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