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Conference Poster
H₂ lines from the first generation star formation process
Author(s): Mizusawa, Hiromi
Publication Date: 2003
Permanent Link: https://doi.org/10.3929/ethz-a-004582412
Rights / License: In Copyright - Non-Commercial Use Permitted
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ETH Library
lines from lines from lines from lines from the firstthe firstthe firstthe first----generation star generation star generation star generation star
formation processformation processformation processformation process
Hiromi Hiromi Hiromi Hiromi Mizusawa MizusawaMizusawaMizusawa(Niigata University)(Niigata University)(Niigata University)(Niigata University)Collaborator
Ryoichi Nishi (Niigata University)Kazuyuki Omukai
(University of Oxford,NAOJ)
2H
STAR AND STRUCTURE FORMATION : FROM FIRST LIGHT TO THE MILKY WAYAstrophysics Conference, August 18-22, 2003, ETH Zurich, Switzerland.
Molecular hydrogen line photons emitted owing to formation events of first-generation stars and their detectability by future observational facilities are explored. The H_2 luminosity evolution from the onset of prestellar collapse tothe formation of a ~100 M_sun protostar is followed by a simplified model for the dynamical evolution. In particular, the calculation is extended not only the early phase of the runaway collapse but also to the later phase of accretion, whose observational feature has not been studied before. Contrary to the runaway collapse phase, where the pure-rotational lines are always dominant, during the accretion phase prominent emission is owing to rovibrational lines. Also, the maximum luminosity is attained in the accretion phase for strong emission lines. The peak intensity of the strongest roviblational line reaches ~10^{-27} (W/m^2), corresponding to the flux density of 10^{-5} (μμμμJy), for a source at the typical redshift of the next-generation infrared satellite, SPICA, Space Infrared Telescope for Cosmology and Astrophysics, is ideal for observing the redshifted rovibrational line emission, to exceed the detection threshold, about 10^6 such forming stars must reach the maximum luminosity simultaneously in a pregalactic cloud. Unfortunately, this situation is excluded by the current theoretical understanding of early structure formation.
Abstract
PurposeWe estimate the luminosities of lines, which can be characteristics of the first star formation process, and evaluate the detectability of lines.
The luminosities of lines for the runaway collapse phase Ripamonti et al (2002) and Kamaya & Silk (2002)
However the luminosities of lines for the main accretion phase haven’t been estimated.
protostellar cloud protostarmain sequence
star
main accretionphase
we calculate them for both phase .
2H
2H
2H
2H
runaway collapsephase
1111
Model
The Larson-Penston-type similarity solution, γ=1.09 (dotted line),reproduces Omukai&Nishi’result (solid line) well.
It is a good approximation to the actual collapse dynamics.center ---- flat density distribution, runaway collapse
envelope ---- leaving the outer part practically unchanged
The thermal and chemical evolution of gravitationally collapsing protostellar clouds is investigated by hydrodynamical calculations for spherically symmetric clouds.
(Omukai&Nishi 1998)The evolutionary sequences
We focus on the central region and calculate the time evolution(e.g.,Omukai 2000).
yr104.1~76yr102.4~65
0.32yr~5412yr~43
yr102.8~32yr108.7~21yr107.5~10
2-
2-
2
3
5
×→×→
→→
×→×→×→
The time interval
2222
1.Dynamics
ααααββββ
・The runaway collapse phase
・The main accretion phase approximation, each mass shell free-fall
the collapse time scale ; the flat core size ;
:free-fall timeρ :the central density
ρ :the density of free-falling mass shell
:the velocity of free- falling mass shell
:the distance from mass shell to the center
r
≤
≥+=
=
=
∑∑
∑
≠≠
→
)(
)(
),H(),H(
),H(1
22
2H2
jiC
jiCAR
RjnRin
hAinL
ij
ijijijij
j
n
ij
n
ijij
ijijjiij
ε
νερ
The central evolution the free-fall relation modified by pressure gradient
ρπρρG
ttdt
d32
3, ffff
==ββββ fft
JλThe modification due to the finite pressure gradient force is represented
by the correction factor αααα,ββββ.
2/32 ,,)( −∝−=<−= rv
dtdr
rrGM
dtdv
rr ρ
rv
For the Larson-Penston-type similarity solution for γ=1.09,
13.2,33.1,11,1,78.0
gravitypressure ==
−=+=≅= βα
δβδαδ
fft
3333
)g/cm( 3−ρ )g/cm( 3−ρ
)cm(r )cm(r
2.2−∝ rρ
2/3−∝ rρJλ~
The runaway collapse phase The main accretion phase
①
②
③
①
②
③time
Contracting region and mass become more and more small.
Inner mass shells fall faster than outer mass shells.
Free-fall determined by
the local densityFree-fall
determined by the gravitational
force of the protostar
4444
2.Energy equation
HH
)(
,1
1
1
mkTp
mkTe
Ldtdp
dtde net
µρ
µγ
ρ
=−
=
−
−=
3. Cooling/Heating processes
:the energy per unit mass , :the pressure , :the temperature ,
:the adiabatic exponent , :the mean molecular weight ,
e p T
Hmµγ
::::the radiative cooling rate, :, :, :, :the chemical cooling rate or heating rate,,,,
::::the cooling rate of line emission, :, :, :, :the cooling rate of continuum emission
radL
contLlineLchemL
: the mass of the hydrogen nucleus
)(,)(contlineradchemrad
net LLLLLL +=+=
The continuum cooling rate is treated with the radiation field from the central protostar which is assumed to be the black body of 6000 K.
contL
5555
--- the population density of in level i
--- the spontaneous transition probability
--- the energy difference between levels I and j
--- the collisional transition rate from level I to level j
ijA ijC ijCi
j
Dv∆
shl
--- the velocity dispersion
--- the shielding length
),H( 2 in
ijA
ijεijhν
ijC
ijτ --- the optical depth averaged over the line
--- the escape probability
・・・・ line coolingline coolingline coolingline cooling
2H
GMrv
vrGMvdrdvvS
2/3
D2DDth 22/2)//(2 ∆=
∆=∆=∆
The runaway collapse phase ;
The main accretion phase ;
≤
≥+=
=
=
∑∑
∑
≠≠
→
)(
)(
),H(),H(
),H(1
22
2H 2
jiCjiCA
R
RjnRin
hAinL
ij
ijijijij
ji
n
ij
n
ijij
ijijji
ij
ε
νερ
( ) ( ) ( )
)/(2,)2/,min(
2/,,8
1
HDthsh
Dsh3
3
mkTvSl
vlixnggjxn
cA
e
J
j
i
ij
ijij
ijij
ij
µαλ
πντ
τε
τ
=∆∆=
∆
−=
−=−
ffDDth 6)//(2 tvdrdvvS β∆=∆=∆
6666
−−
−−
+→++→+
eHHHHeH
2
γ)cm10(~ 38
H−n
4.Chemical reactions( formation processes)
( process)
(three-body process)22
2
2HH2HHH3H
→++→
)cm10~cm10( 31438H
−−n
−H
2H
・continuum cooling/heating
[ ])()()(4)( ννκνηπν Jaacont −=Λ)(νη a
)(νκ a )(νJ: the thermal part of emission coefficient: the absorption coefficient , : the intensity of the central protostar
bound-free absorption of , -H
2H collision induced absorption
The main continuum processes as the radiative effect of the protostar free-free absorption of ,-H
7777
Initial Conditions
The physical condition of fragments (protopstellar clouds)
sun3
J M10~M83
234
H 10)e(,10)H(),K(500),cm(10 −−−− ==== yyTn
The contraction and fragmentation of primordial, metal-free gas clouds is investigated by several authors .(e.g., Uehara et al. 1996; Abel et al. 2002;
Bromm et al. 2002; Nakamura & Umemura 2002)
JM :Jeans mass
)H(/)H()H( i nny i= :the concentration of the i-th species
:the number density of the hydrogen nucleus
)H(n
We adopt the typical values for the star-formingcores from Bromm et al.(2002).
8888
The time evolution of the central abundance of
Results
)K(T
time time
temperature, abundance of , luminosities of the lines
Notice!
The time evolution of the central temperature fraction
)H(y)H( 2y
The runaway collapse phase
-H process
three body process
2H2H
2HH,410
310
210
1
310−
410 810 1210 410 810 1210)cm( -3n )cm( -3n
~ ten orders of magnitude
an order
Effective cooling by2H
9999
Comparison between runaway collapse phase and main accretion phase
)K(T fraction
The main accretion phase
sun2 M10
The runaway collapse phase
)H(210y )H( 25.0y
)H( 2y)H( 2102y
)H(5.0y
)H(y
time time
410 810 1210)cm( 3−n
410 810 1210)cm( 3−n
410
310
210
1
-310
sunM5.0
For the accretion phase, the evolutionary trajectories of the mass shells of ( : protostellar mass) = 0.5, 1, 5, 10, 50, 100 are shown. sunM/M M
10101010
The time evolution of the line luminosities
runaway collapse phase
main accretionphase
Peak luminosityPeak luminosity
(vibrational level,rotational level)→(vibrational level,rotational level)
red:(1,1)→(0,1), green:(1,1)→(0,3), blue:(0,6)→(0,4), purple:(0,5)→(0,3) 2.34μμμμm , 2.69μμμμm , 8.27μμμμm , 10.03μμμμm
Pick up : four of the strongest lines2H
2H
before after
rotational lines
rovibrational lines
rest frame :
The central protostar
sunM26~
11111111
For mid-infrared region( ), SPICA(ISAS),a large(3.5m),cooled(4.5K) telescope, is the best . (better than JWST and ALMA)
Detectability
19=zD)m/W(10~4
2272
19peak
−
=
=z
peak
DL
Fπ peakL
µm40~λ
)µm(34.2:),1,0()1,1( =→ λframerest)µm(8.46:)201 ==+ λz(redshifted
:The luminosity distance to z=19
:The peak luminosity
The line detection limit of SPICA is about in .In this region, the high background of the zodiacal light limits the sensitivity of SPICA to (private communication H.Matsuhara).
If there are more than sources with their luminosity near the peak value,SPICA is able to observe a cluster of forming first-generation stars.
6510 −
)W/m(10 220− µm40~λ
)W/m(10 2)2221( −−
The total cloud mass reaches Galactic scale.The metalicity in the pregalactic clouds must be lower than (Omukai 2000).sun
410~ Z−
Formation of Galactic scale with such low metallicity is clearly excluded in the context of standard cosmology (e.g., Scannapieco,Schneider,& Ferrara 2003)
12121212
Summary・ We estimate the line luminosities from the first-generation star formation
process. ・ the luminosities of both rovibrational lines and rotational lines become
maximum value at the main accretion phase. ・ For the runaway collapse phase, the strongest lines are rotational lines.
But for the main accretion phase , some rovibrational lines overwhelm them.
・ For the peak, rovibratinal lines are stronger than rotational lines.
rotational lines ----- low density region such as envelope of the protostellar cloudsrovibrational lines ----- high density region such as final stage of star formation processrovibrational lines the evidencethe evidence of the first-generation star formation
For observation of the first-generation star rovibrationalrovibrational lines are importantlines are important..
2H
・ Unfortunately, detecting line emission from forming first star by SPICA is highly improbable.
2H
13131313