وابر ِ باریون-فوتون vâbar-e bâriyon-foton
*Fr.: rapport baryon-photon*
The → *baryon number* compared with the number of photons in the
→ *Universe*. The baryon-photon ratio can be estimated in a simple way. The
→ *energy density* associated with
→ *blackbody radiation* of → *temperature*
*T* is *aT*^{4}, and the mean energy per photon is
~*kT*. Therefore, the number density of blackbody photons for *T* = 2.7 K is:
*n*_{γ} = *aT*^{4}/*kT* = 3.7 x 10^{2}
photons cm^{-3}, where *a* = 7.6 x 10^{-15}
erg cm^{-3} K^{-4} (→ *radiation density constant*)
and *k* = 1.38 x 10^{-16} erg K^{-1}
(→ *Boltzmann's constant*). The number density of baryons can be
expressed by ρ_{m}/*m*_{p},
where ρ_{m} is the mass density of the Universe and
*m*_{p} is the mass of the → *proton*
(1.66 x 10^{-24} g). → *CMB*
measurements show that the baryonic mean density is ρ_{m} =
4.2 x 10^{-31} g cm^{-3} (roughly 5% of the
→ *critical density*). This leads to the value of ~ 2 x 10^{-7}
for the number density of baryons.
Thus, the baryon/photon ratio is approximately equal to
η = *n*_{b}/*n*_{γ} =
2 x 10^{-7}/3.7 x 10^{2} ~ 5 x 10^{-10}. In other words,
for each baryon in the Universe there is 10^{10} photons. This estimate
is in agreement with the precise value of the baryon-photon ratio
6.14 x 10^{-10} derived with the → *WMAP*.
Since the photon number and the baryon number are conserved,
the baryon-photon ratio stays constant as the Universe expands. → *baryon*; → *photon*;
→ *ratio*. |