Generic burst waveforms¶

Perhaps the simplest waveforms which Minke is able to produce are so-caled “generic” or “ad-hoc” burst waveforms. These waveform families include gaussian bursts, sine-gaussian wavelets, and white noise bursts.

Gaussian bursts¶

Perhaps the simplest conceivable model of a burst of gravitational waves is one where energy is emitted across a broadband range of frequencies over a fixed period of time, with a smooth rise and decay in amplitude. Such a source can be modelled as with a Gaussian function, and may be a suitable model for broadband sources, such as the core-bounce during a core-collapse abbr:sn.

In searches the model for such a signal is

\[h(t) = A \exp\left( - \frac{ (t - t_{0})^{2} }{ 2 \sigma^{2} } \right),\]

for a strain \(h\) at time \(t\), with an amplitude \(A\), central time \(t_{0}\) and duration \(\sigma\).

Minke supports Gaussian bursts using the minke.sources.Gaussian class.

Sine-Gaussian bursts¶

In addition to searching for broadband, time-constrained bursts of gravitational wave energy, some sources are expected to produce gravitational waves which are in a confined range of frequencies, in addition to being released over a short time-span.

Such a source can be approximated by a sinusoidal signal which is enveloped by a Gaussian rise and decay in amplitude.

The model used in gls:ligo searches for such signals is:

\[h(t) = A \exp \left[ \frac{ - 2(t - t_{0})^{2} \pi^{2} f^{2}}{Q^{2}} \right] \cos\left[ 2 \pi f (t - t_{0}) \right],\]

for a strain \(h\) at time \(t\), with \(A\) the amplitude of the signal, \(t_{0}\) its central time, \(Q\) the quality factor of the burst, and \(f\) is frequency.

A SineGaussian burst can be produced with a short script such as this

import minke
import astropy.units as u

from minke.models.bursts import SineGaussian
from minke.detector import AdvancedLIGOHanford

model = SineGaussian()

parameters = {"centre_frequency": 20,
              "phase": 0,
              "eccentricity": 0,
              "q": 1.,
              "sample_rate": 4096 * u.Hertz,
              "gsptime": 998,
              "hrss": 1e-22,
              "duration": 2*u.second}

data = model.time_domain(parameters)

detector = AdvancedLIGOHanford()

projected = data.project(detector,
             ra=1, dec=0.5,
             iota=0.4,
             phi_0=0,
             psi=0
             )

f = projected.plot()
f.savefig("projected_sinegaussian.png")

Band-limited white noise bursts¶

Astrophysical processes are unlikely to produce emission at a single frequency, or with a smooth evolution of amplitude, and so searches are normally expected to be sensitive to band-limited white noise bursts, which consist of band-limited uncorrelated noise within a Gaussian amplitude envelope.