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HMSF vs. LMSF

- Spatial Distinction
- LMSF region: Taurus
- GMCs: Orion
- “Intermediate”: Ophiuchus
- Higher Star Forming Efficiency for HMSF
- “Thermal” vs.“Turbulent” Cores
- Initial Conditions?
- Super vs. Sub Critical
- Evolutionary Paths?
- No pre-main-sequence for HMSF?

Di Li, NAIC & Cornell U

LMSF: standard model

- Four Stages
- Core: Virial equilibrium, Ambipolar diffusion
- Collapse: Inside-out
- Jets: Deuterium Burning, Stellar energetics start to take over
- Accretion Disk: the termination of infall will determine the final mass of the new star.
- Evidence
- Association between low mass cores and Young Stellar Objects (YSOs)
- Ammonia cores: 0.05pc, 10K, almost thermal support, sign of infall
- outflows and disks around YSOs, such as T Tauri stars

Di Li, NAIC & Cornell U

HMSF: Time Scale

- Different Time Scales/Paths
- Infall time scale:
- Kelvin-Helmholtz:

1 M: tKH~107 yr, M>5MtKH <tinf

no pre-main-sequence!

- Different Initial Conditions
- Massive cores could be supercriticalfragmentation?, cluster formation? Binary?

Di Li, NAIC & Cornell U

Observational Challenge

- Massive young stars are energetic.
- In Orion, a large region are dominated by OB clusters, e.g., filamentary morphology.
- Massive stars tend to be found in clusters
- Massive-Core identification, initial condition, association with HMSF, not clear.
- Smaller Population
- Greater Distances
- Other than Orion, Others identified by remote HII regions, e.g. NGC 3603 at 7 Kpc.
- Limited by angular resolution of mm instruments

Di Li, NAIC & Cornell U

Project Outline

- Identify resolvable by current radio, millimeter and submillimeter instruments:

Effelsberg, FCRAO, 12M, and CSO

- Multiple tracers to measure initial conditions, T, M, n, accurately
- Study energy balance and stability of massive cores
- Chemistry and Core Evolution
- Comparison with LMSF cores
- Future Work and Related Subjects

Di Li, NAIC & Cornell U

Quiescent cores chosen from CS 1-0 catalog (Tatematsu et al. 1993)

Why Orion:

the closest GMC at about 450 pc: 44” ~ 0.1pc

High Density Tracer Map Available (not for Ophiuchus!)

Why These Cores:

Far from BN/KL, at least 30 arcmin away

No IR association

Reasonable Size

Sources SelectionDi Li, NAIC & Cornell U

Ori2 -Ori15

Orion Molecular CloudsSakamoto et al. 1994; Lis et al. 1998; Wiseman & Ho 1998

Di Li, NAIC & Cornell U

Choices of Tracers

- Column density: C18O 1-0 / 2-1

Well known abundance

Less variation compared to rarer species

- Temperature: NH3 inversion lines (1,1)/(2,2)

no need for absolute calibration

especially fit for mid range temperature: 15K-35K

- Density: C18O 2-1/1-0 line ratio, CS 5-4/2-1

different critical densities

- Possible depletion: continuum & N2H+ 1-0

Di Li, NAIC & Cornell U

Observation: Time and Efforts

Di Li, NAIC & Cornell U

Kinetic Temperature

- Importance
- Determines excitation level, along with density
- Affect level population and the derivation of mass
- Affect dust temperature through gas dust coupling
- important factor in the derivation of dust mass
- Sound speed and mass accretion rate: heat up before star forming collapse?
- Judging the importance of turbulence
- Methods
- Thermalized line: CO
- Carbon chain molecules
- Ammonia (NH3) Inversions

Di Li, NAIC & Cornell U

Why Ammonia?

- Only Collisionally Coupled
- Population Concentrated in Metastable States
- Level Structure: at 20K, N(2,1)/N(1,1) ~7.6%
- A Coefficients(1,1) : 1.67x10-7 (2,2) : 2.23x10-7 (2,1) (1,1): 4.35x10-3
- Frequency Proximity Inversions
- (1,1) -- 23,694.495 MHz
- (2,2) -- 23,722.633 MHz

Di Li, NAIC & Cornell U

Derivation of Tk

- Optical Depths
- (1,1): from hyperfine lines
- (2,2): calculated
- Rotational Temperature

(1,1)/ (2,2) => N(1,1)/N(2,2)

- TR -> Tkin : Three level model or more sophisticated excitation models

Di Li, NAIC & Cornell U

Temperature Maps

Di Li, NAIC & Cornell U

Error Analysis

- Error propagation not feasible
- hyperfine fitting
- ratio of two optical depth
- excitation calculations in converting TR to Tk
- Monte Carlo Approach
- Treat the whole derivation as a black box
- Generate noise
- Central Limit Theorem

Di Li, NAIC & Cornell U

Noise Statistics

- 10, 000 runs-> Gaussian distribution for noise
- The spread is determined by S/N
- 5 sigma: 1.8 K
- 10 sigma: 0.9 K

Di Li, NAIC & Cornell U

Getting Serious about Coolness

- Student’s t Test
- Divide data into two sets by the 50% intensity contour:
- Center: 31 -> Mean -1.3 K
- edge: 54 -> Mean 0.76 K
- P(null) = 10-9

Di Li, NAIC & Cornell U

Spatial Correlation: Intensity and Tk

- 3D Correlation: no standard statistics
- Linear correlation test: Pearson’s r

Di Li, NAIC & Cornell U

Column Density

- Usual approximation: optically thin and no background
- Correction Factors

Di Li, NAIC & Cornell U

Column Density Maps

Di Li, NAIC & Cornell U

Finding Cores

- Fit by Gaussian
- 2D Gaussian
- Fit by eye
- if the edge not dropping to a really low level

Di Li, NAIC & Cornell U

Cores

Di Li, NAIC & Cornell U

Kinetic Energy and Gravity: mvir

- Virial Mass and Mass Ratio: gravitationally bond?
- Axis Ratio:

rule out pure oblate

models. Assuming prolate

cores in our calculations

Fall and Frenk 1983

Di Li, NAIC & Cornell U

Stability and Critical Mass

- Critical Mass
- assume B=100 G
- Use 13CO maps

for deriving pressure

confinement

Di Li, NAIC & Cornell U

Core Stability

Di Li, NAIC & Cornell U

Core Stability: Another Look

Stable on this scale!

- Gravitationally bounded
- Pressure confinement significant
- Sufficient internal turbulent support and stable
- Steady magnetic energy density provides insignificant support assuming B~100 G

Di Li, NAIC & Cornell U

A coupled problem

Localized Approximation:

Large Velocity Gradient method (Goldreich & Kwan 1974; Goldsmith, Young, & Langer 1983)

Semi-automatic algorithm

Self-iterating LVG

Inputs: X, n, dv/dr, T, cross-section-, A

outputs: TA,

Define a confidence indicator: Chi square

Minimization of Chi square

Downhill simplex method

Radiative Transfer

Excitation

Radiative Transfer: Chi Square approachDi Li, NAIC & Cornell U

Behaviors of Antenna Temperatures

- Contours of TA on a X-n plane=>
- Critical Density
- C18O 1-0 ~ 2x103 cm-3
- C18O 2-1 ~ 2x104 cm-3
- CS 2-1 ~ 2x105 cm-3
- CS 5-4 ~ 5x106 cm-3
- Only accurate around turning regions!

Di Li, NAIC & Cornell U

What do we learn from CS?

- Reasonable fits for ORI1
- Density upper limit for other cores

Di Li, NAIC & Cornell U

Density Gradients

- Theory
- Hydrostatic equilibrium: r-2for infinite isothermal sphere

and Bonnor-Ebert spheres

- Collapse: r-1.5

Singular isothermal solution by Shu (1977)

&

Uniform density sphere by

Larson (1969); Penston (1969)

- Observational Evidence
- CS 5-4 is more concentrated
- Discrepancy between N/r and n from LVG
- Column density profiles=>

Di Li, NAIC & Cornell U

Radiative Transfer With Density Structures

- Monte Carlo type radiative transfer codes

Ratran by Hogerhieijde & van der Tak (2000)

Spherical symmetrical code publicly available

- Consistent with LVG for a uniform sphere cloud model (test species HCO+)
- Elements of the cloud model for ORI1
- Inner core: r~0.05 pc & n~106 cm-3, Bonnor-Ebert sphere
- Outer envelope: r~0.5pc & n~ 105 cm-3, n drops as an isothermal sphere
- Temperature gradient incorporated (given by observations)

Di Li, NAIC & Cornell U

Comparison with ORI1 Data

- Density differentiation required in self-consistent cloud models
- ORI1 has an inner denser core embedded in the an extended envelope, sign of further evolution than cores south of the Orion Bar

Di Li, NAIC & Cornell U

Dust Emission: Promises and Problems

- Pro: No chemical abundance variation and mapping at higher resolution
- Con: Large uncertainty
- Emissivity
- Q
- Temperature
- M(T)dTT-3-/2

Di Li, NAIC & Cornell U

350 Micron Continuum

Di Li, NAIC & Cornell U

Gas to Dust Ratio

- Using gas temperature TdTk.
- Gas-dust coupling
- is good for n>2x105 cm-3 (Goldsmith 2001)
- Smooth to FCRAO resolution
- Derive GDR from N(C18O)/N(dust)
- Gradients in GDR!

GDR = 30

GDR = 20

GDR = 10

Di Li, NAIC & Cornell U

Depletion

- Standard GDR~100

Knapp & Kerr 1974; Scoville & Solomon 1975, and etc.

- Existing evidence of depletion
- CO isotopes: Gibb & Little 1998
- CS: Ohashi 1999
- Continuum and NH3: Willacy, Langer & Velusamy 1998

depletion factor ranges from 3 to 20

- Evidence for ORI1
- Smaller CS abundance
- Correlation between C18O, 350 m, NH3 and N2H+

Di Li, NAIC & Cornell U

Depletion (cont.)

- Accretion time scale
- ~ [109/n(H2)] yr (Goldsmith 2001)
- Chemical models predict a central hole for carbon bonded molecules at certain ages. Nitrogen bonded molecules have much longer depletion time scales.
- N2H+ depletes even later than NH3 (Aikawa et al. 2001).
- We obtain lower limits for the depletion factor of C18O
- ORI1: 10
- ORI2: 5
- The depletion gradients restrain the cloud chemical age to be within 105 to 106 yr

Di Li, NAIC & Cornell U

Summary

- A rare comprehensive millimeter and submillimeter data set of massive quiescent cores.
- Out of 15 selected targets, 7 well defined cores are identified:
- Mean mass 230 M
- Mean density: 5x104 cm-3
- Elongated cores: mean size ~ 0.3 pc and mean axis ratio ~ 0.6. Not purely oblate.
- Gravitationally bond and Stable, with both pressure confinement and internal turbulence playing significant roles
- Cooler than environment. Statistically significant temperature gradients with temperature dropping toward cloud centers.
- Evidence for depletion of CO and CS with depletion factor > 10
- Evidence for density gradients in ORI1

Not supercritical and no imminent collapse, at 0.1 pc spatial scale.

Di Li, NAIC & Cornell U

Ongoing and Future Work

- Higher resolution mapping of ORI1 and other cores

e.g. SHARC II; APEX; SMA

- Comparative study of cores in Ophiuchus
- Measuring magnetic field using HI narrow line absorption.

Di Li, NAIC & Cornell U

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