Standard Candles

1. Nov 11, 2013

bowlbase

1. The problem statement, all variables and given/known data
Suppose that we observe the redshifts and apparent fluxes of a sample of standard
candles. When observed at a distance of 1 Mpc, the standard candles are known to
have a flux F1Mpc = 1. From this sample of standard candles, we can measure the
Hubble constant H0.

redshift = z
flux = F
flux error = σ

The penalty function
$$\chi^2(H_o)=\sum_i^N(\frac{F_{model}(z_i|H_o-F_i)}{\sigma_i})^2$$

where $F_{model}(z_i|H_o-F_i)$ is the predicted flux of a standard candle at redshift z, given a value of Ho, and {zi, Fi, σi} are the redshift,
flux, and error for the ith standard candle. The best- fitting value of H0 consistent with the data is the value that minimizes $\chi^2$.

a) Explain why $$F_{model}(z_i|H_o-F_i)=F_{1Mpc}(\frac{(1Mpc)H_o}{cz})^2$$

2. Relevant equations
Flux $F=\frac{l}{4 \pi d^2}$
Hubble $H=\frac{\dot{a}}{a}$

3. The attempt at a solution

I was given a data set of standard candle measurements with this problem but since I have no clue where the equation comes from I don't know if I'm suppose to use it for this or not. I'm guessing not since it wants me to explain why the equation is used.

I understand that $z=\frac{v}{c}$ so the equation is $F_{model}(z_i|H_o-F_i)=F_{1Mpc}(\frac{(1Mpc)H_o}{v_{recession}})^2$

But, I dont know why this is necessarily the predicted flux.

Once I have this part understood I may have follow up questions because there is three parts to this. Let me know if I should go ahead and add those.

Thanks for any help.

2. Nov 12, 2013

bowlbase

I'm still struggling to understand this question. Anyone have some insight they might want to share?