Gravitational wave detection with pulsar timing arrays Michael Kramer Max-Planck-Institut für Radioastronomie, Bonn Jodrell Bank Centre for Astrophysics, Univeristy of Manchester Outline • Introduction Pulsar timing Pulsar timing arrays (PTAs) • Science with PTAs Theories of gravity Gravitational Wave Astronomy On-going and future experiments Status & prospects Recent progress • Conclusions Pulsars… • …cosmic lighthouses • …almost Black Holes: mass of ~1.4 Solar Mass within 20km • …objects of extreme matter – 10x nuclear density 13 – B ~ Bcr = 4.4 x 10 Gauss – Voltage drops ~ 1012 volts 10-12 – FEM = 10 Fgravity – High-temperature & superfluid superconductor • …very stable clocks: The best pulsars keep time with an accuracy of 1 millionth of a second over 30 years (comparable to the best atomic clocks) Pulsar Timing “Simple” and clean experiment: - compare arrival times of pulses at telescope with model including… • Astrometric position, proper motion and parallax • Spin-down behaviour • Interstellar dispersion delays • Movement about possible binary companion & rel. effects - Measurement & determination is result of iterative process trying to minimize “post-fit residuals”, e.g Fold Fold Model TOA Residual Coherent timing solution about 1,000,000 more precise than Doppler method! Pulsar Timing “Simple” and clean experiment: - compare arrival times of pulses at telescope with model including… • Astrometric position, proper motion and parallax • Spin-down behaviour • Interstellar dispersion delays • Movement about possible binary companion & rel. effects - Measurement & determination is result of iterative process trying to minimize “post-fit residuals” - extremely precise measurements: PSR J1012+5307: 15 years of observations with EPTA P = 0.005255749014115410 ± 0.000000000000000015 s [ Lazaridis et al. 2009 ] ! 100 billion rotations since discovery & not lost a single count! High precision measurements indeed! – “Best of” examples… Masses: • Masses of neutron stars: m1 = 1.4398(2) M and m2 = 1.3886(2) M (Weisberg et al. 2010) • Mass of WD companion: 0.207(2) M (Hotan et al. 2006) • Mass of millisecond pulsar: 1.67(2) M (Freire et al. 2010) • Main sequence star companion: 1.029(8) M (Freire et al. 2010) -4 • Mass of Jupiter and moons: 9.547921(2) x 10 M (Champion et a. 2010) Spin parameters: • Period: 5.757451924362137(2) ms Note: 2 atto seconds uncertainty! (Verbiest et al. 2008) Orbital parameters: • Period: 0.102251562479(8) day (Kramer et al. in prep.) • Eccentricity: 3.5 (1.1) × 10−7 (Freire et al. in 2012) Astrometry: • Distance: 157(1) pc (Verbiest et al. 2008) • Proper motion: 140.915(1) mas/yr (Verbiest e t al. 2008) Tests of general relativity: • Periastron advance: 4.226598(4) deg/yr (Weisberg et al. 2010) • Shrinkage due to GW emission: 7.152(8) mm/day (Kramer et al. in prep) • GR validity (obs/exp): 1.0000(5) (Kramer et al. in prep.) • Constancy of grav. Constant, dG/dt/G: (9±12) x 10-13 yr-1 (Zhu et al. in prep) Gravitational wave detection: • Change in relative distance: 100m / 1 lightyear (PTAs) But with the SKA…we can do so much more, for instance: • Measure SGR A* properties: mass to 10-6, spin to 10-4 to 10-3, no hair to 10-3 to 10-2: No hair! (Liu et al. 2012) Pulsar Timing - Ability to measure small effects scales with various parameters, mostly sensitivity: 3 / 2 W Tsys 1 Pδ σTOA ≅ ∝ × × S /N Aeff tobsΔν SPSR Telescope Obs. Pulsar - Indicator:€ RMS timing residuals σTOA, current state of art ~ 50 ns σTOA Amin,GWB ∝ 5 / 3 T NPSR × NTOA / PSR - Important factors: - Instrumental calibration € - Interstellar weather - Source specific: Strength, period, pulse shape, “timing noise” - Need to know things accurately: time, solar system ephemerides We even measure the masses of our planets… Champion et al. (2010) Putting the planets on the pulsar scale… • incorrect planet masses have severe impact on our timing residuals = measured – expected pulse times of arrival • in the future, a PTA should measure planet masses very precisely Champion et al. (2010) Champion et al. (2010) Effect of a Jupiter mass modified PTA with biweekly observations -10 by 5x10 M! of 20 pulsars A pulsar time scale • There is not absolutely accurate clock on Earth • Only, some 2clocksG. are Hobbs better et al. than others (or corrected later…) the motion of the Earth about the solar system barycen- tre. Timing residuals are the difference between the arrival times converted to the solar system barycentre and predic- tions of those times based upon the timing model (see e.g., Edwards, Hobbs & Manchester 2006 for details). Non-zero residuals can result from an incorrect conversion from the measured ToAs to barycentric arrival times. Our ability to convert to barycentric arrival times relies, for instance, upon Hobbs et al. (2012) the accuracy of the solar system ephemeris. Many pulsars also display irregularities in rotation and changes in pulse shape that make timing difficult (e.g., Lyne et al. 2011 and references therein). A subset of pulsars, the “millisecond pul- sars”, have shorter pulse periods and much more stable ro- tation than the “normal pulsars”. However, precise observa- tions of millisecond pulsars show some unexplained timing irregularities which we refer to as “timing noise”. Figure 1. The top panel shows the difference between Some of the variations in the timing residuals are caused TT(BIPM11) and TT(TAI) since the year 1994. The bottom If the clock is wrong, all pulsars will be affected in the sameby way! processes that are correlated between different pulsars. panel shows the same, but after a quadratic polynomial has been These can be identified by observing an ensemble of pul- fitted and removed. sars, a so-called “Pulsar Timing Array” (PTA, e.g., Foster &Backer1990).Errorsintheterrestrialtimestandardwill (which does conform to the SI second) from EAL, various introduce exactly the same signal in the residuals for each frequency adjustments are necessary. These are determined pulsar. In contrast, errors in the planetary ephemeris used in using primary frequency standards. Frequency adjustments the timing analysis will induce timing residuals which have a are generally made slowly, a process referred to as “steer- dipolar signature on the sky and gravitational waves prop- ing”. In 1996, a decision was made to change the realization agating past the pulsar and the Earth will induce timing of the SI second that resulted in a frequency shift of about residuals with a quadrupolar signature. As shown later in 2 × 10?14.ThatshiftwasprogressivelyintroducedintoTAI this paper, it is not possible to obtain an unbiased estimate over a period of two years. As TAI itself is never retroac- of the time standard errors simply by forming a weighted tively corrected, only the post-corrected versions of TT, e.g., average of the timing residuals for different pulsars. This is TT(BIPM11), have the earlier data corrected. This leads to because of the coupling between the timing model for each the “bump” that we observe in Figure 1 around the year pulsar and the measurement of the correlated signal as well 1998. as the differing data spans for each pulsar. Although numerous clocks are used in forming TAI and In this paper we analyse data from the Parkes Pulsar there is continuous development of atomic clocks, stability Timing Array (PPTA) project (Manchester et al. 2012) to over decades is difficult to measure and maintain. It is there- develop a pulsar-based timescale which we label an Ensem- fore desirable to have an independent precise timescale valid ble Pulsar Scale (EPS). This scale has similarities to the on such long intervals. In this paper, we describe the devel- free atomic timescale EAL. The frequency of EAL needs to opment of such a timescale based on the rotation of pulsars. be steered using primary frequency standards to realise a Radio pulsars are rotating, magnetised neutron stars timescale based on the SI second. Similarly, since the intrin- that radiate beams of electromagnetic waves. For a fortu- sic pulsar pulse periods and their time derivatives are un- itous line of sight to the pulsar, these can be observed at the known for the pulsars in a PTA, the EPS is not an absolute Earth as pulses. The pulse times of arrival (ToAs) from the timescale and it must be “steered” to a reference timescale brightest and fastest-spinning pulsars can be measured with which conforms to the SI. This is achieved by first forming aprecisionof∼ 100 ns in an observation time of ∼ 1hour. timing residuals for each pulsar with respect to the reference This precision is significantly worse than that obtainable timescale, TT(TAI) in our case, and subsequently fitting a from atomic clocks, but, in contrast to individual clocks, quadratic polynomial to the residuals. Fluctuations in the can be maintained for a very long time. We note that a reference timescale with respect to the EPS can be identified pulsar-based timescale provides: and used to provide a set of corrections to that realisation of TT, thereby realising a new pulsar-based timescale. We • an independent check on terrestrial timescales using a refer to the timescale derived in this paper as TT(PPTA11). system that is not terrestrial in origin. The bottom panel of Figure 1 shows the difference between • atimescalebasedonmacroscopicobjectsofstellarmass TT(BIPM11) and TT(TAI) after a quadratic polynomial instead of being based on atomic clocks that are based on has been fitted and removed. It is this signal that we expect quantum processes. to see in comparing TT(PPTA11) with TT(TAI). • atimescalethatiscontinuousandwillremainvalidfar Earlier attempts to develop a pulsar timescale have been longer than any clock we can construct. made by Guinot & Petit (1991), Petit & Tavella (1996), 2 In order to develop a pulsar-based timescale, all phe- Rodin (2008) and Rodin & Chen (2011) .Wewillshowbe- nomena affecting the pulse ToAs must be taken into ac- low that, in contrast to our method, these earlier attempts count.