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Thread: Starlight energy/number density

  1. #1
    Join Date
    Feb 2018

    Starlight energy/number density

    The energy density u of starlight in the solar neighbourhood is about 0.45 eV cm−3. It is sometimes convenient to approximate the density of the background starlight as a “diluted blackbody” of “dilution factor” W and “color temperature” Tc. The dilution factor is defined to be the ratio of the actual energy density u to the energy density of (undiluted) blackbody radiation of temperature Tc. Take Tc = 5000 K as characteristic of the starlight background.

    a) Estimate W for the starlight background. (And what is W for the CMB?)
    I used the Stefan-Boltzmann law here: u_c = 4 \sigma T^4 /c, to calculate the energy density of the (undiluted) blackbody radiation of temperature Tc. I took the ratio of the energy densities (definition of W) en I got 0.17 $ 10^-12. I was wondering if any one have an idea if this result is acceptable? because I have no idea of a typical value of this quantity
    b) The cosmic background has a temperature of 2.7 K. Estimate the ratio of the number density of microwave background photons to the number density of starlight photons in the solar neighborhood.
    Here using the average photon energy is 3kT = 1.13 10−22 J, I calculated the number density of CMB: n_b = u_cmb / 3kT_cmb. Using the Stefan-Boltzmann equation, I derived the corresponding temperature to be able to calculate the number density with n = u / 3kT . My question is: Is it acceptable to calculate the temperature for the starlight with S.B. law? I got a result of T = 2.44K, is that even possible?

    Thank you guys in advance
    Last edited by Itachi; 2018-Feb-10 at 10:08 PM.

  2. #2
    Join Date
    Jul 2005
    Massachusetts, USA
    Welcome Itachi! Hopefully someone will give you an answer soon.

    Side note: Here in this forum, we reserve colored text for moderator messages. I suggest using bold or italic for contrast in the future.
    Forming opinions as we speak

  3. #3
    Join Date
    Feb 2018
    Hi Antoni, Thanks for your welcome, I just fixed the technical issue


  4. #4
    Join Date
    Dec 2004
    These questions are well beyond my competence to answer, but
    since you give me the opportunity to offer something, I'll say that
    somewhere I recall seeing a figure of about 5 K for the temperature
    of local starlight minus sunlight, and I think that included CMB.
    2.7 + 2.44 is suspiciously close to 5, although I know that is not
    how temperatures are added!

    -- Jeff, in Minneapolis

    "I find astronomy very interesting, but I wouldn't if I thought we
    were just going to sit here and look." -- "Van Rijn"

    "The other planets? Well, they just happen to be there, but the
    point of rockets is to explore them!" -- Kai Yeves

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