Jun’ichi Yokoyama (RESCEU)

(As of 2002, just before WMAP data came.)

0 Photon density

Black body radiation with temperature 0 2.725KT dominated by Cosmic Microwave Background (CMB)

5 2 50 2.47 10 4.76 10h

34 3 51 40 4.6408 10 g cm 2.0003 10 GeV

0 Neutrino Background13

0 0

41.945K

11T T

13

0 0 0

21 40.6813

8 11

for 3 species in the standard model(massless)

-30 410cmn

b0 Baryon density

Luminosity density of galaxies8 32 10 MpcGL hL

333.90 10 erg secL solar luminosity

Mass-to-Light ratio(1 2)

visible

MM

L L

Density of Visible Matter

(It simply means that our Sun is a typical star.)

32 1 3(1 2) (1 2) 10 g cmvisible G

ML h

L

3 1 3visible0 (1 2) 10 (1.4 3) 10h

b0 Baryon density

Big bang Nucleosynthesis (BBN) theory and Observations of light elements (D, He4, Li…) constrain Baryon-to-Photon ratio .

All Baryon density

b0 0.02 0.04

bn n

BBN is one of the most important subjects of the standard cosmology. But I do not discussit here any further, since it will be covered by lectures on Nuclear Physics III.

前ページと左図はApJ600(2004)544右図はastro-ph/0307244による。

m0 Total Matter (Baryon + Cold Dark Matter)

Rotation curve of a spiral galaxy 渦巻き銀河の回転曲線2 ( )( )

M rv r G

r

Mass within radius r

Rotation curve remain constant evenbeyond the size of the galactic disk,which indicates the existence of darkmatter.

10galaxy visible

M Mh

L L

m0 0.2 0.4

m0Random velocities of galaxies in a group of galaxies

Cluster baryon fraction from X-ray emissivity and baryon density from primordial nucleosynthesis

Shape parameter of the transfer function of CDM scenario of structure formation

Many others

m0 0.3

m0 0.2 0.5

m0 0.35 0.07

m0 0.15 0.3h

m0 0.35

Total Matter (Baryon + Cold Dark Matter)

Virial Theorem gives an estimate of gravitational potential energy Mass.

H0 500 km / s / Mpc

2Mpc

2Mpc

Hubble`s discover

y

The Greatest Blunder

Current data

0v H d

Luminosity Distance

Angular Diameter Distance Ad

Ld Absolute Luminosity

Absolute Size

Before turning into observations, some terminologies…

Band central

wavelength

(μm)

band

width

(μm)

0 mag flux

(Jy)

U 0.3652 0.0526 1923

B 0.4448 0.1008 4130

V 0.5505 0.0827 3695

R 0.6588 0.1568 3107

I 0.8060 0.1542 2439

oF

26 2 11 Jy=10 W m Hz

Apparent magnitude 102.5logo

Fm

F

g

r

i

z

Absolute magnitude M

2

10

10pc2.5log 5log 5L

L

m M dd

Apparent magnitude seen 10pc away from the star. 104.72 2.5logM L L Measure of the absolute luminosity

Color, Colours, … e.g.B V B VB V m m M M

Distance modulus5log 5Lm M d 5log 25Lm M d

Ld in parsec Ld in Mpc

Extinction by dusts etc. = ReddeningLight with shorter wavelength is more likely absorbed/scattered.

2.5log extinct extinctA L L m m

(1pc = 3.26ly = 3.0856×1018cm).

Color excess e.g.

( ) ( )extinctB V B VE B V B V A A

Extinction is proportional to color excess.

V V B VA R E 3.1VR standard text-book value

K correctionWhen we observe high-redshift objects, we observe at a longer wavelength than the rest-frame counterpart. Hence depending on the spectral shape of the object, we must correct the flux or the apparent magnitude of each band.

0HCepheids H0 =75±10km/s/Mpc

SNIa H0 =71±2(stat)±6(syst)km/s/Mpc

Tully-Fisher H0 =71±3±7km/s/Mpc

Surface Brightness Fluctuation H0 =70±5±6km/s/Mpc

SNII H0 =72±9±7km/s/MpcFundamental Plane of Elliptical Galaxies H0 =82±6±9km/s/Mpc

Summary 　 H0 =72±8km/s/Mpc

HST Key Project

(Freedman et al ApJ 553(2001)47)

A suffix 0 denotesthe present value.

Cepheid 動径脈動型変光星They change their size with a certain constant period P=5-70 days.Their absolute magnitude M is proportional to logP.

distance to LMC = 51kpc (46kpc previously).

Hubble space telescope (HST)measured 20 cepheids in M100galaxy, for example.

H0 =75±10km/s/Mpc

This method is used to measure the distance to relatively close galaxies andit serves as the second step to the cosmic distance ladder.

This distance is also determined using variable stars (Mira type).NB. Parallax distance can be determined only up to 100pc or so.

Tully Fisher relation

Rotation velocity of a spiral galaxy is correlated with its absolute luminosity.

Line broadening by Doppler effect=Observable

Surface Brightness Fluctuations

Nearby Mountains=Trees can be resolved.

Distant Mountains=Looks homogeneous.

Galaxies consist of stars. Distant galaxies looks more homogeneouswith smaller pixel-to-pixel fluctuations of surface brightness.

0HCepheids H0 =75±10km/s/Mpc

SNIa H0 =71±2(stat)±6(syst)km/s/Mpc

Tully-Fisher H0 =71±3±7km/s/Mpc

Surface Brightness Fluctuation H0 =70±5±6km/s/Mpc

SNII H0 =72±9±7km/s/MpcFundamental Plane of Elliptical Galaxies H0 =82±6±9km/s/Mpc

Summary 　 H0 =72±8km/s/Mpc

HST Key Project

(Freedman et al ApJ 553(2001)47)

A suffix 0 denotesthe present value.

Type I : No H lines, Type II : H lines

GravitationalCollapseand Bounce

Type Ia SupernovaeAccretion to a C+O white dwarf in a binary system

Radius of the white dwarf dropsrapidly with increased centraltemperature, leading to the ignition of Carbon

It approaches Chandrasekharmass (1.38 M), the maximummass that can be supported bydegenerate electron pressure.

Deflagration and Detonation

Type Ia Supernovae

SN1994D in NGC4526

Theoretical studies includingnumerical simulations have beenin difficult situations to realize explosion…

Large luminosity ～ whole galaxy

Measurable at cosmological distances

Observations of nearby SNIaindicate that they can be usedas a standard candle whoseabsolute luminosity can be foundfrom the light curve shape andcolor..

4310 erg/secSNL 333.9 10 erg/secL

Phillips (1993) Astrophys J 413, L105

Measured B, V, I absolute magnitudes of 9 SNIa using host-galaxydistances estimated by the surface-brightness fluctuations orTully-Fisher relation.Light curve observed for > 20 days after the maximum.

Scatter in the maximum absolute magnitudes are quite large: ±0.79mag in B, ±0.59mag in V, ±0.46mag in VThey cannot be used as a standard candle as they are.

But a strong correlation was found between the maximummagnitudes and decline rate of the light curve.

15 ( )m B , drop in the B magnitude during the first 15 daysafter the maximum is strongly correlated to the maximumabsolute magnitude.

)(15 BmMB

0 15 days

Peak luminosity-decline raterelation

The light curve of SNIa is powered by the radiative decay of5656Ni Ni 5656Co Co 5656Fe, so its luminosity depends on the amountFe, so its luminosity depends on the amountof of 5656Ni synthesized in the explosion.Ni synthesized in the explosion.

More More 5656Ni →larger luminosity → higher temperatureNi →larger luminosity → higher temperature→ → higher opacity → broader light curvehigher opacity → broader light curve

Perlmutter et al (1997) Astrophys J 483, 565 (Supernova Cosmology Project)

Light curve width – Luminosity relation

The stretch factor linearly broadens or narrows the rest-frametime scale of an average template light curve.

s

Related to as . 115 1.96 0.17 1 1.07m s 15m

( )corrB B corrm m s Corrected magnitude ( ) ( 1)corr s s

0.27B , 0.19B corr

From 6 distant supernovae with z=0.35-0.46they found no evidence for the dark energy.

Perlmutter et al (1999) Astrophys J 517, 565 (Supernova Cosmology Project)

42 SNIa at z=0.18-0.83, ( ) ( 1) 5log ( , , )B corr R BR R B L m vm z m s K A z M D

BMand are nuisance parameters to be integrated out.

60

42

0.99 0.01Hamuy

s

1.00 0.01SCP

s

Distant SN and closer SNhave the same property.

v0 Type Ia Supernovae m-z relation

v0 m01.25 0.5 0.5

log(dL)

z

d H zq

z

qa

aH

L

tM

FHG

IKJ

0

1 0 2

0 2

1

2

1

22

0

,

b g

various tests

0.3mag

K0Location of 1st peak in the angular power spectrum of CMB anisotropy

K0 0

The angular scale subtending thesound horizon at decoupling depends on spatial geometry.

in accordance with(standard) Inflation

What makes up therest of the Universe?

K m r1 0.7?

SNIa

K0 0

v0

SNIa+CMB

v0

m0

K0 0

v0

SNIa+CMB+Matter density

m0 0.3 v0 0.7

m0 v0 K01, 0 as predicted by Inflation

Cosmic age 10 0(0.9 1.0)t H

H0 =72±8km/s/Mpc, 10 13.61 Gyr2.2 16.9H

0 11 17Gyrt centered around 　　　　　　0 13Gyrt

Observation:

0 11 14Gyrt

0 12 15Gyrt from globular cluster

from cosmological nuclear chronology

Expected accuracy of MAP satellite Present status

will make it possible to determine cosmological parametersmuch more accurately. Perturbation spectrum as well.

0m0 0vK01, 0, 5 0, 0 H

v0 0 00m K0.2, 0, 0, 50 100 H or

m0 v0 K01, 0 as predicted by Inflation

good news

bad newsm0 0.3 v0 0.7 0 70 H