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NonGaussian cosmic shear statistics based on weak-lensing aperture mass($M_{\rm ap}$) maps can outperform the classical shear two-point correlationfunction ($\gamma$-2PCF) in terms of cosmological constraining power. However,reaching the full potential of these new estimators requires accurate modelingof the physics of baryons as the extra nonGaussian information mostly residesat small scales. We present one such modeling based on the Magneticumhydrodynamical simulation for the KiDS-450 and DES-Y1 surveys and a Euclid-likesurvey. We compute the bias due to baryons on the lensing PDF and thedistribution of peaks and voids in $M_{\rm ap}$ maps and propagate it to thecosmological forecasts on the structure growth parameter $S_8$, the matterdensity parameter $\Omega_{\rm m}$, and the dark energy equation of state $w_0$using the SLICS and cosmo-SLICS sets of dark-matter-only simulations. We reporta negative bias of a few percent on $S_8$ and $\Omega_{\rm m}$ and also measurea positive bias of the same level on $w_0$ when including a tomographicdecomposition. These biases reach $\sim 5$% when combining $M_{\rm ap}$statistics with the $\gamma$-2PCF as these estimators show similar dependencyon the AGN feedback. We verify that these biases constitute a less than$1\sigma$ shift on the probed cosmological parameters for current cosmic shearsurveys. However, baryons need to be accounted for at the percentage level forfuture Stage IV surveys and we propose to include the uncertainty on the AGNfeedback amplitude by marginalizing over this parameter using multiplesimulations such as those presented in this paper. Finally, we explore thepossibility of mitigating the impact of baryons by filtering the $M_{\rm ap}$map but find that this process would require to suppress the small-scaleinformation to a point where the constraints would no longer be competitive.

Impact of baryons in cosmic shear analyses with tomographic aperture mass statistics