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Dilepton invariant-mass spectra for heavy-ion collisions at SIS 18 andBEVALAC energies are calculated using a coarse-grained time evolution from theUltra-relativistic Quantum Molecular Dynamics (UrQMD) model. Thecoarse-graining of the microscopic simulations enables to calculate thermaldilepton emission rates by application of in-medium spectral functions fromequilibrium quantum-field theoretical calculations. The results show thatextremely high baryon chemical potentials dominate the evolution of the createdhot and dense fireball. Consequently, a significant modification of the $\rho$spectral shape becomes visible in the dilepton invariant-mass spectrum,resulting in an enhancement in the low-mass region $M_{ee} = 200$ to 600MeV/$c^{2}$. This enhancement, mainly caused by baryonic effects on the $\rho$spectral shape, can fully describe the experimentally observed excess above thehadronic cocktail contributions in Ar+KCl ($E_{\mathrm{lab}}=1.76$ $A$GeV)reactions as measured by the HADES collaboration and also gives a goodexplanation of the older DLS Ca+Ca ($E_{\mathrm{lab}}=1.04$ $A$GeV) data. Forthe larger Au+Au ($E_{\mathrm{lab}}=1.23$ $A$GeV) system, we predict an evenstronger excess from our calculations. A systematic comparison of the resultsfor different system sizes from C+C to Au+Au shows that the thermal dileptonyield increases stronger ($\propto A^{4/3}$) than the hadronic backgroundcontributions, which scale with $A$, due to its sensitivity on the timeevolution of the reaction. We stress that the findings of the present work areconsistent with our previous coarse-graining results for the NA60 measurementsat top SPS energy. We argue that it is possible to describe the dileptonresults from SIS 18 up to SPS energies by considering the modifications of the$\rho$ spectral function inside a hot and dense medium within the same model.

Dilepton production and reaction dynamics in heavy-ion collisions at SIS energies from coarse-grained transport simulations