- #1
bowlbase
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Homework Statement
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
[tex]\chi^2(H_o)=\sum_i^N(\frac{F_{model}(z_i|H_o-F_i)}{\sigma_i})^2[/tex]
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 [tex]F_{model}(z_i|H_o-F_i)=F_{1Mpc}(\frac{(1Mpc)H_o}{cz})^2[/tex]
Homework Equations
Flux ##F=\frac{l}{4 \pi d^2}##
Hubble ##H=\frac{\dot{a}}{a}##
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 don't 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.