line emissionby the first star formation

Hiromi Mizusawa(Niigata University)Collaborators

Ryoichi Nishi (Niigata University)Kazuyuki Omukai (NAOJ)

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　　　　　 Formation of the First Generation of Galaxies December 2-5, 2003, Niigata University, Japan

Outline

PurposeModel : the method of calculation

Results : the evolution of T, y( ), luminosity

Detectability of the first stars by SPICA

Summary & Discussion

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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 accretion phase

we calculate them for both phase .

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2H

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runaway collapse phase

１

Model

The Larson-Penston-type similarity solution, γ ＝ 1.09 (dotted line),　　　　　　 reproduces Omukai&Nishi’ result (solid line) well. 　　　　　 a good approximation to the actual collapse dynamics.

center ---- flat density distribution, runaway collapseenvelope ---- leaving the outer part practically unchanged

The thermal and chemical evolution of gravitationally collapsing protostellar clouds is i

nvestigated by hydrodynamical calculations for spherically symmetric clouds. 　　 (Omukai&Nishi 1998)

The evolutionary sequences

yr104.1:76

yr102.4:65

0.32yr:54

12yr:43

yr102.8:32

yr108.7 :21

yr

2-

2-

2

3

5107.5:10

The time interval

２

)g/cm( 3

)cm(r

2.2 r

J~

①

②

③time

Contracting region and mass

become more and more small.

Free-fall determined by

the local density

３１． Dynamics・ The runaway collapse phase

The central evolution　　　　　 the free-fall relation 　　　　　 modified by pressure gradient

G

ttdt

d

32

3, ff

ff

β

the flat core size ;Jα

the collapse time scale ; fftβ

For the Larson-Penston-type 　　　　　　 similarity solution for γ=1.09,

13.2,33.1

,1

1,1

,78.0gravity

pressure

)g/cm( 3

)cm(r

2/3 r

①

②

③

Inner mass shells fall faster than outer mass shells.

Free-fall determined by the gravitational force of th

e protostar

４・ The main accretion phase

2/3

2

,

,)(

r

vdt

drr

rGM

dt

dv

r

r

： the density of free-falling mass shell

rv ： the velocity of free- falling mass shell

r： the distance from mass shell to the center

Approximation,

　 each mass shell free-fall

２． Energy equation

HH m

kTp

m

kTe

Ldt

dp

dt

de net

,1

1

1 )(

3. Cooling/Heating processes

： the energy per unit mass ，　 ： the pressure , ： the temperature ，： the adiabatic exponent ， ： the mean molecular weight ， : the mass of the hydrogen nucleus

e p T

Hm

： the cooling rate by line emission ，

： the net cooling rate by continuum emission,

： the net cooling rate by chemical reactionscontLlineL

chemL

chemcontline

net LLLL )(

５

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--- 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 ijCijC

i

j

),H( 2 in

ijA

ij

ijh

ijC

ij --- the optical depth averaged over the line

--- the escape probability

・ line cooling

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ij

ij

ije

1

６

)(

)(

),H(),H(

),H(1

22

2H2

jiC

jiCAR

RjnRin

hAinL

ij

ijijij

ij

ji

n

ij

n

ijij

ijijji

ij

eHHH

HeH

2

)cm10(~ 38

Hn

４． Chemical reactions （ formation processes)

（　　process)

（ three-body reactions ）22

2

2HH2H

HH3H

)cm10~cm10( 31438H

n

H

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・ continuum cooling/heating

bound-free absorption of ,

-H

2H collision induced absorption

Protostar ~ the black body of 6000 K (Omukai & Pala 2003) free-free absorption of ,-H

７

In our calculation, these continuum processes are hardly effective.

Initial Conditions

The physical condition of fragments (protopstellar clouds)

832

34 10)(,10)(),(200),(10 eHKcmH yyTn

The contraction and fragmentation of primordial, metal-free gas clouds is investigated by some authors .(e.g., Uehara et al. 1996; Nakamura & Umemura 2002 ;Abel et al. 2002; Bromm et al. 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).

８

MJ

310~M

Results

time

The runaway collapse phase

９

time

an order

Effective cooling by 2H

The time evolution of the central temperature

three body reactions

process -H

)H(y

)H( 2y

The time evolution of the central abundance of 2HH,

~ ten orders of magnitude

time time

Comparison between runaway collapse phase and main accretion phase

For the accretion phase, the evolutionary trajectories of the mass shells of are shown.

M20M5

M102

The main accretion phase

The runaway collapse phase

)H( 2y

)H(y

100,20,5/)( MrM

10

The evolution of line emission

red ： (1,1)→(0,1), green: (1,1)→(0,3), blue ： (0,6)→(0,4), purple ：(0,5)→(0,3)　　　　 2.34μm 　 , 　 　 2.69μm 　 , 　　　　 8.27μm 　 , 　　 　 10.03μm

Pick upPick up : four of the strongest lines

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rest frame :

１１

rovibrational lines

rotational lines

runaway collapse phase

main accretion phase

Peak luminosityPeak luminosityThe central The central protostarprotostar

M20~

The protostar formation

])(log[

))((

(cm)

(erg/s)ch

rd

rd L

(K)T

600

1000

1400

1800

20013 14 15 16 17 18 19

The sources of radiated energy

Compressional heating

formation heating

Until peak luminosity

At the same radius,)()( rTrT ac

)()( ,, rr achcch LL

Area indicates the chemical energy unit time,

(erg/s))( rch L

)()(

)()(

,,

,,

rr

rr

alinecline

achcch

LL

LL The final stage of collapse phase

Three selected time in accretion phase

M5

M20

M50

M20

M50

M52H

For mid-infrared region ( ), SPICA(ISAS), a large(3.5m),cooled(4.5K) telescope, is the best . (better than JWST and ALMA)

19zD)m/W(10~4

227

2

19

peak

z

peak

D

LF

peakL

μm40~

)μm(34.2:),1,0()1,1( framerest

)(8.46:)201 μm z(redshifted

:The luminosity distance to z=19

:The peak luminosity

The line detection limit of SPICA is about 　　　　 in 　　　　 .

more than 　 sources 　　　 　 SPICA can observe.6510

μm40~

13

)(10 21 2W/m

Limited by the high background of the zodiacal light 　　 (private communication H.Matsuhara).

Detectability

Summary & Discussion ・ 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. For the main accretion phase, 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 clouds rovibrational lines ----- high density region such as final stage of star formation processrovibrational lines the strong evidencethe strong evidence of the first-generation star formation

For observation of the first-generation star, rovibrational lines are importanrovibrational lines are importantt..

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@ high z,detecting line emission by SPICA is highly improbable.

@ low z, such as ,detecting it from Pop III stars by SPICA is maybe possible.

Formation of Galactic scaleGalactic scale with such low metallicitylow metallicity is maybe excluded in the context of standard cosmology (e.g., Scannapieco,Schneider,& Ferrara 2003).

Although, it is necessary to investigate how the mixing of metals occur.

IfIf sources @ , SPICA can observe forming first-generation stars.

6510 19~z

To emit mainly in lines,

the metallicity in the pregalactic clouds (Omukai 2000).

Z410~

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3~z

To exist sources is difficult situation at early universe.6510