“Telescope of Theory”: Radiative Transfer Studies of a Young Star Forming Object M. Yamada(ASIAA) 、 M.N. Machida(NAOJ) 、 S. Inutsuka(Nagoya-U.), K. Tomisaka 、 Y. Kurono(NAOJ) I) young embedded outflow II)magnetic flux problem - morphology variance by diffusivity III) synthetic-observation towards ALMA era IV)LTR project - gallery 1
Introduction: Early Stage of Star Formation ✦ Unresolved problems in (low-mass) Star Formation: 1) angular-momentum problem J core >>J * ⇒ outflow launching that transfers J away 2) magnetic flux problem Φ core >> Φ * : how/when “extra” Φ B decreases by a factor of 10 4 -10 5 ? 3) ... and so on ✦ Low-mass star formation site: center of the parent molecular core observational study of earliest stages of star formation is necessary ✦ evolution time scale~free fall time: rapid evolution at the central region ( ρ ∝ r -2 ) ✦ ⇒ need to probe the emission embedded in an infalling envelope ✦ 3D MHD model + line transfer simulation Which line is the plausible tracer? How ALMA can reveal these problems realistically? 2
Introduction: Early Stage of Star Formation ✦ Unresolved problems in (low-mass) Star Formation: 1) angular-momentum problem J core >>J * ⇒ outflow launching that transfers J away 2) magnetic flux problem Φ core >> Φ * : how/when “extra” Φ B decreases by a factor of 10 4 -10 5 ? 3) ... and so on ✦ Low-mass star formation site: center of the parent molecular core observational study of earliest stages of star formation is necessary ✦ evolution time scale~free fall time: rapid evolution at the central region ( ρ ∝ r -2 ) ✦ ⇒ need to probe the emission embedded in an infalling envelope ✦ 3D MHD model + line transfer simulation Which line is the plausible tracer? How ALMA can reveal these problems realistically? 2
0. Physics of ISM/SF: lines as a toolbox obs.: data cube(x, y, ν ) ISM: T kin (x, y, z) n(x, y, z) v=(v x , v y , v z ) τ ν , T ex y mol (x, y, z).. interpreting data sets of I ν in terms ✦ of T kin , n, y(=n mol /n H ), v is not straightforward line RT can form a toolbox to ✦ decipher tangled “riddles” printed in observed line data cube My dear Watson, circumstance evidence is a very tricky thing... and there is nothing more deceptive than an 3 “obvious fact”.
0. Non-LTE Line Transfer: basic equations ✦ rate eq.: non-LTE in S.E. � � ∞ � � ∞ � � � � 1 1 � � n i A ij + B ij I ν d ν d Ω + C ij n j A ji + n j B ji I ν d ν d Ω + n j C ji = 4 π 4 π 0 0 j j out flowing rate from level i = incoming rate into level i B ij (stimulated emission) & C ij (collisional transition) ✦ → dependent on T kin & n [non-LTE] � � n X γ ij ≈ n X � σ ij v � C ij = X X n i & I ν ij are solved iteratively until solution converges ✦ Radiative transfer eq. [ray tracing with long characteristics method] integrate RT eq. along sampling rays for each grid ✦ dI ν ds = − α ν I ν + j ν j ν = h ν 0 4 π n i A ij φ ( ν ) : emission coeff. � � α ν = h ν 1 − g 1 n 2 φ ( ν ) : absorption coeff. 4 π g 2 n 1 average I ν over all sampling rays ✦ 1 ¯ � 4 J = I ν N ray Hogerheijde&van der Tak(2000)
I. Young Embedded Outflow Belloche et al.2002 5
Basic Picture of Low-mass Star Formation 1D Radiative Hydrodynamics Larson (1969) Protostar Tohline (1982) Masunaga & Inutsuka (2000) Log T (K) Adiabatic Phase Second Collapse & Isothermal Phase Protostellar Phases To MS 10 4 Dead region B amplification B amplification B dissipation (10 12 cm -3 <n<10 15 cm -3 ) protostar (second core) 10 3 H 2 dissociation B B B (endoergic reaction) Molecular Cloud Core 10 2 Adiabatic core (First core) Formation 10 Gas Temperature Log n (cm -3 ) 10 5 10 10 10 15 10 20 6 Spatial Scale (AU) 10 4 100 1 0.1
Calculations ✦ Magneto-Hydrodynamic simulations: 3D nested grid, ideal MHD ✦ initial condition : rotating Bonnor-Ebert sphere ✦ (M=0.6Mo, R=2000AU, T kin =10K) EOS: taken from 1D radiation hydro. simulation ✦ (Masunaga & Inutsuka, 2000) + some modification long evolution, and large spatial extent ✦ stop calculations shortly after the first core ✦ 2000AU formation ✦ Radiative Transfer: [ray tracing with long characteristics method] non-LTE level population up to J=16 for each grid ✦ assume uniform chemical abundance distribution ✦ abs. coeffs. profile: ✦ purely thermal velocity, no micro-turbulence 12 CO CS SiO n crit ~10 2 [1/cc] ~10 5 [1/cc] ~10 5 [1/cc] 7 E 10 5.5K 2.35K 2.08K Hogerheijde&van der Tak(2000)
Hydro. data (snapshot) density distribution 1000 1000 11.5 11.5 10.5 10.5 500 500 log 10 (n[cm -3 ]) log 10 (n[cm -3 ]) 9.57 9.57 z[AU] z[AU] 0 0 8.63 8.63 7.69 7.69 -500 -500 6.75 6.75 -1000 protostellar disk -1000 5.81 5.81 -1000 -500 0 500 1000 first core (R~50AU, M~0.01Mo) -1000 -500 0 500 1000 x[AU] x[AU] ✦ we used a snap shot at very young protostellar object (YPO: t~4,000yrs) that shows: bipolar outflow (~1.7 km s -1 ) launched in the vicinity of the first core [magneto- ✦ centrifugal force-driven flow by twisted B by rotation] rotation & magnetic field -> a geometrically thick disk-like structure (“protostellar ✦ disk”)
Column density: dust continuum dust continuum: provides higher angular resolution obs. than lines? NO! ✦ � β � 0 . 25[mm] κ ν = 0 . 1 × T b = B ν (1 − exp( − τ ν )) λ 1000 1000 1000 θ =0(pole-on) θ =30 (a) 150GHz (b) 220GHz (c) 350GHz 500 500 500 y[AU] y[AU] y[AU] 0 0 0 -500 -500 -500 -1000 -1000 -1000 -1000 -500 0 500 1000 -1000 -500 0 500 1000 -1000 -500 0 500 1000 θ =30 x[AU] x[AU] x[AU] θ =60 θ =90(edge-on) 6.00e-02 1000 1000 T d =10K~T gas (d) 650GHz (e) 850GHz 5.00e-02 500 500 4.00e-02 T b [K] ✴ high column density at y[AU] y[AU] 0 0 3.00e-02 disk - difficult to look 2.00e-02 further inside -500 -500 1.00e-02 ✴ emission from outflow -1000 -1000 0.00e+00 component is quite weak -1000 -500 0 500 1000 -1000 -500 0 500 1000 x[AU] x[AU]
Non-LTE results: integrated intensity integrated intensity: full & blue/red almost symmetric ✦ distribution of red/blue components θ =0, 30, 60, 90 deg. [SiO(J=7-6) E 7 =58K], barotropic 1000 1000 θ =0 θ =30 in outflow & disk: red and ✦ blue contours show separate 500 500 peaks outflow not in perfect symmetry ✦ 0 0 z z in red/blue contours due to optical thickness & -500 -500 velocity structure effects 2,000AU envelope -1000 -1000 θ =30, 60deg.: almost circular ✦ -1000 -500 0 500 1000 -1000 -500 0 500 1000 envelope at the outer part x x ⇔ infalling motion of envelope toward the center θ =60 θ =90 1000 1000 Δθ (10AU)=0.07” if D=140pc ✦ 500 500 0 0 z z ALMA can resolve these structures -500 -500 (..and SMA as well?) -1000 -1000 8 -1000 -500 0 500 1000 -1000 -500 0 500 1000 x x
Excitation Temperature: CO adopt “standard” mol. ✦ 12 abundance y=3x10 -4 10 8 n crit (1-0)~10 2 cm -3 , n crit ∝ J 3 ✦ 6 4 J=1-0 J=2-1 J=3-2 J=1-0 J=2-1 J=3-2 huge optical thickness ( τ 0 up ✦ 1-0 2-1 3-2 2 to 4,000) and high density 0 12 (10 6 cm -3 < n < 10 11 cm -3 ) in the T ex [K] T ex [K] 10 simulation box, pop. energy 8 distribution becomes LTE 6 even at high J (J=10-9) J=4-3 J=5-4 J=6-5 4 (T ex = T kin ~10K) J=4-3 J=5-4 J=6-5 4-3 5-4 6-5 2 0 12 coll. excitation 10 dominant: 8 J=7-6 J=8-7 J=9-8 6 CO, 13 CO, C 18 O are not 4 good tracers J=7-6 J=8-7 J=9-8 7-6 8-7 9-8 n[cm -3 ] 2 0 9 10 6 10 7 10 8 10 9 10 10 10 6 10 7 10 8 10 9 10 10 10 6 10 7 10 8 10 9 10 10 10 11 10 11 10 11 n[cm -3 ]
Integrated intensity: CO θ =30deg, contours: I[K km s -1 ] J=1-0 (b) 13 CO (c) C 18 O (a) 12 CO 4000 4000 4000 2000 2000 2000 z[AU] z[AU] z[AU] 0 0 0 -2000 -2000 -2000 -4000 -4000 -4000 -4000 -2000 0 2000 4000 -4000 -2000 0 2000 4000 -4000 -2000 0 2000 4000 x[AU] x[AU] x[AU] huge optical thickness ⇒ the locations of photospheres are almost the same as the ✦ initial Bonnor-Ebert sphere CO and its isotopologue lines are useless for a probe of very young protostellar object qualitative characteristics are quite independent on viewing angle θ ✦
Excitation Temperature: SiO adopt “standard” mol. ✦ 12 abundance y=2x10 -8 10 8 n crit (1-0)~10 5 cm -3 ✦ 6 ⇔ 10 6 cm -3 < n < 10 11 cm -3 4 J=1-0 J=2-1 J=3-2 1-0 2-1 3-2 2 low-J and in dense regime (n ✦ 0 T ex [K] 12 > 10 8 cm -3 ), pop. is LTE 10 high-J and in tenuous regime T ex [K] ✦ 8 6 (n < 10 8 cm -3 ), T ex decreases to 4 ~ 5K J=4-3 J=5-4 J=6-5 4-3 5-4 6-5 2 ⇒ non-LTE effects can be 0 observed 12 ( ⇔ 12 CO, 13 CO, C 18 O) 10 8 6 4 J=7-6 J=8-7 J=9-8 7-6 8-7 9-8 2 n[cm -3 ] 0 10 6 10 7 10 8 10 9 10 10 10 6 10 7 10 8 10 9 10 10 10 6 10 7 10 8 10 9 10 10 10 10 11 10 11 10 11 n[cm -3 ] n[cm -3 ]
Recommend
More recommend
