I carried out most of the work presented here as a member of the LIGO Scientific Collaboration and benefited from interaction with many of its members. I also present constraints on the potential amplitude of nontensorial monochromatic signals from 200 known pulsars in the Milky Way and describe in detail the methods used to obtain them.
NOMENCLATURE
INTRODUCTION
As an example, with the first detection we were able to measure the dispersion of gravitational waves, allowing for the first dynamical constraints on the mass of the graviton. In this thesis, I will explore some of these possibilities, including a discussion of the first results on gravitational-wave polarizations and the prospects of using gravitational waves to detect new particles.
OVERVIEW
- Enhancing confidence in the detection of gravitational waves from compact binaries using signal coherence
- Establishing the significance of continuous gravitational-wave de- tections from known pulsars
- Probing gravitational wave polarizations with signals from compact binary coalescences
- Constraints on gravitational-wave polarizations from compact- binary coalescences
- Detecting beyond-Einstein polarizations of continuous gravitational waves
- Probing Dynamical Gravity with the Polarization of Continuous Gravitational Waves
- First search for nontensorial gravitational waves from known pul- sars
- Measuring stochastic gravitational-wave energy beyond general relativity
- Measuring the speed of continuous gravitational waves
- Towards constraining generic gravitational-wave dispersion rela- tions
- Directed searches for gravitational waves from ultralight bosons Gravitational-wave detectors could be used to search for yet-undiscovered ultralight
This includes a proposal for how to measure the speed of gravitational waves using persistent signals from known pulsars, as well as how to measure anisotropic dispersion relations with several compact-binary coalescences. The direct detection of gravitational waves with the ground-based detectors, like Advanced LIGO, provides the opportunity to measure deviations from the predictions of general relativity.
ENHANCING CONFIDENCE IN THE DETECTION OF GRAVITATIONAL WAVES FROM COMPACT BINARIES USING
SIGNAL COHERENCE
- Introduction
- Searches
- Coherence vs incoherence
- Analysis
This likelihood may be estimated empirically from the value of the ranking statistic for a large representative set of triggers known with certainty to be spurious. We pick the background triggers by sampling from the full trigger-set uniformly in the log of the inverse-FAR.
GW150914 LVT151012
Results
If we consider the intrinsic probabilistic meaning of the BCR, a value of log BCR < 0 indicates a preference for the instrumental-artifact hypothesis (HI) over the coherent-signal one (HS). 3.1, plotted also as a function of the network signal-to-noise ratio (SNR) recovered by our coherent Bayesian analysis.
Future implementation
The values of the α and β weights in Eq. 3.1) have a strong effect on the shape of the distributions of Fig. This may be achieved via any standard optimization scheme that attempts to minimize the overlap between the two populations.
Conclusion
Versions of the ranking statistic used by PyCBC in recent analyses have incorporated some measure of coherence [15], and it remains to be seen whether this introduces some correlation between BCR and IFAR in Fig. Furthermore, while this study focused on detection candidates produced by the two aLIGO detectors during O1, we are currently investigating how the power of the BCR is affected by the addition of new detectors, like Virgo.
Appendix: Effect of BCR weights
This is shown as a function of the BCR prior weights,α(x-axis) and β(y-axis), of Eq. This number then gives a measure of the vertical distance between the centers of the distributions in Fig.
ESTABLISHING THE SIGNIFICANCE OF CONTINUOUS GRAVITATIONAL-WAVE DETECTIONS FROM KNOWN
PULSARS
Introduction
Given this, we may instead attempt to empirically determine the response of the different searches to real detector noise in theabsenceof astrophysical signals. By the same token, time slides themselves would not be feasible in transient analyses if the noise properties of the detectors changed rapidly compared to the sampling time.
Background
- Continuous waves Morphology
- Detector noise
- Searches
The antenna patterns,F+(t;ψ)and F×(t;ψ), encode the amplitude modulation of the signal due to the local geometric effect of a GW acting on a given detector. The timing correction of Eq. 4.5) is heavily dependent on the sky-location of the targeted pulsar and will be the key to the off-sourcing method presented in Sec.
Method
- Off-sourcing
- Blinding and draw-independence
Our goal is to estimate the distribution of the overlap between the noise and the template,hn(t) | Λ(t)i, by studying our proxy statistic, hB(t) | Λ(t)i. Explicitly, the contribution of the signal to the inner product of Eq. 4.23) can be written in terms of a time integral over the observation timeT,.
Analysis
- Case studies
We can then compare the value of the on-source statistic to the off-source background, as we would in a real analysis. For reference, the distribution of the off-source statistic over the whole Northern sky (0° curve on the left) is represented on the right panel of Fig.
Comparison to other methods
In order to determine whether off-sourcing offers an improvement over other strategies, we must go beyond specific examples and study false-alarm and false-dismissal rates. That is, respectively, how likely is off-sourcing to conclude that a noise artifact is a signal (false alarm), and how likely is it to conclude that a signal is a noise artifact (false dismissal), as a function of confidence level.
Conclusion
As long as this is true, off-sourcing will provide independent draws from the background distribution (Sec. 4.3.2). We find that off-sourcing outperforms the standard method for computing significances in the context of the 5-vector search.
PROBING GRAVITATIONAL WAVE POLARIZATIONS WITH SIGNALS FROM COMPACT BINARY COALESCENCES
- Introduction
- Background .1 Polarizations.1Polarizations
- Antenna patterns
- Method
- Toy example
- Conclusion
We may thus exploit the difference in the response of the network to the different polarizations (Fig. 5.3). However, we may already distinguish between some of the possibilities using the current LIGO-Virgo network.
CONSTRAINTS ON GRAVITATIONAL-WAVE POLARIZATIONS FROM COMPACT-BINARY COALESCENCES
Introduction
A measurement of the signal amplitude by multiple (non-coaligned) detectors is the first ingredient needed to study polarizations. Reconstructed waveforms with the maximum a posterioriprobability (MAP) under the assumption of fully tensor (blue), vector (orange) or scalar (green) polarizations, as seen by each of the three detectors in the network.
Conclusion
If the sky location of GW170817 is constrained to NGC 4993, we find overwhelming evidence in favor of pure tensor polarization modes in comparison to pure vector and pure scalar modes with a (base ten) logarithm of the Bayes factor of and respectively. From this analysis, we also see that only the tensor hypothesis is consistent with the location of the electromagnetic counterpart (Fig. 6.7).
DETECTING BEYOND-EINSTEIN POLARIZATIONS OF CONTINUOUS GRAVITATIONAL WAVES
Introduction
Tests of these properties have been proposed which make use of GW burst search methods [145].
Background .1 Polarizations.1Polarizations
- Signal
The few exceptions, presented in Table 7.2, were obtained through the study of the pulsar spin nebula [149]. Accounting for the time dependence of the arm vectors due to the rotation of the Earth, Eqs.
Method
- Data reduction
- Search
We can clearly see already that the data are non-stationary, an issue addressed in the Sec. As before, in the presence of a signal and in the absence of noise, Eqs indicate that the values returned by the fit would be a function of theactual, unknownψandι:.
Analysis
The sensitivity of the template is related to the number of injections recovered with a significance higher than sαn. The same analysis can be done on thesvshinjplots, taking into account proper scaling of the best-fit slope.
Results
- Crab pulsar
- All pulsars
In any case, the accuracy of matching and model-independent searches, given by the width of the confidence bands, are almost identical. While model-independent searches are of the same accuracy as matching semi- model-dependent ones, their strain detection threshold is louder due to the extra degrees of freedom (Fig. 7.9c).
Conclusions
In all cases, the matching template is the best at recovering signals, followed closely by the model-independent one. We will also employ methods to constrain other theories (e.g., scalar-tensor) in the event of a model-independent detection.
Appendix: Statistical properties of LIGO data
The results of the KS and AD tests for each day-segment, together with those for reference Gaussian noise series, are presented in Figs. It can be seen from the results of these tests that the statistical properties of the segments vary considerably from day to day.
PROBING DYNAMICAL GRAVITY WITH THE POLARIZATION OF CONTINUOUS GRAVITATIONAL WAVES
Introduction
Model selection: in the presence of a signal, determine whether the data favor GR or a generic non-GR model, as well as comparing specific alternative theories among themselves and to GR; combine data for multiple sources into a single statement about the validity of GR. Inference: if the data favor the presence of a GR signal, place constraints on specific alternative theories using the tools of Bayesian parameter estimation.
Background .1 Polarizations.1Polarizations
- Continuous waves Signal
This can be pictured by noting that, as the Earth spins on its axis, the angular location of the source with respect to detector will change, tracing an arc on the surfaces of Fig. It is important to remember that, theFp’s are functions of the source orientation and sky location relative to the detector, so we have made this dependence explicit in Eq.
Method
- Model selection
However, in the case of the noise (“null”) hypothesis, as defined by the Student’stlikelihood above, there are no free parameters. Formally, the inadequacy of the naive construction ofHS as proposed in the previous paragraph is related to the logical independence of nested hypotheses.
B N GRBR
Parameter estimation
In the absence of a loud signal, this can be used to obtain credible intervals that yield upper-limits on the amplitudes of GR deviations. As discussed in Sec. 8.61) with the same algorithm used to compute the evidence. 8.61) can be used to place upper limits on model parameters; in particular, we will use it to place limits on the amplitude of GR deviations.
Analysis
GR , we set equal prior probability forHGR andHnGR, distributing the prior equally among non-GR models, as in Eq. described in the previous section; the 95%-credible upper limit on the strength of the breathing mode ish95%s , defined by:. As mentioned in the previous section, the key step in our analysis is the computation of the evidence integral of Eq. 8.40) for the hypotheses under consideration (one noise model, plus seven signal submodels; see Sec.
Results
- Model selection Signal vs noise
- Parameter estimation
The color of each hexagon represents the average value of the log-odds in that region of parameter space; color is normalized logarithmically, except for a linear stretch in the(−1,1)range. The color of each hexagon represents the average value of the upper limit in that region of parameter space.
Summary
Furthermore, the value of this threshold will decrease linearly with the square-root of the observation time [57]. N for detection purposes and may instead wish to adopt one of the strategies suggested in Sec.
Appendix: Tensor models
Each panel consists of acorner plotdisplaying the two-dimensional posteriors for each pair of parameters as indicated by the xand ylabels, with the diagonals showing a histogram of the one-dimensional PDF for each parameter [i.e. Each panel consists of acorner plotdisplaying the two-dimensional posteriors for each pair of parameters as indicated by thex andy labels, with the diagonals showing a histogram of the one-dimensional PDF for each parameter.
Appendix: Amplitude priors
Thus, the dependence of the upper limit on the range defined by the log-uniform prior is quite weak, as illustrated in Fig. However, the flat priors do not properly represent our ignorance of the scale of the signal amplitude.
Appendix: Numerical error
Since xmax is set by the likelihood (by construction), if the prior is changed by rescalingxmin by a factorα,. then, for a given set of data, the upper limit becomes x95%α , satisfying:. 8.80). This explains why upper limits obtained with a log-uniform prior differ only by a factor of a few from those obtained with a flat one, as seen in Fig.
Appendix: Upper-limit ratios
Error in the computation of the logarithm of the GR vs noise Bayes factor as a function of injected GR signal amplitude. The dashed, gray curve shows the theoretical prediction for the error in the logarithm of the evidence, Eq.
FIRST SEARCH FOR NONTENSORIAL GRAVITATIONAL WAVES FROM KNOWN PULSARS
- Introduction
- Analysis
- Results
- Conclusion
The distribution of the odds corresponding to the subhypotheses making up HS is summarized in the box plots of Fig. The upper limits are obtained assuming a signal model including all five independent polarizations (Hstv), and incorporating no information on the orientation of the source (Table B.2 in Supplementary Material).
MEASURING STOCHASTIC GRAVITATIONAL-WAVE ENERGY BEYOND GENERAL RELATIVITY
Introduction
Perhaps the most important example of an assumption that has been dubiously applied beyond GR concerns the form of the effective stress-energy of GWs. This is the case even without considering changes to the potential sources of the background in beyond- GR theories, which may themselves break more of the assumed symmetries.
Formalism