A new way for stochastic gravitational wave background

A new way for stochastic gravitational wave background map making using maximum entropy method Hsiung Chia Hsuan, Tamkang university

Contents 1. 2. 3. 4. Stochastic gravitational wave background SGWB image construction Preliminary result Summary

Stochastic gravitational wave background SGWB can be created by the superposition of independent and unresolved sources (N. Christensen, N. Mazumder). Astrophysical sources (local universe) Cosmological sources (early universe) • CBC (N. Christensen) • Inflation (Michael S. Turner) • Supernoave (Ashish Sharma) • Cosmic string (Alexander C. Jenkins) • rotating neutron stars (Z. Arzoumanian) • Phase transitions (R. Durrer) The background is likely to be anisotropy if it is dominated by the local universe! (Nairwita Mazumder, Sanjit Mitra, Sanjeev Dhurandhar)

https: //www. ligo. caltech. edu/image/ligo 20160211 c https: //www. almaobservatory. org/en/images/this-stunning-aerialimage-of-the-alma-array/

The signal is assuming to be stochastic and uncorrelated. Although the signal is too weak to detect individualiy, we still can collect these signal statistically.

• ∝ Here we use maximum entropy method (MEM) to avoid this problem.

MEM is widely used in image reconstruction in radio interferometry (e. g. , CMB (M. P. Hobson & A. W. Jones), supermassive black hole in the center of M 87(EHT)). (EHT collaboration, First M 87 Event Horizon Telescope Results. IV)

Multiply the entropy function S to the maximum likelihood estimators ∝ The maximum likelihood estimators can be rewrite as ∝

Taking the logarithm, we thus need to maximize the estimators to get the skymap •

Baseline : 1 (H-L) Frequency band : 25 Hz segment duration : 52 sec Total obeservation time : one sidereal day

Baseline : 1 (H-L) Frequency band : 100 Hz segment duration : 52 sec Total obeservation time : one sidereal day

Baseline : 3 (H-L) (H-V) (L-V) Frequency band : 100 Hz segment duration : 52 sec Total obeservation time : one sidereal day

Baseline : 3 (H-L) (H-V) (L-V) Frequency band : 100 Hz segment duration : 52 sec Total obeservation time : one sidereal day

Baseline : 3 (H-L) (H-V) (L-V) Frequency band : 25~505 Hz Bin size : 8 Hz segment duration : 52 sec Total obeservation time : one sidereal day

Baseline : 3 (H-L) (H-V) (L-V) Frequency band : 25~505 Hz Bin size : 8 Hz segment duration : 52 sec Total obeservation time : one sidereal day

Summary • In broadband analysis, the reconstruction is accepted subjectively by visualization. • Quantify the improvement and evolve into spherical harmonic basis in the future