Transcript Diapositiva 1 - Universidad de Guanajuato

Lecture 16
Cosmological Observations
• Curvature, Topology and Dynamics
 Curvature: CMBR
 Topology: Cosmic Cristalography & Circles in the Sky
• Expansion History (Dynamics)




H0
H(z), q0, Λ
Matter-Energy Content
Age
• Light Elements Primordial Abundance
• Reionization
• Non Cosmological Backgrounds
Depto. de Astronomía (UGto)
Astronomía Extragaláctica y Cosmología Observacional
 Curvature, Topology & Dynamics
 According to GR, spacetime is what mathematicians call a manifold, characterized by a
metric and a topology
 the metric gives the local shape of spacetime (the distances and time intervals), relating a
curvature to the presence of matter and energy
 the topology gives the global geometry (shape and extension) of the Universe
 The FRW model specifies completely the metric, but not the global curvature parameter
(k) and a free function given the expansion history (a), which represents the dynamics
of the Universe
 The curvature parameter is related to the “radius of curvature” of the Universe, defined as
Rcurv2 = a 2 =
1
kc2 H2|ΣΩi + ΩΛ – 1|
k = +1, 0, –1
which can have the values:
Rcurv2 > 0
Rcurv = ∞
Rcurv2 < 0
→ Rcurv is the radius of the hypersphere (closed/spherical geometry)
→ there is no Rcurv (flat/Euclidean geometry)
→ Rcurv is an imaginary number (open/hyperbolic geometry)
concerning to the topology, in the first case the Universe has a finite volume, while in the
others the Universe may either be finite or infinite in spatial extent
 Curvature, Topology & Dynamics
 Curvature
 Some possible topologies for flat curvature
simply connected
(only one geodesics)
multiply connected
(more than one geodesics)
 The spherical (positive curvature) spaces and Euclidean (flat) spaces are all classified, but
the hyperbolic (negative curvature) ones are not
 Curvature, Topology & Dynamics)
Curvature
Topology
Dynamics
k < 0 (negative)
finite/infinite
open
k = 0 (Euclidean)
finite/infinite
open
k > 0 (positive)
finite
closed/open
 Curvature: CMBR
 Cosmologists have measured Rcurv using the largest triangle available: one with us at one
corner and the other two corners in the CMBR
 the characteristic angular size
of the temperature fluctuations
(hot and cold spots) can be
predicted theoretically: if the
space is flat, this characteristic
size (or, more rigorously,
the first peak in the CMBR
power spectrum) subtends
about 0.5° (~ Moon size);
positively and negatively
curved spaces have larger
and smaller values, respectively
 Observed values are so close
to 0.5° that we still cannot
tell whether space is
perfectly flat or very slightly
curved either way...
 Topology: Cosmic Cristalography & “Circles in the Sky”
 If the Universe is positively curved or
Euclidean it is, in principle,
possible to verify if it is simply or
multiply connected by the the
cosmic cristalography method
 given a certain class of extragalactic
objects, with known distances, one
may analyze the distribution of
distances of these objects: if the
Universe is multiply connected
(and its curvature radius is smaller
than the deepness limit of the sample) certain values of distances will
occur much more frequently than the others
 Another possible verification for signs of multiple
conexity is the search for “circles in the sky”
in the CMBR
 if the fundamental polyhedron has a size such that
its faces intercept the last scattering surface,
we may see circles (marked by different
temperatures) in these interceptions
 Dynamics: Expansion History
Current Hubble parameter (H0):
 In order to measure the current expansion rate (Hubble
“constant”) one needs to have accurate distances and
radial velocities for a sample of extragalactic objects
covering distances large enough for having vpec << vH
and still in the Local Universe
 radial velocities are directly measured from the redshifts
of object spectra
 distances are very hard to measure –
many methods are available, but all
of them have large uncertainties.
There are two general classes of
methods: the ones that use a series
of distance measurements, each
calibrated to measures at shorter
distances, which compose a
distance ladder, and the
direct ones
 Dynamics: Expansion History
 the Cepheids P-L Relation, Tully-Fisher,
Fundamental Plane and Ia Supernovae
methods are of the first class, using calibrations
from parallaxes (Hipparchus satellite),
statistical parallaxes, main sequence fitting, etc
 Dynamics: Expansion History
 the Surface Brightness Fluctuations, Baade-Wesselink,
Time Delay of Gravitational Lenses and X-Ray + S-Z
methods are of the second class, based only on physical
assumptions
 Dynamics: Expansion History
 HST Key Project
[Freedman et al. 2001, ApJ 553, 47]
 Dynamics: Expansion History
d = cz/H0 [1 + ½ (1 + q0) z]
 BCGs (50´s – 70´s)
 SNe I (80´s – 90´s)
 SNe Ia (90´s – 00´s)
SNe Ia:
• Lmax – dtL relation  correction
(lacks theoretical basis!)
 Dynamics: Expansion History
Expansion History H(z):
 Supernovae Cosmology Project
[Perlmutter et al. 1998, Nature 391, 51]
[Perlmutter et al. 1999, ApJ 517, 565]
 High-z Supernovae Project
[Riess et al. 1998, AJ 116, 1009]
 Dynamics: Expansion History
q(t) = ½ Σ Ωi(t) – ΩΛ(t)
 Dynamics: Matter-Energy Content
Radiation density:
 The density parameter for the radiation is easily found from the temperature of the CMBR
TCMBR = 2.725  0.002 K
[Mather et al. 1999, ApJ 512, 511]

Ωrad = 4.1510–5 h–2
Neutrino density:
 The density parameter of neutrinos depend on their exact mass. If all ν species are massless,
then their energy density is smaller than the γ energy density by a factor 3(7/8)(4/11)4/3
(the first term for 3 generations of ν, the 7/8 because the Fermi-Dirac integral is smaller
than the Bose-Einstein one by this factor, and the third term for difference in
temperatures of the 2 particles). Thus
Ων = 1.6810–5 h–2
 Nevertheless, observations of ν from both the Sun [Bahcall 1989, Neutrino Astrophysics] and
from our atmosphere [Fukuda et al. 1998, Ph. Rev. L 81, 1562] strongly suggest that ν of
different flavors (generations) oscillate into each other. This can happen only if ν have
mass (although probably very small)
 Dynamics: Matter-Energy Content
Baryonic density:
 There are now four established ways of measuring the baryon density, and these all seem to
agree reasonably well [Fukugita, Hogan & Peebles 1998, ApJ 503, 518]
• groups and clusters of galaxies – most of the baryons in groups and clusters are in
the form of a hot intergroup/cluster gas. The current estimates give Ωb ~ 0.02
• Lyα-Forest in the spectra of distant quasars – these estimates suggest Ωbh1.5 ~ 0.02
[Rauch et al. 1997]
• anisotropies in the CMBR – the second peak is direct related to the baryon density;
preliminary results give Ωbh2 ~ 0.0240.004 []
• light elements abundance – are also sensitive to the baryon density, and that estimates
give Ωbh2 ~ 0.0205  0.0018
Since these measurements refer to different redshifts (baryon density fall with a–3), they
are in good agreement
Ωb ~ 0.019 h–2
 Dynamics: Age
Universe Age:
 Since we have the density parameters of the Universe, we can estimate the its age
from the lookback time of the big-bang
tL = 1/H0 ∫0→∞ dz / (1+z) [Ωrad (1+z)4 + Ωmat (1+z)3 – Ωk (1+z)2 + ΩΛ]½
 the best estimates from
the concordance
model (Ωk = 1.0,
Ωmat ~ 1/3 and
ΩΛ ~ 2/3) are
t0 = 13.7 Gy
 Dynamics: Age
Galaxy Age:
 Beyond estimates from H(z), one can obtain lower limits for the Universe age from the
age of our Galaxy
 three methods are usually used for that
• nucleocosmochronology – abundance ratios of long-lived radioactive species
(formed by fast n capture, r-process, in SNe explosions of the early generation stars)
can be predicted and compared with their present observed ratios
235U
0
= 235UG exp(-tG/τU)
(232Th/238U)0 = (232Th/238U)G exp[-tG/(1/τTh– 1/τU)]
where 0 indices are current observed abundances, G indices are original abundances,
τ are the (half-lives / ln2) and tG is the Galaxy age. Half-lives of 235U, 238U and
232Th are, respectively 0.704, 4.468 and 14.05 Gy, respectively (all of them decay
to a stable isotope of Pb)
Cayrel et al [2001, Nature 409, 691], p.e., using these elements and also Os and Ir
derived the age tG = 13.3  3 Gy
 Dynamics: Age
• Globular Clusters age – the oldest stars of the Galaxy are in the Globular Clusters.
These systems form very rapidly in the beginning of the galaxy life, since their
collapse time scale is only about several million years. Their age can be derived
from their H-R diagram, considering that all of their stars were born at the same
time – the turn-off point, obtained by a isochrone fitting, gives the age of the
GC. In the oldest GC the main-sequence turn-off point has reached a mass of about
0.9 M (Z ~ Z/150)
 Dynamics: Age
Krauss & Chaboyer [2003, Science 299, 65], p.e., find tAG = 13.4+3.4-2.2 Gy
[Chaboyer 1998, Cosmological Parameters and Evol. of the Universe, IAU Symp 183] – the 17 oldest GC
 Dynamics: Age
• disc age – the age of the Galaxy disc may be estimated by the luminosity function of
white dwarf stars. These stars represent the final evolutionary state of most
main-sequence stars (M < 8 M), and their luminosity decreases approximately
as L  M t–7/5 [Mestel 1952, MNRAS 112, 583]
Hansen et al [2002, ApJL 574, L155], p.e., find tD = 7.3  1.5 Gy
(and tAG = 12.5  0.7 Gy for M5)
 Dynamics: Age
• quasars – the currently farthest quasar was found at z = 6.4 [SDSS]
The lookback time of this object is about 12.9 Gy, which means that its formation
was at most 0.8 Gy after the Big-Bang.
 Light Elements Abundance
 primordial nucleosynthesis
(200-1000 s, 1×109-5×108 K)
• 12D
• 23He
• 24He
• 37Li
Deuterium:
[D/H]p = 3.39  0.25  10–5
[Burles & Tytler 1998, ApJ 499, 699]
[Burles & Tytler 1998, ApJ 507, 732]
 Light Elements Abundance
Helium:
 There is a relation between the
abundance of metals, Z, and the
abundance of He, Y (both are
produced by stars)
 By extrapolating the Y to Z = 0
(using the O, for example) we get
the primordial abundance of
He  Yp
[Izotov & Thuan 1998,
ApJ 500, 188]
[Peimbert et. al 2007, ApJ 666, 636]
 Light Elements Abundance
 Reionization
The Dark Ages:
 after recombination, HI absorbs
almost all the light of the first stars
(Universe is dark and opaque)
Energy sources for
reionization:
 quasars: by assuming a universal
LF for quasars and extrapolating to
reionization era, they seem not to be
numerous enough to ionize the IGM
alone…
 pop III stars (zero-metallicity,
high-mass, very hot stars): can
account for reionization with a
reasonable IMF, although not
observed yet…
 Reionization
Observables:
 quasars’ spectra (GunnPeterson trough)*: before
reionization, HI absorption
suppress all the light blueward
of Ly
(zreion > 6, from SDSS quasars)**
 CMBR: small scale
anisotropies are erased, while
polarization anisotropies are
introduced
(zreion = 11-7 from WMAP3)***
 21-cm line: ideal probe, for
the near future…
* [Gunn & Peterson 1965, ApJ 142, 1633]
** [Becker et al. 2001, AJ 122, 2850]
*** [Spergel et al. 2007, ApJS 170, 377]
 Other References
Papers:
 A.R. Liddle 1999, astro-ph/9901124 (inflation)
 M.S. Turner 1999, PASP 111, 264
 P.J.E. Peebles 1999, PASP 111, 274
 S.M. Carroll 2000, astro-ph/0004075 (cosmological constant)
 M. Tegmark 2002, astro-ph/0207199
 M.S. Turner 2002, astro-ph/0202007
 Gallerani et al. 2006, MNRAS 370, 1401
Books:
 S. Dodelson 2003; Modern Cosmology, Academic Press
 M. Roos, 1999; Introduction to Cosmology, Wiley Press
 M. Plionis & S. Cotsakis 2002, Modern Theoretical and Observational
Cosmology, ASSL – Kluwer Academic Publishers
 M.H. Jones & R.J.A. Lambourne 2003. An Introduction to Galaxies and
Cosmology, Cambridge Univ. Press