Detecting anisotropies of the stochastic gravitational wave background with TianQin

The investigation of the anisotropy of the stochastic gravitational wave background (SGWB) using the TianQin detector plays a crucial role in studying the early universe and astrophysics. In this work, we examine the response of the $AET$ channel of the TianQin Time Delay Interferometry (TDI) to the anisotropy of the SGWB. We calculate the corresponding angular sensitivity curves and find that TianQin is capable of detecting the anisotropy of the SGWB, with an angular sensitivity reaching $10^{-10}$ for quadrupoles. Due to the fixed $z$-axis of TianQin pointing towards J0806, its overlap reduction functions (ORFs) exhibit specific symmetries, enabling the resolution of different multipole moments $\ell m$. The detection sensitivity is optimal for the $(2, 0)$ mode, with a sensitivity reaching $10^{-10}$. Using the Fisher matrix approach, we estimate the parameters and find that in the power-law spectrum model, higher logarithmic amplitudes lead to more effective reconstruction of the spectral index for all multipole moments. Under the optimal scenario with a signal amplitude of $\Omega_{\mathrm{GW}} (f = f_{\mathrm{c}}) h^2 = 10^{-9}$, the spectral indices can be reconstructed with uncertainties of $10^{-3}$, $10$, and $10^{-3}$ for $\ell = 0$, $1$, and $2$ multipole moments, respectively. For the cases of $(\ell, m) = (0, 0)$, $(1, 1)$, $(2, 0)$, and $(2, 2)$, the spectral indices can be reconstructed with uncertainties of $10^{-3}$, $10$, $10^{-3}$, and $10$, respectively.