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Changeset 3976 in Sophya for trunk/Cosmo
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trunk/Cosmo/RadioBeam/sensfgnd21cm.tex (modified) (13 diffs)
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trunk/Cosmo/RadioBeam/sensfgnd21cm.tex
r3949 r3976 174 174 175 175 Ongoing or future surveys plan to measure precisely the BAO scale in the redshift range 176 $0 \lesssim z \lesssim 3$, using either optical observation of galaxies or through 3D mapping177 Lyman $\alpha$ absorption lines toward distant quasars \citep{baorss}\cite{baolya}.176 $0 \lesssim z \lesssim 3$, using either optical observation of galaxies \citep{baorss} % CHECK/FIND baorss baolya references 177 or through 3D mapping Lyman $\alpha$ absorption lines toward distant quasars \cite{baolya}. 178 178 Mapping matter distribution using 21 cm emission of neutral hydrogen appears as 179 179 a very promising technique to map matter distribution up to redshift $z \sim 3$, … … 227 227 the method envisaged has been mostly through the detection of galaxies as \HI compact sources. 228 228 However, extremely large radio telescopes are required to detected \HI sources at cosmological distances. 229 The sensitivity (or detection threshold) limit $S_{lim}$ for a radio instrument230 characterized by an effective collecting area $A$, and system temperature $\Tsys$ can be written as231 \begin{equation} 232 S_{lim} = \frac{ 2\kb \, \Tsys }{ A \, \sqrt{t_{int} \delta \nu} }229 The sensitivity (or detection threshold) limit $S_{lim}$ for the total power from the of two polarisations 230 of a radio instrument characterized by an effective collecting area $A$, and system temperature $\Tsys$ can be written as 231 \begin{equation} 232 S_{lim} = \frac{ \sqrt{2} \kb \, \Tsys }{ A \, \sqrt{t_{int} \delta \nu} } 233 233 \end{equation} 234 234 where $t_{int}$ is the total integration time $\delta \nu$ is the detection frequency band. In table … … 281 281 \begin{tabular}{|c|c|c|} 282 282 \hline 283 $A (\mathrm{m^2})$ & $ T_{sys} (K) $ & $ S_{lim} \ mathrm{\mu Jy} $ \\283 $A (\mathrm{m^2})$ & $ T_{sys} (K) $ & $ S_{lim} \, \mathrm{\mu Jy} $ \\ 284 284 \hline 285 285 5000 & 50 & 66 \\ 286 286 5000 & 25 & 33 \\ 287 100 000 & 50 & 3. 5\\288 100 000 & 25 & 1. 7\\287 100 000 & 50 & 3.3 \\ 288 100 000 & 25 & 1.66 \\ 289 289 500 000 & 50 & 0.66 \\ 290 290 500 000 & 25 & 0.33 \\ … … 494 494 bandwidth $\delta \nu$, with an integration time $t_{int}$, characterized by a system temperature 495 495 $\Tsys$. The uncertainty or fluctuations of this measurement due to the receiver noise can be written as 496 $\sigma_{noise}^2 = \frac{ 4\Tsys^2}{t_{int} \, \delta \nu}$. This term496 $\sigma_{noise}^2 = \frac{2 \Tsys^2}{t_{int} \, \delta \nu}$. This term 497 497 corresponds also to the noise for the visibility $\vis$ measured from two identical receivers, with uncorrelated 498 noise. If the receiver has an effective area $A \simeq \pi D^2 $ or $A \simeq 4D_x D_y$, the measurement498 noise. If the receiver has an effective area $A \simeq \pi D^2/4$ or $A \simeq D_x D_y$, the measurement 499 499 corresponds to the integration of power over a spot in the angular frequency plane with an area $\sim A/\lambda^2$. 500 500 The sky temperature measurement can thus be characterized by the noise spectral power density in … … 503 503 \begin{eqnarray} 504 504 P_{noise}^{(u,v)} & = & \frac{\sigma_{noise}^2}{ A / \lambda^2 } \\ 505 P_{noise}^{(u,v)} & \simeq & \frac{ \Tsys^2 }{t_{int} \, \delta \nu} \, \frac{ \lambda^2 }{ D^2 }505 P_{noise}^{(u,v)} & \simeq & \frac{2 \, \Tsys^2 }{t_{int} \, \delta \nu} \, \frac{ \lambda^2 }{ D^2 } 506 506 \hspace{5mm} \mathrm{units:} \, \mathrm{K^2 \times rad^2} \\ 507 507 \end{eqnarray} … … 523 523 The three dimensional projected noise spectral density can then be written as: 524 524 \begin{equation} 525 P_{noise}(k) = \frac{\Tsys^2}{t_{int} \, \nu_{21} } \, \frac{\lambda^2}{D^2} \, \dang^2(z) \frac{c}{H(z)} \, (1+z)^4525 P_{noise}(k) = 2 \, \frac{\Tsys^2}{t_{int} \, \nu_{21} } \, \frac{\lambda^2}{D^2} \, \dang^2(z) \frac{c}{H(z)} \, (1+z)^4 526 526 \end{equation} 527 527 … … 560 560 The noise power spectral density could then be written as: 561 561 \begin{equation} 562 P_{noise}^{survey}(k) = \frac{\Tsys^2 \, \Omega_{tot} }{t_{obs} \, \nu_{21} } \, \dang^2(z) \frac{c}{H(z)} \, (1+z)^4562 P_{noise}^{survey}(k) = 2 \, \frac{\Tsys^2 \, \Omega_{tot} }{t_{obs} \, \nu_{21} } \, \dang^2(z) \frac{c}{H(z)} \, (1+z)^4 563 563 \end{equation} 564 564 For a single dish instrument equipped with a multi-feed or phase array receiver system, … … 704 704 \mbox{ 705 705 \hspace*{-10mm} 706 \includegraphics[width=\textwidth]{Figs/p noisea2g.pdf}706 \includegraphics[width=\textwidth]{Figs/pkna2h.pdf} 707 707 } 708 708 \vspace*{-10mm} … … 714 714 715 715 \section{ Foregrounds and Component separation } 716 716 Reaching the required sensitivities is not the only difficulty of observing the large 717 scale structures in 21 cm. Indeed, the synchrotron emission of the 718 Milky Way and the extra galactic radio sources is a thousand time brighter than the 719 emission of the neutral hydrogen distributed in the universe. Extracting the LSS signal 720 using Intensity Mapping, without identifying the \HI point sources is the main challenge 721 for this novel observation method. Although this task might seem impossible at first, 722 it has been suggested that the smooth frequency dependence of the synchrotron 723 emissions can be used to separate the faint LSS signal from the Galactic and radio source 724 emissions. However, any real radio instrument has a beam shape which changes with 725 frequency which significantly increases the difficulty and complexity of this component separation 726 technique. The effect of frequency dependent beam shape is often referred to as {\em 727 mode mixing} \citep{morales.09}. 728 729 In this section, we present a short description of the foreground emissions and 730 the simple models we have used for computing the sky radio emissions in the GHz frequency 731 range. We present also a simple component separation method to extract the LSS signal and 732 its performance. We show in particular the effect of the instrument response and possible 733 way of getting around this difficulty. The results presented in this section concern the 734 total sky emission and the LSS 21 cm signal extraction in the $z \sim 0.6$ redshift range, 735 corresponding to the central frequency $\nu \sim 884$ MHz. 736 717 737 \subsection{ Synchrotron and radio sources } 718 % {\color{red} \large \it Reza (+ J.M. Martin ?) + CMV } \\[1mm] 719 720 Description of the radio foregrounds for LSS@21cm and the sky models used 721 \begin{itemize} 722 \item Galactic synchrotron 723 \item Radio sources : spectral behavior and brightness distribution 724 \item GSM global sky model (Angelica) 725 \item simple sky model : Synchrotron (HASLAM/WMAP) + sources (North20 / NVSS catalogue ) 726 \end{itemize} 738 We have modeled the radio in the form of three dimensional maps (data cubes) of sky temperature 739 brightness $T(\alpha, \delta, \nu)$ as a function of two equatorial angular coordinates $(\alpha, \delta)$ 740 and the frequency $\nu$. Unless otherwise specified, the results presented here are based on simulations of 741 $90 \times 30 \simeq 2500 \mathrm{deg^2}$ of the sky, centered on $\alpha= 10:00 \mathrm{h} , \delta=+10 \mathrm{deg.}$, 742 and covering 128 MHz in frequency. The sky cube characteristics (coordinate range, size, resolution) 743 used in the simulations is given in the table below: 744 \begin{center} 745 \begin{tabular}{|c|c|c|} 746 \hline 747 & range & center \\ 748 \hline 749 Right ascension & 105 $ < \alpha < $ 195 deg. & 150 deg.\\ 750 Declination & -5 $ < \delta < $ 25 deg. & +10 deg. \\ 751 Frequency & 820 $ < \nu < $ 948 MHz & 884 MHz \\ 752 Wavelength & 36.6 $ < \lambda < $ 31.6 cm & 33.9 cm \\ 753 Redshift & 0.73 $ < z < $ 0.5 & 0.61 \\ 754 \hline 755 \hline 756 & resolution & N-cells \\ 757 \hline 758 Right ascension & 3 arcmin & 1800 \\ 759 Declination & 3 arcmin & 600 \\ 760 Frequency & 500 kHz ($d z \sim 10^{-3}$) & 256 \\ 761 \hline 762 \end{tabular} \\ 763 Cube size : $ 90 \, \mathrm{deg.} \times 30 \, \mathrm{deg.} \times 128 \, \mathrm{MHz}$ \\ 764 $ 1800 \times 600 \times 256 \simeq 123 \, 10^6$ cells 765 \end{center} 766 767 Two different methods have been used to compute the sky temperature data cubes. 768 We have used the Global Sky Model (GSM) \citep{gsm.08} tools to generate full sky 769 maps of the emission temperature at different frequencies, from which we have 770 extracted the brightness temperature cube for the region defined above 771 (Model-I/GSM $T_{gsm}(\alpha, \delta, \nu)$). 772 As the GSM maps have an intrinsic resolution of $\sim$ 0.5 degree, it is 773 difficult to have reliable results for the effect of point sources on the reconstructed 774 LSS power spectrum. 775 776 We have thus also created a simple sky model using the Haslam Galactic synchrotron map 777 at 408 Mhz \citep{haslam.08} and the NRAO VLA Sky Survey (NVSS) 1.4 GHz radio source 778 catalog \cite{nvss.98}. The sky temperature cube in this model (Model-II/Haslam+NVSS) 779 has been computed through the following steps: 780 781 \begin{enumerate} 782 \item The Galactic synchrotron emission is modeled as a sum of two power law. 783 We assign a power law index $\beta = -2.8 \pm 0.15$ to each sky direction. 784 $\beta$ has a gaussian distribution centered at -2.8 and with standard 785 deviation $\sigma_\beta = 0.15$. 786 The synchrotron contribution to the sky temperature for each cell is then 787 obtained through the formula: 788 $$ T_{sync}(\alpha, \delta, \nu) = T_{haslam} \times \left(\frac{\nu}{408 MHz}\right)^\beta $$ 789 %% 790 \item A two dimensional $T_{nvss}(\alpha,\delta)$sky brightness temperature at 1.4 GHz is computed 791 by projecting the radio sources in the NVSS catalog to a grid with the same angular resolution as 792 the sky cubes is computed. The source brightness in Jansky is converted to temperature taking the 793 pixel angular size into account ($ \sim 21 \mathrm{mK / mJansky}$ at 1.4 Ghz and $3' \times 3'$ pixels). 794 A sepctral index $\beta_{src} \in [-1.5,-2]$ is also assigned to each sky direction for the radio source 795 map; we have taken $\beta_{src}$ as a flat random number in the range $[-1.5,-2]$, and the 796 contribution of the radiosources to the sky temperature is computed as follow: 797 $$ T_{radsrc}(\alpha, \delta, \nu) = T_{nvss} \times \left(\frac{\nu}{1420 MHz}\right)^{\beta_{src}} $$ 798 %% 799 \item The sky brightness temperature data cube is obtained through the sum of 800 the two contributions, Galactic synchrotron and resolved radio sources: 801 $$ T_{fgnd}(\alpha, \delta, \nu) = T_{sync}(\alpha, \delta, \nu) + T_{sync}(\alpha, \delta, \nu) $$ 802 \end{enumerate} 803 804 The 21 cm temperature fluctuations due to neutral hydrogen in large scale structures 805 $T_{lss}(\alpha, \delta, \nu)$ has been computed using the SimLSS software package 806 \footnote{SimLSS : {\tt http://www.sophya.org/SimLSS} }. 807 {\color{red}: CMV, please add few line description of SimLSS}. 808 We have generated the mass fluctuations $\delta \rho/rho$ at $z=0.6$, in cells of size 809 $1.9 \times 1.9 \times 2.8 \, \mathrm{Mpc^3}$, which correspond approximately to the 810 sky cube angular and frequency resolution defined above. The mass fluctuations has been 811 converted into temperature through a factor $0.13 mK$, corresponding to a hydrogen 812 fraction $0.008x(1+0.6)$. The total sky brightness temperature is then computed as the sum 813 of foregrounds and the LSS 21 cm emission: 814 $$ T_{sky} = T_{sync}+T_{radsrc}+T_{lss} \hspace{5mm} OR \hspace{5mm} 815 T_{sky} = T_{gsm}+T_{lss} $$ 816 817 Table \ref{sigtsky} summarizes the mean and standard deviation of the sky brightness 818 temperature $T(\alpha, \delta, \nu)$ for the different components computed in this study. 819 Figure \ref{compgsmmap} shows the comparison of the GSM temperature map at 884 MHz 820 with Haslam+NVSS map, smoothed with a 35 arcmin gaussian beam. 821 Figure \ref{compgsmhtemp} shows the comparison of the sky cube temperature distribution 822 for Model-I/GSM and Model-II. There is good agreement between the two models, although 823 the mean temperature for Model-II is slightly higher ($\sim 10\%$) than Model-I. 824 825 \begin{table} 826 \begin{tabular}{|c|c|c|} 827 \hline 828 & mean (K) & std.dev (K) \\ 829 \hline 830 Haslam & 2.17 & 0.6 \\ 831 NVSS & 0.13 & 7.73 \\ 832 Haslam+NVSS & 2.3 & 7.75 \\ 833 (Haslam+NVSS)*Lobe(35') & 2.3 & 0.72 \\ 834 GSM & 2.1 & 0.8 \\ 835 \hline 836 \end{tabular} 837 \caption{ Mean temperature and standard deviation for the different sky brightness 838 data cubes computed for this study} 839 \label{sigtsky} 840 \end{table} 841 842 we have computed the power spectrum on the 21cm-LSS sky temperature cube, as well 843 as on the radio foreground temperature cubes computed using our two foreground 844 models. We have also computed the power spectrum on sky brightness temperature 845 cubes, as measured by a perfect instrument having a 25 arcmin gaussian beam. 846 The resulting computed power spectrum are shown on figure \ref{pkgsmlss}. 847 The GSM model has more large scale power compared to our simple model, while 848 it lacks power at higher spatial frequencies. The mode mixing due to 849 frequency dependent response will thus be stronger in Model-II (Haslam+NVSS) 850 case. It can also be seen that the radio foreground power spectrum is more than 851 $\sim 10^6$ times higher than the 21 cm signal from large scale structures. This corresponds 852 to the factor $\sim 10^3$ of the sky brightness temperature fluctuations ($\sim$ K), 853 compared to the mK LSS signal. 854 855 \begin{figure} 856 \centering 857 \mbox{ 858 \hspace*{-10mm} 859 \includegraphics[width=0.5\textwidth]{Figs/comptempgsm.pdf} 860 } 861 \caption{Comparison of GSM (black) Model-II (red) sky cube temperature distribution. 862 The Model-II (Haslam+NVSS), 863 has been smoothed with a 35 arcmin gaussian beam. } 864 \label{compgsmhtemp} 865 \end{figure} 866 867 \begin{figure*} 868 \centering 869 \mbox{ 870 \hspace*{-10mm} 871 \includegraphics[width=\textwidth]{Figs/compmapgsm.pdf} 872 } 873 \caption{Comparison of GSM map (top) and Model-II sky map at 884 MHz (bottom). 874 The Model-II (Haslam+NVSS) has been smoothed with a 35 arcmin gaussian beam.} 875 \label{compgsmmap} 876 \end{figure*} 877 878 \begin{figure} 879 \centering 880 \vspace*{-20mm} 881 \mbox{ 882 \hspace*{-20mm} 883 \includegraphics[width=0.7\textwidth]{Figs/pk_gsm_lss.pdf} 884 } 885 \vspace*{-30mm} 886 \caption{Comparison of the 21cm LSS power spectrum (red, orange) with the radio foreground power spectrum. 887 The radio sky power spectrum is shown for the GSM (Model-I) sky model (dark blue), as well as for our simple 888 model based on Haslam+NVSS (Model-II, black). The curves with circle markers show the power spectrum 889 as observed by a perfect instrument with a 25 arcmin beam.} 890 \label{pkgsmlss} 891 \end{figure} 892 893 727 894 728 895 \subsection{ LSS signal extraction } 729 {\color{red} \large \it CMV + Reza + J.M. Martin } \\[1mm]896 % {\color{red} \large \it CMV + Reza + J.M. Martin } \\[1mm] 730 897 Description of the component separation method and the results 731 898 \begin{itemize} … … 741 908 742 909 \section{ BAO scale determination and constrain on dark energy parameters} 743 {\color{red} \large \it CY ( + JR ) } \\[1mm]910 % {\color{red} \large \it CY ( + JR ) } \\[1mm] 744 911 We compute reconstructed LSS-P(k) (after component separation) at different z's 745 912 and determine BAO scale as a function of redshifts. … … 757 924 758 925 759 \begin{figure*} 760 \centering 761 \includegraphics[width=0.85\textwidth]{Figs/compexlss.png} 762 \caption{Comparison of the original simulated LSS (frequency plane) and the recovered LSS. 763 Color scale in mK } 764 \label{figcompexlss} 765 \end{figure*} 766 767 \begin{figure*} 768 \centering 769 \includegraphics[width=0.85\textwidth]{Figs/compexfg.png} 770 \caption{Comparison of the original simulated foreground (frequency plane) and 771 the recovered foreground map. Color scale in Kelvin } 772 \label{figcompexfg} 773 \end{figure*} 774 775 \begin{figure*} 776 \centering 777 \includegraphics[width=0.7\textwidth]{Figs/pklssfg.pdf} 778 \caption{Comparison of the LSS power spectrum at 21 cm at 900 MHz ($z \sim 0.6$) 779 and the synchrotron/radio sources - GSM (Global Sky Model) foreground sky cube} 780 \label{figcompexfg} 781 \end{figure*} 782 783 784 \begin{figure*} 785 \centering 786 \includegraphics[width=0.7\textwidth]{Figs/exlsspk.pdf} 787 \caption{Recovered LSS power spectrum, after component separation - - GSM (Global Sky Model) foreground sky cube} 788 \label{figexlsspk} 789 \end{figure*} 926 % \caption{Comparison of the original simulated LSS (frequency plane) and the recovered LSS. 927 % Color scale in mK } \label{figcompexlss} 928 929 % \caption{Comparison of the original simulated foreground (frequency plane) and 930 % the recovered foreground map. Color scale in Kelvin } \label{figcompexfg} 931 932 % \caption{Comparison of the LSS power spectrum at 21 cm at 900 MHz ($z \sim 0.6$) 933 % and the synchrotron/radio sources - GSM (Global Sky Model) foreground sky cube} 934 % \label{figcompexfg} 935 936 937 % \caption{Recovered LSS power spectrum, after component separation - - GSM (Global Sky Model) foreground sky cube} 938 % \label{figexlsspk} 790 939 791 940 \bibliographystyle{aa} … … 806 955 \bibitem[Cole et al. (2005)]{cole.05} Cole, S. Percival, W.J., Peacock, J.A. {\it et al.} (the 2dFGRS Team) 2005, \mnras, 362, 505 807 956 957 % NVSS radio source catalog : NRAO VLA Sky Survey (NVSS) is a 1.4 GHz 958 \bibitem[Condon et al. (1998)]{nvss.98} Condon J. J., Cotton W. D., Greisen E. W., Yin Q. F., Perley R. A., 959 Taylor, G. B., \& Broderick, J. J. 1998, AJ, 115, 1693 960 808 961 % Parametrisation P(k) 809 962 \bibitem[Eisentein \& Hu (1998)]{eisenhu.98} Eisenstein D. \& Hu W. 1998, ApJ 496:605-614 (astro-ph/9709112) 810 963 811 % :SDSS first BAO observation964 % SDSS first BAO observation 812 965 \bibitem[Eisentein et al. (2005)]{eisenstein.05} Eisenstein D. J., Zehavi, I., Hogg, D.W. {\it et al.}, (the SDSS Collaboration) 2005, \apj, 633, 560 813 966 … … 815 968 \bibitem[Furlanetto et al. (2006)]{furlanetto.06} Furlanetto, S., Peng Oh, S. \& Briggs, F. 2006, \physrep, 433, 181-301 816 969 970 % Haslam 400 MHz synchrotron map 971 \bibitem[Haslam et al. (1982)]{haslam.82} Haslam C. G. T., Salter C. J., Stoffel H., Wilson W. E., 1982, 972 Astron. \& Astrophys. Supp. Vol 47, {\tt (http://lambda.gsfc.nasa.gov/product/foreground/haslam\_408.cfm)} 973 817 974 % WMAP CMB anisotropies 2008 818 975 \bibitem[Hinshaw et al. (2008)]{hinshaw.08} Hinshaw, G., Weiland, J.L., Hill, R.S. {\it et al.} 2008, arXiv:0803.0732) 819 976 820 977 % HI mass in galaxies 821 \bibitem[Lah et al. (2009)]{lah.09} Philip Lah, Michael B. Pracy, Jayaram N. Chengalur et al. 822 MNRAS 2009,( astro-ph/0907.1416)978 \bibitem[Lah et al. (2009)]{lah.09} Philip Lah, Michael B. Pracy, Jayaram N. Chengalur et al. 2009, \mnras 979 ( astro-ph/0907.1416) 823 980 824 981 % Boomerang 2000, Acoustic pics 825 982 \bibitem[Mauskopf et al. (2000)]{mauskopf.00} Mauskopf, P. D., Ade, P. A. R., de Bernardis, P. {\it et al.} 2000, \apjl, 536,59 983 984 % Papier sur le traitement des obseravtions radio / mode mixing - REFERENCE A CHERCHER 985 \bibitem[Morales et al. (2009)]{morales.09} Morales, M and other 2009, arXiv:0999.XXXX 986 987 % Global Sky Model Paper 988 \bibitem[Oliveira-Costa et al. (2008)]{gsm.08} de Oliveira-Costa, A., Tegmark, M., Gaensler, B.~M. {\it et al.} 2008, 989 \mnras, 388, 247-260 826 990 827 991 % Original CRT HSHS paper
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