Solve Supernova Problem: Apparent Magnitude at Max Luminosity

[Froddo]

Hello community, I really need help with few assignments!

First one would be about Supernova:
In a distant galaxy a supernova flash occured. When supernova reached luminosity maximum, galaxy apparent magnitude
was 17,6. Before the supernova flash the galaxy apparent magnitude was 18,0. What was the supernova's apparent magnitude at it's luminosity maximum?

Could you help me solve this and explain it to me ?

 

[SHISHKABOB]

So basically you've got the following:

m_g, m_sn, and m_{g + sn}

where m_g = 17.6 and m_{g + sn} = 18.0

So we know that m_g + m_sn is NOT m_{g + sn}

but we do know that

L_g + L_sn = L_{g + sn}

Do you have any equations that relate luminosity to magnitude? Or even a relationship between flux and magnitude, since F is proportional to L.

 

[Froddo]

Don't really have any equation or even a far-near one that would help in this problem. There is no actually luminosity mentioned as the numbers only state for apparent magnitude . I searched the whole net for relation between galaxy and supernova apparent magnitude, though did not find anything useful.

By the way , this is not really a homework or something, trying to learn some astroP on my own :)

 

[Froddo]

Of course there's the basic m1 - m2 = -2.5 log10 ( F1 / F2)

Where we can inputed m1 and m2 , though not sure which would I put in first. Like m1=mg and m2=mg+sn.

The final question is what was the Supernova's magnitude in the flash. Not sure this formula is useful in that way.

 

[SHISHKABOB]

you want to do something like

\frac{F_{sn+g}}{F_{g}} = 10^{\frac{m_{sn + g} - m_{g}}{-2.5}}

I just solved your equation for the ratio of the fluxes.

Now we also know that we can just add up the fluxes, i.e.

F_{sn + g} = F_g + F_sn

does this help? Remember that if you get a number for the magnitude, it should be something comparable to the two magnitudes you've already got.

 

[berkeman]

Thread closed temporarily for Moderation...

Thread re-opened. Froddo -- check your PMs.

 

[Froddo]

Done berkman :)

On-topic : I've tried to solve the problem whole night with no results, I think I'm missing something important. Anyone with experience could give me some heads up ? Not sure where to begin..

 

[Bandersnatch]

Let's try doing it in a more step-by-step fashion.

Look at the equation you provided in post #4. You needn't throw your condescension at it by calling it "basic", as this is your workhorse here. You won't be doing much more than playing with it.

Shishkabob solved the first step for you in post #5.
He took the two magnitudes you were given, as defined by yourself in post #4, and after plugging them into the equation and using the definition of the logarithm(http://en.wikipedia.org/wiki/Logarithm#Definition), he got a relation from which it should be easy to extract the value of F_sn as a factor of F_g.
In other words, it'll tell you how many times the supernova was brighter/dimmer than the galaxy.


Notice that it doesn't matter which goes first and which goes second when you plug the values here:

m1 - m2 = -2.5 log10 ( F1 / F2)

the end result is the same as if it were:

m2 - m1 = -2.5 log10 ( F2 / F1)

Now, use the same equation again, only this time with the values for the galaxy(m_g, F_g) and the supernova(m_sn, F_sn). Plug in the value for F_sn from the previous calculations.
The flux will disappear from the equation, and you'll be left with a common logarithm, whose value you can check in the tables, e.g. here:
http://www.sosmath.com/tables/logtable/logtable.html

In the end, you should end up with the ratio of fluxes F_sn=~0,45F_g,
and supernova magnitude around 18,9.
Which is good, as we know that one magnitude difference corresponds to two-and-a-half times difference in flux, and here we've got something in that range.