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Standard Candles

  1. Nov 11, 2013 #1
    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
    [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]


    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. jcsd
  3. Nov 12, 2013 #2
    I'm still struggling to understand this question. Anyone have some insight they might want to share?
     
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