Physics of Primordial Star Formation · Physics of Primordial Star Formation Naoki Yoshida University of Tokyo ... Non-LTE cooling to LTE cooling “loitering”. Molecular frac-on

Physics of Primordial Star Formation

Naoki YoshidaUniversity of Tokyo

SFDE17 Bootcamp, Quy Nhon, August 6th�

1. The standard cosmological model 2. Growth of density fluctuations

3. Assembly of dark matter halos

So far, we learned

ELEMENTS NOW AND THEN

HUMAN BODY EARLY UNIVERSE

Helium

Hydrogen

OBSERVATIONS OF HII REGIONS

Weak dependence on metallicity (O abundance) indicating other source(s) than stars.

HELIUM PRODUCTIONIn cosmology text books, we learn (simply

read) that hydrogen and helium were produced by Big Bang during “the first three minutes”, without thinking why it is needed.

It was not so, historically. All the elements other than hydrogen were thought to be formed in stars.

But it quickly turned out it wouldn’t work....

HYDROGEN BURNING IN STARS

The$net$result$of$hydrogen$burning$is$the$fusion$$of$four$H$nuclei$into$one$4He$nucleus.$The$difference$in$binding$energy$is$26.731$MeV,$hence$~$7MeV$per$H.$(Not$all$this$energy$is$emiEed$as$photons$from$the$surface,$though.$Think$about$“Where$does$the$rest$go$?”)$

Galaxies are not He factoryOne can calculate light-to-helium production ratio as follows: Let’s take a galaxy with L ~ 1011 Lsun. Over a cosmological time of 10 Gyrs, it releases a total energy of ~ 7.5x1073 eV.

Its stellar mass would be ~ a few x1011 Msun. Then it contains ~ 2 x 1068 hydrogen nuclei.

This gives a mean energy output of 0.3 MeV per hydrogen nuclei. This is way too small compared with 7MeV per hydrogen burning.

Galaxies (stars) are luminous, but not as much as it should, in order to produce helium to ~ 25% in mass. There must be another He factory.

GALAXIES ARE NOT HELIUM FACTORIES

BBN PREDICTION

Helium abundance relatively insensitive to the baryon density. Lithium abundance is another, highly

interesting mystery.

In the beginning, there was a sea of light elements

and dark matter…

　　　　　　　　　　　　　　and tiny ripples left over 　　　　　　　　　　　　　　　　　from the Big Bang

1. What Observations Tell Us 2. Formation of Primordial Gas Clouds

3. Thermal Evolution of a Primordial Gas 4. From Big Bang Ripples to a Protostar

Contents

STAR FORMATION AT HIGH-z

WMAP

SURVIVING EARLY GENERATION STARS

Wavelength

Fe Fe Ca

Almost no iron!!

Num

ber o

f sta

rs

Iron abundance wrt sun There are stars in MW with very low metal content.

Progress since last century

metallicity

PrimordialStarForma-on:Theory

Starforma-onintheearlyuniverse

Cosmological recombination at t = 380Kyrs 　　　　　　　　　↓ Non-linear formation of dark matter clumps 　　　　　　　　　↓ Virialization → chemical reactions take place (hydrogen molecules are formed) 　　　　　　　　　↓ Gas condensation at the center of DM clumps 　　　　　　　　　↓ Runaway collapse of a massive molecular cloud = star-formation

• Collisional ionization, recombination

•  Formation of molecules (H2, HD, H3+, H2+, HD+, HeH)

•  Photoionization, photo-dissociation

•  Radiative cooling　collisional excitation, collisional ionization, recombination,　 Bbremsstrahlung, compton cooling, CMB heating

Primordialgaschemistry e, H, H+, H-, H2, H2

+, He, He+, He++ D, D+, D-, HD, HD+

~ 50-70 reactions

Composition: 76% H, 24% He、10-5 D、little Li

Chemicalreac-onsandrates

Above is just a partial list.

PRIMORDIAL GAS CLOUD

HHe

Gravity

Radiative cooling

H2 (0.01%)

Starsareformed…

in a cold, dense, molecular gas cloud. Gravity alone does not make it. Gravity actually compresses and heats the gas. We need a mechanism to cool a gas cloud. Radiative cooling removes the excess energy (i.e., lowers the gas pressure) and makes it possible for the gas to cool and condense. Radiative cooling operates only if there are coolants. How did all this happen in the early universe ?

Inthepresent-dayuniverse…

Interstellar gas can cool by, e.g., - Metallic ions such as Fe, Si, O - Molecules such as CO, OH - Dust thermal emission

None of these coolants existed in the early universe.

Primordialcoolingfunc-on

HHe+

H2 For the gas in a dark halo to cool, hydrogen molecules must be formed in some way.

Galaxies

Photo-a?achmentH2forma-on

H2Forma-on:Gasphasereac-ons

Slowreac-ons,relyingonresidualelectronsasacatalyst. Becomeeffec-veatT>1000K(M~105Msun)Molecularfrac-onreaches~0.001

Comological Recombination

Photo-a?achmentH2forma-on

H2Forma-on:Gasphasereac-ons

Slowreac-ons,relyingonresidualelectronsasacatalyst. Becomeeffec-veatT>1000K(M~105Msun)Molecularfrac-onreaches~0.001

Formation on dust grains

H2Forma-on:Present-day

This reaction is much faster than the gas-phase reactions.

Almost all the hydrogen atoms are converted to molecules at relatively low densities

if there are a sufficient amount of dust grains.

H + H on dust → H2 + dust

H2rota-onaltransi-on A hydrogen atom hits a H2 molecule in the ground-level (J=0). The H2 molecule got excited to J=2. After a while, it emits a photon spontaneously, to be back in the J=0.

H2coolingrate A hydrogen atom hits a H2 molecule in the ground-level (J=0). The H2 molecule got excited to J=2. After a while, it emits a photon spontaneously, to be back in the J=0.

H2cooling:Abriefhistory Late 60’s ) Pregalactic clouds, molecular hydrogen

Matsuda-Sato-Takeda, Yoneyama, Saslaw & Zipoy

Peebles & Dicke (globular cluster)

Early 80’s ) Primordial star formation, fragmentation

Palla-Stahler-Salpeter, Yoshii, Silk, Couchman & Rees (DM)

2000’s) Cosmological simulations, pre-collapse

Omukai-Nishi, Bromm+, Abel+, NY, Greif

2010’s) Protostellar evolution, final masses

Hosokawa, Hirano, …

PrimordialgascloudBromm, Coppi, Larson 2002

Physical properties of H2 molecules connected to thermal evolution. ΔE (J=2 → 0) ~ 512 K sets the minimum temperature. Non-LTE cooling to LTE cooling “loitering”.

Molecularfrac-onWhat you get must be more than what you need

what you need

what you get = asymptotic fraction

Hydrogen recombination

Formation of H2

Radiative cooling

Left-over electroms

H, H-

Electron depletion

H, e-

t_cool ~ t_hubble

+

Tegmark et al. (1997)

Temperature

CosmologicalFirstObjects

Computer simulation by Yoshida et al. (2003)

Web-like structure in the early universe. Halo mass ~ 1,000,000 Msun Gas clouds are ~ 1000 Msun. Strongly clustered.

Matter distribution

Tage = 300 million years

Resultfroma3Dcosmo.simula-on

Halos that host gas clouds are populated above the critical line, as predicted.

THERMAL EVOLUTION OF A PRIMORDIAL GAS

adiabatic contraction

H2 formation line cooling 　(non-LTE)

loitering (~LTE)

3-body reaction

Heat release

opaque to molecular

line

collision induced emission T [K]

104

103

102

opaque to continuum

adiabatic, high-P

dissociation

number density

Cooling rate from NLTE (~ density2) to LTE (~ density) Jeans mass ~ T1.5/n0.5

~ 500 Msun

Fromacloudtoaprotostar

0.3Mpc

5pc

0.01pc A new born proto-star with T* ~ 20,000K

r ~ 10 Rsun!

Self-gravitating cloud

Fully-molecular core

THERMAL EVOLUTION OF A PRE-STELLAR GAS

adiabatic contraction

H2 formation line cooling 　(non-LTE)

loitering (~LTE)

3-body reaction

Heat release

opaque to molecular

line

collision induced emission T [K]

104

103

102 number density

opaque to continuum

adiabatic, high-P

The Physics

dissociation

Ahydrogenmoleculecan

Rotate, and vibrate Emit and absorb photons Be formed, and destroyed Collide with other atoms

Radiative cooling (gas temperature↓）

Chemical cooling and heating (T ↓↑）

Interact with photons, cooling and heating

Quantum energy levels

At high densities, H2 molecules are formed by

H2 formation by 3-body reactions

•  The reaction rate ∝ density3. •  The core becomes almost fully molecular•  Significant heat release (4.48eV per molecule)

Rot-vibra-onaltransi-onsinLTEPar-clenumberdensity～1010/cc,

temperature～1000K

Thelevelpopula-on(energydistribu-on)

isLTEforJ=0-20,v=0-2

H2isahomo-nuclearmolecule;nodipoletransi-on

→quadropoletransi-on(ΔJ=2)

Radia-veTransfer1:molecularlines

Example)H2J=6→4transi-onatT~1000K

For τ >0.1, the cloud core becomes optically thick to H2 lines、and then line cooling is inefficient （τ4,6 ~1 for Lcore~0.0001pc）

1010-14

Netmolecularcoolingrate

CIE cooling

Omukai98 1D full RT

optic

ally

thic

k /

thin

3D calculation

8 10 12 14 16 log (n)

NY, Omukai, Hernquist, Abel (2006)

Λthick = Σ βescape nk,l A k,l hν

Structure of a disk: with/without radiative transfer

3D effect important in post-collapse simulations

3D transferco

olin

g ef

ficie

ncy

line continuum

Hirano & NY, 2013, ApJisotropic

density

CollisionInducedEmission

Duringcollisions,acollisionpairactsasa‘super-molecule’,genera-nganinducedelectricdipole.

hν

continuum emission

1014-17

Op-callythinCIEcoolingrate

η (ν) = σ nH2 exp(-hν/kT) 2hν3 c2

H2-H2 (Borysow et al. 2001) H2-He (Jorgensen et al 2000) @ n ~ 1013 - 1017

Equilibriumchemistry:theSahaequa-ons

A set of coupled equations including the energy equation are solved self-consistently:

H-H2

H-H+

>1016

Cooling/hea-ngprocesses

Chemical reaction

1000 light-years 　　 15 light-years　

0.1 astronomical unit 10 astronomical unit

A clump of dark matter Molecular gas cloud

Newborn proto-star Central core

PrimordialProtostarST

ATE

OF

THE

ART

C

OM

PUTE

R S

IMU

LATI

ON

S Yoshida, O

mukai, H

ernquist, 2008, Science