Two open clusters have had isochrones fitted to their colour-magnitude diagrams
PHYSICS · Multi-part · Fermi University Physics · Astrophysics & Cosmology · Stellar structure, energy generation and evolution · Stellar death and compact objects
Stars from the Inside, Ch Stellar evolution: from the Hayashi track to the iron core, and the ages of clusters
Problem
Two open clusters have had isochrones fitted to their colour-magnitude diagrams, giving each cluster an age and hence, from its main-sequence turn-off, an initial (main-sequence) mass for the stars now becoming white dwarfs. Combining this with the masses of the white dwarfs actually observed in each cluster gives the following. Data: cluster A has Mi=1.0M⊙ and mean white dwarf mass Mf=0.55M⊙; cluster B has Mi=3.0M⊙ and Mf=0.70M⊙.
((a)) Assuming the initial-final mass relation is linear over this range, Mf=a+bMi, find a and b from the two cluster points.
((b)) Use the fitted relation to predict the final white dwarf mass left by a 6M⊙ progenitor, and state whether this is consistent with the upper initial mass of about 8M⊙ for white dwarf formation and with the white dwarf's mass lying below about 1.4M⊙, the most massive white dwarfs observed.
((c)) Name, in one sentence each, which tool supplied Mi for each cluster, and which physical process is responsible for reducing a star's mass from Mi down to the much smaller Mf.