Main sequence lifetime problem

If you set up the equation as T/t = M**-2/m, you will get the correct answer of 3.2 times the mass of the sun.In summary, to find the mass of the most massive main sequence stars in a globular cluster after 1 giga year, you can set up the equation T/t = M**-2/m and solve for M, which will give you a result of 3.2 times the mass of the sun.
  • #1
kranav
34
0
Hello.
The question states that
We have a globular cluster with total mass 10^6 times sun's mass.
Assume that the main sequence lifetime of a solar mass star is 10 giga year, and a main sequence lifetime scales with mass as M^-2. What is the mass of the most massive main sequence stars in the cluster after 1 giga year? (answer - 3.2 times sun's mass)

we have t ~ M^-2

Does this require me to do a differential and find out the maxima (of the mass) by putting it to zero?
or by cutting of the massive stars which would die out within the 1 giga year and somehow see the masses left.
 
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  • #2
1) Hint 1: The cluster mass is extraneous information that you can ignore...

(stop reading before you get to hint 2)2) Hint 2: set it up like a ratio problem.
 
  • #3
so,

T/t = M/m

where t = 10 gy and T = 1 gy and
m = 1 solar mass

is this correct?

thanks.
 
  • #4
kranav said:
so,

T/t = M/m

where t = 10 gy and T = 1 gy and
m = 1 solar mass

Close. What you've set up is the equation for T proportional to M. You are looking for T proportional to M**-2
 

What is the main sequence lifetime problem?

The main sequence lifetime problem refers to the question of how long a star will remain on the main sequence, which is the longest and most stable phase of a star's life. This is an important question in astrophysics as it helps us understand the evolution and lifespan of stars.

What factors affect a star's main sequence lifetime?

Several factors can influence a star's main sequence lifetime, including its mass, composition, and environment. Generally, the more massive a star is, the shorter its main sequence lifetime will be. A star's composition also plays a role, as stars with higher metallicity (amount of elements other than hydrogen and helium) tend to have shorter main sequence lifetimes. Additionally, a star's environment, such as its distance from other stars or the presence of a binary companion, can also affect its main sequence lifetime.

How do scientists calculate a star's main sequence lifetime?

There are several different methods that scientists use to estimate a star's main sequence lifetime, including theoretical models and observational data. The most common method involves using a star's mass and luminosity to determine its position on the Hertzsprung-Russell (H-R) diagram, which is a graph that plots a star's luminosity against its temperature. By comparing a star's position on the H-R diagram to theoretical models, scientists can estimate its main sequence lifetime.

Why is the main sequence lifetime problem important?

The main sequence lifetime problem is important because it helps us understand how stars evolve and how long they will remain in different stages of their life cycle. This knowledge is crucial for understanding the formation and evolution of galaxies, as well as the potential habitability of planets orbiting other stars. Additionally, the main sequence lifetime problem is closely related to other important questions in astrophysics, such as the origin of different types of stars and the fate of our own Sun.

How does the main sequence lifetime problem impact our understanding of the universe?

The main sequence lifetime problem is a fundamental question in astrophysics that has implications for our understanding of the universe as a whole. By studying the main sequence lifetime of stars in different galaxies and at different points in cosmic history, scientists can gain insights into the formation and evolution of galaxies and the overall structure and history of the universe. Additionally, the main sequence lifetime problem is closely linked to our understanding of the origin and distribution of elements in the universe, which is crucial for understanding the conditions necessary for life to exist.

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