Type Ia supernovae arise from thermonuclear explosions of white dwarfs accreting from a binary companion. Following the explosion, the surviving donor star leaves at roughly its orbital velocity. The discovery of the runaway helium subdwarf star US 708, and seven hypervelocity stars from Gaia data, all with spatial velocities $\gtrsim 900$ km/s, strongly support a scenario in which the donor is a low-mass helium star, or a white dwarf. Motivated by these discoveries, we perform three-dimensional hydrodynamical simulations with the $\texttt{Athena++}$ code modeling the hydrodynamical interaction between a helium star or helium white dwarf, and the supernova ejecta. We find that $\approx 0.01-0.02\,M_{\odot}$ of donor material is stripped, and explain the location of the stripped material within the expanding supernova ejecta. We continue the post-explosion evolution of the shocked donor stars with the $\texttt{MESA}$ code. As a result of entropy deposition, they remain luminous and expanded for $\approx 10^{5}-10^{6}$ yrs. We show that the post-explosion properties of our helium white dwarf donor agree reasonably with one of the best-studied hypervelocity stars, D6-2.
Tilt-to-length (TTL) coupling, caused by the jitter of test masses or satellites, is a significant noise source in space-based gravitational wave detection. Calibrating and suppressing TTL coupling noise at the sub-nanometer level is essential. One main challenge in current ground-based TTL coupling testing is the residual translational movement of the tilt actuator. This paper introduces the development of an advanced pure tilt actuator (APTA) specifically designed for testing TTL coupling. The APTA provides precise tilt motion and is monitored by a four-beam interferometer, which measures the displacement of attached array pyramids. We present a detailed theoretical model and experimental setup. Experimental results demonstrate that this optical test bed, equipped with the APTA, can achieve subnanometer-level TTL coupling calibration. In addition, a typical heterodyne interferometer was tested using the APTA test bed. Comparative testing demonstrated that the imaging system is capable of effectively suppressing TTL coupling errors. The TTL coupling coefficients were reduced from over plus-minus 30 micrometers per radian to within plus-minus 5 micrometers per radian across a range of plus-minus 200 microradians, meeting the preliminary requirements for the TianQin mission. This APTA test platform has the potential to be widely utilized for ground-based TTL coupling inspection.
Recently, several pulsar timing array (PTA) projects have detected evidence of the existence of a stochastic gravitational wave background (SGWB) in the nanohertz frequency band, providing confidence in detecting individual supermassive black hole binaries (SMBHBs) in the future. Nanohertz GWs emitted by inspiraling SMBHBs encode the luminosity distances of SMBHBs. They can serve as dark sirens to explore the cosmic expansion history via a statistical method to obtain the redshift information of GW sources' host galaxies using galaxy catalogs. The theoretical analysis of the dark siren method relies on the modeling of the population of SMBHBs. Using a population model consistent with the latest SGWB observations is essential, as the SGWB provides significant information about the distribution of SMBHBs. In this work, we employ a quasar-based model, which can self-consistently account for the SGWB amplitude, to estimate the population of SMBHBs. We constrain the Hubble constant using the mock GW data from different detection cases of PTAs in the future. Our results show that a PTA consisting of 100 pulsars with a white noise level of 20 ns could measure the Hubble constant with a precision close to $1\%$ over a 10-year observation period, and a PTA with 200 pulsars may achieve this goal over a 5-year observation period. The results indicate that modeling the SMBHB population significantly influences the analysis of dark sirens, and SMBHB dark sirens have the potential to be developed as a valuable cosmological probe.