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2MASS Image of the Orion Nebula. Massive Cores in Orion. Di Li NAIC, Cornell University February, 2002. HMSF vs. LMSF. Spatial Distinction LMSF region: Taurus GMCs: Orion “Intermediate”: Ophiuchus Higher Star Forming Efficiency for HMSF “Thermal” vs.“Turbulent” Cores

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2MASS Image

of the Orion Nebula

Di Li, NAIC & Cornell U

massive cores in orion

Massive Cores in Orion

Di Li

NAIC, Cornell University

February, 2002

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

1 M: tKH~107 yr, M>5MtKH <tinf

no pre-main-sequence!

  • Different Initial Conditions
    • Massive cores could be supercriticalfragmentation?, cluster formation? Binary?

Di Li, NAIC & Cornell U

observational challenge
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
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

sources selection
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 Selection

Di Li, NAIC & Cornell U

orion molecular clouds


Ori2 -Ori15

Orion Molecular Clouds

Sakamoto et al. 1994; Lis et al. 1998; Wiseman & Ho 1998

Di Li, NAIC & Cornell U

choices of tracers
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
Observation: Time and Efforts

Di Li, NAIC & Cornell U

kinetic temperature
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
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 t k
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
Temperature Maps

Di Li, NAIC & Cornell U

error analysis
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
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
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 t k
Spatial Correlation: Intensity and Tk
  • 3D Correlation: no standard statistics
  • Linear correlation test: Pearson’s r

Di Li, NAIC & Cornell U

spatial correlation r p
Spatial Correlation: R & p

r ~ -0.6

p(null)~ 0.01

Credible anti-correlation

Di Li, NAIC & Cornell U

column density
Column Density
  • Usual approximation: optically thin and no background
  • Correction Factors

Di Li, NAIC & Cornell U

lvg analysis of correction factors
LVG analysis of Correction Factors

Recipe for N(C18O)

Di Li, NAIC & Cornell U

column density maps
Column Density Maps

Di Li, NAIC & Cornell U

finding cores
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


Di Li, NAIC & Cornell U

virial equilibrium
Virial Equilibrium
  • The Virial Theorem

Steady state:

Di Li, NAIC & Cornell U

kinetic energy and gravity m vir
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
Stability and Critical Mass
  • Critical Mass
    • assume B=100 G
    • Use 13CO maps

for deriving pressure


Di Li, NAIC & Cornell U

core stability
Core Stability

Di Li, NAIC & Cornell U

core stability another look
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

radiative transfer chi square approach
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


Radiative Transfer: Chi Square approach

Di Li, NAIC & Cornell U

density and abundance
Density and Abundance
  • Solutions for ORI2, typical of cores other than ORI1

Di Li, NAIC & Cornell U

density and abundance1
Density and Abundance
  • Solutions for ORI1

Di Li, NAIC & Cornell U

behaviors of antenna temperatures
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
What do we learn from CS?
  • Reasonable fits for ORI1
  • Density upper limit for other cores

Di Li, NAIC & Cornell U

density gradients
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
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
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
Dust Emission: Promises and Problems
  • Pro: No chemical abundance variation and mapping at higher resolution
  • Con: Large uncertainty
    • Emissivity
      • Q
    • Temperature
      • M(T)dTT-3-/2

Di Li, NAIC & Cornell U

350 micron continuum
350 Micron Continuum

Di Li, NAIC & Cornell U

gas to dust ratio
Gas to Dust Ratio
  • Using gas temperature TdTk.
  • 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

  • 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
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

  • 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
Ongoing and Future Work
  • Higher resolution mapping of ORI1 and other cores


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

Di Li, NAIC & Cornell U