be excluded by the data, leading to the conclusion that interaction between the accretion disc and the magnetic field of the star must be leading to the observed behaviour (Haskell & Patruno, 2011). This led us to analyse the population of accreting systems as a whole. It had been suggested that the fact that no accreting neutron stars are observed to be spinning faster than approximately 700 Hz (which is well below the limit at which the star would be torn apart by rotation), is due to gravitational waves being emitted at a rate that is sufficient to halt the accretion induced spin up.
We found that by taking the most up to date observational constraints and accretion disc models, such behaviour can be explained by the disc / magnetic field interaction, without invoking gravitational wave emission (Patruno, Haskell & D'Angelo, 2011).
Although such a conclusion may seem discouraging for gravitational wave detection at first, we did in fact find that hotter, faster systems, are more likely to be active as gravitational wave sources. This conclusion was also verified by a bachelor student, supervised by myself, Manuel Oppenoorth. His work focused on the 'mountain' mechanisms, in which thermal fluctuations give rise to small mountains on neutron stars, which lead to gravitational wave emission. Manuel found that for systems that are close enough even temperature asymmetries of a few percent will lead to signals that could be detected by the Einstein Telescope (Oppenoorth, UvA bachelor thesis, 2012).
We also analysed in detail the r-mode mechanism for gravitational wave emission. In this case it is a fluid mode of oscillation that becomes large and provides the necessary perturbation that leads to gravitational wave emission. In particular one of the best candidates is the so-called r-mode, a fluid mode that exists in a rotating star for which the restoring force is the Coriolis force (analogous to Rossby waves on Earth).
We found that the standard neutrons star model of a star composed of neutrons, protons and electrons that does not account for other components or strong superfluidity / superconductivity in the core, is not consistent with observations (Ho, Andersson & Haskell 2011, Haskell, Degenaar & Ho, 2012). In fact, the standard models would predict that nearly all the observed systems should be emitting gravitational waves and not only be spinning down much faster than observed, but also be much hotter. This is perhaps a surprising result, as it already allows us to place some constrains on the interior physics of neutron stars, and to suggest possible mechanisms that could be consistent with the data.
Let us note that also for the r-mode mechanism we find that a few of the faster, hotter, systems may still be consistent with spin equilibrium due to gravitational wave emission. During the whole project we also continued to develop the theoretical framework that is needed to model the interior dynamics of superfluid neutron stars (Haskell 2011, Andersson, Haskell & Samuelsson 2011, Haskell, Andersson & Comer 2012).
In conclusion we have found that available X-ray data can strongly constrain gravitational wave emission mechanisms for accreting systems. In most cases the data indicates that gravitational waves do not play an important role in the evolution of the system and allow to constrain both the interior composition of the neutron star and the nature of the interaction between the accretion disc and the magnetic field of the star. Our results do, however, point to faster and hotter systems as the best targets for gravitational wave detection. This is a very important point when evaluating detection strategies for future gravitational wave observatories such as the Einstein Telescopes and suggests that even persistently accreting systems for which the spin is not known may be emitting gravitational waves. If such a signal were detected, and allowed us to measure the spin of the star, it would, for the first time, provides us with information that electromagnetic waves cannot provide.