1. LIGO-G07XXXX-00-Z Beating the Crab pulsar spin-down and other upper limits: new results from the LIGO S5 known pulsar search Matthew Pitkin for the LIGO Scientific Collaboration matthew@astro.gla.ac.uk LIGO-G07XXXX-00-Z

2. Beating the Crab pulsar spin-down and other upper limits: new results from the LIGO S5 known pulsar search Matthew Pitkin for the LIGO Scientific Collaboration matthew@astro.gla.ac.uk LIGO-G0XXXX-00-Z

3. LIGO-G07XXXX-00-Z Targeted pulsar search - Why? Rapidly spinning neutron stars provide a potential source of continuous gravitational waves To emit gravitational waves they must have some degree of non-axisymmetry e.g. triaxial deformation due to elastic stresses or magnetic fields Size of distortions can reveal information about the neutron star equation of state Many millisecond and fast young pulsars have very well determined parameters and are generally very stable - good candidates for a targeted search using gravitational detectors! The greatly reduced unknown parameter space allows deep, relatively computational inexpensive searches using long time spans of data

4. LIGO-G07XXXX-00-Z Targeted search - method Pulsar signal parameterised by: h 0 - gravitational wave amplitude,  - pulsar orientation,  -  gravitational wave phase, and  - polarisation angle Signal is Doppler modulated by detector and source motion Assume that the gravitational wave emission from triaxial neutron star that is tightly coupled and phase locked with the EM emission  Heterodyne time domain data using the known phase evolution of the pulsar  Bayesian parameter estimation of unknown pulsar parameters using data from all interferometers Within the LIGO sensitive band ( gw > 50 Hz) there are currently 163 known pulsars We have rotational and positional parameter information for 97 of these

5. LIGO-G07XXXX-00-Z Preliminary results preliminary results for use Joint 95% upper limits from 4 Nov 05 – 22 Jan 07 of S5 using H1, H2 and L1 (97 pulsars) Lowest h 0 upper limit: PSR J1435-6100 ( n gw = 214.0 Hz, r = 3.3 kpc) h 0_min = 3.1x10 -26 Lowest ellipticity upper limit: PSR J2124-3358 ( n gw = 405.6Hz, r = 0.25 kpc)  = 7.3x10 -8 Due to pulsar glitches the Crab pulsar result uses data up to the glitch on 23 Aug 2006, and the PSRJ0537-6910 result uses only three months of data between two glitches on 5th May and 4th Aug 2006

6. LIGO-G07XXXX-00-Z preliminary Black curve represents one full year of data for all three interferometers running at design sensitivity Blue stars represent pulsars for which we are reasonably confident of having phase coherence with the signal model Green stars represent pulsars for which there is uncertainty about phase coherence

7. LIGO-G07XXXX-00-Z Crab pulsar – spin-down limit Spin-down limit assumes all the pulsars rotational energy loss is radiated by gravitational wave We know some goes is emitted electromagnetically and is powering the expansion of the Crab nebula This is poorly constrained and allows room for gravitational wave emission Braking index  The braking index of the Crab is n=2.5, not n=3 for purely magnetic dipole radiation, and not n=5 for purely gravitational radiation emission  Palomba (2000) allows for a combination of mechanisms to account for this braking index and ends up with a GW spin-down limit which is 2.5 times below the n=5 standard limit. Standard spin-down limit:

8. LIGO-G07XXXX-00-Z preliminary results for use Crab pulsar - result These results give upper limits for the Crab pulsar of  < 2.6x10 -4, h 0 < 5.0x10 -25  this value of the ellipticity is now in the range of some of the more speculative equations of state (Owen 2005, Haskell et al 2007, Lin 2007) These beat the spin-down limit of h 0 < 1.4x10 -24 by a factor of 2.9 – for canonical moment of inertia I = 10 38 kgm 2 Start to constrain the amount of spin-down energy in GWs to less than 10% of overall emitted and known spin-down (Palomba 2000, Santostasi).  This is significant: the uncertainties on all non-GW contributions add up to 80% of the total! Moment of inertia is uncertain by about a factor of three, but we can plot the result on the moment of inertia – ellipticity plane to give exclusion regions (Pitkin for the LSC, 2005)

9. LIGO-G07XXXX-00-Z Crab prior constraints There are potentially observational constraints on the values of  and  for the Crab pulsar that we can include as priors within our posterior calculation The observation of an interpulse and polarisation properties of the pulsar suggest that the inclination angle is around 90 degrees (uncertainty?) Observations of the pulsar wind nebula give a value of the pulsar position angle (the angle on the plane of the sky) of 124(1) degree  This converts to a value of  of 34 degrees

10. LIGO-G07XXXX-00-Z Priors If you restrict cos  to be around zero then it decreases sensitivity as you would just be seeing linearly polarised waves On simulated data (Gaussian noise) with cos  restricted with a flat prior between -0.05 and 0.05 there is an average upper limit increase of 20(4)% over that with a flat prior over the whole range

11. LIGO-G07XXXX-00-Z Priors For the Crab pulsar there is quite a large difference in the antenna pattern amplitude between LHO and LLO This means that the posteriors on  for the different detectors are slightly different with LHO peaking more at  For LHO if  is restricted, with a flat prior, between +/- 5 degrees of 34 degrees then on average the upper limit (on Gaussian noise) is 13 +/- 17% smaller For LLO if  is restricted, with a flat prior, between +/- 5 degrees of 34 degrees then on average the upper limit (on Gaussian noise) is the same with +/-14% fluctuations

12. LIGO-G07XXXX-00-Z Result with restricted prior Our actual data is not totally stationary and has different amplitudes and lengths for the different detectors Using the above prior ranges on the real data, and producing a joint upper limit gives h 0 =4.6x10 -25 which is 9% smaller than that using flat priors over the whole range It seems that the detrimental effect of the cosi prior is compensated for by the  prior!

13. Motivation for a Wide Parameter Search for the Crab Pulsar We can imagine some simple physical mechanisms by which the GW and EM pulses would have different frequencies  Free precession  Two component model

14. Free Precession The Crab pulsar is not undergoing large angle precession, since that would show up clearly in the radio timing data However, very small angle precession could be occurring If we assume a simple axisymmetric model for the neutron star where I 1 = I 2 ≠I 3, we can write the precession angular frequency, p, as where is the angular rotation, is the ellipticity, and is the wobble angle GWs will occur at frequencies of  and 2 , while the frequency of the electromagnetic radiation will be  +  p An ellipticity of order 10 -5 to 10 -4 combined with  << 1 could cause a shift of order of 10 -3 Hz for the Crab pulsar

15. Two Component Model and Glitches The Crab pulsar occasionally glitches, resulting in a sudden speed up of the pulse frequency, of order The glitches could be caused by a sudden transfer of angular momentum between two components, from an inner core to an outer crust These glitches relax back to the original frequency evolution on timescales of days to weeks, which could be caused by a friction-like torque connecting the two distinct components ~ 2x10 -9 to 6x10 -8

16. Two Component Model The recovery time scale, t coupling, of weeks to days would be inversely proportional to the strength of the friction-like torque between the components The steady state frequency lag between the two components would be depend on the ratio of the strength of torque connecting the two components to the total torque spinning down the pulsar, effectively measured by the spin down age, t spin-down, of the pulsar A relation would hold in this case For the Crab pulsar this would estimate a difference in frequency also of order 10 -3 Hz

17. Parameter Space We also need estimates for differences in and Begin by writing by the GW frequency in terms of the EM frequency and the small deviation away, d By taking time derivatives of this equation, and making the assumption that the GW frequency evolution follows the EM frequency evolution and does not drift away over time we can estimate the size of the bands

18. Final Parameter space The size of the final parameter space with regards to the frequency and its derivatives is: It should be emphasized that this parameter space was chosen in part because its computationally reasonable in addition to being physically motivated - taking approximately one day on 400 nodes of the Caltech computer cluster to complete