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:
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.
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 $`Y(\alpha)`$.
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, the variance of $`p(\beta \mid \mathcal{H}_0 )`$ increases for real LIGO data.
## References
**Unveiling the spectrum of inspiralling black holes*: [arXiv:1910.04565](https://arxiv.org/abs/1910.04565),
presentated in [R&D call 2019-08-19](https://dcc.ligo.org/G1901496)
**Detection of Nonquadrupole mode from inspiralling compact binary mergers*:
[Link](https://wiki.ligo.org/CBC/InspiralHOM)
**Analysis of GW190814 for detection of higher-order inspiral modes*: [Link](https://dcc.ligo.org/G1901969),
presented in [CBC call 2019-10-08](https://wiki.ligo.org/CBC/MainAgenda20191008)
**Analysis of GW190412 for detection of higher-order inspiral modes*: [Link](https://dcc.ligo.org/G1902017),
presented in [R&D call 2019-10-21](https://wiki.ligo.org/CBC/TechAgenda20191021),
| [Haris K](https://git.ligo.org/haris-k), [Nathan K. Johnson-McDaniel](https://git.ligo.org/nathan-johnson-mcdaniel) | Inject study for S190412m event using C00 \& C01 data | cell | [Link](https://git.ligo.org/soumen.roy/o3inspiralhom/wikis/injection-Study-for-S190412m-event) | cell | cell | cell |
| [Nathan K. Johnson-McDaniel](https://git.ligo.org/nathan-johnson-mcdaniel) | Choise on ending frequency of the $`22-`$mode track | cell | [Link](https://git.ligo.org/soumen.roy/o3inspiralhom/wikis/overelap33) | cell | cell | cell |
