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Aug 5, 2011, 7:40:16 PM (14 years ago)
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Version du papier soumis a A&A - cmv+reza, 05/08/2011

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  • trunk/Cosmo/RadioBeam/sensfgnd21cm.tex

    r4013 r4014  
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    1515%\documentclass[onecolumn]{aa} % for a paper on 1 column 
    1616%\documentclass[longauth]{aa} % for the long lists of affiliations
    … …  
    2929
    3030%% Commande pour les references
    31 \newcommand{\citep}[1]{ (\cite{#1}) }
     31\newcommand{\citep}[1]{(\cite{#1})}
    3232%% \newcommand{\citep}[1]{ { (\tt{#1}) } }
    3333
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    5858
    5959%% Definition fonction de transfer
    60 \newcommand{\TrF}{\mathrm{Tr}}
     60\newcommand{\TrF}{\mathbf{T}}
    6161
    6262
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    117117   }
    118118
    119    \date{Received July 15, 2011; accepted xxxx, 2011}
     119   \date{Received August 5, 2011; accepted xxxx, 2011}
    120120
    121121% \abstract{}{}{}{}{}
    … …  
    146146  competitive with optical surveys. }
    147147
    148    \keywords{ Cosmology:LSS --
    149                  Cosmology:Dark energy -- Radio interferometer -- 21 cm
    150                }
     148   \keywords{ large-scale structure of Universe --
     149                 dark energy -- Instrumentation: interferometers --
     150                 Radio lines; galaxies -- Radio continuum: general }
    151151
    152152   \maketitle
    … …  
    165165(\HI) as a tracer with intensity mapping, has been proposed in recent years \citep{peterson.06} \citep{chang.08}.
    166166Mapping the matter distribution using HI 21 cm emission as a tracer has been extensively discussed in literature
    167 \citep{furlanetto.06} \citep{tegmark.08} and is being used in projects such as LOFAR \citep{rottgering.06} or
     167\citep{furlanetto.06} \citep{tegmark.09} and is being used in projects such as LOFAR \citep{rottgering.06} or
    168168MWA \citep{bowman.07} to observe reionisation  at redshifts z $\sim$ 10.
    169169
    … …  
    187187length  of $\sim 150 \mathrm{Mpc}$.
    188188These features have been first observed in the CMB anisotropies
    189 and are usually referred to as {\em acoustic peaks} \citep{mauskopf.00} \citep{hinshaw.08}.
     189and are usually referred to as {\em acoustic peaks} (\cite{mauskopf.00}, \cite{larson.11}).
    190190The BAO modulation has been subsequently observed in the distribution of galaxies
    191191at low redshift ( $z < 1$) in the galaxy-galaxy correlation function by the SDSS
    … …  
    201201a very promising technique to map matter distribution up to redshift $z \sim 3$,
    202202complementary to optical surveys, especially in the optical redshift desert range
    203 $1 \lesssim z \lesssim 2$.
     203$1 \lesssim z \lesssim 2$, and possibly up to the reionization redshift \citep{wyithe.08}.
    204204
    205205In section 2, we  discuss the intensity mapping and its potential for measurement of the
    … …  
    245245
    246246Although the application of 21 cm radio survey to cosmology, in particular LSS mapping has been
    247 discussed in length in the framework of large future instruments, such as the SKA (e.g \cite{ska.science}),
     247discussed in length in the framework of large future instruments, such as the SKA (e.g \cite{ska.science}, \cite{abdalla.05}),
    248248the method envisaged has been mostly through the detection of galaxies as \HI compact sources.
    249249However, extremely large radio telescopes are required to detected \HI sources at cosmological distances.
    … …  
    341341  \frac{c}{H(z)} \, (1+z)^2 \times  \etaHI (\vec{\Theta}, z) 
    342342\end{equation}
    343 where $A_{21}=2.85 \, 10^{-15} \mathrm{s^{-1}}$ \citep{lang.99} is the spontaneous 21 cm emission
     343where $A_{21}=2.85 \, 10^{-15} \mathrm{s^{-1}}$ \citep{astroformul} is the spontaneous 21 cm emission
    344344coefficient, $h$ is the Planck constant, $c$ the speed of light, $\kb$ the Boltzmann
    345345constant and $H(z)$ is the Hubble parameter at the emission redshift.
    … …  
    371371fraction at $z=1.5$ in the intergalactic medium \citep{wolf.05},
    372372compared to its present day value $\gHI(z=1.5) \sim 0.025$.
    373 The 21 cm brightness temperature and the corresponding power spectrum can be written as \citep{wyithe.07} :
     373The 21 cm brightness temperature and the corresponding power spectrum can be written as
     374(\cite{barkana.07} and \cite{madau.97}) :
    374375\begin{eqnarray}
    375376 P_{T_{21}}(k) & = & \left( \bar{T}_{21}(z)  \right)^2 \, P(k)    \label{eq:pk21z} \\
    … …  
    443444& &
    444445I(\vec{\Theta},\lambda)  =  | A(\vec{\Theta},\lambda) |^2  \hspace{2mm} , \hspace{1mm} I \in \mathbb{R}, A \in \mathbb{C} \\
    445 & & < A(\vec{\Theta},\lambda) A^*(\vec{\Theta '},\lambda) >_{time}  = 0 \hspace{2mm} \mathrm{for}   \hspace{1mm} \vec{\Theta} \ne \vec{\Theta '}   I(\vec{\Theta},\lambda)
     446& & < A(\vec{\Theta},\lambda) A^*(\vec{\Theta '},\lambda) >_{time}  = 0 \hspace{2mm} \mathrm{for}   \hspace{1mm} \vec{\Theta} \ne \vec{\Theta '} 
    446447\end{eqnarray}
    447448A single receiver can be  characterized by its angular complex amplitude response $B(\vec{\Theta},\nu)$ and
    … …  
    827828brightness $T(\alpha, \delta, \nu)$ as a function of two equatorial angular coordinates $(\alpha, \delta)$
    828829and the frequency $\nu$. Unless otherwise specified, the results presented here are based on simulations of
    829 $90 \times 30 \simeq 2500 \, \mathrm{deg^2}$ of the sky, centered on $\alpha= 10\mathrm{h}00\mathrm{m} , \delta=+10 \, \mathrm{deg.}$, and  covering 128 MHz in frequency. We have selected this particular area of the sky to in order to minimize
     830$90 \times 30 \simeq 2500 \, \mathrm{deg^2}$ of the sky, centered on $\alpha= 10\mathrm{h}00\mathrm{m} , \delta=+10 \, \mathrm{deg.}$, and  covering 128 MHz in frequency. We have selected this particular area of the sky in order to minimize
    830831the Galactic synchrotron foreground. The sky cube characteristics (coordinate range, size, resolution)
    831832used in the simulations are given in the table \ref{skycubechars}.
    … …  
    881882The synchrotron contribution to the sky temperature for each cell is then
    882883obtained  through the formula:
    883 $$ T_{sync}(\alpha, \delta, \nu) = T_{haslam} \times \left(\frac{\nu}{408 MHz}\right)^\beta $$
     884$$ T_{sync}(\alpha, \delta, \nu) = T_{haslam} \times \left(\frac{\nu}{408 \, \mathrm{MHz}}\right)^\beta $$
    884885%%
    885886\item A two dimensional $T_{nvss}(\alpha,\delta)$ sky brightness temperature at 1.4 GHz is computed
    … …  
    890891map; we have taken $\beta_{src}$ as a flat random number in the range $[-1.5,-2]$, and the
    891892contribution of the radiosources to the sky temperature is computed as follows:
    892 $$ T_{radsrc}(\alpha, \delta, \nu) = T_{nvss} \times \left(\frac{\nu}{1420 MHz}\right)^{\beta_{src}} $$
     893$$ T_{radsrc}(\alpha, \delta, \nu) = T_{nvss} \times \left(\frac{\nu}{1420 \, \mathrm{MHz}}\right)^{\beta_{src}} $$
    893894%%
    894895\item The sky brightness temperature data cube is obtained through the sum of
    … …  
    905906of the power spectrum $P(k)$ at $z=0$ computed according to the parametrization of
    906907\citep{eisenhu.98}. We have used the standard cosmological parameters,
    907  $H_0=71 \mathrm{km/s/Mpc}$, $\Omega_m=0.27$, $\Omega_b=0.044$,
     908 $H_0=71 \, \mathrm{km/s/Mpc}$, $\Omega_m=0.27$, $\Omega_b=0.044$,
    908909$\Omega_\lambda=0.73$ and $w=-1$.
    909 An inverse FFT was then performed to compute the matter density fluctuations
     910An inverse FFT was then performed to compute the matter density fluctuations $\delta \rho / \rho$
    910911in the linear regime,
    911 $\delta \rho / \rho$ in a box of $3420 \times 1140 \times 716  \, \mathrm{Mpc^3}$ and evolved
     912in a box of $3420 \times 1140 \times 716  \, \mathrm{Mpc^3}$ and evolved
    912913to redshift $z=0.6$.
    913914The size of the box is about 2500 $\mathrm{deg^2}$  in the transverse direction and
    … …  
    10411042The LSS signal extraction depends indeed on the white noise level.
    10421043The results shown here correspond to the (a) instrument configuration, a packed array of
    1043 $11 \times 11 = 121$ 5 meter diameter dishes, with a white noise level corresponding
     1044$11 \times 11 = 121$ dishes  (5 meter diameter), with a white noise level corresponding
    10441045to $\sigma_{noise} = 0.25 \mathrm{mK}$ per $3 \times 3 \mathrm{arcmin^2} \times 500$ kHz
    10451046cell.
    … …  
    12681269
    12691270In order to estimate the precision with which BAO peak positions can be
    1270 measured, we  used a method similar to the one established in \citep{blake.03}.
     1271measured, we  used a method similar to the one established in
     1272\citep{blake.03} and \citep{glazebrook.05}.
    12711273
    12721274
    … …  
    15791581to perform a cosmological neutral hydrogen survey over a significant fraction of the sky. We have shown that
    15801582a nearly packed interferometer array with few hundred receiver elements spread over an hectare or a hundred beam
    1581 focal plane array with a $\sim 100 \, \mathrm{meter}$ primary reflector will have the required sensitivity to measure
     1583focal plane array with a $\sim \hspace{-1.5mm} 100 \, \mathrm{meter}$ primary reflector will have the required sensitivity to measure
    15821584the 21 cm power spectrum. A method to compute the instrument response for interferometers 
    15831585has been developed and we have  computed the noise power spectrum for various telescope configurations.
    … …  
    16031605
    16041606%%%
     1607%% reference SKA - BAO / DE en radio avec les sources
     1608\bibitem[Abdalla \& Rawlings (2005)]{abdalla.05} Abdalla, F.B. \& Rawlings, S.  2005,  \mnras, 360,  27     
     1609
     1610\bibitem[Albrecht et al. (2006)]{DETF}  Albrecht, A., Bernstein, G., Cahn, R. {\it et al.} (Dark Energy Task Force) 2006, arXiv:astro-ph/0609591
     1611
    16051612\bibitem[Ansari et al. (2008)]{ansari.08} Ansari R., J.-M. Le Goff, C. Magneville, M. Moniez, N. Palanque-Delabrouille, J. Rich,
    16061613    V. Ruhlmann-Kleider, \& C. Y\`eche , 2008 , arXiv:0807.3614
    16071614
    1608 %%%% References extraites de la section fournie par C. Yeche
    1609 \bibitem[Abdala \& Rawlings(2005)]{SKA} Abdalla, F.B. \& Rawlings, S.  2005,  \mnras, 360,  27     
    1610 
    1611 \bibitem[Albrecht et al.(2006)]{DETF}  Albrecht, A., Bernstein, G., Cahn, R. {\it et al.} (Dark Energy Task Force) 2006, arXiv:astro-ph/0609591
    1612        
    1613 \bibitem[Barkana \& Loeb(2007)]{h1temp} Barkana, R., and Loeb, A. 2007, Rep. Prog. Phys, 70 627
    1614 
    1615 \bibitem[Binney \& Merrifield(1998)]{binneymerrifield} Binney, J. \&  Merrifield, M. 1998, Galactic Astronomy.
    1616 (Princeton Univ. Press, Princeton)
    1617 
    1618 \bibitem[Blake and Glazebrook(2003)]{blake.03} Blake, C. \& Glazebrook, K. 2003, \apj, 594, 665;
    1619 Glazebrook, K. \&  Blake, C. 2005 \apj, 631, 1
     1615%%   Temperature HI 21 cm (Valeur pour la reionisation)
     1616\bibitem[Barkana \& Loeb (2007)]{barkana.07} Barkana, R., and Loeb, A. 2007, Rep. Prog. Phys, 70,  627
     1617
     1618%% Methode de generation/fit k_bao  (Section 5 - C. Yeche)
     1619\bibitem[Blake and Glazebrook (2003)]{blake.03} Blake, C. \& Glazebrook, K. 2003, \apj, 594, 665
     1620\bibitem[Glazebrook and Blake (2005)]{glazebrook.05} Glazebrook, K. \&  Blake, C. 2005 \apj, 631, 1
    16201621
    16211622% WiggleZ BAO observation
    1622 \bibitem[Blake et al. (2011)]{blake.11} Blake, Davis, T., Poole, G.B.  {\it et al.}  2011, \mnras  (arXiv/1105.2862)
     1623\bibitem[Blake et al. (2011)]{blake.11} Blake, Davis, T., Poole, G.B.  {\it et al.}  2011, \mnras,  (accepted, arXiv/1105.2862)
    16231624
    16241625% Galactic astronomy, emission HI d'une galaxie
    … …  
    16541655% Haslam 400 MHz synchrotron map
    16551656\bibitem[Haslam et al. (1982)]{haslam.82} Haslam  C. G. T.,  Salter C. J., Stoffel H., Wilson W. E., 1982,
    1656 Astron. \& Astrophys.  Supp.  Vol 47, {\tt (http://lambda.gsfc.nasa.gov/product/foreground/haslam\_408.cfm)}
    1657 
    1658 %  WMAP CMB anisotropies 2008
    1659 \bibitem[Hinshaw et al. (2008)]{hinshaw.08}  Hinshaw, G., Weiland, J.L., Hill, R.S.  {\it et al.} 2008, arXiv:0803.0732)
     1657Astron. \& Astrophys.  Supp.  Vol 47,  \\ {\tt (http://lambda.gsfc.nasa.gov/product/foreground/)}
     1658
    16601659
    16611660% Distribution des radio sources
    1662 \bibitem[Jackson(2004)]{jackson.04} Jackson, C.A. 2004, \na, 48, 1187 
     1661\bibitem[Jackson (2004)]{jackson.04} Jackson, C.A. 2004, \na, 48, 1187 
    16631662
    16641663% HI mass in galaxies
    1665 \bibitem[Lah et al. (2009)]{lah.09}  Philip Lah, Michael B. Pracy, Jayaram N. Chengalur et al.  2009,  \mnras
    1666 ( astro-ph/0907.1416)
     1664\bibitem[Lah et al. (2009)]{lah.09}  Philip Lah, Michael B. Pracy, Jayaram N. Chengalur et al.  2009,  \mnras, 399, 1447
     1665% ( astro-ph/0907.1416)
    16671666
    16681667% Livre Astrophysical Formulae de Lang
    1669 \bibitem[Lang (1999)]{radastron} Lang, K.R. {\it Astrophysical Formulae}, Springer, 3rd Edition 1999
     1668\bibitem[Lang (1999)]{astroformul} Lang, K.R. {\it Astrophysical Formulae}, Springer, 3rd Edition 1999
     1669
     1670%  WMAP CMB 7 years power spectrum 2011
     1671% \bibitem[Hinshaw et al. (2008)]{hinshaw.08}  Hinshaw, G., Weiland, J.L., Hill, R.S.  {\it et al.} 2008, arXiv:0803.0732)
     1672\bibitem[Larson et al. (2011)]{larson.11}  Larson, D.,  {\it et al.}  (WMAP) 2011, \apjs, 192, 16
    16701673
    16711674% LSST Science book
    … …  
    16731676{\it LSST Science book}, LSST Science Collaborations, 2009, arXiv:0912.0201 
    16741677
     1678% Temperature du 21 cm
     1679\bibitem[Madau et al. (1997)]{madau.97} Madau, P., Meiksin, A. and Rees, M.J., 1997, \apj 475, 429
     1680 
    16751681% Foret Ly alpha - 1
    16761682\bibitem[McDonald et al. (2006)]{baolya} McDonald P., Seljak, U. and Burles, S.  {\it et al.}  2006, \apjs, 163, 80
    … …  
    16891695\mnras, 388, 247-260
    16901696
    1691 % Original CRT HSHS paper
    1692 \bibitem[Peterson et al. (2006)]{peterson.06} Peterson, J.B.,  Bandura, K., \& Pen, U.-L. 2006, arXiv:astro-ph/0606104 
     1697% Original CRT HSHS paper (Moriond Cosmo 2006 Proceedings)
     1698\bibitem[Peterson et al. (2006)]{peterson.06} Peterson, J.B.,  Bandura, K., \& Pen, U.-L. 2006, arXiv:0606104 
    16931699
    16941700% SDSS BAO 2007
    … …  
    16961702
    16971703% SDSS BAO 2010  - arXiv:0907.1660
    1698 \bibitem[Percival et al. (2010)]{percival.10}   Percival, W.J., Reid, B.A., Eisenstein, D.J. {\it et al.},  2010, \mnras 401, 2148-2168   
     1704\bibitem[Percival et al. (2010)]{percival.10}   Percival, W.J., Reid, B.A., Eisenstein, D.J. {\it et al.},  2010, \mnras, 401, 2148-2168   
    16991705
    17001706%% LOFAR description
    1701 \bibitem[Rottering et a,. (2006)]{rottgering.06} Rottgering H.J.A., Braun, r., Barthel, P.D. {\it et al.}  2006, arXiv:astro-ph/0610596
     1707\bibitem[Rottering et al. (2006)]{rottgering.06} Rottgering H.J.A., Braun, r., Barthel, P.D. {\it et al.}  2006, arXiv:astro-ph/0610596
    17021708%%%%
    17031709
    … …  
    17161722
    17171723% FFT telescope
    1718 \bibitem[Tegmark \& Zaldarriaga (2008)]{tegmark.08} Tegmark, M. \& Zaldarriaga, M. 2008, arXiv:0802.1710
     1724\bibitem[Tegmark \& Zaldarriaga (2009)]{tegmark.09} Tegmark, M. \& Zaldarriaga, M., 2009, \prd, 79, 8, p. 083530 % arXiv:0802.1710
    17191725
    17201726%  Thomson-Morane livre interferometry
    … …  
    17251731\bibitem[Wolf et al.(2005)]{wolf.05} Wolfe, A. M., Gawiser, E. \& Prochaska, J.X. 2005  \araa, 43, 861
    17261732
    1727 % 21 cm temperature
    1728 \bibitem[Wyithe et al.(2007)]{wyithe.07} Wyithe, S., Loeb, A. \& Geil, P. 2007 http://fr.arxiv.org/abs/0709.2955, submitted to \mnras
     1733%  BAO à 21 cm et reionisation
     1734\bibitem[Wyithe et al.(2008)]{wyithe.08} Wyithe, S., Loeb, A. \& Geil, P. 2008, \mnras, 383, 1195 %  http://fr.arxiv.org/abs/0709.2955,
    17291735
    17301736%% Today HI cosmological density
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