Transcript final_form_jpm.pptx

The Analysis of Astrophysical
‘Weeds’ Using 3-D Submillimeter
Spectroscopy
SARAH M. FORTMAN, JAMES P. MCMILLAN, CHRISTOPHER F. NEESE, and FRANK C.
DE LUCIA
The 67th International Symposium on Molecular Spectroscopy
June 21, 2012
The Ohio State University
Motivations
Primary: Understand the
complete contribution of each
‘Weed’ to the Astrophysical data
Methodology: A
Temperature Dependent
Approach to Spectroscopy
Bonus: Obtaining Dipole
Moments and Lower State
Energies which may aide in QM
assignments
ALMA Science Verification Data
Acquiring the Intensity Calibrated
Complete Experimental Spectrum (CES)
10 Heaters
Sample
Detector
Transmitter
THz Source
6 meters
Steps:
0𝑡ℎ : Contamination
1𝑠𝑡 : Pressure vs. Doppler Broadening
2𝑛𝑑 : Acquire CES
Peak rate:~1.5 K / Spectral Average
166 Spectral Averages
Butterfly
Valve
Catalog Line Approach
ln
𝑃
= 𝛼𝐿 = 𝐴
𝑃𝑜
Actually measured and known
are 𝑃 and 𝑃𝑜
Peak Integrated Absorption Coefficient :
𝛼𝑝 𝑇 = 𝑛ν𝑜 (1 −
ℎν
𝑔𝑙 𝑒
− 𝑘𝑇𝑜
𝑒
)𝑆𝑖𝑗 μ2
−𝐸𝑙
𝑄
𝑘𝑇
1 8𝜋 3
𝛿ν 3𝑐ℎ
ln 2
𝜋
Goal: Acquire "𝐸𝑙 ” and “𝑆𝑖𝑗 μ2 𝑔𝑙 ” for unassigned lines
Doppler width:
𝛿ν = ν𝑜
2𝑁𝑎 𝑘 𝑙𝑛(2)
𝑀𝑐 2
𝑇 = Wν𝑜 𝑇
Catalog Line Approach
Choose Catalog Lines and Feed in their
𝑛𝐿
"𝐸𝑙 ” , “𝑆𝑖𝑗 μ2 𝑔𝑙 ” ‘s : Return T’s and for
Input
Output
𝑄
each scan
ℎν
𝐴𝑝 = (1 − 𝑒
−𝑘𝑇
𝑛𝐿
)(𝑆𝑖𝑗 μ2 𝑔𝑙 )( 𝑄 )𝑒
−𝐸𝑙
𝑘𝑇
𝐾
𝑇
Best fit over 10’s -> 100’s of lines
Measured
Next reverse the process and find the
"𝐸𝑙 ” , “𝑆𝑖𝑗 μ2 𝑔𝑙 ” ‘s for the Unassigned
Lines
𝐴𝑝 = (1 −
ℎν
𝑛𝐿 −𝐸𝑙
−𝑘𝑇
2
𝑘𝑇
𝑒
)(𝑆𝑖𝑗 μ 𝑔𝑙 )( )𝑒
𝑄
𝐾
Best fit over 100’s -> 1000’s of temperatures
𝑇
Measured
Note: burying constants
8𝜋3
K = 𝑊(3𝑐ℎ
ln 2
𝜋
)
Catalog Line Approach
Choose Catalog Lines and Feed in their
𝑛𝐿
"𝐸𝑙 ” , “𝑆𝑖𝑗 μ2 𝑔𝑙 ” ‘s : Return T’s and for
Input
Output
𝑄
each scan
ℎν
𝐴𝑝 = (1 − 𝑒
−𝑘𝑇
𝑛𝐿 −𝐸𝑙
𝐾
2
)(𝑆𝑖𝑗 μ 𝑔𝑙 )( 𝑄 )𝑒 𝑘𝑇 𝑇
Finally Make a Prediction:
Measured
Next reverse the process and find the
"𝐸𝑙 ” , “𝑆𝑖𝑗 μ2 𝑔𝑙 ” ‘s for the Unassigned
Lines
𝐴𝑝 = (1 −
𝐴𝑝 = (1 −
ℎν
𝑛𝐿 −𝐸𝑙
−𝑘𝑇
2
𝑘𝑇
𝑒
)(𝑆𝑖𝑗 μ 𝑔𝑙 )( )𝑒
Prediction
ℎν
𝑛𝐿 −𝐸𝑙
−𝑘𝑇
2
𝑘𝑇
𝑒
)(𝑆𝑖𝑗 μ 𝑔𝑙 )( )𝑒
𝑄
𝐾
𝑇
Measured
Note: burying constants
8𝜋3
K = 𝑊(3𝑐ℎ
ln 2
𝜋
)
𝑄
𝐾
𝑇
Point by Point Approach
Step 1: Massage Doppler Broadened
Absorbance into a form with Effective 𝐸𝑙 and 𝑆
which are in fact "𝐸𝑙 ” and “𝑆𝑖𝑗 μ2 𝑔𝑙 ” on line
center
A(ν) = (1 − 𝑒
ℎν
− 𝑘𝑇𝑜
A(ν) = (1 − 𝑒
− 𝑘𝑇𝑜
ℎν
𝑛𝐿 −𝐸𝑙
2
)(𝑆𝑖𝑗 μ 𝑔𝑙 )( 𝑄 )𝑒 𝑘𝑇 (𝑒
ln 2
ν
− 2 (1−ν )2
𝑊 𝑇
𝑜
)
𝐾
𝑇
𝑆 = 𝑆𝑖𝑗 μ2 𝑔𝑙
ln 2
ν 2
𝐸𝑙 = 𝐸𝑙 + 𝑘
(1 − )
𝑊2
ν𝑜
−𝐸𝑙
𝑛𝐿
𝐾
)( )𝑆𝑒 𝑘𝑇
𝑄
𝑇
Step 2: Fit each data point across the
spectrum using 𝑆 and 𝐸𝑙 as fitting parameters
1.2 ∗ 106 Data Points
∆ν = 0.0625MHz
Making A Prediction
1.)Simply Download the table of 𝑆 and 𝐸𝑙 .
2.)Choose your temp and plot!
𝐴
𝑛𝐿
ℎν
= (1 − 𝑒
−𝑘𝑇
) 𝑆𝑒
1.2 ∗ 106 Data Points
∆ν = 0.0625MHz
−𝐸𝑙
𝑘𝑇
𝐾
𝑄 𝑇
Key Notes:
Good Agreement of the data (green line)
and prediction (black line)
The process agrees with the catalog lines
(red dash) and picks up more
Comparisons with the Astrophysical
Data
Strategy:
MeCN
• Identify the line shape for the molecule
• Convolve the line shape with the CES
EtCN
• Scale/Fit the prediction to the astrophysical
data
VCN
“An Analysis of a Preliminary ALMA Orion KL Spectrum via the use of Complete
Experimental Spectra from the Laboratory” Fortman S. M., McMillan J.P., Neese C.F.,
Randall S., Remijan A.J., Wilson T.L., De Lucia F.C. (Submitted to J. Mol. Spec.)
Convolution
Predicted Spectrum Width:
~1’s MHz
Line Shape Width :
~10’s MHz
The purpose of the
convolution is to
predict the SHAPE and
RELATIVE intensities of
spectral features.
Convolution Definition:
𝑓∗𝑔 𝑡 =
𝑓 𝜏 𝑔 𝑡 − 𝜏 𝑑𝜏
The relative width of the CES lets
it act much like a delta function
Assume Local
Thermodynamic
Equilibrium (LTE)
190K
Scaling for Intensity
Perform best fit of :
Astrophysical Data =
scaling factor*
Predicted Convolved
Data
Recall:
𝐴
𝑛𝐿
= (1 − 𝑒
ℎν
−𝑘𝑇
) 𝑆𝑒
−𝐸𝑙
𝑘𝑇
𝐾
𝑄 𝑇
This region is dominated by EtCN
Others clearly by MeCN , VCN
Band Studied: 213739.8 – 246654.6 MHz
Confirm Local Thermodynamic Equilibrium
(LTE) 190K
Conclusion
• Shown 2 separate ways to experimentally acquire
physically meaningfully 𝑆𝑖𝑗 μ2 𝑔𝑙 and 𝐸𝑙
• Demonstrated the ability to predicted Intensity
resolved spectra for arbitrary temperature
• Shown the applicability in studying astrophysical data