Weeding the Spectra

[Preliminary Results with a new ‘Experimental’ Approach]

 Frank C. De Lucia

 Department of PhysicsOhio State University

USA

May 5, 2008, Arcachon

courtesy of J. Cernicharo C. Comito, P. Schilke, T. G. Phillips, D. C. Lis, F. Motte, and D. Mehringer; Ap. J. S.S. 156, 127 (2005).

The Discussion Today1. Meetings for ‘spectroscopy in support of ‘X’ are becoming popular

2. The spectroscopists’ dirty little secret: We measure, assign, and model what we can - not what you need - the catalogues are massively incomplete.

3. We have proposed an alternative: Use of fast recording of complete, intensity calibrated spectra as a function of temperature – without quantum mechanical assignment - to provide the usual astrophysical catalogues.

4. Today: Preliminary results (project is < 5 days old) to illustrate and use as a case study of the strengths, weaknesses, challenges, and symbiotic relation to the usual quantum mechanical modeling approach.

Background

AN EXPERIMENTAL APPROACH TO THE PREDICTION OF COMPLETE MILLIMETER AND SUBMILLIMETER SPECTRA AT ASTROPHYSICAL TEMPERATURES: APPLICATIONS TO CONFUSION-LIMITED ASTROPHYSICAL OBSERVATIONS, Ivan R. Medvedev and Frank C. De Lucia, The Astrophysical Journal 656, 621-628 (2007)

The Fundamental Problem: A Brief History of Bootstrap Astrophysical Spectroscopy and Models

In the beginning there were only a few astrophysical lines: H2CO, NH3, CO, . . .

Laboratory mm/submm spectroscopy was ahead of the astronomy

Then there were U-lines - exotic species like HCO+

Astrophysical reality made it easy in the lab - astronomers got use to complete catalogues:

Small Molecules: Astrophysically abundant and spectroscopically strong (good partition function)

Easy to characterize from lab studies: ‘simple’ models were ‘complete’ generate ‘complete’ catalogues

But then along came methanol, methyl formate, and others:

Spectral complexity is a very steep function of molecular size

The difficulty of complete spectroscopic modeling is also a very steep function of molecular size

It is not possible to over emphasize this last point about molecular size

The Nature of the ChallengeThe problem is not that there are so many lines (QM models are very good at calculatinglots of spectral frequencies), but rather:

1. These lines come from many different low lying vibrational/torsional states.2. Each of these states is a new assignment problem3. The difficulty of these problems can increase very rapidly with energy a. Approach barrier heights b. Perturbations and mixings among states

We have worked on this problem for > 50 years with model based approachesWith existing telescopes: Examples for which large fractions of lines are unknownHerschel and ALMA dramatically expand frequency and sensitivity limits

The Nature of a Solution

What do we need/want? We Need Complete Spectra at Arbitrary Temperature/Excitation Maintain the catalog format for the interface between spectroscopists and astronomers

How can we get it? Quantum Mechanical Models are the backbone of what we do But, now in laboratory we can record rapidly complete spectra at selected T By recording spectra at multiple (at least two) temperatures 1. the usual catalog of transition strength and lower state energy can be calculated for all of the lines of the complete spectra, and

2. the spectra at an arbitrary/astrophysical temperature can be calculated

What do we need to worry about? Where are we?

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

The Classical Weed: Methyl Formate

< 0.01 sec

FASSST Gives us Complete Two Dimensional Spectroscopy

1000 such spectra expanded to visible resolution extend to Paris

Variable Temperature Leads to Third Dimension

The Calculation of Line Frequencies and Lower State Energies from Unassigned Experimental Data

An Example of the Formalism

l u n (1 e h / kT )8 3

3chi,l u

2

ix,y,z

gl e E l / kT

gn e En / kT

n0

Unassigned Line (1)

Assigned Line (2)

l u n (1 e h / kT )8 3

3chi,l u

2

ix,y,z

gl e E l / kT

gn e En / kT

n0

1(T) /2(T) C1e (E1 E2 ) / kT

or

ln[1(T) /2(T)] C2 (E1 E2) /kT

Ratio of Assigned and Unassigned Lines to Provide Lower State Energy

Divide:

C1

1. Ramp Temperature from -50 C to 150 C @ ~0.50/min2. Measure Spectrum every 15 Seconds (~800 Spectra at ~ 30 MBytes/spectra)3. If everything is stable, easy to understand (normalize to line strength of assigned reference line), straight line in log (1/T) space

An Example of the Energy Plot

Scatter

SystematicRipples

TemperatureCalibration?

AstronomicalTemperatures?

Collisional Cooling: 1 K - 300 K

Three Dimensional Spectroscopy gives back to Assignment Spectroscopy

163 163.5 164GHz

Lower State Energy vs. Thermal Behavior

600 cm-1

0 cm-1

A Symbiotic Relation ‘Experimental’ 3-D Spectroscopy depends heavily on Quantum Mechanical Assignment Spectroscopy

‘Experimental’ 3-D Spectroscopy is a very advantageous data base for Quantum Mechanical Assignment Spectroscopy

Intensity calibrated Known lower state energies Large amounts of complete data Useful even before best/final analysis for astronomy

We will archive these data in a public place They represent much more data than we can analyze

Analysis Strategies

Preliminary Demonstration – Shake out of Approach Single assigned line chosen for reference Temperatures from thermocouples Intensities from peak finder

Production Scheme – A Grand Fit Typically hundreds of assigned lines available for reference/statistical calibration Temperatures from intensity fit of hundreds of assigned lines Intensities from spectral analysis (linewidth issues)

Of the Astronomical Parameters – Propagation of Error: Astronomical Intensities should have error similar to the measured laboratory errors if the lab measurements include the astronomical temperature region.

Accuracy - What are the Challenges?

Of 3-D Spectroscopy Parameters

Scatter - Amplitude from Peak Finder – can improve by at least an order of magnitudeReflections/baseline ripple – no suppression – order of magnitude? plus?Limited Temperature Range – Have used Collisional Cooling with temperature calibration to below 2 KTemperature calibration - Will do from known spectra, not thermometersUse a Grand Fit for reference, not a single line

Model Integration for Accuracy and Surety Combined Model - Grand Fit

Quantum Model Experimental Model

Line Frequencies Calculated Measured

some lines all lines, interpolated all vibrational states extrapolated

redundant model accuracy?

Intensities Calculated Measured

some lines all lines

redundant, model accuracy?

1. Standard output (frequencies, transition moments and lower state energies) for catalogues

2. Redundant QM model guards against blunders in direct measurement (from errors to impurities)

3. Measurement of all lines eliminates errors in extrapolated frequencies (especially for model challenged species)

4. Quantum Mechanical intensities provide cross check on reliability and accuracy of experimental intensities

5. Experimental intensities provide cross check for model errors in the QM models of complex spectra

The Relationships Among Spectroscopy, Catalogues, and Astrophysics have Changed Dramatically:

We Need a New StrategyFrom experimental measurements at two temperatures T1 and T2, it is possible to calculate spectrum (with intensities) at an arbitrary T3.

For low T3, a relatively low T2 improves the accuracy of the calculated spectrum.

Collisional cooling provides a general method for achieving this low T2

FASSST is a means of obtaining the needed data rapidly and with chemical concentrations constant over the data collection period.

It is realistic in a finite time to produce catalogs complete enough to account even for the quasi-continua that sets the confusion limit.

In the limit of ‘complete’ spectroscopic knowledge, the confusion limit will probably be set by the unknowns associated with the complexity of the astrophysical conditions, but the high spatial resolution of large telescopes and modern arrays may reduce this complexity.

The 3-D spectroscopic data will be archived. The quantum mechanical method and the ‘experimental’ method are symbiotic Needed so that progress can be cumulative