PROSPECTS FOR GRAVITATIONAL-WAVE POLARIZATION TEST FROM COMPACT BINARY COALESCENCES WITH NEXT-GENERATION DETECTORS

Hiroki Takeda1, Atsushi Nishizawa2, 3, Koji Nagano4 , Yuta Michimura1, Kentaro Komori1, Masaki Ando1, and Kazuhiro Hayama51Department of Physics, University of Tokyo, 2RESCEU, University of Tokyo, 3KMI, Nagoya University, 4 ICRR, University of Tokyo, 5Department of Applied Physics, Fukuoka University,

Email: takeda@granite.phys.s.u-tokyo.ac.jp

1. Motivation

22nd International Conference on General relativity and Gravitation & 13th Edoardo Amaldi Conference on Gravitational Waves in Valencia, Spain

Background

- General metric theory of gravity allows six polarization modes of gravitational waves [1].

3. Results

There exist six possible polarization modes of gravitational waves in a general metric theory of gravity, while two tensor modes are allowed in general relativity. For transient signals, the number of detectors needs to be basically equal to the number of modes for polarization separation. However, a next-generation detector having great sensitivity at lower frequency such as Einstein telescope and Cosmic Explorer could be regarded as a virtual detector network due to the Earth's rotation for chirp signal. For compact binary coalescences, we study polarization separability of next-generation detectors and show that future observations of multi-sources would be able to reach the compatible level to the current constraint on the nontensorial modes from PSR B1913+16 in a much stronger gravity regime.

4. Conclusion

References

- Properties of polarizations depend on gravity theories. Search for gravitational-wave polarizations can be used to test gravity theories.

(The number of detectors) ≥ (The number of polarizations) [2] .

2. Model and method

Next-generation detectors and polarization separation for compact binary

- Einstein telescope (ET) [3] - Cosmic Explorer (CE) [4]

Separability improvement. (Earth’s rotation)

Statistical improvement.(multi-sources)

- Stationary phase approximation gives the time-dependent signal.Tensor-scalar dipole model:

Virtual detector network [5].

Better sensitivity at low frequency region.

Time-dependent antenna pattern functions.

Earth’s rotation need to be considered.

11 model parameters in GR + additional polarization amplitude parameter, AS1 uniformly random

Binary neutron star (BNS)

Binary black hole (BBH)

- Parameter estimation by Fisher matrix.

! , z=0.1, !1.4M⊙ − 1.4M⊙ AS1 = 1

! , z=0.5, !10M⊙ − 10M⊙ AS1 = 1

Multiple sources

ΔA < (fiducial value) ⇔ separable- Separation criterion: based on SNR scaling.

In polarization test…

Polarization model

Method

?

Sensitivity improvement.(including low frequency region)

- Single detector: inseparable, but

[1] D. M. Eardley et al., Physical Review Letters 30, 884 (1973). [2] H. Takeda et al., Physical Review D 98, 022008 (2018). [3] M. Punturo et al., Classical and Quantum Gravity 27, 194002 (2010). [4] B. P. Abbott et al., Classical and Quantum Gravity 34, 044001 (2017). [5] W. Zhao et al., Physical Review D 97, 064031 (2018).

- Even a single ET-D could test three polarizations. - The range below 5 Hz is essential for the polarization test.

- Two detectors including ET-D could test three polarization. - They could also take advantage of the Earth rotation for BBHs.

- Merger rate distributions following Madau plot.

- Median values of ! within each redshift bin. - Improvement inversely

proportional to expected number of detections ! .

ΔAS1

Nz

- The expected error from future observations can be obtained by sum of inverse square.

Formation rate: Madau plot

Delay time distribution: log flatMerger rate

- The number of polarizations that next-generation detectors can probe is larger than the number of detectors.

- Observations of multi-sources would reach the compatible level to the current constraint on the nontensorial modes from PSR B1913+16 ! in a much stronger gravity regime.AS1 ≲ 1 × 10−3

Plus mode

Cross mode

Vector x mode

Vector y mode

Breathing mode

Longitudinal mode

x

x

y

y

z

z

x

y

x

y

z

x, y

SignalAntenna pattern functions

Separable!!

arXiv:1904.09989