# 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?