3-D SUBMILLIMETER SPECTROSCOPY FOR ASTROPHYSICS AND SPECTRAL

ASSIGNMENT

SARAH M. FORTMAN, IVAN R. MEDVEDEV, FRANK C. DE LUCIA, Department of Physics, The Ohio State University,

Columbus, OH 43210-1106, USA.

OSU International Symposium on Molecular Spectroscopy

Columbus, OH

June 16th, 2008

Two Related Objectives

Spectroscopy Challenge• Bootstrap Assignment in Complex Spectra• FASSST spectra may contain >10^5 lines in many

vibrational states

Traditional Approach• Use 2D (intensity, frequency) spectra to assign and

bootstrap in each vibrational state

New Approach• Observe intensity calibrated variable temperature

spectrum and calculate lower state energies.• Use intensity, frequency and lower state energies in

the bootstrap assignment

Astronomy Challenge• Current telescopes approach confusion limit• Many unassigned lines• New systems (Alma, Herschel) will be more

powerful

Traditional Approach• Quantum Mechanical predictions of astrophysical

spectra give intensity and frequency as a function of temperature

• Spectroscopists calculate and fit what we can, not what astronomers need

New Approach• Predict intensity and frequency as a function of

temperature without assignment

courtesy of J. Cernicharo

Intensity Calibrated Variable Temperature Spectroscopy• Observe 2D spectra at many temperatures• Calculate intensity, frequency and lower state

energies for assigned and unassigned lines• Give astronomers what they want• Give spectroscopists more information

FREQ ERR LGINT DR ELO GUP TAG QNFMT QN’ QN”222205.8884 0.0141 -7.0138 3 1502.8669 81 630061404402218 1 402119 1 222206.5102 0.0142 -7.0138 3 1502.8675 81 630061404402318 1 402219 1 222216.2472 0.0128 -6.1572 3 916.1480 21 63006140410 8 2 0 9 8 1 0 222222.2687 0.0241 -7.3542 3 1502.8669 81 630061404402318 1 402119 1 222662.1685 0.1481 -7.8356 3 2033.0142109 630061404543718 0 543619 0 222662.5968 0.0071 -6.0426 3 915.3357 21 63006140410 7 3 0 9 7 2 0 222665.1993 0.1573 -7.8356 3 2033.0133109 630061404543618 0 543519 0 222696.0695 0.0098 -6.7291 3 900.5161 17 630061404 8 6 2 0 7 4 3 0 222725.9166 0.1222 -7.8669 3 1956.8275105 630061404523319 1 523320 1 222746.5775 0.1175 -8.1094 3 1956.8268105 630061404523319 1 523220 1 222800.4652 0.1143 -8.1092 3 1956.8275105 630061404523419 1 523320 1 222821.1262 0.1312 -7.8664 3 1956.8268105 630061404523419 1 523220 1

Spectroscopic Challenge

NEW PARAMETER (EST. ERROR) 1 910099 1.468190000( 0) 0.000000000 2 0 26355017.840800( 0) 0.000000 3 10000 12962.3189(307) 0.0000 4 20000 12085.7215(308) -0.0000 5 30000 6242.05887( 35) 0.00000 6 610000 -196.061( 69) 0.000 7 610100 2.464( 33)E-03 -0.000E-03 8 611000 -2.3201(144)E-03 -0.0000E-03 9 610200 -0.0928( 48)E-06 -0.0000E-0610 612000 -0.06750(269)E-06 -0.00000E-0611 1000000000 -17.7136( 60) -0.0000 12 1000000100 -0.4134(150)E-03 0.0000E-03

Predicted lines from SPFIT .cat file Fitted Constants from SPFIT .fit file

Graphing in Two and Three Dimensions

Frequency (MHz)

Intensity

(nm2*MHz)

Lower State Energy (cm-1)

162977 5.1963711 631.1015

163119 17.025509 113.2438

163568 5.0442872 400.8251

163606 37.162086 65.264397

163925 4.3062572 488.5152

• Traditional approach uses a 2D (intensity vs. frequency) plot

• New approach creates a 3D plot from the intensity, frequency and lower state energy data

Interference fringes Spectrum

InSb detector 1

InSb detector 2

Ring cavity: L~15 m

Mylar beam splitter 1

Mylar beam splitter 2

High voltagepower supply

Slow wave structuresweeper

Aluminum cell: length 6 m; diameter 15 cm

Trigger channel /Triangular waveform channel

Sig

na

l ch

an

ne

l

BWO

Magnet

Lens

Filament voltagepower supply

Length ~60 cm

Steppermotor

Reference channel

Lens

Stainless steel rails

Path of microwaveradiation

Preamplifier

Fre

qu

en

cy

ro

ll-o

ffp

rea

mp

lifi

er

Referencegas cell

Glass rings used to suppress reflections

Data acquisition system

Computer

FAst Scan Submillimeter Spectroscopic Technique (FASSST) spectrometer

Thermal enclosure

Temperature Control

• Ran experiment once• Temperature Range: 228 – 405 K (-45 – 132 °C) at ~.8 degrees/min• Took 700 scans over 3.5 hours totaling 29.6 GB of data

Spectra as a Function of Temperature

• The physical basis of the calculation of the lower state energy is the differential change in line strength with temperature.

Subset of Data

(in total experiment 700 traces over 50 GHz)

Ratios to Obtain Lower State Energy

kTEE uaeC /)(1

sgnsgn

0

/

/

,,

2

,

3/

sgnsgn

3

8)1 )( )(

sgn

sgn

n

kTEn

kTEl

zyxiuli

kThuu

n

u

u

eg

eg

che(TnT

0

/

/

,,

2

,

3/

sgnsgn

3

8)1 )( )(

sgn

sgn

n

kTEn

kTEl

zyxiuli

kThaa

n

a

a

eg

eg

che(TnT

kT

EEC

T

Tor ua

u

a )(]

)(

)(ln[ sgnsgn

2sgn

sgn

sgnsgn * au EkslopeE

We can plot the log of the ratio in log(1/T) space and expect to see a straight line.

• Scatter from the peak finder

• Ripples (variation in reflection with T?)

• Temperature calibration (currently thermocouples, starting to use spectroscopic temperature)

Consider taking the ratio of two lines of which one is assigned and the other is unassigned.

Lower State Energy vs. Thermal Behavior

Okay but not great

Astronomy

• The smallest errors in intensities will come when the calculated temperature is bounded by experimental temperatures

• The error in the predicted intensity will be of the order the error in the observations (or better because we make many observations).

Propagation of Error and Uncertainties

Spectroscopy

We expect to reduce uncertainties by a factor of 10 by:• Replacing the peak finder with analysis• Fitting a model to the baseline ripple• Using a grand fit of all assigned lines as the reference line

instead of a single line• Getting a proper average over the ends by using the

spectroscopic temperature• Operating over a larger temperature range (using a

collisional cooling cell to 2K)

221

213

223

31,

32,

31,

32,

)/1/1(

)/1/1()/1/1(2

)(

)(

)(

)(

TT

TTTT

T

T

T

T

ul

ul

ul

ul

ul

ul