Question

3. The angular size of the Crab Nebula is about 4 arcminutes across, and its distance is approximately 2000 pc. You take a spectrum of the ionized gas in the nebula and find that the Hydrogen Alpha emission line has split into two lines -- one line is at 6594.7 Angstroms and the other is at 6531.3 Angstroms. (Note that Ziemann splitting is not at work here, since there are only 2 lines.) Given this information, estimate the date of the supernova explosion. Compare this to the observed date of 1054 AD. Why might your number be different (hint: think about physical reasons, not just measurement error)?

Answer 1

Given :

The size of the Crab Nebula = 4 arcmin = 240 arcsec

Solution:

The size of the crab Nebula is increasing at the rate of 0.23 arcsec/year. The time,t, since the supernova occurred can be written as

t = (240arcsec) / (0.23 arcsec/year) = 1043 years

Therefore, the nebula probably exploded in (2019-1043)=976 AD.

But the known year of the supernova explosion = 1054 AD

There is a possibility of the rate of expansion not being constant. For instance, if the rate of expansion was estimated to be greater than 0.23 arcsec/yr, the time passed since the supernova occurred would be lesser than the current calculated 1043 years.