Question

Suppose a star 1000 times brighter than our Sun (that is, emitting 1000 times the power) suddenly goes supernova. Using data from Table 7.3:

(a) By what factor does its power output increase?

(b) How many times brighter than our entire Milky Way galaxy is the supernova?

(c) Based on your answers, discuss whether it should be possible to observe supernovas in distant galaxies. Note that there are on the order of 10¹¹ observable galaxies, the average brightness of which is somewhat less than our own galaxy.

Short answer

(a) The factor by which power output of the star 1000 times brighter than the Sun has increased on going supernova is${10}^8$.

(b) The factor by which the supernova explosion is brighter than out galaxy is 5.

(c) Yes, it is possible to observe the supernova explosion in distant galaxies.

Step-by-step solution

Definition of Concepts

Power: Power is defined as the rate at which energy is expended. Greater power means a large amount of work or energy developed in a short time.

Power output of the star and a supernova

(a)

The power output of the sun is,

$P_{sun}=4\times {10}^{26}W$

Since, the power output of the star is 1000 times to that of power output of the Sun. Therefore, the power output of the start is,

$$\begin{gathered} P_s=1000\times \left(4\times {10}^{26}\right) \\ =4\times {10}^{29}W \end{gathered}$$

The power output of the supernova is,

$P_N=5\times {10}^{37}$

The factor by which the power output has increased is,

$$\begin{gathered} \frac{P_N}{P_S}=\frac{5\times {10}^{37}W}{4\times {10}^{26}W} \\ =1.25\times {10}^8 \end{gathered}$$

Therefore, the factor by which the power output of the star, 1000 times brighter than the sun has increased ongoing supernova is ${10}^8$.

Power output of Milky Way galaxy and a supernova

(b)

The power output of the Milky way galaxy is,

$P_G={10}^{37}W$

The factor by which the supernova explosion is brighter than Milky way is,

$$\begin{gathered} \frac{P_N}{P_G}=\frac{5\times {10}^{37}W}{{10}^{37}W} \\ =5 \end{gathered}$$

Thus, the factor by which the supernova explosion is brighter than our Milky way galaxy is 5.

Observation of supernova explosion in distant galaxies

(c)

The average brightness of observable galaxies is less than our Milky way galaxy. And we know that the supernova explosion is 5 times brighter than our Milky way galaxy. Hence, it is possible to observe supernova explosion in distant galaxies.