Searches for Continuous Gravitational Waves

Transcription

1 Searches for Continuous Gravitational Waves Keith Riles University of Michigan LIGO Scientific Collaboration and the Virgo Collaboration Guenakh Fest University of Florida March 30, 2018 LIGO-G

2 Generation of Continuous Gravitational Waves q Radiation generated by quadrupolar mass movements: h µν = 2G d 2 I rc 4 dt 2 µν No GW from axisymmetric object rotating about symmetry axis (I μν = quadrupole tensor, r = source distance) q Spinning neutron star with equatorial ellipticity ε equat ε equat = I xx I yy I zz gives a strain amplitude h (f GW = 2!f Rot ): Courtesy: U. Liverpool h = kpc r f GW khz 2 ε 10 6 I zz kg m 2 2

3 Gravitational CW mechanisms q Equatorial ellipticity (e.g., mm-high bulge ): h ε equat with f GW = 2 f rot q Poloidal ellipticity (natural) + wobble angle (precessing star): h ε poloidal θ wobble with f GW = f rot ± f precess (precession due to different L and Ω axes) q Two-component (crust+superfluid)! f GW = f rot and 2 f rot q r modes (rotational oscillations CFS-driven instability): N. Andersson, ApJ 502 (1998) 708 S. Chandrasekhar PRL 24 (1970) 611 J. Friedman, B.F. Schutz, ApJ 221 (1978) 937 h α r-mode with f GW 4 3 f rot 3

4 Gravitational CW mechanisms Assumption we (LSC, Virgo) have usually made to date: Bulge is best bet for detection! Look for GW emission at twice the EM frequency e.g., look for Crab Pulsar (29.7 Hz) at 59.5 Hz (troublesome frequency in North America!) What is allowed for ε equat? Old maximum (?) [σ/10-2 ] ( ordinary neutron star) with σ = breaking strain of crust G. Ushomirsky, C. Cutler, L. Bildsten MNRAS 319 (2000) 902 More recent finding: σ 10-1 supported by detailed numerical simulation C.J. Horowitz & K. Kadau PRL 102, (2009) Recent re-evaluation: ε equat < 10-5 N.K. Johnson-McDaniel & B.J. Owen PRD 88 (2013)

5 Gravitational CW mechanisms Strange quark stars could support much higher ellipticities B.J. Owen PRL 95 (2005) , Johnson-McDaniel & Owen (2013) Maximum ε equat 10-1 (!) But what ε equat is realistic? What could drive ε equat to a high value (besides accretion)? Millisecond pulsars have spindown-implied values lower than " 5

6 Finding a completely unknown CW Source Serious technical difficulty: Doppler frequency shifts w Frequency modulation from earth s rotation (v/c ~ 10-6 ) w Frequency modulation from earth s orbital motion (v/c ~ 10-4 ) à Coherent integration of 1 year gives frequency resolution of 30 nhz à 1 khz source spread over 6 million bins in ordinary FFT! Additional, related complications: Daily amplitude modulation of antenna pattern Spin-down of source Orbital motion of sources in binary systems 6

7 Finding a completely unknown CW Source Modulations / drifts complicate analysis enormously: w Simple Fourier transform inadequate w Every sky direction requires different demodulation Computational scaling: Single coherence time Sensitivity improves as (T coherence ) 1/2 but cost scales with ~ (T coherence ) 6+ à Restricts T coherence < few days for all-sky search à Exploit coincidence among different spans Alternative: Semi-coherent stacking of spectra (e.g., T coherence = 30 min) à Sensitivity improves only as (N stack ) 1/4! All-sky survey at full sensitivity = Formidable challenge Impossible? 7

8 But three substantial benefits from modulations: w Reality of signal confirmed by need for corrections w Corrections give precise direction of source w Single interferometer can make definitive discovery Can zoom in further with follow-up algorithms once we lock on to source V. Dergachev, PRD 85 (2012) M. Shaltev & R. Prix, PRD 87 (2013) A. Singh et al, PRD 96 (2017) Sky map of strain power for signal injection (semi-coherent search) 8

9 Recent results Targeted search for 200 known pulsars in O1 data B. Abbott et al., Ap. J (2017) 12 O1 sensitivity estimate O1 results spin-down limits surpass spin-down limits Initial detector results Lowest (best) upper limit on strain: h 0 < Lowest (best) upper limit on ellipticity: ε < Strain Sensitivity h Crab limit at 0.2% of total energy loss (beats spindown limit ) arxiv: (Sept 2013) Gravitational-wave Frequency (Hz)

10 Another take on the 200* 10 *Also looked for non-tensorial polarizations none seen B. Abbott et al, PRL 120 (2018)

11 Recent results Narrowband Search Targeted search assumes exact agreement between EM and GW phase, but differential rotation can lead to slight mismatch à Additional search ( narrowband ) for nearby phase templates O(10-3 ) relative frequency mismatch à Can still beat spindown limit for handful of pulsars Vela B. Abbott et al., PRD 96, (2017) Crab h min J J J J J J J J J Frequency [Hz]

12 Recent results Scorpius X-1 Low-mass X-ray binary (LMXB) brightest X-ray source outside Sun For an LMXB, equating accretion rate torque (inferred from X-ray luminosity) to gravitational wave angular momentum loss (steady state) gives: [R.V. Wagoner, ApJ 278 (1984) 345; J. Papaloizou & J.E. Pringle, MNRAS 184 (1978) 501; L. Bildsten, ApJ 501 (1998) L89] Marginalized Upper Limits Courtesy: McGill U. 12 h0 upper limit B. Abbott et al., PRD 96, (2017) Radiometer O1 Viterbi O1 CrossCorr O1 torque balance Frequency (Hz)

13 Recent results All-sky search B. Abbott et al., arxiv: , Feb 2018 h0 1e 25 1e 24 1e 23 PowerFlux worst case (linear) PowerFlux best case (circular) TimeDomain F stat pop. average SkyHough population average Frequency (Hz)

14 Recent results All-sky search Powerflux lin. pol B. Abbott et al., PRD 96, (2017) Powerflux circ. pol. TD Fstat Sky Hough Freq. Hough h 95% Lower frequency band badly contaminated with instrumental spectral lines Frequency (Hz)

15 Recent results All-sky search Powerflux O1 search Time-domain F-stat O1 search Sky Hough O1 search Frequency Hough O1 search Results from this search B. Abbott et al., PRD 96, (2017) permits deepest search at lowest frequencies 15

16 No CW discoveries yet, but Summary Still examining data we have taken in O2 run Future: More sensitive detectors Longer (and cleaner) data sets Improved algorithms à Could be on cusp of new type of GW discovery Nature sometimes bestows golden gifts 16

17 Extra Slides 17

18 Recent results All-sky search B. Abbott et al., arxiv: , Feb

19 What is the direct spindown limit? It is useful to define the direct spindown limit for a known pulsar, under the assumption that it is a gravitar, i.e., a star spinning down due to gravitational wave energy loss Unrealistic for known stars, but serves as a useful benchmark Equating measured rotational energy loss (from measured period increase and reasonable moment of inertia) to GW emission gives: kpc 1kHz h SD = df / dt GW I d f GW Hz / s g cm 2 Example: Crab à h SD = (d=2 kpc, f GW = 59.5 Hz, df GW /dt = Hz/s ) 19

20 What is the age-based spindown limit? If a star s age is known (e.g., historical SNR), but its spin is unknown, one can still define an indirect spindown upper limit by assuming gravitar behavior has dominated its lifetime: τ = And substitute into h SD to obtain [K. Wette, B. Owen, CQG 25 (2008) ] f 4 (df / dt) h Example: ISD 24 kpc 1000yr I 45 2 = d τ 10 g cm Cassiopeia A à h ISD = (d=3.4 kpc, τ=328 yr) 20

21 What is the X-ray flux limit? For an LMXB, equating accretion rate torque (inferred from X-ray luminosity) to gravitational wave angular momentum loss (steady state) gives: [R.V. Wagoner ApJ 278 (1984) 345; J. Papaloizou & J.E. Pringle MNRAS 184 (1978) 501; L. Bildsten ApJ 501 (1998) L89] h 600Hz F x X ray fsig 10 erg cm s Example: Scorpius X-1! h X-ray [600 Hz / f sig ] 1/2 (F x = erg cm -2 s-1 ) Courtesy: McGill U. 21

22 Not all known sources have measured timing Compact central object in the Cassiopeia A supernova remnant Birth observed in 1681 One of the youngest neutron stars known Star is observed in X-rays, but no pulsations observed Other results Requires a broad band search over accessible band Cassiopeia A 22

23 Other results Directed search Search for Cassiopeia A Young age (~300 years) requires search over 2 nd derivative S.J. Zhu et al., PRD 94 (2016) indirect upper limit (based on age, distance) 23

24 Other results All-sky binary search Circular polarization limits Random orientation limits h 0 95% upper limit J. Aasi et al., PRD 90 (2014) Frequency (Hz)

25 Searching for continuous waves Several approaches tried or in development: Summed powers from many short (30-minute) FFTs with skydependent corrections for Doppler frequency shifts! Semicoherent (StackSlide, Hough transform (2 types), PowerFlux) Frequency bin Time Time Push up close to longest coherence time allowed by computing resources (~few days) and look for coincidences among outliers in different data stretches (demodulation-based F-Statistic) 25

26 q q q q q q q GEO-600 Hannover LIGO Hanford LIGO Livingston Current search point Current search coordinates Known pulsars Known supernovae remnants Your computer can help too! 26