Changeset 4044 in Sophya for trunk/Cosmo/RadioBeam/sensfgnd21cm.tex

Timestamp:

Dec 20, 2011, 5:51:40 PM (14 years ago)

Author:

ansari

Message:

version quasi finale, V3, 2nd revision, soumise a A&A, Reza 20/12/2011

File:

• trunk/Cosmo/RadioBeam/sensfgnd21cm.tex (modified) (7 diffs)

trunk/Cosmo/RadioBeam/sensfgnd21cm.tex

@@ -354 +354 @@
 {\changemark and assuming high spin temperature, $\kb T_{spin} \gg h \nu_{21}$},
 the brightness temperature for a given direction and wavelength $\TTlam$ would be proportional to 
-the local \HI number density $\etaHI(\vec{\Theta},z)$ through the relation:
+the local \HI number density $\etaHI(\vec{\Theta},z)$ through the
+relation {\changemarkb (\cite{field.59} , \cite{zaldarriaga.04})}:
 \begin{equation}
   \TTlamz  =   \frac{3}{32 \pi}  \, \frac{h}{\kb} \,  A_{21}  \, \lambda_{21}^2 \times
@@ -362 +363 @@
 coefficient, $h$ is the Planck constant, $c$ the speed of light, $\kb$ the Boltzmann 
 constant and $H(z)$ is the Hubble parameter at the emission 
-redshift {\changemarkb (\cite{field.59} , \cite{zaldarriaga.04})}.
+redshift.
 For a \LCDM universe and neglecting radiation energy density, the Hubble parameter
 can be expressed as:
@@ -659 +660 @@
 and measurements at regularly spaced frequencies centered on a central frequency $\nu_0$ or redshift $z(\nu_0)$.
 The noise spectral power  density from equation (\ref{eq:pnoisekxkz}) would then be  
-constant, independent of $(k_x, k_y, \ell_\parallel(\nu)$. Such a noise power spectrum corresponds thus 
+constant, independent of $(k_x, k_y, \ell_\parallel(\nu))$. Such a noise power spectrum corresponds thus 
 to a 3D white noise, with a uniform noise spectral density:}
 \begin{equation}
@@ -789 +790 @@
 This last parameter is obtained through the relation 
 $t_{int} = t_{obs} \Omega_{FOV}  / \Omega_{tot}$ using the total survey duration 
-$t_{obs}=1 \mathrm{year}$ and the instantaneous field of view 
-$\Omega_{FOV} \sim \left( \frac{\lambda}{D} \right)^2$, for a total survey sky coverage 
-of $\pi$ srad. }
+$t_{obs}=1 \mathrm{year}$, the instantaneous field of view 
+$\Omega_{FOV} \sim \left( \frac{\lambda}{D} \right)^2$, and the total sky coverage 
+$\Omega_{tot} = \pi$ srad. }
 \end{itemize} 
 
@@ -1072 +1073 @@
 We haven't taken into account the curvature of redshift shells when 
 converting SimLSS euclidean coordinates to angles and frequency coordinates 
-of the sky cubes analyzed here, which introduces distortions visible at large angles $\gtrsim 10^\circ$. 
-These angular scales, corresponding to small wave modes $k \lesssim 0.02 \mathrm{h \, Mpc^{-1}}$ 
+of the sky cubes analyzed here. This approximate treatment causes distortions visible at large angles $\gtrsim 10^\circ$. 
+These angular scales correspond to small wave modes $k \lesssim 0.02 \mathrm{h \, Mpc^{-1}}$ and
  are excluded for results presented in this paper.
 }  
@@ -1397 +1398 @@
 
 \begin{table}[hbt]
-\caption{Value of the parameters for the transfer function (eq. \ref{eq:tfanalytique}) at different redshift 
-for instrumental setup (e), $20\times20$ packed array interferometer.  }
+\caption{Transfer function (eq. \ref{eq:tfanalytique}) parameters
+  $(k_A,k_B,k_C)$  at different redshifts
+for instrumental setup (e), $20\times20$ packed array interferometer. 
+{\changemarkb Note that the parameters are given in
+  $\mathrm{Mpc^{-1}}$ unit, and not in $\mathrm{h \, Mpc^{-1}}$.}
+}
 \label{tab:paramtfk}
 \begin{center}
@@ -1406 +1411 @@
 \hspace{2mm} 1.5 \hspace{2mm} & \hspace{2mm} 2.0 \hspace{2mm}  & \hspace{2mm} 2.5 \hspace{2mm} \\
 \hline 
-$k_A$ & 0.006 & 0.005 & 0.004 & 0.0035 & 0.003 \\
-$k_B$ & 0.038 & 0.019 & 0.012 & 0.0093 & 0.008 \\
-$k_C$ & 0.16   & 0.08   & 0.05   & 0.038   & 0.032 \\
+$k_A \, (\mathrm{Mpc^{-1}})$ & 0.006 & 0.005 & 0.004 & 0.0035 & 0.003 \\
+$k_B \, (\mathrm{Mpc^{-1}})$ & 0.038 & 0.019 & 0.012 & 0.0093 & 0.008 \\
+$k_C \, (\mathrm{Mpc^{-1}})$ & 0.16   & 0.08   & 0.05   & 0.038   & 0.032 \\
 \hline 
 \end{tabular}