Question

5. The HR Diagram. Suppose we consider a main sequence “O star” much more massive than the sun. According to the formulae shown in lecture:

a. What is the luminosity of a main-sequence O star (in solar units, L_sun) of mass 100 solar masses?

b. If the sun were a 100 solar mass main-sequence O star, how much brighter would it appear from the earth?

c. What is the hydrogen fusing lifetime of this star in years?

d. If the core of this star contains 5 solar masses, to what radius must the core shrink to become a black hole? (Quote your answer in km.)

Answer 1

d)

I solar man 5. -- 2x 1030kg. 5x2 < 10 30 31 - 2 x 10 - 10 kg/v₂ 3x lo m/s TG 6-67xlo" M₂ 1031 kg Escape relocity, 31 16 3x10 2 x 10 2 x 86.67 x 10 R 20 2) R- 2x G 67 x 10 9 10 6 ? 1.482 x 10 - 14820 m

a) They are between 40,000 and 1,000,000 Lsun times as luminous as the Sun.

In the present arrangement of excellent characterization, stars are gathered by temperature, with the gigantic, youthful and lively Class O stars bragging temperatures in overabundance 30,000 K while the less monstrous, regularly more established Class M stars show temperatures under 3,500 K. Since luminosity is corresponding to temperature to the fourth force, the enormous variety in outstanding temperatures creates a significantly vaster variety in excellent luminosity. Since the luminosity relies upon a high intensity of the excellent mass, high mass brilliant stars have a lot shorter lifetimes. The most iridescent stars are constantly youthful stars, close to two or three million years for the most extraordinary. In the Hertzsprung–Russell graph, the x-pivot speaks to temperature or otherworldly sort while the y-hub speaks to luminosity or magnitude.

b) If the sun has 100 solar mass like that of main sequence O star then the luminosity of the sun would be like 1000000 solar luminosity as like the Main Sequence star .

c ) Since the mass of O star is very large their lifespan is very short . The most iridescent stars are constantly youthful stars, close to two or three million years for the most extraordinary.