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\def\bes{\begin{slide}}
\def\ens{\end{slide}}


\def\etal{et al. }
\def\nifsx{${}^{56}$Ni}
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\def\n{\mathrm n}


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%\def\ens{\ } %{\end{slide}}
%\def\bes #1 {\begin{slide}{#1}}
\def\bes{\begin{slide}}
\def\ens{\end{slide}}


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    \includegraphics*[#3]{#2}%
    \\ \parbox{10cm}{%
    \caption{\label{#1}#4}}%
  \end{center}\end{figure}%
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\title{Астрометрия, космография, решения Фридмана}
% \subtitle{в нашей Вселенной}
\author{С.И.Блинников}
\email{sergei.blinnikov@itep.ru,  sblinnikov@gmail.com}
\institution{ИТЭФ, ГАИШ, НГУ}
\slideCaption{Novosibirsk - \texttt{Prosper}}

\begin{document}

\maketitle

\begin{slide}{ }
% \begin{center}

%
    \textit{S.I.Blinnikov${}^{1,2}$}
\pv{1}
    \begin{minipage}[c]{6cm}
{${}^1$\it ИТЭФ = ITEP = Institute for Theoretical and  Experimental Physics,
Moscow}%\pv{1}
    \end{minipage}
    \begin{minipage}[c]{4cm}
 \IG{width=.6\textwidth}{itepm.ps}%\pv{1}
    \end{minipage} \hfill    %\pv{1}
\vskip 0.3cm
    \begin{minipage}[c]{6cm}
{${}^2$\it  ГАИШ = SAI = Sternberg Astronomical \\Institute, Moscow}\pv{1}
    \end{minipage}
    \begin{minipage}[c]{4cm}
   \IG{width=.6\textwidth}{sai-main.ps}\pv{1}
    \end{minipage}\hfill %\pv{1}
%     \begin{minipage}[c]{6cm}
% {${}^3$\it MPA, Garching}\pv{1}
%     \end{minipage}
%     \begin{minipage}[c]{4cm}
%    \IG{width=.6\textwidth}{MPA.ps}\pv{1}
%     \end{minipage}\hfill \pv{1}

%\end{center}

  \centerline{НГУ 26 сентября 2012}

\end{slide}

\bes{\small Элементы астрономии: Небесные координаты}
% \vglue -1.7cm
\begin{figure}
\epsfxsize=0.55\textwidth
\centering{\epsfbox{zomb110a.ps}}
%\caption{Celestial coordinates and Zodiac (Zombeck 1990)}
%  \label{z110}
\end{figure}
\ens

\bes{Экваториальные координаты}
% \vglue -0.7cm

    \begin{minipage}[c]{3cm}
{\tiny

Экваториальные координаты, по существу, являются проекциями земных географических
координат: прямое восхождение RA или $ \alpha $, аналогично долготе,
{\dred --- но измеряется в часах, а не в градусах! --- }
 а склонение $ \delta $ --- аналог  широты.
}
    \end{minipage}
    \begin{minipage}[c]{7.5cm}
 \IG{width=0.7\textwidth}{zomb39.ps}%\pv{1}
    \end{minipage} %\hfill    %\pv{1}
\ens

\bes{Equatorial coordinates-2}
% \vglue -0.7cm
 \CIG{width=0.8\textwidth}{celestialCoord.ps}
\ens

\bes{Equatorial coordinates-3}
% \vglue -0.7cm
 \CIG{width=0.5\textwidth}{radecchart.ps}
\ens


\bes{Galactic coordinates}
% \vglue -0.7cm
For more distant objects more natural system is the
Galactic one: longitude (measures from the center of our Galaxy -- Milky Way) and
latitude (from the plane drawn in the `middle' of  Milky Way).

\begin{minipage}[c]{5.5cm}
 \CIG{width=0.95\textwidth}{800px-Milky_Way_infrared.ps}
\end{minipage}
\begin{minipage}[c]{5cm}
 \CIG{width=\textwidth}{galactic_coordinates.ps}
\end{minipage}

\ens

\bes{Milky Way infrared}
% \vglue -0.7cm
 \IG{width=1.1\textwidth}{Milky_Way_infrared.ps}
\ens

\bes{Measuring radiation}
% \vglue -0.7cm


{\red Luminosity} $L$ is just the power emitted by an object: $ L={d \mathcal{E} \over dt}$.

{\red Flux} $S$ in astrophysics is the power coming per unit time per
unit area of a detector
$ S={d\mathcal{E} \over dt dA}$
(called {\em illumination} in some branches of laboratory physics). %of a surface normal to the beam

{\red Exposition (fluence)} $F$ -- the integral energy coming per unit area  of a detector,
$ F={d\mathcal{E} \over dA}$
useful for bursting objects.

\ens



\bes{Forms used for describing spectra}
% \vglue -0.7cm

1) The photon number spectrum $N(E)$, or $N(\nu)$, with
$E=h\nu$, units of photons per second per cm$^2$ per unit
energy.

2) The differential energy flux density $S(E)=E N(E)$, written also as
$S_\nu=h\nu N(\nu)$.
The notation $F_\nu$ is often used for the flux instead of $S_\nu$,
but I will use the letter $F$ for the fluence.

3) The second moment of $N(E)$ is the so called $\nu S_\nu$ distribution,
(or $\nu F_\nu$ distribution), $\nu S_\nu \propto E^2 N(E)$,
which peaks where the maximum radiation power comes
(per decade of the photon energy).
\ens

\overlays{3}{%
\bes{Intensity}
\begin{minipage}[c]{6cm}
{\small
A very important quantity is {\red\em intensity} {\dred (brightness)} $I$ it is the flux density per solid angle:
$$ I={d\mathcal{E} \over dt dA d\Omega}$$
or spectral intensity
$$ I_\nu={d\mathcal{E} \over d\nu dt
\fromSlide*{2}{\rnode{NA}{\pscirclebox[linecolor=red]{dA}}}
\onlySlide*{1}{\rnode{NA}{\pscirclebox[linecolor=red,linestyle=none]{dA}}}
d\Omega}
$$
\FromSlide{2}%
OK for $dA$ normal to beam\FromSlide{3}, else \rnode{NB}{$dA \cos\theta$}
\fromSlide*{3}{\nccurve[linecolor=red,angleA=90,angleB=270]{->}{NB}{NA}}
}
\end{minipage}
\begin{minipage}[c]{4.5cm}
 \hfill\IG{width=\textwidth}{intensity.ps}
\end{minipage}

\ens
}
%------------------------------------------------------------------------------

\bes{Intensity-2}
% \vglue -0.7cm

 $I_\nu\; $.
Here the subscript $\nu$ refers to frequency.
The observations and experiments always work with
$I_\nu$, but the physics is actually described by the occupation number $f(\mathbf{p})$.

One can see that $I_\nu$ and $f$ are simply connected:
$$
 I_\nu={gc\over {(2\pi\,\hbar)}^3}\,f p^2\,{dp\over d\,\nu}\,c p={g f p^3c\over {(2
\pi\,\hbar)}^2}={g f h\,\nu\over \lambda^2}
$$
(here $dp/d\,\nu=2\pi\hbar/c$, and {\red $g=2$} for photons).
$I_\nu$ has the meaning of energy coming through the area
$\lambda^2$ in unit time per unit frequency interval,
so $[I_\nu]=\mbox{erg}/\mbox{cm}^2\,\mbox{s}\,\mbox{Hz}=\mbox{erg}/\mbox{cm}^2$.
\ens


\bes{Stellar magnitudes}
% \vglue -0.7cm

A traditional way of measuring fluxes in astronomy is the stellar magnitude (mag):
$$
    m_1-m_0 = - 2.5(\lg S_1  - \lg S_0) = - 2.5\lg (S_1 / S_0)
$$
-- a zero point ({\red ZP}) $m_0$ must be defined at some standard star
(usually Vega $= \alpha$ Lyrae). {\small\dred All m's and S's here may have subscripts ($\nu$, or $U$, $B$, $V$ etc. for filters).}

Absolute stellar magnitude ${\cal M}$ is mag at the standard distance $d$ of 10 parsecs.
Since $S \propto d^{-2} $ the {\em\blue distance modulus} is
$$
    m-{\cal M} \equiv - 2.5[\lg S(d)  - \lg S(10 \, \mbox{pc})]
$$
$$
    = +5[\lg( d / 10 \, \mbox{pc} )] = 5\lg d_{\rm pc} - 5 \; .
$$

\ens


\bes{Importance of units}
% \vglue -0.7cm

The role of units used for measuring distances and other physical parameters
of celestial objects is very important.

{\blue Let us consider one example from old astronomy}

One astronomical unit 1 AU $\approx 1.5 \times 10^{13}$ cm
 -- the mean distance of Earth from Sun.
\ens

\bes{Measuring angles}
%\vglue -0.7cm

    \begin{minipage}[c]{6cm}
{\small
Ancient astronomers knew distance of Venus from the Sun in
AU with a reasonable accuracy, because in AU everything reduces to measuring angles
and time, but in terrestrial units they were wrong by orders of magnitude.}
    \end{minipage}
    \begin{minipage}[c]{4.5cm}
 \IG{width=\textwidth}{sunven.ps}%\pv{1}
    \end{minipage} \hfill    %\pv{1}

{\small
So if you measure the {\red angle} $\alpha$ between the Sun and Venus at the moment of
their maximum departure  (elongation) you have the {\red distance} Sun-Venus equal to
$\sin\alpha$ AU.
}

\ens

\bes{Parallax}
\vglue -.2cm
% \begin{center}
\hspace{-.25cm}\includegraphics[width=.9\textwidth]{ladder8}
% \end{center}

\ens

\bes{Trigonometric Parallax}
% \begin{minipage}{6cm}

\large

Measure the change in
	the apparent position
	of the star as the
	viewers position
	changes
$$
 d = 1  \mbox{AU}/ \tan(\theta)
$$

	If $\theta=1''$ then    d= 206265 AU = 1pc

 One can measure up to 40 pc from Earth

 Up to 100 pc with  Hipparcos satellite

% \end{minipage}

\ens

\bes{Astronomical Unit,  AU}

Modern determinations

Very precise measurements of the relative positions of the inner planets can be made by radar
and by telemetry from space probes.
As with all radar measurements, these rely on measuring the time taken for light to be
reflected from an object.

% These measured positions are then compared with those calculated by the laws of celestial mechanics:
% the calculated positions are often referred to as an ephemeris, and are usually calculated
% in astronomical units.
% The comparison gives the speed of light in astronomical units,
% which is 173.144 632 6847(69) AU/d (TDB).[7]
% As the speed of light in metres per second (cSI) is fixed in the International System of Units,
% this measurement of the speed of light
% in AU/d (cAU) also determines the value of the astronomical unit in metres (A):
%
% $$
% A = 86\,400 \frac{c_{\rm SI}}{c_{\rm AU}}.
% $$

The International Astronomical Union (IAU) currently accepted best estimate (2009)
of the value of the astronomical unit in metres is

$$
\mbox{AU} = 149 597 870 700(3) \; \mbox{m} \approx 1.5 \times 10^{13} \; \mbox{cm} .
$$

\ens



\bes{Parsecs}

The unit for interstellar distances, parsec: 1 pc = 206265 AU$\approx 3 \times 10^{18}$ cm,
is again derived from
measuring angles (parallax), it is the distance from which 1 AU is visible at
the angle of 1 sec of arc (since 1 radian = 206265 arcsecs).

{\dblue Eventually this leads to \emph{angular} and \emph{parallactic}
distances.}
\ens



\bes{Kepler-Einstein}

{\bf\red Discovery of Kepler's laws and hence of the Newton's gravity.}

{\blue In one of his popular papers, Einstein gave the most brilliant account of that story.}


\ens


\bes{Kepler: use Mars as a lighthouse}
%\vglue -0.7cm

    \begin{minipage}[c]{6cm}
{\small\dblue
One cannot directly measure the distance Sun-Mars, because Mars moves outside
the terrestrial orbit.
The idea of Kepler essentially was to use a rotating frame
of reference where Mars is at rest and to find from terrestrial observations
(made by Tycho Brahe)}
    \end{minipage}
    \begin{minipage}[c]{4.5cm}
 \IG{width=\textwidth}{sunmars.ps}%\pv{1}
    \end{minipage} \hfill    %\pv{1}

{\small
the position of Earth corresponding to two elongations of our planet as viewed
from Mars - then one can find all angles and the  distance Sun-Mars in AU.
}
\ens

\bes{Kepler's laws}

This resulted in the great Kepler's laws.
{\dblue
The most important is the 3rd Kepler's law, that the square of the period
of planet's revolution around the Sun is proportional to the cube of its orbit
semimajor axis.}
{\dblue This great discovery led Newton to the formulation of classical dynamics and
to the law of gravity.}

For a circular orbit of the radius $r$ around a star of mass
$M$ we have for the speed $u$:
$$
   u^2 = G_{\rm N} M / r ,
$$
from Newton's mechanics.
\ens

\bes{Kepler's laws-2}

This derivation is OK while $ u^2 \sim |\phi| \ll c^2$.
If the period  is ${\cal P}$, then $u=2\pi r/{\cal P}$ and
$$
   r^3/{\cal P}^2 = M/\msun
$$
if $r$ is in AU, ${\cal P}$ in years.
And this is the 3rd Kepler's law.
Note that $G_{\rm N}$ does not enter in the units that we used, and
it is convenient to take the solar mass \Msun\ as a unit of mass $M$.

\ens

\bes{Solar mass in grams}
% \vglue -0.7cm

How accurate is the mass of the Sun $\msun \approx 1.9884\times 10^{33}$ in grams?
We get it from 1 AU in cm (radar location of planets and asteroids  with a very high accuracy,
better than $10^{-11}$)
and ${\cal P}=1$ year $\approx 3.16\times 10^7$  in seconds (accuracy is much higher than 3 digits in 3.16).

1) Laboratory measurements of $G_{\rm N}=(6.6742 \pm 0.0010) \times 10^{-8}$
   cm$^3$/(g$\cdot \mbox{s}^2$), according to Particle Data Group (2004):
it is the lowest accuracy among fundamental constants.
%(And the accuracy is even reduced in more recent tables of fundamental constants).

{\small\red So we cannot get $\msun$ in grams (or kg) with accuracy higher than $\sim 0.2\times 10^{-3}$
which is absolutely not sufficient for computing the orbits of interplanetary
missions etc.
But everything is OK in the units AU, year, $\msun$.}
\ens

\bes{Fifth force?}

2) Yukawa type deviations from Newton's law of gravity are possible in principle:
instead of
$$
 \phi = G_{\rm N} M / r
$$
one can have
$$
 \phi = {G_{\rm N} M \over r}\bigl(1+\alpha \exp (-\mu r)\bigr)
$$
and $\alpha$ can be as high 0.1 - 0.3 if $\mu$ is $\sim 1\, \mbox{km}^{-1}$!
(See, e.g. Sugimoto 1972, Blinnikov 1978, Hoskins et al. 1985.)
\ens

\bes{\Msun\ accurate $\sim 20 $\% ?}

{\dblue
Astrophysics is a science for testing models: in the General Relativity (GR)
model (which reduces to pure Newtonian gravity for  small speeds $u$)
we know \Msun\ in grams with accuracy of laboratory $G_{\rm N}$.
In the model-free case we know \Msun\ with accuracy $\sim 20 $ \%
(the same is true for the mass of Earth!).
}
\ens




\bes{Elementary Cosmography}
%\vglue -0.7cm
  \begin{minipage}[c]{4.9cm}
\begin{center}
\IG{width=\textwidth}{transp_lamp}
\end{center}
\end{minipage}
  \begin{minipage}[c]{4.9cm}
\dred
Angular size halved -- distance doubled.
Flux 1/4, brightness not changed.
\begin{center}
\IG{width=0.5\textwidth}{transp_lamp}
\end{center}
\end{minipage}
\ens

\bes{Distances: angular diameter}
%\vglue -0.7cm

  \begin{minipage}[c]{4.5cm}
Standard ruler length
$R$:
$\theta=R/d \to d_A=R/\theta$
(for small  $\theta$)
  \end{minipage}
  \begin{minipage}[c]{6.cm}
\IG{width=0.95\textwidth}{epm1.ps} % breaks vlatex corrected
\end{minipage}
\ens

\bes{Distances: photometric}
%\vglue -0.7cm

  \begin{minipage}[c]{4.5cm}
Standard candle power
$L$:
$F={L \over 4\pi d^2} \to  d^2_{\rm ph} = {{L}\over{4\pi F}}$.

\bigskip
The same flux if the brightness is
$I$:
$F=\pi\theta^2 I = \pi I R^2/d_A^2$.

\end{minipage}
\begin{minipage}[c]{6cm}
\IG{width=0.95\textwidth}{epm1.ps} % breaks vlatex corrected
\end{minipage}
\ens

\bes{Distances}
%\vglue -0.7cm


The {\red photometric} or luminosity
{\red distance} is defined as
$$ %\begin{equation*}
  d^2_{\rm ph} = {{L}\over{4\pi F}}\ ,
$$ %\end{equation*}
where $L$ is the absolute luminosity of the source and $F$ is
the flux measured by the observer (the energy per unit time per
unit area of some detector).

The {\red angular diameter distance}
$d_A =  d_{\rm ph}$ only in a {\red static} flat space.
They differ in an {\dblue expanding} universe.

\ens



\bes{Luminosity $L$ is crucial}
% \Large

{\dblue Светимость должна быть высокой. А самые мощные звёзды -- сверхновые.
Что это такое?}


В нашей Галактике, около $10^{11}$ звёзд.

Каждый год заканчивает эволюцию примерно одна звезда.

Почему далеко не все из них ({\dblue а только $\sim 1/50$}) взрываются как сверхновые?

Что остаётся после взрыва?

Как объяснить свечение самых мощных сверхновых?

%и в каких диапазонах наблюдаются сверхновые и их остатки
%наземными и космическими телескопами.

\ens

\begin{slide}{\Large Взрывающиеся звезды}
%\vglue -0.7cm
{\Huge
\centerline{\dblue  -- новые и сверхновые.}

\vskip 0.5cm

НОВАЯ звезда ({\bf nova}) --- это яркая вспышка на  $\mathbf{\sim 10 - 12 }$ mag,
причём светимость достигает $\mathbf{L \sim 10^5 L_\odot}$, где
 $\mathbf{L_\odot}$ -- светимость Солнца.
}
\end{slide}

\bes{Звёздные величины}
\vglue -0.2cm
{\Large
По традиции, чем меньше $m$ {\dred (mag, magnitude)}, тем
выше блеск звезды. Например Вега $m=0$. Слабые звёзды, видные глазу
$m\approx 5$.
Разница  $m_1-m_2=5$ -- это различие в потоках в 100 раз.

{\dred
Звёздная величина является логарифмической мерой светового потока.
}
}
\ens


\bes{\Huge Вспышки новых}
{\Large
 --- это взрыв водорода на поверхности белого карлика
в двойной системе.

Выбрасывается малая доля массы звезды $\la 10^{-4} \msun$.

\bigskip

``Stella Nova'' по Латыни значит ``новая звезда'' --- так думали древние
увидев вспышку, но на самом деле звезда старая.
}
\ens


\bes[Blinds]{Tycho ``Nova'' 1572}
%\vglue -0.7cm
\begin{center}
\includegraphics[width=0.6\textwidth]{tyc_sn.ps}
\end{center}
\ens

\bes[R]{SNR Tycho in X-rays (Chandra)}
\begin{center}
\includegraphics[width=0.6\textwidth]{tychoCh.ps}
\end{center}
\ens


\bes{\Huge СВЕРХНОВЫЕ}
{\Large

{\dblue (Supernova = SN, Supernovae = SNe)} ---
светимость $\mathbf{ L \sim 10^{10} L_\odot}$ и выше.

Это одни из наиболее сильных взрывов во Вселенной.

Разрушается и выбрасывается \emph{\dred б\'{о}льшая} часть массы звезды.

}

\ens


\bes{\Huge Открытие сверхновых}
%\vglue -0.7cm
\CIG{width=0.8\textwidth}{small_compare_SN2005-m51.ps}

SN2005cs in M51 (see center of right image).

 Discovered by Wolfgang Kloehr, June 28, 2005
\ens

\bes[Replace]{\normalsize Сверхновая в галактике Centaurus-A}
% \Large

\vskip 1cm
\begin{center}%
Click below for web:
\vskip 1cm

\fbox{\href{http://dau.itep.ru/lections/saulsm.qt.mov}{\dred Фото, кривая блеска, спектры,
\textcopyright\ S.Perlmutter}}%
\vskip 1cm

  \fbox{\href{run:saulsm.qt.mov}{SN Movie: for files saved  locally, \textcopyright\ S.Perlmutter}}

\end{center}

\ens

\bes[Blinds]{SN Light Curves - Кривые блеска }
% \vskip -0.35cm
\CIG{width=0.9\textwidth}{Filippf3.ps}
\ens

\bes{SN1987A в БМО}

\begin{center}

    \includegraphics[width=0.89\textwidth]{aat050_72c_sn87a}
\end{center}

\ens


\bes[Dissolve]{SN1998bu in M96}
\begin{center}%
    \includegraphics[width=0.7\textwidth]{sn98bu.ps}
\end{center}
\ens

\bes[Box]{SNII 2001du in NGC1365}
% \vglue -0.7cm
\centering{SNeII are close to spiral arms}
\begin{center}%
    \includegraphics[width=\textwidth]{sn01du_n1365.ps}
\end{center}
\ens

\bes{SNIa 1994D in NGC4526}
% \vglue -0.7cm
\centering{SNeIa may be away of spiral arms}
\begin{center}%
    \includegraphics[width=0.6\textwidth]{sn94d.ps}
\end{center}
\ens



\bes{SNR Cas A Chandra}
\begin{center}
\includegraphics[width=0.7\textwidth]{casa2011}
\end{center}
\ens

\bes{SNR 1006}
\vglue -0.3cm
\begin{center}
\includegraphics[width=0.6\textwidth]{sn1006c}
\end{center}

\begin{center}%
\small
 \fbox{\href{http://dau.itep.ru/lections/sn1006_expansion2.mov}{\dred movie -- click here for web}}
 \fbox{\href{run:sn1006_expansion2.mov}{\dred movie -- for files saved  locally}}
\end{center}

\ens

\bes{Most Luminous SNe}
\vglue -0.3cm
    \CIG{width=0.85\textwidth}{sn2006gyf2.ps}
\ens

\bes{\normalsize SN~2006gy -- сверхмощная сверхновая}
\vglue -0.3cm
    \begin{minipage}[c]{2.9cm}
{\small
{Ofek et al. 2007, ApJL,  astro-ph/0612408)}\pv{1}

{Smith et al. 2007, Sep. 10 ApJ, astro-ph/0612617)}\pv{1}
}
    \end{minipage}
    \begin{minipage}[c]{7.9cm}
    \CIG{width=0.95\textwidth}{sn2006gyf1.ps}\pv{1}
    \end{minipage}\hfill %\pv{1}
\ens

% На всякий случай красивый мультик:
% http://www.youtube.com/watch?v=17jymDn0W6U

\bes{Distance Ladder}
\vglue -1.3cm
% \begin{center}
% \hspace{-.5cm}\includegraphics[clip,width=1.05\textwidth]{Extragalactic_distance_ladder}
\hspace{-.25cm}\includegraphics[width=1.0\textwidth]{Extragalactic_Distance_Ladder1}
% \end{center}

\ens


\bes{Distance Ladder Cone}
\vglue -.3cm
% \begin{center}
% \hspace{-0.25cm}
\includegraphics[width=0.92\textwidth]{ladder23.eps}
% \end{center}

\ens


\bes{Distance Ladder - 2}
\vglue -1.3cm
% \begin{center}
% \hspace{-.5cm}\includegraphics[clip,width=1.05\textwidth]{Extragalactic_distance_ladder}
\hspace{-.25cm}\includegraphics[width=1.0\textwidth]{Extragalactic_Distance_LadderSnII1}
% \end{center}

\ens

\bes{Distance Ladder - 3}
\vglue -1.3cm
% \begin{center}
% \hspace{-.5cm}\includegraphics[clip,width=1.05\textwidth]{Extragalactic_distance_ladder}
\hspace{-.25cm}\includegraphics[width=1.0\textwidth]{Extragalactic_Distance_LadderSnIIMarked1}
% \end{center}

\ens


\bes{Hubble diagram, Feb 2004}
% \vglue -0.7cm
\centerline{\dred \large for SN~Ia (A.Riess et al.)}

%\IG{bb=56 56 566 566}{ariess04fig4}
%\IG{bb= 0 56 570 466}{ariess04fig4.ps}
\CIG{width=0.65\textwidth}{ariess04fig4.ps}
\ens

%\bes{$\Omega$  from SN~Ia: Riess et al. Feb 2004}
%{\blue Cosmological parameters from SN~Ia: Riess et al. Feb 2004}

%\begin{center}
%\IG{width=0.55\textwidth,angle=0}{ariess04fig8.ps}
%\end{center}

%\ens


\bes{Hubble diagram {\red SNLS}}
% \vglue -0.7cm
\begin{minipage}[c]{5cm}
\begin{center}
\includegraphics[width=\textwidth]{hubbleCorr.eps}
\end{center}
\end{minipage}
\begin{minipage}[c]{5cm}
{\small
The bottom plot shows the residuals for $\mu_B$
when $d_{\rm ph}(z)$ is for the best fit flat $\Lambda$-cosmology ($\Omega_M = 0.26, \; \Omega_\Lambda=0.74$). Dashed line is for the flat zero $\Lambda$ model.
Adopted with corrections from (Astier et al., 2006).
}
\end{minipage} \hfill    %\pv{1}
\ens


\bes{$(\Omega_m,\Omega_\Lambda)$ cosmology,  {\red SNLS}}
% \vglue -0.7cm
\begin{minipage}[c]{5cm}
\begin{center}
\includegraphics[width=\textwidth]{omol_contours.eps}
\end{center}
\end{minipage}
\begin{minipage}[c]{5cm}
{\small  {\red 68.3\%, 95.5\% and 99.7\%} confidence levels for
 the {\red SNLS} Hubble diagram
(solid contours),
 the {\dgreen SDSS} baryon acoustic oscillations (Eisenstein et al. 2005,
dotted lines), and the joint confidence contours (dashed lines).
(Astier et al., 2006).
}
\end{minipage} \hfill    %\pv{1}
\ens

\bes{$(\Omega_m,w)$ cosmology}
% \vglue -0.7cm
\begin{minipage}[c]{5cm}
\begin{center}
\includegraphics[width=\textwidth]{omw_contours.eps}
\end{center}
\end{minipage}
\begin{minipage}[c]{5cm}
{\small Contours at  {\red 68.3\%, 95.5\% and 99.7\%} confidence levels
for the fit to  cosmology with equation of state  $P=w\mathcal{E}$ for flat 3D space, from the {\red SNLS} Hubble diagram
alone, from the {\dgreen SDSS} baryon acoustic oscillations alone (Eisenstein et al. 2005),
and the joint confidence contours.
From (Astier et al., 2006).
}
\end{minipage} \hfill    %\pv{1}
\ens

\bes{Hubble diagram {\red SNLS}}
% \vglue -0.7cm
\begin{minipage}[c]{5cm}
\begin{center}
\includegraphics[width=\textwidth]{hubbleCorr.eps}
\end{center}
\end{minipage}
\begin{minipage}[c]{5cm}
{\small
The bottom plot shows the residuals for $\mu_B$
when $d_{\rm ph}(z)$ is for the best fit flat $\Lambda$-cosmology ($\Omega_M = 0.26, \; \Omega_\Lambda=0.74$). Dashed line is for the flat zero $\Lambda$ model.
Adopted with corrections from (Astier et al., 2006).
}
\end{minipage} \hfill    %\pv{1}
\ens


\bes{\small D.Rubin, E.V.Linder, M.Kowalski et al. ApJ 2009}
\begin{center}%
\includegraphics[width=0.47\textwidth]{colorOm-w0_sysinterp2}
\includegraphics[width=0.48\textwidth]{colorOm-w0_sys+sys_curvinterp2}
\end{center}
{\tiny 68.3\%, 95.4\%, and 99.7\% conf. levels on a constant
EOS $w$ and  $\Omega_m$ for the individual and combined data
sets.  The left panel shows individual and combined probes in the flat
universe case; the right panel repeats the combined systematics contour,
and also compares to the statistical only contour, and to the systematics
contour when simultaneously fitting for spatial curvature.
}
\ens



\bes[Wipe]{Surface of Last  Scattering}

\CIG{width=0.9\textwidth}{LastScatSurf.ps}

\ens


\bes{Structure formation simulations}

\vskip 1 cm


\begin{center}
%   \fbox{\href{run:/home/seb/Pres/movies/S2_960x640.avi}{Movie}}
\tiny
\url{http://www.mpa-garching.mpg.de/galform/data_vis/S2_960x640.avi}
\end{center}
\ens

\bes{Что нас окружает: SDSS}

\vskip 1 cm

\begin{center}%

{\dred
SDSS = Sloan Digital Sky Survey, проект на Apache Point обсерватории с аккуратными
измерениями положений (угловых координат) и спектров (т.е. и красных смещений $\boldsymbol z$)
сотен тысяч галактик и квазаров.
}

{\dblue
Данные выкладываются в открытый доступ.
Угловые координаты и $\boldsymbol z$ позволяют построить трёхмерную картину распределения видимого
вещества во Вселенной. Эта картина показана в фильме:
}
%  \fbox{\href{run:../../../c/pres/movies/vv1a_9-25.mpg}{\dblue movie -- click here}}
%  \fbox{\href{run:/home/seb/Pres/movies/april18.mov}{\dblue movie -- click here}}

{\tiny
\url{http://astro.uchicago.edu/cosmus/projects/sloanmovie/april18.mov}
}
\end{center}
\ens

\bes{Конец 3-й лекции}

\ens

\end{document}

