1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Redshift (Ryden 5.2), confusing step.

  1. Mar 4, 2012 #1
    1. The problem statement, all variables and given/known data
    A light source in a flat, single-component universe has a redshift z when observed at a time [itex] t_{0} [/itex]. Show that the observed redshift changes at a rate

    [tex]
    \frac{dz}{dt_{0}} = H_{0}(1+z) - H_{0}(1+z)^{3(1+w)/2}
    [/tex]



    2. Relevant equations
    [tex]H_{0} = (\frac{\dot{a}}{a})|_{t = t_{0}} = \frac{2}{3(1+w)t_{0}} [/tex]

    [tex] (1+z) = \frac{a_{t_{0}}}{a_{t_e}} = \left( \frac{t_{0}}{t_{e}}\right )^{2/3(1+w)} [/tex]

    [tex] \frac{dz}{dt_{0}} = \frac{dz}{da_{0}}\frac{da_{0}}{dt_{0}} + \frac{dz}{da_{e}}\frac{da_{e}}{dt_{e}}\frac{dt_{e}}{dt_{0}} [/tex]

    [tex] t_{e} = \frac{t_0}{(1+z)^{3(1+w)/2}} [/tex]

    w is the component index (matter, radiation, lambda), not sure what its formal name is.
    3. The attempt at a solution

    Everything goes ok following my work below until the last step:

    [tex]\frac{dz}{dt_{0}} = \frac{2}{3(1+w)t_{0}}\left( \frac{t_{0}}{t_{e}} \right)^{2/3(1+w)}
    - \frac{2}{3(1+w)t_{e}}\left( \frac{t_{0}}{t_{e}} \right)^{2/3(1+w)}\frac{dt_{e}}{dt_{0}}[/tex]

    [tex] = H_{0}(1+z) - \frac{2}{3(1+w)t_{e}}(1+z)\frac{dt_{e}}{dt_{0}} [/tex]



    Here is where I am stuck. Using the definition for [itex] t_{e} [/itex], as given in the chapter, we get:

    [tex] \frac{dt_{e}}{dt_{0}} = (1+z)^{-3(1+w)/2} = \frac{t_e}{t_{0}} [/tex]

    But when subbing this in we end up with 0!

    I have no idea how to proceed.
     
    Last edited: Mar 4, 2012
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Redshift (Ryden 5.2), confusing step.
  1. Step potentials (Replies: 0)

  2. Redshift question (Replies: 0)

  3. Step down potential (Replies: 0)

  4. Redshift Parameter (Replies: 0)

Loading...