TUESDAY, 28 June 2016, 12:00
Δημήτριος Μ. Χριστοδούλου
By solving analytically the various types of Lane-Emden equations with rotation, we have discovered two new coupled fundamental properties of rotating, self-gravitating, gaseous discs in equilibrium: isothermal discs must, on average, exhibit strict power-law density profiles in radius x on their equatorial planes of the form Ax^(k-1), where A and k-1 are the integration constants; and “flat” rotation curves precisely such as those observed in spiral galaxy discs. Polytropic discs must, on average, exhibit strict density profiles of the form [ln(Ax^k)]^n, where n is the polytropic index; and “flat” rotation curves described by square roots of upper incomplete gamma functions. By “on average”, we mean that, irrespective of the chosen boundary conditions, the actual profiles must oscillate around and remain close to the strict mean profiles of the analytic singular equilibrium solutions. We call such singular solutions the “intrinsic” solutions of the differential equations because they are demanded by the second-order equations themselves with no regard to the Cauchy problem. The results are directly applicable to gaseous galaxy discs that have long been known to be isothermal and to protoplanetary discs during the extended isothermal and adiabatic phases of their evolution.
Το σεμινάριο θα μεταδοθεί ζωντανά στην ιστοσελίδα:
Στην αίθουσα διαλέξεων "Β. Ξανθόπουλος" στο Εργαστήριο Αστρονομίας, ΑΠΘ