This is the home page for the review of the detection of non-quadrupole modes using scaled tracks method for O3. The technique is described in a recent paper *Unveiling the spectrum of inspiralling black holes*. Note that the review is only focussed on reviewing scaled tracks method for the case of individual detections of non-quadrupole modes from compact binary coalescences.
This is the home page for the review of the detection of non-quadrupole modes using scaled tracks method for O3. The technique is described in a recent paper *Unveiling the spectrum of inspiralling black holes*. Note that the review is only focussed on reviewing scaled tracks method for the case of individual detections of non-quadrupole modes from compact binary coalescences.
## Method:
## Method:
1. Extract the mass-spin parameters and the event time from the GraceDB link.
2. Construct the time-frequency map of the whitened data surroundings the event.
1. Extract the parameters of the event from PE summary page or GraceDB.
3. Collect the energies along various scaled 22-track. Especially, the arbitrary track is defined as $`f_{\alpha}(t) = \alpha f_{22}(t)`$, where the 22-track is generated using the GraceDB mass-spin parameters. The summed energy along the $`f_{\alpha}(t)`$ track is defined as $`Y(\alpha)`$.
2. Construct the time-frequency map (by wavelet transform using Morlet wavelet: Details: ) of the whitened data surroundings the event. The wavelet used in the analysis is different from the one described in the method paper. Details on the wavelet tranform is summarised [here](https://git.ligo.org/soumen.roy/o3inspiralhom/-/wikis/uploads/bf743a417b1494559a3613d8d3aed501/cwt_doc.pdf).
3. Collect the energies in the pixels along various scaled 22-track. Especially, the arbitrary track is defined as $`f_{\alpha}(t) = \alpha f_{22}(t)`$, where the 22-track is generated using parameters obtained from PE/GraceDB. The summed energy along the $`f_{\alpha}(t)`$ track is defined as $`Y(\alpha)`$.
4. The template model $`S(\alpha)`$ is constructed using the same mass-spin parameters.
4. The template model $`S(\alpha)`$ is constructed using the same mass-spin parameters.
5. Two consecutive points in $`Y(\alpha)`$ are highly correlated; thereby, the covariance matrix is necessary for hypothesis testing. The covariance matric is computed using the off-source data surrounding the event.
5. Two consecutive points in $`Y(\alpha)`$ are highly correlated; thereby, the covariance matrix is necessary for hypothesis testing. The covariance matric is computed using the off-source data surrounding the event.
6. Finally, we defined a statistic ($`\beta`$) for detecting the higher-order modes from the inspiral part of the signal. For pure Gaussian noise case, the statistic $`\beta`$ follows a Gaussian distribution with zero mean and unit variance when no gravitational wave presents in the data, i.e., $`p(\beta \mid \mathcal{H}_0 ) \sim \mathcal{N}(0, 1)`$. However, the variance of $`p(\beta \mid \mathcal{H}_0 )`$ increases for real LIGO data.
6. Finally, we defined a statistic ($`\beta`$) for detecting the higher-order modes from the inspiral part of the signal. For pure Gaussian noise case, the statistic $`\beta`$ follows a Gaussian distribution with zero mean and unit variance when no gravitational wave presents in the data, i.e., $`p(\beta \mid \mathcal{H}_0 ) \sim \mathcal{N}(0, 1)`$. However, $`p(\beta \mid \mathcal{H}_0 )`$ need not to be pure Gaussian for real LIGO data.
## References
## References
**Unveiling the spectrum of inspiralling black holes*: [arXiv:1910.04565](https://arxiv.org/abs/1910.04565),
**Unveiling the spectrum of inspiralling black holes*: [arXiv:1910.04565](https://arxiv.org/abs/1910.04565),
...
@@ -37,14 +38,9 @@ This is the home page for the review of the detection of non-quadrupole modes us
...
@@ -37,14 +38,9 @@ This is the home page for the review of the detection of non-quadrupole modes us
## Review statements
## Review statements
We have reviewed the implementation of 'search of higher modes in the gravitational wave strain assuming the detection of 22 mode' using time-frequency map of the data. The method was introduced in (https://arxiv.org/abs/1910.04565) and presented in [R&D call 2019-08-19](https://dcc.ligo.org/G1901496). The brief summary of analysis is as below:
We have reviewed the implementation of 'search of higher modes in the gravitational wave strain assuming the detection of 22 mode' using time-frequency map of the data. The method was introduced in (https://arxiv.org/abs/1910.04565) and presented in [R&D call 2019-08-19](https://dcc.ligo.org/G1901496). The brief summary of analysis can be found [here](https://git.ligo.org/soumen.roy/o3inspiralhom/-/wikis/Home):
1. Extract the parameters of the event from PE summary page or GraceDB.
2. Construct the time-frequency map (by wavelet transform using Morlet wavelet: Details: ) of the whitened data surroundings the event. The wavelet used in the analysis is different from the one described in the method paper. Details on the wavelet tranform is summarised [here](https://git.ligo.org/soumen.roy/o3inspiralhom/-/wikis/uploads/bf743a417b1494559a3613d8d3aed501/cwt_doc.pdf).
3. Collect the energies in the pixels along various scaled 22-track. Especially, the arbitrary track is defined as $`f_{\alpha}(t) = \alpha f_{22}(t)`$, where the 22-track is generated using parameters obtained from PE/GraceDB. The summed energy along the $`f_{\alpha}(t)`$ track is defined as $`Y(\alpha)`$.
4. The template model $`S(\alpha)`$ is constructed using the same mass-spin parameters.
5. Two consecutive points in $`Y(\alpha)`$ are highly correlated; thereby, the covariance matrix is necessary for hypothesis testing. The covariance matric is computed using the off-source data surrounding the event.
6. Finally, we defined a statistic ($`\beta`$) for detecting the higher-order modes from the inspiral part of the signal. For pure Gaussian noise case, the statistic $`\beta`$ follows a Gaussian distribution with zero mean and unit variance when no gravitational wave presents in the data, i.e., $`p(\beta \mid \mathcal{H}_0 ) \sim \mathcal{N}(0, 1)`$. However, $`p(\beta \mid \mathcal{H}_0 )`$ need not to be pure Gaussian for real LIGO data.
The python implementation of the analysis cam be found [here](). We have done a line-by-line code review here.
The python implementation of the analysis cam be found [here](). We have done a line-by-line code review here.
