Eccentric search for Neutron star-black hole (NSBH) and binary neutron star (BNS) mergers within O3 advanced LIGO and advanced VIRGO data

[Rahul Dhurkunde]^{1, 2}, Alexander H. Nitz³,

<sub>1. Max-Planck-Institut for Gravitationsphysik (Albert-Einstein-Institut), D-30167 Hannover, Germany
2. Leibniz Universitat Hannover, D-30167 Hannover, Germany
3. Department of Physics, Syracuse University, Syracuse, NY 13244, USA</sub>

(Image credits: Soheb Mandhai)

Introduction

The possible formation histories of neutron star binaries remain unresolved by current gravitational-wave catalogs. The detection of an eccentric binary system could be vital in constraining compact binary formation models. We present the first search for aligned spin eccentric neutron star-black hole binaries (NSBH) and the most sensitive search for aligned-spin eccentric binary neutron star (BNS) systems using data from the third observing run of the advanced LIGO and advanced Virgo detectors. No new statistically significant candidates are found; we constrain the local merger rate to be less than 150 $\text{Gpc}^{-3}\text{Yr}^{-1}$ for binary neutron stars in the field, and, 50, 100, and 70 $\text{Gpc}^{-3}\text{Yr}^{-1}$ for neutron star-black hole binaries in globular clusters, hierarchical triples and nuclear clusters, respectively, at the 90$%$ confidence level if we assume that no sources have been observed from these populations. We predict the capabilities of upcoming and next-generation observatory networks; we investigate the ability of three LIGO (A#) detectors and Cosmic Explorer CE (20km) + CE (40km) to use eccentric binary observations for determining the formation history of neutron star binaries. We find that 2 -- 100 years of observation with three A# observatories are required before we observe clearly eccentric NSBH binaries; this reduces to only 10 days -- 1 year with the CE detector network. CE will observe tens to hundreds of measurably eccentric binaries from each of the formation models we consider.

```
Eccentric-search-O3/
├── configs/                                   # Configuration files for the analysis
    ├── data/                                  # Config files specific to LIGO observing run data
├── injections/                                # Files used to generate injections for the search
├── Jupyter-notebooks/                         # Notebooks for plotting upper limits (observational and idealized)
├── measurability-analysis/                    # Files to investigate measurable eccentric systems
│   ├── Full-simplified-PE-comparision-plots/  # Comparision corner plots for the different PE runs
│   ├── inferenc-configs/                      # Configs for the PE analysis
│   ├── results/                               # Measurable eccentric systems as a function of mchirp and eccentricity
├── psds/                                      # Contains various PSDs used in the study
├── sensitivity/                               # Directory containing scripts and results used to obtain the observational constraints of our search
│   ├── idealized-search/                      # Script for computing detectability of sources
│   ├── injections-results/                    # Found and missed injections results from our search
│   ├── library/                               # Custom PyCBC scripts to get VT and merger rate for our injection set.
│   ├── pop-models/                            # Mchirp and eccentricity distributions for astrophysical models used.
│   └── precession-bais/                       # Files to compute bias in merger rate due to neglecting precession.
├── README.md                # Project documentation
└── LICENSE                  # License information
```

A preprint version of the paper is available on arXiv. This release contains the following:

• Search
  • Configuration files for the search, template bank, and injections used for the analysis.
• Search results
  • List of top candidates
  • The search sensitivity as a function of mchirp and eccentricity (HDF5 files).
• Constraints
  • Population synthesis data -- Mchirp and eccentricity samples.
  • Noise ASDs used to compute the optimal SNRs for the idealized searches.
  • Jupyter-lab notebooks to obtain the 90 % upper limits on the local merger rate.
• Measurability analysis
  • Scripts to compute the simplified Bayesian inference.
  • Dictionary of measurable binary sources for given SNRs (keys).

** The simulated data for the idealized searches is not provided due to the file size limit on GITHUB. This can be made available upon reasonable requests.

Constraints on the local merger rate

Modeled predicted rates

Isolated binary (Belczynski et al. (2018a))	[8.0, 50.0]
Globular cluster (Arca Sedda (2020b))	<=0.1
Triples (Trani et al. (2021))	[0.04, 0.34]
Nuclear cluster (Fragione et al. (2019))	[0.06. 0.1]

Observational constraints for O3

Isolated binary (Belczynski et al. (2018a))	149.02243058810643
Globular cluster (Arca Sedda (2020b))	53.36526395563427
Triples (Trani et al. (2021))	97.976810617951
Nuclear cluster (Fragione et al. (2019))	70.44463776334753

Idealized constraints for various detector networks

We have estimated constraints for an idealized search that covers the entire parameter space of the astrophysical model, and captures the signal SNR perfectly. We provide three different types of constraints on each population:

• Full population
• Eccentric systems above a fixed eccentricity >= 0.01
• Measurable eccentric systems

Full population constraints

• Three A+ detectors

Isolated binary (Belczynski et al. (2018a))	3.8967851099830795
Globular cluster (Arca Sedda (2020b))	0.8313479171178976
Triples (Trani et al. (2021))	0.5604497225737369
Nuclear cluster (Fragione et al. (2019))	0.7834932299108661

• Three Asharp detectors

Isolated binary (Belczynski et al. (2018a))	0.48555766392578537
Globular cluster (Arca Sedda (2020b))	0.10645969508981815
Triples (Trani et al. (2021))	0.0778671896131999
Nuclear cluster (Fragione et al. (2019))	0.10731093611667676

• CE (40km baseline) + CE(20km baseline)

Isolated binary (Belczynski et al. (2018a))	0.0021919213943572277
Globular cluster (Arca Sedda (2020b))	0.0011257530053556922
Triples (Trani et al. (2021))	0.0010080234416283082
Nuclear cluster (Fragione et al. (2019))	0.001082967826882465

• ET

Isolated binary (Belczynski et al. (2018a))	0.010134497215643601
Globular cluster (Arca Sedda (2020b))	0.00249218885268609
Triples (Trani et al. (2021))	0.001648579773221853
Nuclear cluster (Fragione et al. (2019))	0.0019435434126820943

Fixed ecc >= 0.01 constraints

• Three A+ detectors

Isolated binary (Belczynski et al. (2018a))	5757.5
Globular cluster (Arca Sedda (2020b))	26.77906976744186
Triples (Trani et al. (2021))	0.8303288145370638
Nuclear cluster (Fragione et al. (2019))	0.8947859196518766

• Three Asharp detectors

Isolated binary (Belczynski et al. (2018a))	677.3529411764706
Globular cluster (Arca Sedda (2020b))	3.330922765403529
Triples (Trani et al. (2021))	0.1157658744520851
Nuclear cluster (Fragione et al. (2019))	0.12335693701993637

• CE (40km baseline) + CE(20km baseline)

Isolated binary (Belczynski et al. (2018a))	2.6722573839662442
Globular cluster (Arca Sedda (2020b))	0.034350762054564186
Triples (Trani et al. (2021))	0.0014993702562062906
Nuclear cluster (Fragione et al. (2019))	0.0012444783733012645

• ET

Isolated binary (Belczynski et al. (2018a))	12.179326923076921
Globular cluster (Arca Sedda (2020b))	0.07535994764397905
Triples (Trani et al. (2021))	0.0024534832818740725
Nuclear cluster (Fragione et al. (2019))	0.002231164612793901

Measurable eccentric systems

• Three A+ detectors

Isolated binary (Belczynski et al. (2018a))	11520.0
Globular cluster (Arca Sedda (2020b))	62.92
Triples (Trani et al. (2021))	5.388
Nuclear cluster (Fragione et al. (2019))	1.922

• Three Asharp detectors

Isolated binary (Belczynski et al. (2018a))	1279.0
Globular cluster (Arca Sedda (2020b))	8.53
Triples (Trani et al. (2021))	0.7375
Nuclear cluster (Fragione et al. (2019))	0.2632

• CE (40km baseline) + CE(20km baseline)

Isolated binary (Belczynski et al. (2018a))	1.712
Globular cluster (Arca Sedda (2020b))	0.06979
Triples (Trani et al. (2021))	0.009821
Nuclear cluster (Fragione et al. (2019))	0.004279

• ET

Isolated binary (Belczynski et al. (2018a))	11.73
Globular cluster (Arca Sedda (2020b))	0.08415
Triples (Trani et al. (2021))	0.003113
Nuclear cluster (Fragione et al. (2019))	0.002463

License and Citation

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