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TUESDAY, 28 June 2016, 12:00
Δημήτριος Μ. Χριστοδούλου
Abstract: 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
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