What is the estimated total lifetime for a star with mass 0.7 Msun ? (in billions of year)

To estimate the total lifetime of a star, we need to consider its mass. A star's mass determines its fuel consumption rate and, consequently, its lifespan. A common approach to estimate the lifetime of a star is to use the main sequence lifetime, which is the time spent by a star on the main sequence, where it burns hydrogen into helium.

For a star with a mass of 0.7 times the mass of the Sun (0.7 Msun), we can utilize a known relationship between a star's mass and its main sequence lifetime. This relationship is known as the mass-luminosity relation, which provides a correlation between a star's mass and its luminosity (brightness).

According to this relation, the luminosity of a star is proportional to the mass raised to the power of approximately 3.5. Hence, for a star with 0.7 Msun, its luminosity will be roughly (0.7)^3.5.

To estimate the total main sequence lifetime, we need to consider the star's fuel supply, which is primarily related to its mass. Higher-mass stars have more fuel and burn it at a faster rate than lower-mass stars. As a result, lower-mass stars tend to have longer lifetimes.

Stars similar to the Sun (1 Msun) typically have main sequence lifetimes of around 10 billion years. By using the mass-luminosity relation, we can estimate the main sequence lifetime of our star with 0.7 Msun relative to the Sun's lifetime:

Lifetime of 0.7 Msun star = Lifetime of 1 Msun star * (Luminosity of 0.7 Msun / Luminosity of 1 Msun)

Plugging in the values:

Lifetime of 0.7 Msun star ≈ 10 billion years * (0.7^3.5 / 1^3.5)

Calculating the expression:

Lifetime of 0.7 Msun star ≈ 10 billion years * 0.176

Hence, the estimated total lifetime for a star with a mass of 0.7 Msun is around 1.76 billion years.