“c2d” project of theory: towards construction of a new low-mass

star formation scenario by numerical studies

“c2d” project of theory: towards construction of a new low-mass

star formation scenario by numerical studies

M. Yamada(ASIAA), M.N. Machida(Kyushu-U.), K. Tomisaka(NAOJ),Y. Aikawa(Kobe-U.), T. Hosokawa(JPL), K. Tomida(SOKENDAI), K. Saigo(NAOJ), Ya. Pavlyuchenkov(IARAS), D. Wiebe(IARAS)+

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CFD-MHD seminar May.2011

Introduction: Overview✦ Low-mass (~1Msun) star formation studies - great progresses in

the past decade

1)(M)HD modeling: covers a wide dynamic range required to star formation(e.g., 105~1022 cm-3)

2)high-resolution obs. - radio, IR, optical...

3)detailed matter evolution studies - chemistry, dust...✦ ... but still far from complete

1) many physical processes are involved in a non-linear manner

1) almost impossible to incorporate all the relevant processes (limitation of computational resources

2) subgroups - subsubgroups... N(groups)∝exp(N) :p→sometimes mutually inconsistent assumptions and scenarios

✦ matter (theory) - radiation (obs) relation is complicated (“Telescope of Theory”)→synthetic observation experiments just working

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What is the status? Integrated Model is needed for comprehensive understanding!

What is the status? Integrated Model is needed for comprehensive understanding!

Introduction: Classical picture ✦ Classical pictures - based on

theories of grav. collapse of a dense core & observations of YSOs

1)age of class 0/1~105 years (statistical studies) - need to know (at least) modeling over 105 years from the onset of core collapse

2)how kinds of forces (grav. magnetic, radiative) work in 3D?

3)possible missing process - early embedded stage

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Shu, Adams & Lizarno (1987)→MHD studies

Introduction: Classical to Modern picture.. ✦ Numerical (M)HD studies

revealed dynamical evolution in detail, beyond 1D Classical pictures

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Shu, Adams & Lizarno (1987)

Masunaga & Inutsuka (2000)

Tomisaka (2002)Machida, Inutsuka & Matsumoto (2008)

Introduction: Observation-based Picture

✦ High angular resolution obs: protostar, disk, envelope structure

✦ High frequency res. obs: “chemical clock”, organic molecules, dust (crystalized/amorphous)...

✦ Recent R(M)HD studies→radiation force is important even in low mass star formation

✦ B-field and matter coupling: depends on gas status (ionization deg. ...)⇒Matter evolution and ⇒Matter evolution and dynamics should be coupleddynamics should be coupled

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However,

Belloche et al.2002

Introduction: contents

✦ compile (M)HD, chemical, radiative studies from a dense molecular core to circumstellar disk formation (“c2d”) to a model with minimum arbitrary assumptions

✦ onset of gravitational collapse of a core to end of main acc. phase

prestellar core protostar+diskmain sequence

protostar heats up the center* “hot-core” chemistry*destruction/reformation of dust

blow away the envelope & formation of circumstellar/protoplanetary disk

grav. collapse and angular momentum transfer by outflows

protostellar core

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I. Dynamical EvolutionI. Dynamical Evolution

Dynamical Evolution (Overview)✦ Forces at work in low-mass molecular core

✦ Egrav~Emag>Eth>>Erad (⇔ Egrav~Erad~Eth>>Emag: massive star formation)✦ so many MHD simulations, with simplified EOS

✦ thermal, chemical & radiative processes determine the dynamical evolution (e.g., Masunaga & Inutsuka, 1998, 2000)

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✦ Which kind of modeling should we take?✦ recently some groups have shown that radiative force is not negligible (Offner et al.2008, Tomida et al. 2009)

✦ However, RHD modeling has still numbers of assumptions and simplifications

✦ Frad = (Frad(x), Frad(y), Frad(z), ν, Ω, θ[propagating direction of rays])6 additional variables

✦ gray app., FLD(flux limited diffusion), ...

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☆our goal: establishment of a

evolution picture from core to disk

⇒ long term calculation necessary

◎barotropic relation adopted

☆our goal: establishment of a

evolution picture from core to disk

⇒ long term calculation necessary

◎barotropic relation adopted

Offner et al. (2008)

Dynamical Modeling

Barotropic Relation v.s. R(M)HD✦ Barotropic relation - a relation law of pressure and density (P=P(ρ))

✦ (in Machida’s simulations) adopted 1D RHD results of Masunaga & Inutsuka (2000)the barotropic relation at the center is applied to the whole system

✦ no additional heating or cooling by dissipation -- entropy is conserved -> entropy generated at the accretion shock at the surface of the first core (and so on)cannot be included

✦ fluid elements with different initial radius have different shock speed -> have different entropy increases

3Tomida et al. (2010a)

(until the formation of first core++)*gas temperature becomes higher above/below the first core, because of infall of fluid elements with larger radius* dynamically not very important, but changes emission in the radio band drastically

(until the formation of first core++)*gas temperature becomes higher above/below the first core, because of infall of fluid elements with larger radius* dynamically not very important, but changes emission in the radio band drastically

Barotropic Relation v.s. R(M)HD✦ Barotropic relation - a relation law of pressure and density (P=P(ρ))

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Tomida et al. (2010a)t=3e4 yrs

☆one model needs months of CPU time - future☆barotropic relation enables a long term calculation ☆one model needs months of CPU time - future☆barotropic relation enables a long term calculation

✦ resistive MHD equations

✦ resistivity: taken from Nakano et al.(2002)

✦ barotropic relations: adopted 1D results of Masunaga & Inutsuka(2000)

✦ initial conditions: Mcore= 0.5Msun, Rcore=2745AU, T=10K, nc = 3x106 cm-3

B0 = 5.6x10-5 G, Ω0=2.35x10-13 s-1

✦ nested grid simulations: 64*64*32 cells/grid, lmax=9, Grid generation: resolving Jeans wavelength

Basic Equations Bonnor-Ebert Sphere

Rotation Axis

Magneti

c Fi

eld

Lin

e

Ω

B

1300 AU

L=4

Basic Equation (cont.)

ohmic dissipation phaseohmic dissipation phase

Machida et al.2006+

decoupleddecoupled

coupled

coupled

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*Barotropic relation *resistivity

Dynamical Evolution (Results of MHD sim.)

~105yrs after formation of the first core (almost end of main accretion phase)

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II. Feedback from the Formed ProtostarII. Feedback from the Formed Protostar

Radiation Feedback to Dust Temperature✦ Radiation emitted by the formed protostar

heats up dust grains

✦ affects dynamics/chemistry/opacity (radiative force)

✦ low-mass core - dynamical effects are unlikely to be important (should be confirmed in future)

✦ T>1000K: dust grains melt down

✦ T>100K: molecules in the mantle of dust grains evaporate-> “hot core chemistry”

✦ How to include these feedbacks

✦ calculate accretion rate (dM/dt) from MHD simulation

✦ solve (quasi-static) evolution of protostar with thus obtained dM/dt & M*

θ=60

Evolution of a Protostar

θ=60

Hosokawa & Omukai (2009)

✦ 1D RHD simulation, solved quasi-equil. evolution with a constant acc. rate

✦ In our modeling, dM/dt & Mproto are taken from MHD simulation

Radiative Feedback to Tdust

θ=60

✦ Basic Equation: radiative transfer & energy balance equations

✦ We solved equilibrium temperature for each snap shot of MHD simulations

✦ radiative transfer -- basically the same algorithm of line transfer simulation code

✦ hybrid code of Monte-Carlo and Ray-tracing

✦ 2D code - xz-slices of MHD resultsare adopted (later results were assigned to 3D cartesian grid)

✦ opacity - extension of Ossenkopf & Henning(1994) (dust grains with thin ice mantle)

Hogerheijde&van der Tak(2000)

Radiative Feedback to Tdust (results)

θ=60

✦ Feedback from the central protostar makes warm (T up to ~80K) region

barotropic w/ feedbackdensity, 5x103yrs

barotorpicw/feedback

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III. ChemistryIII. Chemistry

Formation of Major Molecules ✦ Dust is the key

✦ “mother” molecules evaporate from the dust grain mantle

✦ gas-phase chemical reactions starting from “mother molecules” form “daughter” moleculese.g., CO, HCO+,H2CO, H2O, methanol....

✦ sublimation temperatures for these mother molecules: ~100 K

⇒ T>Tsub: hot core chemistry T<Tsub: many molecules frozen

✦ Time-dependent chemical models: a drastic change in abundance at t~104-105 yrs

n[cm-3]

J=1-0 J=2-1 J=3-2

J=4-3 J=5-4

J=8-7

J=6-5

J=9-8

Nomura et al.(2009)

time(yr)

Chemistry Modeling ✦ Equil. v.s. non-Equil.

✦ non-equil. calculation: a drastic change in abundance at t~104-105 yrs

✦ dynamical time 10≦ 4-105 yrs

✦ On the other hand, observation results supports a simple modeling (“jump model”)

n[cm-3]

J=1-0 J=2-1

J=4-3 J=5-4

J=8-7

J=6-5

J=9-8

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tchem~tdyn: non-equil. modeling along with MHD is

necessary!(nightmare in 3D

modeling...)

tchem~tdyn: non-equil. modeling along with MHD is

necessary!(nightmare in 3D

modeling...)

T<Tsub: obs. of molecular cloudsT>Tsub: obs. of hot core and/or ice

T

abundance

T_sub

Yamamoto et al.(1983)

Tsub

log(n)

Chemistry Modeling (cont.) ✦ We adopted a simplest version of “jump model”

✦ jump model: hot core chemistry in gas phase with initial condition described with step function a(T)

✦ in several obs. of low-mass protostellar cores, a simple step function can reproduce abundance pattern

n[cm-3]

J=2-1

J=4-3 J=5-4

J=8-7

J=6-5

J=9-8

9Schoier et al.(2002)

IRAS 16293-2422

Chemistry Modeling (cont.) ✦ We adopted simplest version of “jump model”

✦ abundance data were taken from obs. of a low-mass protostellar core

IRAS 16293-2422 (Schoier et al. 2002) with Tsub=90 K (fixed).

✦ MHD model has high density-> Tdust=Tgas well applies (except for the most evolved snapshot, where envelope density drops as low as 104 cm-3)

✦ ..at this moment, feedback from the protostar (up to ~0.1 Msun) does not heat up the dust significantly above Tsub

J=2-1

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1) calculate L* and T*, using dM/dt & M*

obtained in MHD calc.

2) calculate Tdust irradiated with protostar

of L*

3) replace Tgas with Tdust

(heated)

4) assign abundance using step

function of Tgas (jump@Tsub)

☆procedures of construction of abundance distribution

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IV. Synthetic ObservationIV. Synthetic Observation

✦ “Observational Visualization” (K. Tomisaka) ⇒”Numerical Astronomy” (MY)

✦ Hydrodynamic simulations + Radiative Transfer -> pseudo obs. tool✦ hydro. (theoretical models) : ρ(x), T(x), v(x), ymol(x) ....

✦ real observation : Iν(θ) ✦ currently we do not pay much attention to TA⇔Tb, or responseof obs. instruments...

simulation(Wada&Tomisaka2005)

obs.(Kohno et al.)

radiation transfer

RT simulation

Members:(phase1)K. Tomisaka, K.Wada, K. Omukai, K.Saigo, MY.+..

RT Simulation Project @ NAOJ+ASIAA

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Physics of ISM/SF: lines as a toolbox

✦ interpreting data sets of Iν in terms of Tkin, n, y(=nmol/nH), v is not straightforward

✦ line RT can form a toolbox to decipher tangled “riddles” printed in observed line data cube

obs.: data cube(x, y, ν)ISM: Tkin(x, y, z)n(x, y, z)

v=(vx, vy, vz)ymol(x, y, z)..

τν, Tex

My dear Watson, circumstance evidence is a very tricky thing... and there is nothing more deceptive than an “obvious fact”. 3

Non-LTE Line Transfer: basic equations✦ rate eq.: non-LTE in S.E.

✦ Bij (stimulated emission) & Cij (collisional transition)→dependent of Tkin & n [non-LTE]

✦ Radiative transfer eq. [ray tracing with long characteristics method]✦ integrate RT eq. along sampling rays for each grid

✦ average Iν over all sampling rays

Hogerheijde&van der Tak(2000)

out flowing rate from level i = incoming rate into level i

: absorption coeff.

ni & Iνij are solved iteratively until solution converges

: emission coeff.

4

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V. “First Light” ResultsV. “First Light” Results

Dynamical Evolution

✦ as time goes on, outflows driven near the first core appears, and it blows away the infall envelope at ~105yrs

✦ Protostellar feedback generates warm region at the center (Tdust=Tgas<100K)

t=1x103 yrs

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t=5x103 yrs t=1x105 yrs

den

sity

Tdu

st(=

Tgas)

Radiative Feedback from the Protostar

✦ Protostellar feedback warms up the central ~100 AU

✦ Barotropic relation: includes compressional heating implicitly...

⇒ Tgas = max(Tdust[processed], Tgas[bartoropic])

✦ radiation hydro. simulation is necessary for a full-consistent model

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t=1x103 yrs t=5x103 yrs t=1x105 yrs

barotorpicw/feedback

Synthetic Observation: mol. lines

✦ Rapid evolution from 103-5x103 years, though outflows are still embedded in the envelope

✦ 105 years snapshot shows outflow familiar with observers

t=1x103, 5x103, 1x105 years; 13CO(2-1), θ=60deg

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Synthetic Observation: mol. lines

✦ In early stages, inclination angle does not affect the morphology (deeply embedded in a spherical envelope

✦ at t~105 yrs, a geometrically thin disk & outflow cavity will work to determine θ 8

t=1x103 years; 13CO(2-1)

t=1x105 years; 13CO(2-1)

θ=30deg θ=60deg θ=90deg

Synthetic Observation: mol. lines (cont.)

✦ Compact rotating outflow components are seen in velocity first moment map

✦ geometrically thick pseudo-disk around the first core is very weakly shown(pseudo-disk is thermal pressure-supported)

t=1x103 years; 13CO(2-1)

outflow axis

θ=30deg θ=60deg θ=90deg

Synthetic Observation: mol. lines (cont.)

✦ Compact rotating outflow components are seen in velocity first moment map

✦ geometrically thick pseudo-disk around the first core is very weakly shown(pseudo-disk is thermal pressure-supported)

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t=5x103 years; 13CO(2-1)

outflow axis

still tentative - might be a possible rot. supported disk as well?

θ=30deg θ=60deg θ=90deg

Synthetic Observation: mol. lines (cont.)

✦ Compact rotation supported disk components are seen in velocity first moment map (⇒PV diagram)

✦ geometrically thick pseudo-disk around the first core almost disappear, as outflow blow away the surrounding matter

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t=1x105 years; 13CO(2-1)

outflow axis

θ=30deg θ=60deg θ=90deg

Synthetic Observation: mol. lines (cont.)

✦ Position-velocity diagram of 105 yrs snapshot shows a typical pattern of Kepler-rotating thin disk

✦ similar features appear in earlier snapshots, but very weak and concentrated in a small region (unlikely to be seen in existing telescopes)

θ=30 deg. C18O(J=2-1), t=105yrs

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v los[

km

/s]

distance along the cut outflow axis

Synthetic Observation: mol. lines (cont.)

✦ obs: Class I object w/ SMA, signatures of rotationally-supported disk detected

✦ simulation - similar pattern appears at ~1000 AU@center

θ=30 deg. C18O(J=2-1), t=105yrs

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Yen et al. (in prep.)

vlos[km/s]

dista

nce

alo

ng

the c

ut

13CO(2-1), t=103yrs

13CO(2-1), t=103yrs

✦ At around t~103 yrs, inclination angle does not change the result(embedded in spherically infalling envelope)

outflow axis

Synthetic Observation: mol. lines (cont.)incl=30deg

incl=60deg

incl=90deg (edge-on)

13CO(2-1), t=105yrs

13CO(2-1), t=105yrs

✦ At t~105 yrs, (spherical) envelope is blown away by the outflows, so that inclination angle drastically change the emission morphology⇒ easier to identify each component (disk, outflow...)

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outflow axis

Synthetic Observation: mol. lines (cont.)incl=30deg

incl=60deg

incl=90deg (edge-on)

HCO+(4-3), 90deg, t=105yrs

HCO+(4-3), 90deg, t=105yrs

✦ high critical density (~106 cm-

3) line show disk rotation clearly

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outflow axis

Synthetic Observation: mol. lines (cont.)

12CO(2-1), 90deg, t=105yrs

12CO(2-1), 90deg, t=105yrs

✦ low critical density (~102-3 cm-3) line show rotating outflow and low density (relic) envelope

✦ cavity like structure of rotating outflow at |vlos|>1km/sec(disk/envelope component vanishes at this velocity range)

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outflow axis

Synthetic Observation: mol. lines (cont.)

13CO(3-2), 0deg, t=105yrs

13CO(3-2), 0deg, t=105yrs

✦ high transition line of CO (and its isotope) can probe disk fragmentation??

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outflow axis

Synthetic Observation: mol. lines (cont.)

12CO(3-2), 60deg, t=105yrs

12CO(3-2), 60deg, t=105yrs

✦ very messy....

✦ further analysis is necessary

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outflow axis

Synthetic Observation: mol. lines (cont.)

Synthetic Observation for ALMA✦ line transfer simulation of YSO outflow

✦ rotation of magnetocentrifugal-force driven flow appears in velocity channel maps

2000AU

Yamada, Machida, Inutsuka & Tomisaka, 2009outflow axis

SiO(7-6), 30deg

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Synthetic Observation for ALMAmodelmodel ALMAALMA

Y.Kurono & MY, private comm.

✦ diffuse component from the geometrically thick protostellar disk: the total power array is inevitably necessary in ALMA obs.

✦ exposure time: ~14 hours for SiO(7-6) @0.1”, 0.3K sensitivity w/ALMA

@140pc, dec=-30

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outflow axis

Misc.

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CPU time comment

MHD (machida)~1

months/1.6TFlops*even for low-

res(64^3) calc.

protostellar evol (hosokawa)

~ 1 week(?)

protostellar feedback (MY, pavlyuchenkov)

~1 months/snapshot

*diffusion approx.?

chemistry(MY, aikawa, wiebe)

10min.*non-eq. model requires a lot

more

mol. line transfer(MY)

~1day/snapshot/~1TFlops

64-128 cores

imaging simulation

20min.-a few days

VERY expensive, but (I believe) it deserves its cost.

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