The recent past witnesses the growing interdependence between the physics of hadrons, the physics of relativistic heavy-ion collisions, and the physics of compact objects in astrophysics. A notable example is the kaon which plays special roles in all the three fields. In this paper, we first review the various theoretical investigations of kaon properties in nuclear medium, focusing on possible uncertainties in each model. We then present a detailed transport model study of kaon production in heavy-ion collisions at SIS energies. We shall discuss especially the elementary kaon and antikaon production cross sections in hadron-hadron interactions, that represent one of the most serious uncertainties in the transport model study of particle production in heavy-ion collisions. The main purpose of such a study is to constrain kaon in-medium properties from the heavy-ion data. This can provide useful guidances for the development of theoretical models of the kaon in medium. In the last part of the paper, we apply the kaon in-medium properties extracted from heavy-ion data to the study of neutron star properties. Based on a conventional equation of state of nuclear matter that can be considered as one of the best constrained by available experimental data on finite nuclei, we find that the maximum mass of neutron stars is about 2M⊙, which is reduced to about 1.5M⊙ once kaon condensation as constrained by heavy-ion data is introduced.pacs: 25.75. Dw, 97.60.Jd, 26.60.+c, 24.10.Lx

The momentum dependence of the empirical scalar and vector potentials needed for describing relativistic heavy-ion collisions at 1 GeV/nucleon is compared with that derived from self-consistent Dirac-Brueckner calculations using the Bonn-A potential. Our calculated scalar and vector potentials exhibit a weak momentum dependence and their magnitudes decrease with nucleon momentum, in close similarity with the momentum dependence required by the empirical potentials. The effects of explicit momentum dependence on the properties of equilibrium nuclear matter are found to be small.

Dilepton spectra from the decay of phi mesons produced in heavy-ion collisions at SIS/GSI energies (∼ 2 GeV/nucleon) are studied in the relativistic transport model. We include phi mesons produced from baryon-baryon, pion-baryon, and kaon-antikaon collisions. The cross sections for the first two processes are obtained from an one-boson-exchange model, while that for the last process is taken to be the Breit-Wigner form through the phi meson resonance. For dileptons with invariant mass near the phi meson peak, we also include contributions from neutron-proton bremsstrahlung, pion-pion annihilation, and the decay of rho and omega mesons produced in baryon-baryon and meson-baryon collisions. Effects due to medium modifications of the kaon and vector (rho, omega and phi) meson properties are investigated. We find that the kaon medium effects lead to a broadening of the dilepton spectrum as a result of the increase of phi meson decay width. Furthermore, the dropping of phi meson mass in nuclear medium leads to a shoulder structure in the dilepton spectrum besides the main peak at the bare phi meson mass. The experimental measurement of the dilepton spectra from heavy-ion collisions is expected to provide useful information about the phi meson properties in dense matter.