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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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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..

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・ Unfortunately, detecting line emission from forming first star by SPICA is highly improbable.

2H

１３１３１３１３