Sky Localization and Parameter Estimation¶
Immediately after one of the search pipelines reports an event, sky localization and parameter estimation analyses begin. These analyses all use Bayesian inference to calculate the posterior probability distribution over the parameters (sky location, distance, and/or intrinsic properties of the source) given the observed gravitational-wave signal.
There are different parameter estimation methods for modeled (CBC) and unmodeled (burst) events. However, in both cases there is a rapid analysis that estimates only the sky localization, and is ready in seconds, and a refined analysis that explores a larger parameter space and completes up to hours or a day later.
Note
A sky map is sent out with each of the two preliminary GCN notices, (see Superevents); these are distinguished by a sequential number if they come from the the same localization pipeline.
For example, they might be labeled
bayestar.multiorder.fits,0 and bayestar.multiorder.fits,1 or
cwb.multiorder.fits,0 and cwb.multiorder.fits,1.
These may be different or not depending on whether the preferred event changed in the meantime; one may check this in the sky localization section of the GraceDB superevent, where visualizations of the sky maps are also available.
Together with the refined analysis, whose sky map would be labeled Bilby.multiorder.fits in the case of a modeled event, this means that three public sky maps are sent out for a typical event.
This can increase if more notices are sent out: this may happen, for example, if there is an Early Warning alert, or if the significance of the event changes. As a general rule, a sky map is sent out with each successive notice, and the latest should be considered the most reliable.
Modeled Events¶
BAYESTAR [1] is the rapid CBC sky localization algorithm. It reads in the matched-filter time series from the search pipeline and calculates the posterior probability distribution over the sky location and distance of the source by coherently modeling the response of the gravitational-wave detector network. It explores the parameter space using Gaussian quadrature, lookup tables, and sampling on an adaptively refined HEALPix grid. The sky localization takes tens of seconds and is included in the preliminary alert. CBC signals containing a SSM component can last tens of minutes in the detector bandwidths. Owing to computing constraints, SSM searches start filtering from higher frequency as compared to the stellar mass CBC searches, effectively shortening the filtered signals.
AMPLFI [2] is a machine-learning-based, rapid parameter estimation algorithm that uses simulation-based inference to estimate the posterior probability distribution of sky location, distance, and source masses. Specifically, a normalizing flow neural-network is trained using simulated BBH and NSBH signals to estimate the posterior. Posterior samples can then be drawn rapidly using the normalizing flow. AMPLFI is used to provide sky localization and source property estimates for candidates identified by Aframe. Within a few seconds of candidate identification, AMPLFI provides a sky localization by using an adaptive histogram from ligo.skymap. This is followed by a more refined sky localization from the posterior samples using a KDE via ligo-skymap-from-samples.
Bilby [3] is a full CBC parameter estimation pipeline in Python. Bilby provides a user-friendly and accessible interface with the latest stochastic sampling methods built-in. It explores a greatly expanded parameter space including sky location, distance, masses, and spins, and performs full forward modeling of the gravitational-wave signal and the strain calibration of the gravitational-wave detectors. It explores the parameter space using stochastic sampling methods such as MCMC and nested sampling. For all events, there is an automated Bilby analysis whose settings depend on the initial estimate of chirp mass from the search pipeline. The table below summarizes the waveform model and spin prior employed for parameter estimation. The analysis is accelerated with the reduced order quadrature basis elements constructed for the employed waveform models [4], and completes within tens of minutes for BNS and hours for NSBH and BBH.
Chirp-mass from the search pipeline |
Waveform model |
Spin prior |
|---|---|---|
\(\mathcal{M} < 1.465M_{\odot}\) |
Aligned with the orbital angular momentum, dimensionless magnitude from 0 to 0.05 |
|
\(1.465M_{\odot} \leq \mathcal{M} < 12M_{\odot}\) |
IMRPhenomPv2 [7] |
Any orientation, dimensionless magnitude from 0 to 0.99 |
\(\mathcal{M} \geq 12M_{\odot}\) |
IMRPhenomXPHM [8] |
RapidPE-RIFT [9] [10] is a fast CBC parameter estimation pipeline in Python. RapidPE-RIFT parallelizes parameter estimation by fixing the intrinsic parameters (such as the masses and spins of the binary) to a grid around a search-identified intrinsic point and by integrating over the extrinsic parameters (such as sky location, distance, etc) via Monte Carlo sampling. For all events, there is an automated RapidPE-RIFT analysis that explores the masses holding the spins fixed to the search identified values. The analysis is accelerated using a variety of tricks and completes within a few minutes.
Unmodeled Events¶
cWB, the burst search pipeline, also performs a rapid sky localization based on its coherent reconstruction of the gravitational-wave signal using a wavelet basis and the response of the gravitational-wave detector network [11]. The cWB sky localization is included in the preliminary alert.
MLy, the machine-learning-based burst search pipeline, transforms the time-series data into a time-frequency map. It stacks the time frequency-map from all detectors, groups together the loudest time-frequency pixels, and calculates the SNR. It also computes a rapid sky localization using a combination of coherent and incoherent null energy [12] producing a log likelihood. The log likelihood is then normalized as described in [13]. For the two detector case it uses an approximation of the null stream that assumes a single dominant polarization [14].
Refined sky localizations for unmodeled bursts are provided by two algorithms that, like Bilby, use MCMC and nested sampling methodologies. LALInference Burst (LIB) [15] models the signal as a single sinusoidally modulated Gaussian. BayesWave [16] models the signal as a superposition of wavelets and jointly models the background with both a stationary noise component and glitches composed of wavelets that are present in individual detectors.