The Hagedorn temperature, TH, is the temperature in theoretical physics where hadronic matter (i.e. ordinary matter) is no longer stable, and must either "evaporate" or convert into quark matter; as such, it can be thought of as the "boiling point" of hadronic matter. It was discovered by Rolf Hagedorn. The Hagedorn temperature exists because the amount of energy available is high enough that matter particle (quark–antiquark) pairs can be spontaneously pulled from vacuum. Thus, naively considered, a system at Hagedorn temperature can accommodate as much energy as one can put in, because the formed quarks provide new degrees of freedom, and thus the Hagedorn temperature would be an impassable absolute hot. However, if this phase is viewed as quarks instead, it becomes apparent that the matter has transformed into quark matter, which can be further heated.
The Hagedorn temperature, TH, is about 150 MeV/kB or about 1.7×1012 K,[1] little above the mass–energy of the lightest hadrons, the pion.[2] Matter at Hagedorn temperature or above will spew out fireballs of new particles, which can again produce new fireballs, and the ejected particles can then be detected by particle detectors. This quark matter may have been detected in heavy-ion collisions at SPS and LHC in CERN (France and Switzerland)[3] and at RHIC in Brookhaven National Laboratory (USA).[4]
In string theory, a separate Hagedorn temperature can be defined for strings rather than hadrons. This temperature is extremely high (1030 K) and thus of mainly theoretical interest.[5]