Gravity Wave Detection By Pulsar timing arrays

1. Gravity Wave Detection By Pulsar timing arrays Zack Carson Introduction to Cosmology Department of Physics and Astronomy, University of Utah April 16, 2014

2. Outline • Background and motivation • Einstein, general relativity, and gravity waves • Current gravity wave detection efforts • Neutron stars • Pulsar Timing Arrays • Laser Interferometry • Results and future projections • IPTA “Data Challenge”

3. Background of gravity and general relativity

4. Background • In 1687, Isaac Newton published PhilosophiaeNaturalis Principia Mathematica, with reference to Kepler’s laws of planetary motion. • Principia stated his 3 laws of motion, which resulted in his universal law of gravitation. • This law explains how objects contain “gravitas” (or weight) which in effect describe the force of gravity between massive objects. • Where G is a universal constant, are the individual masses, and r is the distance between centers of mass. • This universal law of gravitation was so complete that is was accepted for 200 years.

5. Background • 200 years later, Einstein and many others noticed slight flaws in predictions from Newton's equations, particularly in the fact that the precession of Mercury’s perihelion was unaccounted for by 43” per century. • In formation of his famous theory on general relativity, Einstein first needed the use Special Relativity and the Equivalence Principle.

6. Special relativity • In 1905 Einstein published his paper “On the Electrodynamics of Moving Bodies.” This paper laid the foundation for special relativity, the relationship between time and space. It is based on two postulates: • The laws of physics are invariant in all inertial systems (non-accelerating frames of reference). • The speed of light in a vacuum is identical to all observers, regardless of frame or motion of source. • Special Relativity also shows that space and time coordinates are intimately woven together and can be treated identically and as a 4-dimensional space. • Galilean relativity is now considered an approximation for special relativity at low speeds, and special relativity is considered an approximation for general relativity within weak gravitational fields. • The famous relationship between mass and energy, , is also derived.

7. The equivalence principle • The principle of equivalence states that “events performed in a uniformly accelerating reference frame with acceleration a are indistinguishable from the same experiments performed with in a non-accelerating frame situated in a gravitational field with acceleration due to gravity being ”. • This implies that the inertial mass from is equivalent to the gravitational mass in . • This also implies that light ejected perpendicular to the acceleration should be bent identically in both situations.

8. General relativity • As had been discovered, the perihelion of Mercury precessedwas about 5.75” per year. This phenomena was unexplained by Newton’s sense of gravity. • In response, Einstein started work on his theory of General Relativity, using both special relativity and the principle of equivalence. • In the theory of general relativity, Einstein explains that instead of acting on each other, massive/energetic objects influence space-time, which bends and in turns influences the motion of objects.

9. General Relativity • Massive and/or energetic objects bend the “fabric of space-time”. • “Spacetime tells matter how to move, and matter tells spacetime how to curve.” • This bending of space-time affects the geodesic followed by other objects. • This includes photons! • Space near massive objects is stretched. • Time near massive objects is dilated. • This comes into play in our daily lives as clocks on orbiting GPS satellites experience time differently than we do on Earth.

10. Geodesics about massive objects • As a consequence of general relativity, it was predicted that light would bend around massive objects, following its null geodesic. • The light incoming from Hyades was observed by Arthur Eddington bending around the sun on May 29th, 1919 during an eclipse. • As predicted by Einstein, the incoming light from Hyades was shifted by 0.75” • Light is also bent around large super clusters, allowing the indirect detection of dark matter via “gravitation lensing.”

11. Gravity waves • Similar to any other type of interactions, gravitationally bound objects were predicted to emit “gravitational radiation” in the form of gravitational waves. • These waves are identifiable ripples through space-time which physically stretches space and time by measurable amounts as they pass. • The waves passing through our Earth waves are predicted to strain space-time by about 1 part in , and travel at the speed of light, making measurements very difficult. • Shown on the left is the effect of a cross-polarized gravitational wave on a ring of particles.

12. The Mathematics of general relativity

13. General Relativity • The Minkowski spacetime metric is formulated by: • Using Einstein’s notation where summation is assumed over repeated Greek indices, and are the spacetime tensors, and is the metric tensor. • Subscripts denote covariant tensors and superscripts denote contravariant tensors. • The Geodesic Equation defines the path taken by an object in a curved spacetime • Where g is the general form of the metric tensor (not Minkowski-specific).

14. General Relativity • After determining that the Riemann curvature Tensor was too restrictive (flat spacetime implied no gravitational fields), Einstein used the Ricci Tensor by summing over the curvature tensor. Setting this tensor equal to zero gave Einstein’s Vacuum Field Equations: • Einstein’s field equations can be more aptly written in terms of the stress-energy tensor : • Where is Newton's gravitational constant, and is the Einstein Tensor.

15. General Relativity • Using the normal Minkowski metric, and letting represent the linearized gravitational field, a Lorentzian invariance can be created with a gauge invariance using the coordinate transformations: • Now the linearized Einstein equations are gauge-invariant, the form of the field equations can be simplified.

16. General Relativity • Now the trace-reversed field: Can be related to the stress energy tensor via Einstein’s Wave Equation: • Now another gauge can be applied to the gravitational field in order to keep only the physical degrees of freedom.

17. General Relativity • One of the most popular gauges at this stage is as follows: • Where are the two possible polarizations of the gravitational wave (plus polarized and cross-polarized.) • This is called the transverse traceless (TT) gauge, where the above matrix describes a plane gravitational wave propagating in the z-direction.

18. General Relativity • Now by introducing a perturbation through an expansion in (v is the characteristic velocity of masses in the system), the Quadrupole Radiation Formula can be obtained using the TT gauge and taking the lowest-order contribution: • Where Q is the trace-free quadrupole moment of the sources energy-density distribution, r is the distance to the source, and ret implies that time-derivatives should be taken at the retarded time .

19. General Relativity • Using the Quadrupole formula, multiple new equations may be derived. The gravitational wave luminosity from any given source becomes: • The natural dynamic frequency associated with any self-gravitating system can be described as: • And the time variation of the quadrupole moment is described by:

20. General Relativity • Combining these two equations gives an estimate of the amplitude and luminosity of the gravitational wave: • Next, calculating the time for system to radiate half of its gravitational energy gives us:

21. Detection of Gravitational waves

22. Laser Interferometer gravitational wave observatory • Alternative to pulsar timing arrays which use 1000’s of light-years long arms for measurement, LIGO measures the time-of-flight of a laser beam along a 4-km path, and compares it to an orthogonally oriented 4 km path. • Three observatories: • Two in Hanford, Washington. • Livingston, Louisiana. • Ground based observatories such as LIGO allow us to probe frequencies between 10 and 1000 Hz. • Pulsar timing arrays allow us to probe between 10 and 100 G.

23. Laser Interferometer gravitational wave observatory • On each of the two 4 km arms, two mirrors are hung at opposite ends. • A laser enters a beam splitter in the corner of the two arms and divides the light equally between the arms. • The light bounces repeatedly in each arm before returning to the beam splitter. • If the arms have identical lengths, there will be no interference and the light returns unchanged. • If a passing gravity wave altered the path length in either arm, interference will cause some light to be directed to a photo detector. • At least 2 widely separated detectors needed in order to rule out false signals.

24. General Relativity • Taking the earlier equations into account gives an estimate on the amplitude and frequency of a gravitational wave emitted from any given source: • Proportional to • Proportional to mass profile of the system

25. Gravitational Wave Sources • As shown in the previous equations, gravitational waves are only emitted if the mass profile is spherically asymmetric and forms a quadrupole moment. • As two object orbit each other, they slowly spiral inwards as energy is lost via gravitational radiation, until merging • Gravitational waves are emitted by multiple sources such as:

26. Neutron Stars • When a large enough star dies and collapses (1.5 solar masses) enough for gravitational pressure to overcome electron degeneracy pressure, a neutron star will be formed. • Due to extreme masses and miniscule diameters, these stars have enormous gravitational fields of around . • Due to high pressure and compression, they have temperatures normally around . • Due to the release of embedded magnetic fields in the original star, these neutron stars have magnetic fields of around .

27. Pulsars • In order to conserve angular momentum, the slow spinning original star must speed up considerably as the radius shrinks so enormously during the process of becoming a neutron star. • These neutron stars can have spin rates of up to 1000 per second, or a period of 0.001 seconds. • The spin rate is so incredibly precise that they are commonly known as the universes most precise clocks. • Pulsar timing arrays commonly using millisecond pulsars because of the extreme accuracy. • Charged particles are accelerated around magnetic field lines, creating synchrotron radiation, which is launched out of the magnetic poles creating a circular jet pattern around the rotation axis. • When oriented with respect to Earth so that we see the jet’s appearance once per rotation, these neutron stars are called pulsars.

28. Hulse-Taylor Pulsar • Using the Arecibo radio satellite in 1974, RusselHulse and Joseph Taylor discovered a binary pulsar system. • According to general relativity, as two massive bodies orbit each other, they emit gravitational waves as they lose energy; moving closer and closer until merging. • As can be seen, this cumulative shift between the bodies matches the predictions of general relativity with high accuracy.

29. Pulsar Timing arrays • Due to pulsar’s extreme stability, accuracy and precision in time-keeping as we monitor the sweeping beams from Earth; they become excellent tools for the detection of gravity waves. • For example, PSR B1937+21 has a period of which is accurate up to • This means we can accurately predict the arrival time of each next pulse, and can thus observe any minute deviations in the arrival times. • Any passing gravitational wave between Earth and any set of neutron stars would thus change the effective light travel distance; creating a time residual from the next expected pulse. • If the arrival times of light from multiple pulsars from known locations in the universe are compiled for long periods of time, correlations of varying time residuals can be used to detect the gravitational waves.

30. Pulsar timing array

31. International pulsar timing array • Monitors precise emission timings of over 30 individual pulsars in order to detect passing gravitational waves. • Composed of the European Pulsar Timing Array (EPTA), the Parkes Pulsar Timing Array (PPTA), and the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). • The goal is shared by each participant, however was formed as a collaboration to achieve success more quickly.

32. European pulsar timing array • The EPTA is currently monitoring 18 priority 1 pulsars with high-energy emissions and/or low orbital eccentricity. • The Effelsberg Radio Telescope in Effelsberg, Germany. • The Lovell Telescope in Cheshire, UK. • The NancayDecimetric Radio Telescope in Nancay, France. • The Sardinia Radio Telescope in PranuSanguni, Italy. • The Westerbork Synthesis Radio Telescope in Westerbork, The Netherlands.

33. European Pulsar Timing Array • The Effelsberg Radio Telescope • 100 m radio telescope monitoring frequencies between 0.395 to 95.5 GHz. • The Lovell Telescope • 76.2 m telescope observing 1.4 GHz frequencies. • The NancayDecimetric Radio Telescope • 94 m telescope monitoring frequencies between 1.1 and 3.5 GHz. Meridional nature allows it to track any source above declination for one hour. • The Sardinia Radio Telescope • 64 m telescope monitoring frequencies between 23 and 100 GHz. • The Westerbork Synthesis Radio Telescope • Array of 14 parabolic dishes working together, creating the equivalent of 94 m. Observes frequencies of 120 MHz to 8.3 GHz. Equatorially mounted East to West, allowing them to move without changing the orientation of receivers.

34. European Pulsar Timing Array

35. North American nanohertz observatory for gravitational waves • The NANOGravis currently monitoring 26 millisecond (very high precision) pulsars. • Monitored using the following radio telescopes: • The Arecibo Observatory in Puerto Rico. • 305 m radio telescope. Due to its large size and fixed location, Arecibo is limited by the portion of sky available; 20 degrees to each side overhead. It is the largest and most sensitive telescope in the world, and thus can observe very weak radio signals, such as the 19 millisecond pulsars it is currently monitoring. • The Green Bank Telescope in Green Bank, West Virginia. • 100 m telescope. Smaller then Arecibo, however it can be positioned so that it can see 85% of the total sky. It is extremely sensitive, and is located in the U.S. National Radio Quiet Zone, eliminating much unwanted background noise.

36. North American nanohertz observatory for gravitational waves

37. Parkes pulsar timing array • The PPTA is the newest addition to the IPTA and is composed of a single telescope, the Parkes Radio Telescope located in Parkes, New South Whales. It is a 64 m telescope, which can be tilted a maximum of , allowing it to see a majority of the sky.

38. International pulsar timing array data challenge • In order to open the project to the public, and to encourage development of gravitational wave research, IPTA hosts data challenges. • A simulated set of pulsar data containing an unknown gravity wave signal is released. • The challenge is to develop algorithms to detect or limit the presence of gravity wave signals in the data. • Open data set solutions are released at the start of the challenge for testing and calibration use. • Closed data set solutions are not revealed until the end of the challenge, making them the real challenge.

39. International Pulsar timing array results • Although pulsar timing arrays have yet to find any solid evidence of gravitational waves, much interesting data has been recovered. • On the left is a 7-hour pulse profile of J1731+0747. • Averaged over this time, the signal is 6000 times stronger than the noise.

40. International Pulsar timing arrayresults • On the left are the plots comprising of many telescope’s data plotted consecutively. • This shows how stable the pulsars behavior is, and allows us to create more accurate algorithms for finding gravitational waves. • Any point shifted above or below the x-axis corresponds to a time residual in which the signal came before or after what was expected. • Earth’s motion, pulsars motion, etc. has already been subtracted out.

41. International Pulsar timing array results Above is the pulse arrival times from the Green Bank Telescope.

42. The future of gravitational wave astronomy • Gravitational wave astronomy has only just begun and many projects are either just beginning, or still in the works. • All current pulsar timing arrays have many years-worth of data to be taken in order to perfectly calibrate instruments, methods, and algorithms. • There are several plans for making larger, more precise telescopes and ground based laser interferometers. • Successful detection of gravity waves would have enormous consequences. • They would enable more tests of general relativity, • They would allow us to probe many things the electromagnetic spectrum can not, such as black holes.

43. References • Simpson, David. "A Mathematical Derivation of the General Relativistic Schwarzschild Metric." East Tennessee State University. East Tennessee State University, 30 Apr 2007. Web. 19 Mar 2014. <http://faculty.etsu.edu/gardnerr/math-honors/theses/Simpson-Thesis.pdf>. • Camp, Jordan, ed. "Gravitational Wave Astronomy.“ Laboratory for High Energy Astrophysics. Goddard Space Flight Center. Web. 20 Mar 2014. <http://www.nikhef.nl/~jo/quantum/qm/virgo/vidi/annurev.nucl.54.070103.pdf>. • Hughes, Scott. "The Basics of Gravitational Wave Theory.“ Arxiv.org. Massechussets Institute of Technology, 5 october 2005. Web. 31 Mar 2014. <http://arxiv.org/pdf/gr-qc/0501041v3.pdf>. • http://nanograv.org/ • http://www.ipta4gw.org/ • http://www.epta.eu.org/ • http://www.astro.cardiff.ac.uk/research/gravity/tutorial/?page=3thehulsetaylor • http://www.atnf.csiro.au/research/pulsar/ppta/index.php?n=Main.PPTA • http://www.astro.umd.edu/~miller/nstar.html