Fractional Follow Up Metric

---
name: fractional-follow-up-metric
description: Evaluates the sky localization precision and detection sensitivity of gravitational-wave detector networks for multi-messenger follow-up of compact binary mergers. It quantifies how well a network can identify and pinpoint sources within a specific distance and localization area threshold. Use when the user has predictions and gold and needs to compute fractional follow-up metric.
metadata:
  skill_kind: metric
  source_arxiv: 2308.13103
  bibtex_key: [REDACTED]
  confidence: high
---

# fractional-follow-up-metric

> Multi-messenger astronomy with a Southern-Hemisphere gravitational-wave observatory — James W. Gardner et al. (arXiv:2308.13103, 2023)

## What this evaluates

Evaluates the sky localization precision and detection sensitivity of gravitational-wave detector networks for multi-messenger follow-up of compact binary mergers. It quantifies how well a network can identify and pinpoint sources within a specific distance and localization area threshold.

## Datasets

- **Simulated compact binary coalescence population (GWTC-3 rate)** — total ?; splits: simulation (-1)

## Metrics

- `fractional follow-up metric` **(primary)** — range: [0, 1]
  - Fraction of simulated sources within 500 Mpc that have a network signal-to-noise ratio greater than 25 and are localized within a specified area threshold (10 deg² for loose, 1 deg² for tight).

## Input / output format

**Input**: Simulated gravitational-wave signals from compact binary mergers within 500 Mpc, detector network configurations, and sky localization uncertainties.

**Output**: Fraction of sources meeting the SNR and localization area thresholds, and expected joint observation rates (yr⁻¹).

## Scoring recipe

```python
def compute_metric(simulated_sources, snr_threshold=25, area_threshold=10.0):
    count = 0
    for source in simulated_sources:
        if source.distance <= 500 and source.snr > snr_threshold and source.localization_area <= area_threshold:
            count += 1
    return count / len(simulated_sources)
```

## Common pitfalls

- Confusing arithmetic improvement (absolute difference in observation rates) with geometric improvement (multiplicative factor).
- Applying the metric outside the 500 Mpc distance bound or ignoring the SNR > 25 requirement.
- Assuming the metric is independent of detector duty cycles and network configurations.

## Evidence (verbatim from paper)

> Fractional follow-up metrics from Table 2, i.e., the fraction of sources within 500 Mpc that have a network signal-to-noise ratio greater than 25 and are localised within 10 deg^2 [panels (a) and (c)] or 1 deg^2 [panels (b) and (d)].

## Citation

```bibtex
@misc{gardner2023southern,
  title={Multi-messenger astronomy with a Southern-Hemisphere gravitational-wave observatory},
  author={James W. Gardner et al.},
  year={2023},
  note={arXiv:2308.13103}
}
```

- arXiv: 2308.13103