Rate of supernovae

[Erenjaeger]

Which option is closest to scientists' current best estimate for the rate at which a supernova explosions occur somewhere in the milky way galaxy?
a) once a day
b) once a year
c) once every hundred years
d) once every thousand years

From what I have found online, the current estimate is one every 50 years but the question on my practice exam doesn't offer that as an option. Anyone got any links or know anything to help me.
Thanks.

 

[PeterDonis]

the current estimate is one every 50 years but the question on my practice exam doesn't offer that as an option

It asks you which option is closest to the current best estimate. Which of the four is closest to one every 50 years?

 

[Vanadium 50]

Well, if I wanted to quibble, I would say 50 years is only 49 years away from 1 year but 50 years away from 100.

The last known supernova in our galaxy was in 1868. (It was not visible because of dust, but the remnant has been found) The only one ever visible in M31 (the nearest large galaxy) was in 1885 (on the opening night of The Mikado). Given that, which answer looks the best to you?

 

[Chronos]

The generally accepted supernova rate for an average galaxy [like the Milky Way] is roughly 1 per century - re: http://candels-collaboration.blogspot.com/2012/09/supernova-hunting_28.html. This, however, varies somewhat depending on redshift as well as other factors as discussed here http://arxiv.org/abs/1509.04496.

 

[Chalnoth]

Well, if I wanted to quibble, I would say 50 years is only 49 years away from 1 year but 50 years away from 100.

Estimates like this work best by thinking about multiplicative differences instead.

For example, 50 years is fifty times the amount of time as 1 year, so those two numbers are very far apart.

Fifty years is only half of 100 years, though, so those two are quite close.

To do this a little bit more rigorously, you can use order-of-magnitude rounding. With this, numbers that are greater than $\sqrt{10}$ (about 3.1) round up to 10, while numbers below this round down to 1. So in this case, 50 rounds up to 100.

 

[newjerseyrunner]

Well, if I wanted to quibble, I would say 50 years is only 49 years away from 1 year but 50 years away from 100.

Estimates like this work best by thinking about multiplicative differences instead.

The question is about rate per year. That's a ratio, not a number by itself. 50 is not one of the options, 1/50 is.

1/50 is a lot closer to 1/100 than is 1/1.

 

[jbriggs444]

The question is about rate per year. That's a ratio, not a number by itself. 50 is not one of the options, 1/50 is.

If one is considering multiplicative differences than it is irrelevant whether one is counting supernovae per year or years per supernova.

log(1/50) is closer to log(1/100) than it is to log(1) and for identical reasons, log(50) is closer to log(100) than to log(1).