If an 0.8 M _$\odot$ white dwarf could accrete matter from a binary companion at a rate of 10 ^- ⁹ M _$\odot$ /yr, how long would it take before it exploded as a Type I supernova? A) 600 thousand years B) 20 million years C) 200 million years D) 600 million years E) 1 billion years

Question

Quizplus · Accepted Answer

The time it takes for a white dwarf to accumulate enough mass to trigger a Type I supernova is dependent on the Chandrasekhar limit, which is the maximum mass a white dwarf can attain before collapsing. This limit is around 1.4 solar masses. In this problem, we are given the accretion rate of the white dwarf, so we can calculate the mass it will accumulate over time using:

Mass accreted = accretion rate x time

We need to solve for time, so we can rearrange the equation to:

Time = mass accreted/ accretion rate

The initial mass of the white dwarf is given as 0.8 solar masses. We can calculate the time it takes for it to reach the Chandrasekhar limit of 1.4 solar masses:

Mass accreted = 1.4 - 0.8 = 0.6 solar masses
Accretion rate = 10^-7 solar masses/year
Time = 0.6/10^-7 = 6 x 10^6 years

Therefore, it would take about 600 million years for the white dwarf to explode as a Type I supernova. The correct answer is choice D.

If an 08 M ⊙\odot⊙ White Dwarf Could Accrete Matter from a Binary

If an 08 M _$\odot$ White Dwarf Could Accrete Matter from a Binary