First narrow-band search for continuous gravitational waves from known pulsars in advanced detector data
Spinning neutron stars asymmetric with respect to their rotation axis are potential sources of continuous gravitational waves for ground-based interferometric detectors. In the case of known pulsars a fully coherent search, based on matched filtering, which uses the position and rotational parameters obtained from electromagnetic observations, can be carried out. Matched filtering maximizes the signal-to-noise (SNR) ratio, but a large sensitivity loss is expected in case of even a very small mismatch between the assumed and the true signal parameters. For this reason, narrow-band analyses methods have been developed, allowing a fully coherent search for gravitational waves from known pulsars over a fraction of a hertz and several spin-down values. In this paper we describe a narrow-band search of eleven pulsars using data from Advanced LIGO’s first observing run. Although we have found several initial outliers, further studies show no significant evidence for the presence of a gravitational wave signal. Finally, we have placed upper limits on the signal strain amplitude lower than the spin-down limit for 5 of the 11 targets over the bands searched: in the case of J1813-1749 the spin-down limit has been beaten for the first time. For an additional 3 targets, the median upper limit across the search bands is below the spin-down limit. This is the most sensitive narrow-band search for continuous gravitational waves carried out so far.
On September 14th 2015 the gravitational wave (GW) signal emitted by a binary black hole merger was detected by the LIGO interferometers (IFOs) abbot:detection () followed on 26th December 2015, by the detection of a second event again associated to a binary black hole mergerabbot:detection2 (), thus opening the era of gravitational waves astronomy. More recently, the detection of a third binary black hole merger on Jan 4th 2017 has been announcedref:GW170104 (). Binary black hole mergers, however, are not the only detectable sources of GW. Among the potential sources of GW there are also spinning neutron stars (NS) asymmetric with respect to their rotation axis. These sources are expected to emit nearly monochromatic continuous waves (CW), with a frequency at a given fixed ratio with respect to the star’s rotational frequency, e.g. two times the rotational frequency for an asymmetric NS rotating around one of its principal axis of inertia. Different flavors of CW searches exist, depending on the degree of knowledge on the source parameters. Targeted searches assume source position and rotational parameters to be known with high accuracy, while all-sky searches aim at neutron stars with no observed electromagnetic counterpart. Various intermediate searches have also been developed. Among these, narrow-band searches are an extension of targeted searches for which the position of the source is accurately known but, the rotational parameters are slightly uncertain. Narrow-band searches allow for a possible small mismatch between the GW rotational parameters and those inferred from electromagnetic observations. This can be crucial if, for instance, the CW signal is emitted by a freely precessing neutron star LVC:old (), or in the case no updated ephemeris is available for a given pulsar. In both cases a targeted search could assume wrong rotational parameters, resulting in a significant sensitivity loss. In this paper we present the results of a fully coherent, narrow-band search for 11 known pulsars using data from the first observation run (O1) of the Advanced LIGO detectorsLIGO:adv (). The paper is organized as follows. In Sec. II we briefly summarise the main concepts of the analysis. Sec. III is dedicated to an outline of the analysis method. Sec. IV describes the selected pulsars. In Sec. V we discuss the analysis results, while the reader can refer to the Appendix for some technical details on the computation of upper limits. Finally, Sec. VI is dedicated to the conclusions and future prospects.
The GW signal emitted by an asymmetric spinning NS can be written, following the formalism first introduced in pia:articolo (), as the real part of:
where is the GW frequency, an initial phase. The polarisation amplitudes are given by:
being the ratio of the polarisation ellipse semi-minor to semi-major axis and the polarization angle, defined as the direction of the major axis with respect to the celestial parallel of the source (measured counter-clockwise). The detector sidereal response to the GW polarisations is encoded in the functions . It can be shown that the waveform defined by Eq. 1 is equivalent to the GW signal expressed in the more standard formalism of matt:O1_known (), given the following relations:
where is the angle between the line of sight and the star rotation axis, and
where and are respectively the star’s distance, its moment of inertia with respect to the rotation axis and the ellipticity, which measures the star’s degree of asymmetry. The signal at the detector is not monochromatic, i.e. the frequency in Eq. 1 is a function of time. In fact the signal is modulated by several effects, such as the Römer delay due to the detector motion and the source’s intrinsic spin-down due to the rotational energy loss from the source. In order to recover all the signal to noise ratio all these effects must be properly taken into account. If we have a measure of the pulsar rotational frequency , frequency derivative and distance , the GW signal amplitude can be constrained, assuming that all the rotational energy is lost via gravitational radiation. This strict upper limit, called spin-down limit, is given bykrolak:fstat ():
where is the star moment of inertia in unit of . The corresponding spin-down limit on the star equatorial fiducial ellipticity can be easily obtained from Eq. 4.
Even in the absence of a detection, establishing an amplitude upper limit below the spin-down limit for a given source is an important milestone, as it allows us to put a non-trivial constraint on the fraction of rotational energy lost through GWs.
Iii The analysis
The results discussed in this paper have been obtained by searching for CW signals from 11 known pulsars using data from the O1 run from the Advanced LIGO detectors (Hanford - LIGO H, and Livingston - LIGO L jointly). The run started on September 12th 2015 at 01:25:03 UTC and 18:29:03 UTC, respectively, and finished on January 19th 2016 at 17:07:59. LIGO H had a duty cycle of 60% and LIGO L had a duty cycle of 51%, which correspond respectively to 72 and 62 days of science data available for the analysis. In this paper we have used an initial calibration of the data abbott:calibration (). In order to perform joint search between the two detectors a common period from September 13th 2015 to January 12th 2016 111An exception is pulsar J0205+6449, see later., with a total observation time of about is selected. The natural frequency and spin-down grid spacings of the search are and . A follow-up analysis based on the LIGO’s second observation Run (O2) has been carried out, for this dataset we have analysed data from December 16th 2016 to May 8th 2017, more details will be given in Appendix C. The analysis pipeline consists of several steps, schematically depicted in Fig. 1, which we summarise here. The starting point is a collection of FFTs obtained from several interlaced data chunks (the short FFT Database - SFDB) built from calibrated detector data chunks of duration 1024 seconds astone:short (). At this stage, a first cleaning procedure is applied to the data in order to remove large, short-duration disturbances, that could reduce the search sensitivity. A frequency band is then extracted from the SFDBs covering typically a range larger (of the order of a factor of 2) than the frequency region analysed in the narrow-band search. The actual search frequency and spin-down bands, and , around the reference values, and , have been chosen according to the following relations rob:obs ():
being a factor parametrizing a possible discrepancy between the GW rotation parameters and those derived from electromagnetic observations. Previous narrowband searches used values of of the order , motivated partly by astrophysical considerationsLVC:old (), and partly by computational limitations rob:method (). Here we exploit the high computation efficiency of our pipeline to enlarge the search somewhat, depending on the pulsar, to a range between . The frequency and spin-down ranges explored in this analysis are listed in Tab. 5.
The narrow-band search is performed using a pipeline based on the 5-vector method rob:method () and, in particular, its latest implementation, fully described in mastrogiovanni:method (), to which the reader is referred for more details. The basic idea is that of exploring a range of frequency and spin-down values by properly applying barycentric and spin-down corrections to the data in such a way that a signal would become monochromatic apart from the sidereal modulation. While a single barycentric correction applied in the time domain holds for all the explored frequency band, several spin-down corrections, one for each point in the spin-down grid, are needed. A detection statistic (DS) is then computed for each point of the explored parameter space. By using the FFT algorithm for each given spin-down value it is possible to compute the statistic simultaneously over the whole range of frequencies, this process is done for each detector, and then data is combined. The frequency/spin-down plane is then divided into frequency sub-bands ( Hz) and, for each of them, the local maximum, over the spin-down grid, of the DS is selected as a candidate. The initial outliers are identified among the candidates using a threshold nominally corresponding to 1% (taking into account the number of trialsrob:method ()) on the p-value of the DS’s noise-only distribution222The noise-only distribution is computed from the values of the DS excluded in each frequency sub-band when selecting the local maxima and then an extrapolation of the long tail of the done and are subject to a follow-up stage in order to understand their nature. The follow-up procedure consists of the following steps: check if the outlier is close to known instrumental noise lines; compute the signal amplitude and check if it is constant throughout the run, compute the time evolution of the SNR (which we expect to increase as the square root of the observation time for stationary noise) and compute the 5-vector coherence, which is an indicator measuring the degree of consistency between the data and the estimated waveform pia:articolo (). For each target, if no outlier is confirmed by the follow-up we set an upper-limit on the GW amplitude and NS ellipticity, see Appendix A for more details.
Iv Selected targets
We have selected pulsars whose spin-down limit could possibly be beaten, or at least approached, based on the average sensitivity of O1 data, see Fig.2. Pulsar distances and spin-down limits are listed in Tab. 1. As distance estimations for the pulsars we have used the best fit value and relative uncertainties given by each indipendet measure, see pulsars list below and Tab. 1 for more details. The uncertainty on the spin-down limit in Tab. 1 can be computed using the relation for the variance propagation333If variable is defined from random variables with variance , then the variance can be estimated as: .For two of these pulsars (Crab and Vela) the spin-down limit has been already beaten in a past narrow-band search using Virgo VSR4 data rob:obs (). The other targets are analysed in a narrow-band search for the first time. The timing measures for the 11 pulsars were provided by the 76-meters Lovell telescope and the 42-foot radio telescopes at Jodrell Bank (UK), the 26-meters telescope telescope at Hartebeesthoek (South Africa), the 64-meters Parkes radio telescope (Australia) and the Fermi Large Area Telescope (LAT) which is a space satellite. For 7 of these pulsars (Crab, Vela, J0205+6449, J1813-1246, J1952+3252, J2043 +2740 and J2229+6114) updated ephemerides covering O1 period were available and a targeted search was done in a recent work matt:O1_known () beating the spin-down limit for all of them, while for the remaining 4 pulsars we have used older measures extrapolating the rotational parameters to the O1 epoch. A list of the analysed pulsars follows:
J0205+6449: Ephemerides obtained from Jodrell Bank. This pulsar had a glitch on November 11th 2015 which can affect the CW search greg:glitch (). For this reason we have performed the narrow-band search only on data before the glitch as done in matt:O1_known (). The distance are set accordingly to kko ().
J0534+2200 (Crab): One of the high value targets for CW searches matt:O1_known () due to its large spin-down value. For this pulsar it was possible to beat the spin-down limit in a narrow-band search using Virgo VSR4 data rob:obs (). Ephemerides have been obtained from Jodrell Bank telescope 444http://www.jb.man.ac.uk/pulsar/crab.html. The nominal distance for the Crab pulsar and it’s nebula is quoted in literature as kpc art:kaplan () we therefore assume the uncertainty correspond to confidence level.
J0835-4510 (Vela): Like the Crab pulsar, Vela is one of the traditional targets for CW searches. Although it spins at a relatively low frequency (compared to the others), it is very close to the Earth (), thus making it a potentially interesting source. Ephemerides obtained from the Hartebeesthoek Radio Astronomy Observatory in South Africa555http://www.hartrao.ac.za/. The distance and its uncertainty are taken accordingly to ddd ().
J1400-6326: First discovered as an INTEGRAL source and then identified as a pulsar by Rossi X-ray Timing Explorer (RXTE). This NS is located in the galactic supernova remnant G310.6-1.6 and it is supposed to be quite young, the distance and its uncertainty correspond to confidence level renaud:J1400 ().
J1813-1246: Ephemerides covering the O1 time span have been provided by the Fermi-LAT Collaborationmatt:O1_known (). Only a lower upper-limit is present on the distance.
J1813-1749: Located in one of the brightest and most compact TeV sources discovered in the HESS Galactic Plane Survey, HESS J1813-178. It is a young energetic pulsar that is responsible for the extended X-rays, and probably the TeV radiation as well. Timing obtained from Chandra and XMM Newton data halpern:J1813 (), pulsar’s distance and uncertainty are taken from m:messi () and correspond to confidence level.
J1833-1034: Located in the Supernova remnant G21.5-0.9. This source has been known for a long time as one of the Crab-like remnants. The evidence for a pulsar was found by analysing Chandra data, the distance and its uncertainty is set accordingly to camilo:J1833 () and correspond to confidence level.
J2022+3842: It is a young energetic pulsar that was discovered in Chandra observations of the radio supernova remnant SNR G76.9+1.0. Distance and uncertainty are set accordingly to arumugasamy:J2022 ().
J2043+2740: Ephemerides obtained from the Fermi-LAT Collaborationmatt:O1_known (). The distance is estimated using dispersion measure by man:cat () and using the model from yao (). The uncertainty on distance is set accordingly to the model and correspond to confidence level.
In this section we discuss the results of the analysis. First, in Sec. V.1 we briefly describe the initial outliers, for most of which the follow-up described in III has been enough to exclude a GW origin. Two outliers, belonging respectively, to the Vela and J1833-1034 pulsars needed a deeper study. The studies discussed in detail in the next section, disfavour the signal hypothesis and seem to suggest these outliers as marginal noise events. Nevertheless the outliers showed some promising features and for this reason a follow-up using O2 data has been carried out and described in Appendix C. The outliers were no longer present in O2 data and therefore inconsistent with persistent CW signals. Finally, in Sec. V.2 upper limits on the strain amplitude for the eleven targets are discussed.
v.1 Outliers outlook
We have found initial outliers for 9 of the 11 analysed pulsars. More precisely, for most pulsars we have found one or two outliers, with the exception of J1813-1749 (36 outliers) and J1952+3252 (6 outliers). For J2043+2740 and J2229+6114 no outlier has been found. A summary of the outliers found in the analysis is given in Tab. 6. The follow-up has clearly shown that in the case of J1952+3252 and J1813-1749 the outliers arise from noise disturbances in LIGO H (for J1813-1749) and in LIGO L (for J1952+3252), see Appendix B for more details. Most of the remaining outliers show an inconsistent time evolution of the SNR together with a low coherence between LIGO H and LIGO L and hence have been ruled out. As mentioned before, two outliers, one for J1833-1034 and one for Vela, have shown promising features during the basic follow-up steps: no known noise line is present in their neighborhood, the amplitude estimation is compatible and nearly constant among the LIGO L and LIGO H runs and their SNR appears to increase with respect to the integration time (see Fig. 3). Even if the trend of the SNR does not increase monotonically with time, as expected for real signals, we have decided to follow-up this outliers due to the fact that they show a completely different SNR trend with respect to all the other outliers found in this work. Moreover each outlier’s significance increases in the multi-IFOs search, suggesting a possible coherent source.
J1833-1034 and Vela outliers:
In order to establish if the outliers were not artefacts created by the narrow-band search, we also looked for the two outliers using two other analysis pipelines for targeted searches, which used a Bayesian approach: one designed for searching for non-tensorial modes in CW signals isi:nGR (), the other developed for canonical CW target searches 666frequency and spin-down value fixed to the outlier’s value found in the narrow-band search and parameter estimation matt:bayes (). Both pipelines produced odds, listed in Tab 2, which show a small preference for the presence of a candidate compatible with general relativity. The odd values are not surprising due to the fact that we are using values for the frequency and the spin-down which are fixed to the ones found in the narrow-band search. Hence, a trial factor should be taken into account in order to make a robust estimation on the signal hypothesis preference. Besides the previous considerations, the values in Tab. 2 clearly shows that the outliers are not artefacts created by the narrow-band pipeline. We have also compared the estimation of the outlier parameters obtained from the 5-vector, -statistic and Bayesianpia:articolo (); krolak:fstat (); matt:bayes () pipelines. The inferred parameters are listed in Tab.3 and seems to be compatible among the three independently developed targeted pipelines, thus suggesting the true presence of these outliers inside the data.
In order to establish each outlier’s nature, a complete understanding of the noise background is needed. For this reason the first check was to look at the DS distribution in the narrow-band search. In the presence of a true signal we expect to see a single significant peak in the DS. Figure 4 shows the distribution of the DS (maximized over the spin-down corrections) for J1833-1034 and for Vela over the frequency band analysed. We notice that for J1833-1034 the outlier is the only clear peak present in the analysis, surrounded by several lower peaks in the detection statistic which are not above the corresponding p-value threshold. On the other hand, for Vela, several peaks in the DS are present, with significance below but similar to that of the outlier, thus suggesting that the Vela outlier can be due to non-gaussian background.
A further test consist of checking the distribution of the DS in a narrow-band search performed using the same frequency/spin-down region but in a sky-position shifted by about 0.5 degrees. Using this method we keep the contribution of non-Gaussian noise in the DS while removing a possible signal contribution. Figure 5 shows the distribution of the DS obtained for J1833-1034 and Vela outliers. In both cases no over-threshold peak are present, however the analysed bands seem similarly polluted by non-Gaussian contributions which produce peaks in the DS. We have also studied the significance of the outliers using two of the three targeted search pipelines. As done previously, we have built a noise-distribution of the DS, performing the targeted searches in other sky positions in order to compute the outliers p-value. Using the trials factor from the narrow-band search we have found the outliers to have a higher resulting p-value with respect to the 1% threshold used in the initial outliers selection process during the narrow-band search, increasing the likelihood that these outliers were generated from noise. Some of the previous tests disfavour the signal hypothesis and seem to indicate the presence of a coherent noise disturbance among the interferometers. Previous works such as matt:O1_known (); eath:all () have already pointed out the presence of some non-trivial coherent noise artefacts among the IFOs which can produce outliers. For this reason, in the spirit of what is done in eath:all (), we have looked at O2 data. If the outliers are really due to a “standard” CW signal, they are expected to be present also in O2 data, due to their persistent nature. We have analysed the data using the narrow-band pipeline but no evidence for these outliers was found in data. In conclusion the outliers are not true CW signals. More details on the O2 analysis can be found in Appendix C.
v.2 Upper limits
Following the procedure described in Appendix A we have set 95% C.L. upper-limits on GW strain amplitude in every sub-band. In each of these bands the upper-limit was computed by injecting simulated GW signals with several different amplitudes and finding the amplitude such that 95% of the injected signals with that amplitude produce a value of the DS corresponding to the nominal overall p-value of 1%. Tab. 4 gives an overview of the overall sensitivity reached in our search using the median of the upper-limits among the analysed frequency band: graphs of the upper-limits see Fig. 6. For J2043+2740, J1952+3252 and J2022+3842 our overall sensitivity is clearly above the spin-down limit. For J1813-1246 and J1833-1034 our overall sensitivity is close to the spin-down limit, producing values of the upper-limits both below and above the spin-down limit. For J1400-6326 we have obtained a large fraction of the upper-limits in the narrow-band search below the spin-down while for J0205+6449 and J2229+6114 we have beaten the spin-down limit in a narrow-band search for the very first time. For Crab and Vela pulsars we have obtained upper-limits respectively 7 and 3.5 times lower than those computed in a past analysis rob:obs (). This improvement is due to a combination of two factors: the enhanced sensitivity of advanced detectors and the choice to compute upper limits over Hz sub-bands instead of the full analysis band, thus reducing the impact of the look-elsewhere effect in each sub-band rob:method (). Finally the narrow-band search for J1813-1749 beats the spin-down limit (if we exclude from the search the frequency region around the LIGO H artefact), constraining for the first time their CW emission. Pulsars J1813-1749 and J1400-6326 have not been previously analysed in targeted searches, due to the lack of ephemeris covering O1 or previous runs. Even if we consider the uncertainties on the pulsars distance, propagated in Tab. 4 for the spin-down limit and upper-limit ratio, we are still able to beat the spin-down for those 5 pulsars.