2MASS Image

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2MASS Image of the Orion Nebula
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Massive Cores in Orion

• Di Li
• NAIC, Cornell University
• February, 2002

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HMSF vs. LMSF

• Spatial Distinction
• LMSF region Taurus
• GMCs Orion
• Intermediate Ophiuchus
• Thermal vs.Turbulent Cores
• Initial Conditions?
• Super vs. Sub Critical
• Evolutionary Paths?
• No pre-main-sequence for HMSF?

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LMSF standard model

• Four Stages
• Core Ambipolar diffusion
• Collapse Inside-out
• Jets Deuterium Burning, Stellar energetics
  starts 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

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HMSF Time Scale

• Different Time Scales/Paths
• Infall time scale
• Kelvin-Helmholtz
• 1 M? tKH107 yr, M?5M? tKH
• ?no pre-main-sequence!
• Different Initial Conditions
• Massive cores could be supercritical?fragmentation
  ?, cluster formation? Binary?

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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

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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

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Sources Selection

• Quiescent cores chosen from CS 1-0 catalog
  (Tatematsu et al. 1993)
• Why Orion
• the closest GMC 44 0.1pc
• High Density Tracer Map Available (not for
  Ophiuchus!)
• Why These Cores
• Far from BN/KL
• No IR association
• Reasonable Size

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Orion Molecular Clouds
BN/KL
Ori2 -Ori15
Sakamoto et al. 1994 Lis et al. 1998 Wiseman
Ho 1998
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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

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Observation Time and Efforts
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Calibration

• Millimeter Chopper wheel method
• Radio Direct calibration using point source
• All quantities convert to main beam antenna
  temperature for consistency and best estimate of
  mass in the beam

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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

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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
• Inversion (1,1) -- 23,694.495 MHz
  (2,2) -- 23,722.633 MHz

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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

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Temperature Maps
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Temperature Maps (Cont.)
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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

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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

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Getting Serious about Coolness

• Students 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

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Spatial Correlation Intensity and Tk

• 3D Correlation no standard statistics
• Linear correlation test Pearsons r

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Spatial Correlation R p
r -0.6 p 0.01 Credible anti-correlation
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Column Density

• Usual approximation optically thin and no
  background
• Correction Factors

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LVG analysis of Correction Factors
Recipe for N(C18O)
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Column Density Maps
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Finding Cores

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

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Cores
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Virial Equilibrium

• The Virial Theorem
• Steady state

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Kinetic Energy and Gravity mvir

• Virial Mass and Mass Ratio
• Axis Ratio
• rule out
• pure oblate
• models

Fall and Frenk 1983
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Stability and Critical Mass

• Critical Mass
• Use 13CO maps
• for deriving pressure
• confinement

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Core Stability
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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 B100 micro G

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Coupled Radiative Transfer Excitation
Radiative Transfer
Excitation
Localized Approximation Large Velocity Gradient
method (Goldreich Kwan 1974 Goldsmith, Young,
Langer 1983)
local
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Minimization approach Chi Square

• Self-iterating LVG
• Inputs X, n, dv/dr, T, cross-section-?, A
• outputs TA, ?, Tx
• Define a confidence indicator Chi square
• Minimization of Chi square
• Downhill simplex method

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Density and Abundance

• Solutions for ORI1

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Density and Abundance

• Solutions for ORI2, typical of others

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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!

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What do we learn from CS?

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

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Density Gradients

• Theory
• Hydrostatic equilibrium ?? r-2 for 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

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Radiative Transfer With Density Structures

• Monte Carlo type radiative transfer codes
• Ratran by Hogerhieijde van der Tak (2000)
• 1D code publicly available
• Consistent with LVG for a uniform sphere cloud
  model (test species HCO)
• Elements of the cloud model for ORI1
• Inner core r0.05 pc n106 cm-3,
  Bonnor-Ebert sphere
• Outer envelope r0.5pc n 105 cm-3, n drops as
  an isothermal sphere
• Temperature gradient incorporated (given by
  observations)

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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
  core in the Orion south

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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

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350 Micron Continuum
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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
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Depletion

• Standard GDR100
• 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

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Depletion (cont.)

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

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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.
• Gravitation bounded 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
  the 0.1 pc spatial scale. Further fragmentation
  or dramatic change of environment for starting
  massive collapse is expected

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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.