The impact of differential rotation on the stochastic excitation of acoustic modes in solar-like pulsators

Context. Acoustic modes are excited by turbulent convection in the outer convective envelope of solar-like stars. Observational results from asteroseismic studies have shown that 44% of solar-like stars do not present detectable stochastically excited acoustic modes. This phenomenon appears to be related to their rotation rate and magnetic activity. Indeed, rotation locally modifies the properties of convection, which in turn influences the stochastic excitation of stellar oscillation modes. In a first paper, we showed that uniform rotation tends to diminish the mode amplitudes significantly. However, convective envelopes in solar-type stars differentially rotate, and the rotation rate difference between mid-latitudes and the equator can reach up to 60%, as shown by recent asteroseismic works. Aims. In this paper, we examine the impact of differential rotation on the stochastic excitation of acoustic modes in solar-like stars. Methods. We provide theoretical predictions for the excitation of acoustic modes in a differentially rotating solar-like star. We used rotating mixing length theory to model the local influence of differential rotation on convection. We then estimated the resulting impact on power injection by turbulent convection into oscillation modes numerically, using a combination of the MESA stellar structure and evolution code and GYRE stellar pulsation code. Results. We show that the power injected in acoustic modes differs by up to 30% for stars with the same mean rotation rate (i.e. 5Ω⊙) but a distinct differential rotation rate. The excitation of axisymmetric acoustic modes is further inhibited in the anti-solar differential rotation regime, where the poles of stars rotate faster than their equators compared to the uniform rotation case. This could hinder mode detection in such configurations. In contrast, in solar differential rotation regimes, where the equator rotates faster than the poles, acoustic mode excitation is less inhibited compared to the uniform rotation case. We also studied the influence of the azimuthal order and show that the amplitudes can differ by up to 30% for modes with the same order, ℓ, and a different azimuthal order, m. The trends for sectoral modes (with |m|=l) is the opposite than the one observed for the axisymmetric modes. Conclusions. This study permits a first prediction of the excitation of acoustic modes as a function of the differential rotation in solar-like pulsators. On the one hand, efficient mode excitation may enable the detection of rotational frequency splittings. On the other hand, weaker-than-expected or stronger-than-expected excitation compared to predictions based on uniform rotation could provide valuable hints into differential rotation. The results are crucial to interpret data from past and ongoing asteroseismic space missions, such as Kepler/K2 and TESS, and to prepare for PLATO.