josé alberto rubiño-martín (iac) ( in collaboration with...

Lin

es i

n t

he

CM

B s

pec

tru

m f

rom

th

e L

ines

in

th

e C

MB

sp

ectr

um

fro

m t

he

epo

ch o

f C

osm

olo

gic

al

Rec

om

bin

ati

on

ep

och

of

Co

smo

log

ica

l R

eco

mb

ina

tio

n

José A

lbe

rto R

ubiñ

o-M

art

ín

(IA

C)

Be

na

sq

ue

, A

ug

ust

4th,

20

06

( In

co

llab

ora

tio

n w

ith

: R

.A. S

un

ya

ev,

C.H

ern

án

de

z-M

on

tea

gu

do

, J. C

hlu

ba

)

Rec

om

bin

ati

on

R

eco

mb

ina

tion

(z (z ~~

10

00

)1

00

0)

zz~

6~

6

PopI

II s

tars

?

Dark

Ages

Dark

Ages

(Uni

vers

eac

cesi

ble

with

op

tical

/IR

tele

scop

es)

(Neu

tral

hyd

roge

n.

Acc

esib

le w

ith 2

1cm

line

su

rvey

sas

SK

A o

rL

OFA

R)

(GP

trou

ghob

serv

edin

QSO

)

(Mic

row

ave

back

grou

nd)

Ga

lax

ies

form

an

d

Ga

lax

ies

form

an

d

evo

lve

evo

lve

Ang

ular

flu

ctua

tions

of

the

CM

B

VSA

CM

B

CM

B a

nis

otr

op

ies

an

iso

tro

pie

s : : D

yn

am

ics

Dy

na

mic

s

•Ini

tial c

ondi

tions

(in

flat

ion)

•Cos

mol

ogic

al p

aram

eter

s

The

CM

B S

pect

rum

•E

ncod

es in

form

atio

n ab

out e

ner

get

ics

ener

get

ics

in th

e U

nive

rse

(pha

se tr

ansi

tions

in e

arly

un

iver

se;r

elic

dec

ay D

M p

artic

les;

rei

oniz

atio

n).

T0

= 2.

725

±0.

001

K

|µ|<

9 x

10-5

(95%

CL

)

|y| <

15 x

10-6

(95%

CL

)

Bla

ckbo

dy s

pect

rum

with

ex

trem

ely

high

pre

ciss

ion

(FIR

AS,

Fixs

en&

Mat

her

2002

)

PopI

II s

tars

?

Is is

pos

sibl

e to

obt

ain

spec

tral

info

mat

ion

from

th

e ep

och

of

reco

mbi

natio

n?

Or,

in o

ther

wor

ds:

Wh

ere

Wh

ere

are

are

th

eth

eL

yL

y-- αα

ph

oto

ns

ph

oto

ns

from

from

the

the

epoch

epoch

of

of

reco

mb

inati

on

reco

mb

inati

on

??

Overvie

w

�In

trod

uctio

n. T

he C

osm

olog

ical

Hyd

roge

n R

ecom

bina

tion.

�

Obs

ervi

ng s

pect

ral f

eatu

res

from

re

com

bina

tion.

�H

ydro

gen

Spec

trum

fro

m R

ecom

bina

tion.

�E

ffec

t on

the

angu

lar

pow

er s

pect

rum

.�

Obs

erva

bilit

y of

the

lines

.�

Con

clus

ions

How

did

the

Uni

vers

e be

cam

e ne

utra

l?

•Z

el´d

ovic

h, K

urt &

Sun

yaev

(19

68)

and

Peeb

les

(196

8) w

ere

the

firs

t des

crib

ing

how

the

reco

mbi

natio

n oc

curs

in th

e U

nive

rse.

•T

wo

mai

n ar

gum

ents

toun

ders

tand

Rec

ombi

natio

n:

•D

ue to

the

high

ent

ropy

of

the

Uni

vers

e (~

1.6x

109

phot

ons

per

bary

on)

reco

mbi

natio

noc

curs

at z

= 10

00. (

Not

e th

at 1

3.6e

V =

157

800

K, b

ut30

00K

= 0

.26e

V).

In

addi

tion,

col

lisio

nal p

roce

sses

are

not

impo

rtan

t.

•The

Lym

an-a

lpha

pho

tons

are

opt

ical

ly th

ick

(Cas

e B

rec

ombi

natio

n).

The

mai

n ch

anne

l of

the

reco

mbi

natio

n is

the

2s tw

o-ph

oton

dec

ay.

How

did

the

Uni

vers

e be

cam

e ne

utra

l? (

II)

2p2s 1s

Con

tinuu

m

Gro

und

2p2s 1s

Con

tinuu

m

Gro

und

•E

ffec

tive

3-le

vel a

tom

.

•D

irec

t rec

ombi

natio

ns to

gr

ound

sta

tedo

notp

rodu

ce

a ne

trec

ombi

natio

n.

•Ly-α

phot

ons

are

optic

ally

th

ick

and

can

not r

edsh

ift

befo

re b

eing

re-

abso

rbed

. L

evel

2 o

verp

opul

ated

.

•Tw

o ph

oton

2s

deca

y is

the

m

ain

chan

nel,

but

the

Ein

stei

nA

-coe

ffic

ient

is

A2s

1s=8

.22

s-1.

a)

a)

Ly

Ly

-- ααp

ho

ton

is

ph

oto

n i

sa

bso

rbed

by

ab

sorb

ed b

yo

ther

ato

mo

ther

ato

m

b)

b)

Tw

o p

ho

ton

s T

wo

ph

oto

ns

can

esc

ap

e.ca

n e

sca

pe.

RE

CO

MB

INA

TIO

N I

S D

EL

AY

ED

Whe

re a

re th

e L

y-α

phot

ons

from

the

epoc

h

of r

ecom

bina

tion?

In th

e W

ien

tail

of th

e B

lack

body

spe

ctru

m.

The

pro

blem

is th

at in

this

spe

ctra

l reg

ion,

dus

t em

issi

on d

omin

ates

(C

IB).

How

the

Uni

vers

e be

cam

e ne

utra

l? (

III)

•Z

el´d

ovic

h, K

urt &

Sun

yaev

(1

968)

•Pe

eble

s (1

968)

•L

yuba

rsky

& S

unya

ev (

1983

)

•Jo

nes

& W

yse

(198

5)

•H

u et

al.

(199

5, H

SSW

)

•Se

ager

, Sas

selo

v &

Sco

tt (1

999,

200

0).

Thi

s cu

rve

is a

key

ingr

edie

nt to

pre

dict

the

angu

lar

pow

er s

pect

rum

of

the

CM

B, b

ecau

se it

dir

ectly

giv

es th

e fr

actio

n of

fre

e el

ectr

ons.

The

(T

hom

son)

visi

bilit

y fu

nctio

n

•The

rel

evan

t qua

ntity

is th

e T

hom

son

optic

al d

epth

.

•The

vis

ibil

ity f

un

ctio

nvis

ibil

ity f

un

ctio

ngi

ves

the

prob

abili

ty th

at a

pho

ton

obse

rved

now

was

last

sca

ttere

d at

red

shif

t z:

V =

exp

(-τ)

dτ/

dη

τ= ∫σ

Tn e

dl

Prio

r to

the

reco

mbi

natio

n ep

och,

the

phot

ons

and

the

elec

tron

s ar

e tig

hly

coup

led

due

to T

hom

son

scat

teri

ng. W

hen

the

num

ber

dens

ity o

f el

ectr

ons

decr

ease

s, th

e ph

oton

s ar

e re

leas

ed a

nd th

e C

MB

is f

orm

ed.

z max

=107

9

∆z

= 8

0

Rec

om

bin

ati

on

. B

asi

c eq

ua

tio

ns

1.T

he r

adia

tion

fiel

d. G

iven

by

the

rad

iati

ve

tran

sfer

eq

uati

on

rad

iati

ve

tran

sfer

eq

uati

on

. For

an

hom

ogen

eous

and

isot

ropi

c (I

->

J)ex

pand

ing

med

ium

:

Thi

s eq

uatio

n is

in it

s m

ost g

ener

al f

orm

and

is d

iffi

cult

to s

olve

, but

we

can

do tw

o as

sum

ptio

ns:

•T

he s

pect

ral d

isto

rtio

ns a

re v

ery

smal

l (FI

RA

S:Fi

xsen

et a

l. 19

96,

show

ed th

at ∆

I/I 0

< 10

-4).

Thu

s, J

(ν,t)

=B(ν

,t).

•Q

uasi

-sta

tic s

olut

ion

for

spec

tral

-lin

e pr

ofile

is v

alid

(R

ybic

ki &

D

ell´

Ant

onio

199

4). W

e ca

n us

e th

e So

bole

ves

cape

pro

babi

lity

met

hod

to d

eal w

ith th

e ev

olut

ion

of a

ll lin

es.

Ba

sic

equ

ati

on

s (I

I)2.

2.

Th

e ra

teT

he

rate

equ

ati

on

seq

uati

on

s.

•C

ollis

iona

l rat

es a

re o

f m

inor

impo

rtan

ce (

Peeb

les

68, S

eage

r et

al.

2000

).

•Ph

otoi

oniz

atio

n/Ph

otor

ecom

bina

tion

rad

iati

ve

rate

sar

e co

mpu

ted

by

inte

grat

ing

the

blac

kbod

y ra

diat

ion

fiel

d, e

.g.

Ba

sic

equ

ati

on

s (I

II)

3.

3.

Sob

ole

vS

ob

ole

ves

cap

e es

cap

e p

rob

ab

ilit

yp

rob

ab

ilit

ym

eth

od

met

hod

. T

he n

et b

ound

-bou

nd r

ate

is:

The

esc

ape

prob

abili

ty p

ijen

code

s th

e pr

obab

ility

that

pho

tons

ass

ocia

ted

to

the

cons

ider

ed tr

ansi

tion

will

“es

cape

” w

ithou

t bei

ng f

urth

er s

catte

red

or

abso

rbed

. The

con

cept

is s

imila

r to

ste

llar

atm

osph

eres

.

In th

is c

ase,

it c

an b

e sh

own

that

(Se

ager

et a

l. 20

00; D

ubro

vich

& G

rach

ev

2004

)

Ba

sic

equ

ati

on

s (I

V)

4.

4.

Matt

er t

emp

eratu

reM

att

er t

emp

eratu

reev

olut

ion

(Com

pton

cool

ing

+ ad

iaba

ticex

pans

ion)

5.O

ther

equ

atio

ns.

1.H

ubbl

e co

nsta

nt e

volu

tion

2.H

eliu

m r

ecom

bina

tion.

Rec

ombi

natio

n. S

tatu

s of

the

art (

I)

•A

fter

ZK

S68

and

P68,

man

y au

thor

s ha

ve r

efin

ed th

e co

mpu

tatio

n of

the

reco

mbi

natio

n pr

oces

s, b

ased

on

the

effe

ctiv

e 3-

leve

l ato

m m

odel

(e.g

.Jon

es&

W

yse

1985

).

•T

o so

lve

the

com

plet

e se

t of

OD

Es

(ord

inar

y di

ffer

entia

l equ

atio

ns)

is

com

puta

tiona

lly d

iffi

cult.

The

pro

blem

is v

ery

stif

f, a

nd th

e ac

cura

cy

requ

iere

men

tsar

e ve

ry h

igh.

•If

one

is n

ot in

tere

sted

in th

e lin

es, b

ut in

the

tota

l ele

ctro

n fr

actio

n, th

e ac

cura

cy r

equi

erem

ents

can

be

rela

xed.

•In

add

ition

, one

can

ass

ume

stat

istic

al e

quili

briu

m b

etw

een

the

l-su

bsta

tes,

i.e.

th

at th

esu

blev

els

are

popu

late

d ac

cord

ing

to N

(n,l)

=(2l

+1)

N(n

,l=0)

. Thi

s is

not

ob

viou

s fo

r th

e co

smol

ogic

al r

ecom

bina

tion,

whe

re c

ollis

ions

are

not

impo

rtan

t.

•B

est d

eter

min

atio

n to

date

:Sea

ger,

Sass

elov

&Sc

ott(

1999

, 200

0),u

sed

a 30

0-le

vel h

ydro

gen

atom

(sta

tistic

al e

quili

briu

m b

etw

een

l-su

bsta

tes

assu

med

).T

his

is th

eR

EC

FA

ST

RE

CF

AS

Tco

de.F

ocus

ed o

nn e

.

Rec

ombi

natio

n. S

tatu

s of

the

art (

II)

•D

ubro

vich

(19

75)

prop

osed

to lo

ok f

or s

pect

ral d

isto

rtio

ns f

or h

ighe

r tr

ansi

tions

.

•D

ubro

vich

& S

toly

arov

(19

97)

cons

ider

ed a

lso

He

lines

.

•M

any

com

puta

tions

to d

ate

(Bur

gin

2003

, Dub

rovi

ch 2

004,

Kho

lupe

nko

et a

l. 20

05,W

ong

et a

l. 20

06)

but u

sing

sim

plif

ying

ass

umpt

ions

to d

eal w

ith th

e eq

uatio

ns: q

uasi

-sta

tic e

volu

tion

of th

e po

pula

tions

for

n>2

. The

am

plitu

de o

f th

e lin

es is

ver

y sm

all (

10-6

to 1

0-8).

•O

nly

one

atte

mpt

to s

olve

the

full

prob

lem

(R

ybic

ki&

del

l´A

nton

io 1

993)

, but

th

e re

sult

was

not

con

clus

ive,

and

onl

y co

nsid

ered

nm

ax=1

0.

Ou

r w

ork

: h

ow

to

ob

serv

e sp

ectr

al

fea

ture

s fr

om

th

e ep

och

of

reco

mb

ina

tio

n

••F

req

uen

cy S

pec

tru

mF

req

uen

cy S

pec

tru

m. W

e ha

ve c

ompu

ted

the

spec

tral

dis

tort

ions

to th

e bl

ackb

ody

aris

ing

from

H

reco

mbi

natio

nin

the

freq

uenc

y ra

nge

1-35

00 G

Hz.

••R

eso

na

nt

Res

on

an

t(( c

oh

eren

tco

her

ent ))

sca

tter

ing

of

sca

tter

ing

of

CM

B

CM

B p

ho

ton

sp

ho

ton

s.

Use

ang

ular

flu

ctua

tions

and

obs

erva

tions

at d

iffe

rent

fr

eque

ncie

s.

Hy

dro

gen

Rec

om

bin

ati

on

Sp

ectr

um

•A

ll st

ates

(in

clud

ing

angu

lar

mom

entu

m s

uble

vels

) tr

eate

d in

de

tail

up to

n=3

0. T

hus,

465

leve

lsar

e so

lved

sim

ulta

neou

sly

for

the

hydr

ogen

atom

. (W

eus

e a

vari

able

-ord

er, v

aria

ble-

step

met

hod

impl

emen

ting

the

back

war

d di

ffer

entia

tion

form

ulae

).

•In

tegr

atio

n ra

nge

in r

edsh

ift:

[500

, 350

0]

•Sp

ectr

al d

isto

rtio

n du

e to

the

2s tw

o ph

oton

dec

ay in

clud

ed.

•L

ines

(bo

und-

boun

dtr

ansi

tions

) ar

e co

mpu

ted

as:

(Rub

iño-

Mar

tín, C

hlub

a&

Sun

yaev

200

6 M

NR

AS

acce

pted

, ast

ro-p

h/06

0737

3)

Hy

dro

gen

Rec

om

bin

ati

on

Sp

ectr

um

...

or

in w

avel

eng

ths

Thi

s os

cilla

tory

be

havi

our

is u

niqu

e, a

nd

coul

d be

use

d to

det

ect

thes

elin

es.

Rel

ati

ve

inte

nsi

ty o

f th

e li

nes

Rel

ati

ve

inte

nsi

ty o

f th

e li

nes

Po

siti

on

s a

nd

wid

ths

of

the

fea

ture

s

The

y ar

e br

oad

feat

ures

. Ele

ctro

n br

oade

ning

is

not

cha

ngin

g th

is p

ictu

re.

Co

nv

erg

ence

of

the

resu

lt

Lin

es a

re

form

ed p

rior

to

the

epoc

h of

re

com

bina

tion

Red

shif

t o

f fo

rma

tio

n o

f th

e li

nes

Imp

ort

an

ce o

f d

eta

iled

l-tr

eatm

ent

Imp

ort

an

ce o

f d

eta

iled

l-t

rea

tmen

t

Imp

act

on

th

e re

sid

ua

l el

ectr

on

fra

ctio

n

Eff

ect

of

the

l-tr

eatm

ent

in t

he

Cls

•T

he e

ffec

t is

larg

er a

t low

red

shif

ts. T

he n

et (

inte

grat

ed)

effe

ct o

n th

e po

wer

sp

ectr

um is

of

the

orde

r of

1%

.

•N

ew p

aper

in p

repa

ratio

n in

clud

ing

n=10

0 sh

ells

, plu

s de

taile

d tr

eatm

ent o

f co

llisi

ons.

EE

TT

Coh

eren

t sca

tteri

ng o

f th

e C

MB

pho

tons

(Rub

iño-

Mar

tín, H

erná

ndez

-Mon

teag

udo

& S

unya

ev 2

005

A&

A 4

38, 4

61)

z=0

z=10

00

CM

B p

hoto

n

λ12

: R

est f

ram

e w

avel

engt

h 2 1

Hyd

roge

n at

om a

t re

dshi

ft z

λ12

λ12

(1+z

)

Coh

eren

t sca

tteri

ng o

f th

e C

MB

pho

tons

(Rub

iño-

Mar

tín, H

erná

ndez

-Mon

teag

udo

& S

unya

ev 2

005)

z=0

z=10

00

CM

B p

hoto

n

Hyd

roge

n at

om a

t re

dshi

ft z

λ12

λ12

(1+z

)

Cl

Cl +

δC

l(B

asu

et a

l. 20

05)

Coh

eren

t sca

tteri

ng o

f th

e C

MB

pho

tons

Co

mp

uti

ng

th

e ch

an

ge

in t

he

Cl

•C

ompu

te th

e op

tical

dep

th f

or th

e lin

e of

inte

rest

.

•C

ompu

te th

e lin

ear

term

usi

ng a

n st

anda

rd B

oltz

man

n co

de to

inte

grat

e th

e C

MB

ani

sotr

opie

s (C

MB

FAST

)

•T

o ob

serv

e th

e ef

fect

, we

com

pare

pow

er s

pect

ra a

t tw

o fr

eque

ncie

s:

δC

l=

Cl(w

ithlin

e) -

Cl(w

ithou

t lin

e)

Com

puta

tions

for

th

is w

ork

•A

ll st

ates

(in

clud

ing

angu

lar

mom

entu

m

subl

evel

s) tr

eate

d in

det

ail

up to

n=1

0.

•O

ptic

al d

epth

s fo

r th

e m

ain

tran

sitio

ns: a

ll ve

ry

smal

l.

(Rub

iño-

Mar

tín, H

erná

ndez

-Mon

teag

udo

& S

unya

ev 2

005)

Th

e li

nea

r te

rm

•O

ptic

al d

epth

s in

the

lines

are

ver

y sm

all:

this

term

is s

uffi

cien

t.

•Fo

r a

give

n lin

e, th

is r

edsh

ift i

nter

val t

rans

late

s in

to f

requ

ency

inte

rval

.

(se

e ad

ditio

nalm

ovie

sat

http

://w

ww

.iac.

es/g

aler

ia/ja

lber

to)

Th

e Hα

lin

e

The

red

shif

t tra

nsla

tes

into

fre

quen

cy a

s 6

562.

8Å(1

+z )

Th

e Hα

lin

e (I

I)

Th

e Hα

lin

e (I

II)

The

eff

ects

that

we

are

disc

ussi

ng a

re v

ery

smal

l, bu

t:

•Fi

xsen

&M

athe

r(2

002)

poin

tout

that

cur

rent

tech

nolo

gy

perm

it us

to r

each

the

leve

l of

10-7

in b

road

reg

ions

of

the

freq

uenc

y sp

ectr

um.

•N

ext g

ener

atio

n of

CM

B in

stru

men

ts m

easu

ring

B-m

odes

(p

olar

izat

ion)

will

rea

ch le

vels

of

sub-

mic

roke

lvin

(0.

01-0

.1 µ

K),

w

hich

is e

noug

h to

det

ect t

hese

eff

ects

on

the

pow

er s

pect

rum

.

•B

ut w

e w

ill b

e lim

ited

by th

e co

ntro

l of

fore

grou

nds

(rad

ioga

laxi

es, d

ust e

mis

sion

,...)

•H

owev

er, N

O F

OR

EG

RO

UN

D C

AN

MIM

IC th

ese

feat

ures

.

Ob

serv

ab

ilit

y o

f th

e ef

fect

s

Ob

serv

ab

ilit

y o

f th

e ef

fect

s

(Lon

gair

& S

unya

ev 1

972)

Ob

serv

ab

ilit

y o

f th

e sp

ectr

al

dis

tort

ion

s

•L

yαis

dom

inan

t, bu

t the

CIB

is

inte

nse.

•H

owev

er, t

he

sens

itivi

ty is

im

prov

ing:

e.g

. Sp

itzer

(D

ole

et a

l. 20

06)

have

res

olve

d pr

actic

ally

¾ o

f th

e M

IB a

t 160

mic

rons

in

to lu

min

ous

IR

gala

xies

at z

~1.

•T

he r

egio

n ar

ound

21

cm s

eem

s m

ost

prom

isin

g. I

n ad

ditio

n, th

ere

is

new

phy

sics

ther

e (d

ecay

ing

dark

m

atte

r pa

rtic

les)

.

Ob

serv

ab

ilit

y o

f th

e ef

fect

on

th

e C

l´s

Ob

serv

ab

ilit

y o

f th

e ef

fect

on

th

e C

l´s

Con

clus

ions

�O

bser

vatio

ns o

f th

ese

spec

tral

fea

ture

s pr

ovid

ea

dir

ect

dir

ect

mea

sure

men

tm

easu

rem

ent

of th

e ep

och

of r

ecom

bina

tion,

as

wel

las

anin

depe

nden

tdet

erm

inat

ion

ofco

smol

ogic

alpa

ram

eter

s.

�W

e ha

ve o

btai

ned

the

mos

tpre

cise

det

erm

inat

ion

of th

e C

osm

olog

ical

Rec

ombi

natio

n sp

ectr

um to

date

.

�Sp

ectr

al f

eatu

res

from

the

epoc

hof

Rec

ombi

natio

nar

e ver

y

ver

y

small

small

, bei

ng o

f th

e or

der

of s

ub-m

icro

kelv

ins

for

pow

er s

pect

rum

di

stor

tions

, and

10-7

-10-8

for

the

spec

trum

itse

lf.

�E

xqui

site

cont

rol o

n fo

regr

ound

con

tam

inat

ion

is e

ssen

tial t

o m

easu

re th

ese

feat

ures

, but

...

�A

ll th

ese

feat

ures

hav

e a

very

pec

ulia

r os

cilla

tory

beh

avio

ur

whi

ch c

an n

ot b

e m

imic

ed b

y an

y ot

her

fore

grou

nd a

nd m

ight

hel

p in

sep

arat

ing

thes

e lin

es.