“c2d” project of theory: towards construction of a new low-mass star formation scenario by...
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“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)+
1
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
2
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
2
Shu, Adams & Lizarno (1987)→MHD studies
Introduction: Classical to Modern picture.. ✦ Numerical (M)HD studies
revealed dynamical evolution in detail, beyond 1D Classical pictures
2
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
2
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
5
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)
3
✦ 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), ...
3
☆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))
3
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
12
*Barotropic relation *resistivity
Dynamical Evolution (Results of MHD sim.)
~105yrs after formation of the first core (almost end of main accretion phase)
5
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
8
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
8
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
8
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)
8
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
8
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
8
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
8
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...)
21
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
21
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)
21
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??
21
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
21
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
20
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.
8
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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