Question

Q4. (5 marks) Assuming an average stellar mass of 0.5M , bmax = re (the core radius; see table 3.1 in lecture 13), and b min=1AU, determine the relaxation time trelax at the center of the globular cluster 47 Tucanae. Show that the crossing time tcross ~ 10-3trelax. What are some implications of this result in terms of modeling the orbits of stars in 47 Tucanae-like systems?

Answer 1

Given that Crossing Time Terors - R/v Tevens 5.2 Yc fra mer √3 or 28 Tcross We know that Trelay N 6 ln (N) T.cross if N=tos Then 6 ln (N) Trelax Tcross N -3 eln (10%) Tcross 10 Trelas. Trelax For Tucarie Cluster 47 ar = 11 km/sec rc =0.7 Pe 1.24X10 yr 2x0.7x 3.08 X10 Tcross ~ 11 Tcross = 10 Trelax 8 = 1.24 210 4y Trelas ~ Scanned with CamScanner