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The gravitational wave (GW) signal from binary black hole (BBH) mergers is a promising probe of Population III (Pop III) stars. To fully unleash the power of the GW probe, one important step is to understand the relative importance and features of different BBH evolution channels. We model two channels, isolated binary stellar evolution (IBSE) and nuclear star cluster-dynamical hardening (NSC-DH), in one theoretical framework based on the semi-analytical code a-sloth, under various assumptions on Pop III initial mass function (IMF), initial binary statistics and high-z nuclear star clusters (NSCs). The NSC-DH channel contributes $\sim 8-95{{\%}}$ of Pop III BBH mergers across cosmic history, with higher contributions achieved by initially wider binary stars, more top-heavy IMFs, and more abundant high-z NSCs. The dimensionless stochastic GW background (SGWB) produced by Pop III BBH mergers has peak values $\Omega ^{\rm peak}_{\rm GW}\sim 10^{-11}-8\times 10^{-11}$ around observer-frame frequencies $\nu \sim 10-100\ \rm Hz$. The Pop III contribution can be a non-negligible ($\sim 2-32{{\%}}$) component in the total SGWB at $\nu \lesssim 10\ \rm Hz$. The estimated detection rates of Pop III BBH mergers by the Einstein Telescope are $\sim 6-230\ \rm yr^{-1}$ and $\sim 30-1230\ \rm yr^{-1}$ for the NSC-DH and IBSE channels, respectively. Pop III BBH mergers in NSCs are more massive than those from IBSE, so they dominate the Pop III SGWB below 20 Hz in most cases. Besides, the detection rate of Pop III BBH mergers involving at least one intermediate-mass BH above $100\ \rm M_\odot$ by the Einstein Telescope is $\sim 0.5-200\ \rm yr^{-1}$ in NSCs but remains below $0.1\ \rm yr^{-1}$ for IBSE.
The gravitational wave (GW) signal from binary black hole (BBH) mergers is a promising probe of Population III (Pop III) stars. To fully unleash the power of the GW probe, one important step is to understand the relative importance and features of different BBH evolution channels. We model two channels, isolated binary stellar evolution (IBSE) and nuclear star cluster-dynamical hardening (NSC-DH), in one theoretical framework based on the semi-analytical code a-sloth, under various assumptions on Pop III initial mass function (IMF), initial binary statistics and high-z nuclear star clusters (NSCs). The NSC-DH channel contributes $\sim 8-95{{\%}}$ of Pop III BBH mergers across cosmic history, with higher contributions achieved by initially wider binary stars, more top-heavy IMFs, and more abundant high-z NSCs. The dimensionless stochastic GW background (SGWB) produced by Pop III BBH mergers has peak values $\Omega ^{\rm peak}_{\rm GW}\sim 10^{-11}-8\times 10^{-11}$ around observer-frame frequencies $\nu \sim 10-100\ \rm Hz$. The Pop III contribution can be a non-negligible ($\sim 2-32{{\%}}$) component in the total SGWB at $\nu \lesssim 10\ \rm Hz$. The estimated detection rates of Pop III BBH mergers by the Einstein Telescope are $\sim 6-230\ \rm yr^{-1}$ and $\sim 30-1230\ \rm yr^{-1}$ for the NSC-DH and IBSE channels, respectively. Pop III BBH mergers in NSCs are more massive than those from IBSE, so they dominate the Pop III SGWB below 20 Hz in most cases. Besides, the detection rate of Pop III BBH mergers involving at least one intermediate-mass BH above $100\ \rm M_\odot$ by the Einstein Telescope is $\sim 0.5-200\ \rm yr^{-1}$ in NSCs but remains below $0.1\ \rm yr^{-1}$ for IBSE.
The gravitational wave (GW) signals from a large number of double white dwarfs (DWDs) in the Galaxy are expected to be detected by space GW detectors, e.g., the Laser Interferometer Space Antenna (LISA), Taiji, and Tianqin in the millihertz band. In this paper, we present an alternative method by directly using the time-domain GW signal detected by space GW detectors to constrain the anisotropic structure of the Galaxy. The information of anisotropic distribution of DWDs is naturally encoded in the time-domain GW signal because of the variation of the detectors’ directions and consequently the pattern functions due to their annual motion around the Sun. The direct use of the time-domain GW signal enables simple calculations, such as utilizing an analytical method to assess the noise arising from the superposition of random phases of DWDs and using appropriate weights to improve the constraints. We investigate the possible constraints on the scale of the Galactic thin disk and bulge that may be obtained from LISA and Taiji by using this method with mock signals obtained from population synthesis models. We further show the different constraining capabilities of the low-frequency signal (foreground) and the high-frequency signal (resolvable sources) via the Markov Chain Monte Carlo method, and find that the scale height and length of the Galactic thin disk and the scale radius of the bulge can be constrained to a fractional accuracy of ∼30%, 30%, 40% (or 20%, 10%, 40%) by using the low-frequency (or high-frequency) signal detected by LISA or Taiji.
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