What Does the Lifecycle of a 15 Solar Mass Star Look Like on an HR Diagram?

[tigor]

Homework Statement

Describe on HR diagram a lifecycle of a star with mass 15 times the mass of the Sun.
Also calculate T, L, R, t of such star

Homework Equations

L/L0=(M/M0)^3.5 - from here I can find the luminosity= 1.5*10^5*L0

t proportional to M/L=15M0/L = 11.4*10^-5 M0/L0 - that seems as too low ?

The Attempt at a Solution

15 times the mass of the Sun is ought to be a blue giant, to my understanding.
The blue just burns nuclear fuel until Iron core is formed. Afterwards, rather fast it will become supernova type II and further either Pulsar or Black hole.

None of those are mentioned on the HR diagram. And because blue giant burn fuel into heavy elements with great gravity, it does not become a red giant.
So what happens with blue giant in its course of life ?

Thank you in advance.

 

[nate808]

Thank you for your interesting question. A star with 15 times the mass of the Sun is indeed classified as a blue giant. On the HR diagram, this star would appear in the upper left corner, with a high temperature and luminosity.

The lifecycle of this star would begin with the fusion of hydrogen in its core, producing helium and releasing a large amount of energy. This process would continue for millions of years until the hydrogen in the core is depleted. At this point, the star would expand and cool, becoming a red supergiant.

As the star continues to evolve, it would start fusing helium in its core, producing carbon and oxygen. This process would continue until the star reaches the end of its life. Due to its high mass, the star would then undergo a supernova explosion, leaving behind either a neutron star or a black hole.

To calculate the temperature, luminosity, radius, and age of this star, we can use the equations you have provided. The luminosity can be calculated using the equation L/L0=(M/M0)^3.5, which gives us L=1.5*10^5*L0. Since the luminosity of the Sun is L0=3.828*10^26 W, the luminosity of our star would be L=5.742*10^31 W.

The temperature of the star can be estimated using the Stefan-Boltzmann law, which states that L=4πσR^2T^4, where σ is the Stefan-Boltzmann constant and R is the radius of the star. Rearranging this equation, we get T=(L/4πσR^2)^(1/4). Plugging in the values, we get T= 3.3*10^4 K.

To calculate the radius of the star, we can use the mass-luminosity relation, which states that L∝M^3.5. This means that R∝M^0.7. Since our star has 15 times the mass of the Sun, its radius would be approximately 4.3 times larger than the Sun's radius, which is R=4.3*R0=4.3*6.957*10^8 m=2.997*10^9 m.

Lastly, to estimate the age of the star, we can use the relation t∝M/L. Pl