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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

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

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

BN/KL

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


Cores

Cores

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

      confinement

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

Excitation

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


Depletion

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

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

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

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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