Periodic Sources Working Group

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Presentation transcript:

Periodic Sources Working Group Results from the LSC Periodic Sources Working Group Alicia M. Sintes On behalf of the LIGO Scientific Collaboration LIGO-G030185-00-Z Recontres de Moriond Gravitational Waves and Experimental Gravity Les Arcs 1800, France 22-29 March 2003

Periodic Sources Working Group B.Allen, S.Anderson, S.Berukoff, P.Brady, D.Chin, R.Coldwell, T.Creighton, C.Cutler, R.Drever, R.Dupuis, S.Finn, D.Gustafson, J.Hough, Y.Itoh, B Krishnan, M.Landry, G.Mendell, C.Messenger, S.Mohanty, S.Mukherjee, M.A.Papa, B.Owen, K.Riles, B.Schutz, X.Siemens, A.M.Sintes, A.Vecchio, H.Ward, A.Wiseman, G.Woan, M.Zucker The group is working on methods to search for continuous gravitational waves from rotating neutron stars: We have exercised different analysis pipelines, established methods for setting upper limits on the strain amplitude of continuous gravitational waves from known pulsars, analyzed data collected during the first science run (S1) of GEO and LIGO, set upper limits on waves emitted by pulsar J1939+2134

Content GEO600 and LIGO first science run (S1) Two complementary analysis approaches: time domain method frequency domain method Future plans Results for a target pulsar Statistical properties of the S1 data

In-Lock Data Summary from LIGO S1 Red lines: integrated up time Green bands (w/ black borders): epochs of lock H1: 235 hrs H2: 298 hrs L1: 170 hrs August 23 – September 9, 2002: 408 hrs (17 days). H1 (4km): duty cycle 57.6% ; Total Locked time: 235 hrs H2 (2km): duty cycle 73.1% ; Total Locked time: 298 hrs L1 (4km): duty cycle 41.7% ; Total Locked time: 170 hrs Double coincidences: L1 && H1 : duty cycle 28.4%; Total coincident time: 116 hrs L1 && H2 : duty cycle 32.1%; Total coincident time: 131 hrs H1 && H2 : duty cycle 46.1%; Total coincident time: 188 hrs Triple Coincidence: L1, H1, and H2 : duty cycle 23.4% ; 95.7 hrs

In-Lock Data Summary from GEO S1 First lock lasted over ~5 days Total Locked time: 396 hrs Duty cycle: 98.5% Including maintenance periods: 453 hrs I have computed the duty cycle for GEO600 during the S1 run: The calculation was based on day-trend data (1 minute resolution) of the channel G1:LSC_MID_LS (microcontroller lock status). Maintenance periods were excluded (only the time where actually work was being done according to the labbook). Times were the data acquisition system was recording data with questionable quality in the low frequency band (<50 Hz) were considered as in-lock-time. Times when the DAQS was down (no data recorded) were considered as out-of-lock-time. Based on this calculation the overall duty cycle is 98.52%.

Limits on gravitational waves radiated by periodic sources -- GEO -- LHO 2km -- LHO 4km -- LLO 4km Crab pulsar hc S1 sensitivities hc: Amplitude detectable with 99% confidence during observation time T: hc = 4.2 [Sh(f)/T]1/2 Limit of detectability for rotating NS with equatorial ellipticity, e = dI/Izz: 10-3 , 10-4 , 10-5 @ 10 kpc Known EM pulsars Values of hc derived from measured spin-down IF spin-down were entirely attributable to GW emissions Rigorous astrophysical upper limit from energy conservation arguments Sensitivity to a continuous wave source with known parameters:sky location, frequency and spin-down Theories of emission mechanisms make it unlikely that one could detect pulsars with data from S1. The methods developed here are the optimal ones for detection. In this decade we expect instrumental sensitivity to increase enough that these methods will enable the direct observation of continuous GW . The fastest pulsar. E< 10^-5 ususally False dismissal 50%, 1% false alarm This slide shows that with the S1 sensitivity and observation time we cannot set astrophysically interesting ULs – this is why I highlit “methods” in the title. This is what the S1 analysis is about:methods. In fact we have exercised the analysis pipeline, established methods for setting UL that we will use when we get to a more interesting sensitivity region and are anyway setting upper limits that, using GW data, have not been set before. PSR J1939+2134 P = 0.00155781 s fGW = 1283.86 Hz P = 1.0519 10-19 s/s D = 3.6 kpc .

The signal – a reminder We use the standard model for the detected strain signal from a non-precessing neutron star: The GW signal from a pulsar will be frequency modulated by the motion and rotation of the Earth, and amplitude modulated due to the varying sensitivity of the detector with respect to a fixed source. Accurate timing routines (~2s) have been developed to convert between GPS and SSB time. Maximum phase mismatch ~10-2 radians for a few months. Two signal generation codes.

Two different analysis methods Time domain search – process signal to remove frequency variations due to Earth’s motion around Sun Best suited for targeted searches Efficiently handless missing data Adaptable to complicated phase evolutions Upper limits interpretation straightforward: Bayesian approach Frequency domain search – conceived as a module in a hierarchical search Efficient method for wide parameter searches -when signal characteristics are uncertain Straightforward implementation of standard matched filtering technique (maximum likelihood detection method): Cross-correlation of the signal with the template and inverse weights with the noise Frequentist approach used to cast upper limits.

Time domain target search Data are successively heterodyned to reduce the sample rate and take account of pulsar slowdown and Doppler shift, reducing the data rate to 1 sample per minute Bk Noise level is estimated from the variance of the data over each minute k Fit a model to this signal model. We take a Bayesian approach, and determine the joint posterior distribution of the probability of our unknown parameters, using uniform priors on over their accessible values, i.e. posterior prior likelihood The likelihood (that the data are consistent with a given set of model parameters) The likelihood is proportional to exp(-2 /2), where Marginalize over the uninteresting parameters to leave the posterior distribution for the probability of h0:

Upper limit definition & detection The 95% confidence upper limit is set by the value h95 satisfying A detection would appear as a maximum significantly offset from zero Most probable h0 h95 h95

Time domain S1 analysis We looked for the expected signal from PSR J1939+2134 at f=1283.86 Hz, with the entire accessible datasets from LHO 2km, LHO 4km, LLO 4km, and GEO. Set upper limits from all four interferometers and a joint upper limit. Analysis can easily be expanded to other pulsars. PSR1939+2134 is our ‘generic pulsar’.

Data (black) and noise estimates (yellow) for the LIGO S1 datasets. Time series for the GEO S1 data (~20 days). Black line is the heterodyned data, the red dots our estimate of the corresponding noise level. Data (black) and noise estimates (yellow) for the LIGO S1 datasets. Ratio of |data| / |noise| over the same period. The distribution is close to Gaussian, with the exception of a few outliers.

Gaussianity of Bk data if the data is Gaussian: the histogram should be Gaussian with m=0 s=1. The dots in the figures are the expected distribution. N: number of degrees of freedom = 2*number of Bks

“Results” (EM pulsar) PSR J1939+2134 Data Injected signal, h = x Injected signal, h = 2x Injected signal, h = 3x Injected signal, h = 5x Time domain analysis: No evidence of signal from PSR J1939 at f = 1283.86 Hz So the search for GW signal from this pulsar has not been carried out before at the level of sensitivity achieved here. Ref. -- hmax < 3 x 10-20 for PSR J1939 -- Hough, J. et al., Nature, 303 (1983) 216 hmax < 3 x 10-24 at f =921.35 (+/- 0.03) Hz - Astone, Phys.Rev. D65 (2002) 022001 (untargeted search)

Frequency domain search The input data are a set of SFTs of the time domain data, with a time baseline such that the instantaneous frequency of a putative signal does not move by more than half a frequency bin (60s for S1 to ensure stationarity) Data are studied in a narrow frequency band (0.5 Hz) and Sh(f) is estimated for each SFT. Detection statistic used is described in [Jaranoski, Krolak, Schutz, Phys. Rev. D58(1998)063001] The F detection statistic provides the maximum value of the likelihood ratio with respect to the unknown parameters, , given the data and the template parameters that are known f0min < f0 < f0max HIGH-PASS FILTER WINDOW ComputeFStatistic x(t) Sh is estimated in the band of interes Is it optimal. F is the statistic of choice for matched filtering methods with the lowest false dismissal rate and fixed false alarm rate FT F(f0) SFTs

F statistic & frequentist upper limit The outcome of a target search is a number F* that represents the optimal detection statistic for this search. 2F* is a random variable, for Gaussian stationary noise, follows a c2 distribution with 4 degrees of freedom. If the data contains the signal, 2F* follows a c2 dist. with 4 degrees of freedom and non-centrality parameter l, pc(2F|l). l  (h|h) Fixing , for every value of h0, we can obtain a pdf curve: The frequentist approach says the data will contain a signal with amplitude  h0 , with confidence C, if in repeated experiments, some fraction of trials C would yield a value of the detection statistics  F* is the functional inverse of is estimated by means of Monte Carlo simulations, injecting fake signals with fixed amplitude (for many different h0), using the worse case for If this is the signal we are searching for! Pdf probability density function

S1 analysis for PSR J1939+2134 Noise studies Value of  Sh  over a band of 1Hz over the entire S1 data. Bands 1281-1282 Hz and 1283.5-1284.5 Hz We have performed many noise analysis to check if the data in a narrow frequency band was Gaussian and stationary. That I’ll not enter in details here. or If the data was Gaussian in each frequency bin. GEO LHO 2km

Results for PSR J1939+2134 at f=1283.86 Hz Measured pdf for the F statistic Injected signals at h0= ? Dots: Monte Carlo simulations Line: c2 distribution (4 dof, l=?) Area: integral pdf between 2F* and  IFO F * h0(95%) lfit ltheory GEO LLO 4km LHO 4km LHO 2km 0.75 1.95 2.51 2.56 ? UL here are more conservative than before. We always have taken the worse case, not uniform distributions for our unknowns Frequency domain search The 95% confidence upper limit values of h0

Future plans Expand analysis to all known isolated pulsars whose emission frequency lies in the sensitivity band of the detectors Extend the targeted searches to pulsars in binary systems (work in progress for LMXRBs, e.g. Sco X-1) With time domain method, track systems with complex phase evolutions, e.g. Crab pulsar Extend searches to unknown sources using the frequency domain method Use incoherent methods (under development) to perform extensive parameter space surveys (e.g. unbias search, Hough transform)