If a 1 M_⨀protostar starts out on the Hayashi track with a temperature of 3300 K and a luminosity of 320 L_⨀,what is its approximate radius? A)25 R_⨀ B)55 R_⨀ C)75 R_⨀ D)105 R_⨀ E)125 R_⨀

Question

Quizplus · Accepted Answer

Using the Hayashi track, we can calculate the radius of the protostar using the relation: L = 4πR2σT4 where L is the luminosity, R is the radius, σ is the Stefan-Boltzmann constant, and T is the temperature. Plugging in the given values, we get: 320 L_⨀ = 4πR2σ(3300 K)4 Simplifying, we get: R = (L/4πσT4)1/2 R = (320 L_⨀ / 4π(5.67×10-8 W m-2 K-4)(3300 K)4)1/2 R ≈ 55 R_⨀ Therefore, the best choice is (B), with a radius of approximately 55 solar radii.

If a 1 M⨀protostar Starts Out on the Hayashi Track

If a 1 M_⨀protostar Starts Out on the Hayashi Track