Approximation of distance to a Type Ia

[SHISHKABOB]

Homework Statement

The Type Ia supernova SN 1963p in the galaxy NGC 1084 had an apparent blue magnitude of B = 14.0 at peak brilliance. Then, with an extinction of 0.49 mag to that galaxy, the distance to the supernova is approximately

d = 10^{(m - M - A + 5)/5} = 41.9 Mpc​

Homework Equations

as above

The Attempt at a Solution

when I stick in m = 14.0, M = -19.3 and A = 0.49, I get only about 36.5 Mpc

I'm really not sure where I'm going wrong

 

[SHISHKABOB]

augh, turns out they used the MAXIMUM for the absolute peak magnitude where M = 19.6

which gives the entirely correct answer.

 

[cepheid]

Homework Statement

The Type Ia supernova SN 1963p in the galaxy NGC 1084 had an apparent blue magnitude of B = 14.0 at peak brilliance. Then, with an extinction of 0.49 mag to that galaxy, the distance to the supernova is approximately

d = 10^{(m - M - A + 5)/5} = 41.9 Mpc​

Homework Equations

as above

The Attempt at a Solution

when I stick in m = 14.0, M = -19.3 and A = 0.49, I get only about 36.5 Mpc

I'm really not sure where I'm going wrong

The short answer is, "because they used M = -19.6."

This was the maximum value of the standard template SN Ia light curve that was obtained using a method described here (they talk about your very example):

http://hyperphysics.phy-astr.gsu.edu/hbase/astro/snovcn.html#c4

EDIT I didn't see that you had already posted while I was typing.

 

[SHISHKABOB]

yeah that's exactly where I went to find the solution :P

thanks anyways

and by the way, that's a pretty huge jump in the distances. From reading the book, they say that the Type Ia supernovae are pretty good standard candles. But a difference of five Mpc seems like a big deal. Am I missing something?

 

[cepheid]

yeah that's exactly where I went to find the solution :P

thanks anyways

and by the way, that's a pretty huge jump in the distances. From reading the book, they say that the Type Ia supernovae are pretty good standard candles. But a difference of five Mpc seems like a big deal. Am I missing something?

Well, here's what it says on that site:

the Type Ia supernova SN 1963p in the galaxy NGC 1084 which had a measured apparent blue magnitude of B = m = 14.0 at peak brilliance. There was a measured extinction of A = 0.49 magnitude. Using the template maximum of M=19.6 as a standard candle gives a distance to the supernova

Emphasis mine. You want to compare the *peak* apparent magnitude to the *peak* absolute magnitude. So it would seem that, according to the template light curve, -19.6 is the peak value, and -19.3 is simply wrong. But I'm confused as to why, higher up on the page, it says that the average *maximum* absolute magnitude is indeed -19.3, and Carroll and Ostlie cite this value, and yet use -19.6 in their example. Maybe one is just older.

EDIT: or maybe -19.3 is the result of simply taking a statistical average of the peak values of several different light curves, whereas -19.6 comes from what is thought to be the more proper method of scaling and stretching the light curves using the observed relation between peak magnitude and decay time, until they all match each other. I'm just speculating, I don't know for sure.

The site also says that, after applying all of the appropriate scaling and stretching to the various light curves, they all reach the template with very little scatter, and as a result:

Distance uncertainties for Type Ia supernovae are thought to approach 5% or an uncertainty of just 0.1 magnitude in the distance modulus, m-M.

5% is 2 Mpc at this particular distance. I guess it's up to you to decide whether that's a big deal. I think the real question is whether the uncertainties in your distance estimate are comparable to, or much smaller than the differences between cosmological models that you are trying to differentiate amongst using Type Ia SNe as standard candles. I assume the answer is that they are much smaller, since these data have allowed us to strongly rule out or disfavour models with 0 cosmological constant.