Timing Relativistic Binary Pulsars to test Gravitation and measure NS masses Paulo C. C. Freire Arecibo Observatory / Cornell University

Neutron stars Neutron stars have been theorized since the 1930s. Baade and Zwicky predicted they are the result of the collapse of the cores of massive stars during a supernova. Their radii should be of the order of 7-16 km, and their masses of the order of the Chandrasekhar mass (1.4 solar masses) or higher. Their central densities are of the order of a billion tons per cubic cm! Neutron stars should spin fast due to conservation of angular momentum from the parent stellar core! They should be highly magnetized due to conservation of magnetic flux from the parent stellar core.

Pulsars In August 1967, Jocelyn Bell, then a graduate student at Cambridge, finds a radio source in the constellation Sagitta (the Little Arrow) pulsating with a period of 1.33 seconds. She found this to appear 4 minutes earlier every day, indicating a sidereal source. For this discovery, Anthony Hewish earns the Nobel Prize in Physics 1974.Nobel Prize in Physics 1974 It was originally thought that pulsars were white dwarf stars.

Pulsar model Pulsars are the radio equivalent of lighthouses on a neutron star. Non-thermal radiation at a variety of wavelengths is emitted through the magnetic poles, which are generally misaligned with the spin axis. We see a pulse at the Earth every time this magnetic axis points towards us. No one knows what causes the radio emission!

The Binary Pulsar Russel Hulse and Joe Taylor discovered PSR B , in the constellation Aquila (the Eagle), during a systematic 430-MHz survey of the Galactic plane at Arecibo.

A Clean System! The pulsar is recycled. This means it soins fast and it is a very good clock. The orbital period is 7 h 45 m and the eccentricity is The companion is another neutron star. We have two point masses with motion influenced solely by their mutual gravitation, and one of them is pulsing with the stability of an atomic clock!

Doppler Shift When timing pulsars (or measuring radial velocities with the aid of spectral lines) one has access to the line-of-sight velocity, which causes a Doppler shift on the wavelength of the spectral line or a modulation on the period of the pulsar.

Ranging In the case of pulsar timing, having a clock in the system allows us to measure the range relative to the center of mass of the binary, sometimes with precision of the order of meters! This is makes pulsar timing many orders of magnitude more precise for measuring orbital parameters. This feature is unique to pulsars, and is the fundamental reason why they are superior astrophysical tools.

Keplerian Orbits Five Keplerian parameters can normally be measured from fitting the velocity (or, preferably, the delay) curves: orbital period (P b ), projected size of the orbit, in light seconds (x), eccentricity (e), longitude of periastron (ω) and time of passage through periastron (T 0 ). A non-changing Keplerian orbit is exactly what is predicted by Newtonian gravity. Without access to information on transverse velocities, the individual masses of the components (m 1 and m 2 ) and the inclination of the system (i) cannot be measured, but…

Mass Function: One Equation for Three Unknowns The mass function, a relation between these three quantities, can be measured to excellent precision, as it depends on two observable parameters: Three unknowns, only one equation! For most binary pulsars this is as far as we can go. However, the PSR B system is so extreme, and pulsar timing is so precise, that some effects of general relativity became detectable!

Advance of Periastron Perihelion advance due to general relativity had been observed for the orbits of several planets in the solar system, most notably Mercury. The periastron of PSR B advances (7) degrees/year. The daily periastron advance is the same as Mercury’s perihelion advance in a century…

Einstein Delay The Einstein delay was also measured:  = (1) s. The pulsar slows down visibly when it is near the companion, accumulating a delay relative to the prediction of constant rotational period. General relativity predicts that time itself slows down in an intense gravitational field (in this case, that of the companion object). The pulsar also rotates more slowly due to special-relativistic time dilation – it is traveling faster near the companion object.

Three Equations! These two effects determine the mass and inclination of the system! This happens because, assuming that general relativity applies, they depend on the known Keplerian parameters and the masses of the two objects:

Mass Determination Combining these three equations, we can solve for the three unknowns and obtain the most precise measurement of any mass outside the solar system!

One More Equation! A third relativistic effect is measurable: The orbital period is becoming shorter! General relativity predicts this to be due to the loss of energy caused by emission of gravitational waves. This depends only on quantities that are already (supposedly) known: The system of equations is over-determined. Prediction: the orbital period should vary – x 10 –12 s/s (or –75  s per year!)

GR Wins! Value observed (after subtraction of the Galactic motion of the pulsar) is – (52) x 10 –12 s/s. The agreement is perfect! GENERAL RELATIVITY GIVES A SELF- CONSISTENT ESTIMATE FOR THE MASSES OF THE TWO COMPONENTS OF THE BINARY! GRAVITATIONAL WAVES EXIST!

Gravitational Waves For this measurement, Hulse and Taylor were awarded the 1993 Nobel Prize in Physics.1993 Nobel Prize in Physics This emboldened astronomers to build giant gravitational wave detectors! This will be one of the great new areas of research in the 21 st century!

Three Current Pulsar Arecibo A Necessarily Biased View

Was Einstein Right? Tests of general relativity continue unabated after more than 30 years! Two tests of general relativity were made in PSR B , GR passed both (inclusively a Shapiro delay test) (Stairs et al. 2002). An asymmetric “Nordtvedt” test was done at Arecibo using an array of wide binary Millisecond Pulsar - White Dwarf (MSP-WD) systems (Stairs et al. 2005) Asymmetric radiative tests are being conducted for the MSP-WD system PSR J (Freire et al. 2008). These asymmetric tests can strongly constrain alternative theories of gravitation!

How Massive Can a Pulsar Be? New Arecibo timing results for PSR B B suggest that pulsars could have masses of the order of 2 solar masses (Freire et al. 2007b)! This implies that the pressures at the center of neutron stars are higher than expected. This constrains the behavior of cold, super-dense matter (see B. Link’s talk!). Neutron stars are probably quite “large” (radii of more than 13 km or so).

Finding new Millisecond Pulsars Finding new MSPs is the main objective of the ALFA pulsar survey. The first new MSP discovered in this survey, PSR J , is a 2.15-ms pulsar in an eccentric orbit with a massive companion (Champion 2007). This system represents a major challenge to all presently accepted stellar evolution theories! This survey will discover many more physics laboratories - excellent for GR tests, NS mass measurements and gravitational wave detection (see A. Lommen and F. Jenet’s talks)!

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