Weeds, Flowers, Clutter and a New Approach to Removing the Spectroscopic Bottleneck in Millimeter and Submillimeter Astrophysical

Spectra - A DiscussionFrank C. De Lucia

Ivan MedvedevDepartment of PhysicsOhio State University

National Radio Astronomical ObservatoryCharlottesville, VANovember 28, 2006

Confessions of a Laboratory Spectroscopist

The Discussion1. 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:

Spectroscopic strategies and custom vs astrophysical advances

3. Growing consensus that conventional approach will not work: a semi-infinite job

4. An alternative: Complete, intensity calibrated spectra as a function of temperature - experiment and theory

5. Really here to discuss flowers and grand fits

The integration of laboratory and astrophysical spectroscopy to detect the unobservable

Large molecules emit more photons/GHz into a multiplex telescope receiver than do small molecules

An example of this type of spectroscopy is called FASSST, an acronym for FAst Scan Submillimeter-wave Spectroscopic Technique developed by Dr. F. De Lucia, which has the potential to obtain needed data rapidly and with the accuracy required. . . . In this approach the entire spectrum is collected at multiple temperatures and compared with known calibration lines allowing the line strengths and energy levels to be determined.

courtesy of J. Cernicharo

1 mm Survey of Orion with IRAM 30-m Telescope

courtesy of J. Cernicharo

U-Lines in the IRAM Survey

After 50 years of submillimeter spectroscopy:

>5000 ‘U’ lines

~40% of total

Most attributable to large molecules -Very large number of low lying vibrational/torsional states

-Many have perturbations; we often analyze the portion of the spectrum that we can or have time to

-In some lab spectra assign and fit ~10000 out of 100000 lines

Baseline often confusion, not noise limited

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:

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

Also, easy to characterize in lab: ‘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

A Few Days Work

Many Years of Work

Stated Another Way

In the beginning it was easier to model/predict line frequencies than to measure them

Small, easy to model species - measure a few well selected transitions, predict the rest

As an important by-product, these models gave astronomers intensities

As an additional by-product, this led naturally to catalogues based on these models

Now it is easier to measure spectra than to predict them

Orders of magnitude increase in the difficulty of modeling (large molecules)

Improvements in experimental approaches

Our cataloging strategy does not reflect this change

Catalogues have become very incomplete in unpredictable ways - unknown bounds

But even with experimentally measured spectral frequencies, we have to deal with the intensity/temperature problem

Methyl Formate

We spent a lot of time assigning these A and E ground state lines (which have 10 - 20% of the total intensity), and they don’t have much in the way of perturbations

Methanol

Non-Bootstrap Approach:

Measure every line

FASSST Spectrum of the Classical Weed: Methyl Formate

< 0.01 second of data

BUT! 1. We rarely measure intensities

2. Even if we did, we need to know them over the range of astronomical temperatures

3. Traditional bootstrap Quantum Mechanical models do this very well

The Effect of Temperature on the Spectrum of CH3OH

We need spectrum that is not just complete in frequency, but also in intensity at all temperatures

Observed | C

alculated

The Calculation of Line Frequencies and Intensities from Experimental Data

Overview of New Approach

A MOLECULAR LINE SURVEY OF ORION KL IN THE 350 MICRON BAND C. Comito, P. Schilke, T. G. Phillips, D. C. Lis, F. Motte, and D. Mehringer; Ap. J. S.S. 156, 127 (2005).

Can we fit astrophysical data as opposed to simply identifying the lines?

Analytical Chemistry (with intensity calibrated reference spectra): Number of data points = number of spectral resolution elements Number of molecular variables = number of molecules (their concentrations)Astrophysics: Number of astrophysical variables = ? (temperature(s)-velocity component(s), . .)

Qast 1

ABC

Qst 1

AB2

Q 1

R3

Rotational Partition Functions At a given observational frequency:

the distance between band heads is

the number of K-levels associated with each band head is:

the number of MJ levels associated with each K - line is:

BH ~ 2R

NK 1

R

Sum of line strengths/frequency interval - the number of spectral photons available to a multi-channel telescope

NMJ

1

R

/ MHz NK NmJ

QrBH

1

R3 / 2

Because the spectral space occupied by these lines grows as R2 (the MJ factor above adds intensity, but not spectral space)

SN ~

1

R

A Motivation: From Weeds to Flowers?

Is it possible to recover astronomical molecular concentrations without

individually observable lines?

Some Thoughts and Questions

1. Fit for individually identifiable ‘U’ lines and QM assigned lines.

2. Will fits to complete spectral libraries eliminate the background clutter?

3. Are there individually hidden, but collectively observable flowers in the astronomical garden?

4. Note the lineshape problems in the astrophysical spectrum - how big is this impact?

Questions -> A modest Program?

1. What is the state of the art for already having done this (i.e. subtract the contributions from assigned lines) Turbulence and lineshape effects?

2. As a function of telescope/telescope type/ molecule/astronomical source, how bad is the approximation that there is an effective temperature? To drive down clutter to 20% of current level, this linear average approximation only needs to be good to a factor of 5?

How well can you use the spectra from simple molecules to establish the effective temperature?

Are there families of molecules which occupy similar regions inside of a spatial resolution element?

3. A simpler molecular problem? A ‘glycine-like’ molecule for which there may be individually observable lines, but lines near the clutter limit.

4. If/When ‘Complete’ Spectra become available, what might the best astronomical sources be for which to try this grand fit approach? Not too hard - Not too easy

5. Alternatives to ‘effective’ temperature Let regions within resolution element have different temperatures/velocities and use the very redundant spectral information to choose sets of concentrations/temperature

Include chemistry models to link species in space (temperature and turbulence)

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

Need a New Strategy

Elimination of Weeds by use of ‘Experimental’ Models From 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, with 77 K convenient and suitable for all but the lowest temperatures.

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.

Finding Flowers - Understanding Chemistry and Astrophysics With good telescope intensity calibration and high spatial resolution there is a good prospect to use a global fitting approach to detect larger molecules than commonly assumed.

Are analyses which include chemistry and nonlinearity of spectral signature to temperature to link concentrations/temperatures/turbulence within a spatial resolution element possible?

The path laid out has challenges, but they are small in comparison to other challenges that must be met to get maximum return on investment for $109 instruments

How do We Spend Our Time and Effort in Traditional Submillimeter Spectroscopy

The Bootstrap Model: Prediction (Infrared, quantum chemistry, etc. . . ) Use predictions to search for a few relatively low J, ground vibrational state lines; assign and measure them Run quantum mechanical analysis, make improved predictions Iterate the process

Keep Bootstrap Going Until: Can predict all observable lines to experimental accuracy Enough to publish Run into lines that are hard to assign or fit (perturbations)

Sometimes extend to excited vibrational states, other conformers, etc.

The Rotational Community has been Good About Publishing Data Makes possible good catalogs based on all useful data But we need to have concern about citation count problems for young faculty

Integration of Bootstrap Predictive Quantum Models and Complete Experimental Measurement:

A New Approach to the Spectroscopy Challenge1. A time efficient solution to the astronomical weed problem based on

the measurement of complete spectra at multiple temperatures

2. Review of ACS (Atlanta), ALMA (Denmark), Snyderfest (Greenbank),

Spectral Catalogue Meeting (Pasadena)

3. Integration of Approaches

-Measurement and predictions of frequencies

-Measurement and predictions of intensities

-Redundancy and errors

-Catalogues for astronomers

-Spectroscopic challenges and effort requirements

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

3ch i ,l u

2

ix,y,z

gl e El /kT

gn e En /kT

n0

The total number density (chemistry and pressure issues).

But, for an unassigned line, one does not know

-The matrix element

-The lower state energy

-The partition function

The large molecules of interest have many assigned lines => Form ratios of spectra at well defined temperatures and concentrations

Absorption Coefficients

What You Need to Know to Simulate Spectra at an Arbitrary Temperature T3 without Spectral Assignment

Eliminate Astronomical ‘Weeds’ at T3 from Laboratory Measurements at T1 and T2

l u, u sgn(T3 )

l u, a sgn(T3 )

l u, u sgn(T1)

l u, a sgn(T1)

l u, u sgn(T1)

l u, u sgn(T2 )

l u, a sgn(T1)

l u, a sgn(T2 )

1/ T3 1/ T1

1/ T1 1/ T2

Along the way, this procedure also yields catalogue data

(1) Complete in line frequencies, and

(2) Upper state energies and line intensities

But it does not include quantum mechanical line assignments

Comparison of Energy Levels Calculated from Experimental and

Quantum Calculations for SO2

Collisional Cooling for low T2

Do we have rotational equilibrium and a well defined rotational temperature? Yes, and we can test.

Do we have vibrational equilibrium and a well defined vibrational temperature? For the relatively low lying levels of interest, probably yes, but we can both optimize and test.

Propagation of Uncertainty (T2 = 300 K)

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

T1 = 77 K

T1 = 77 K

l u, u sgn(T3 )

l u, a sgn(T3 )

l u, u sgn(T1)

l u, a sgn(T1)

l u, u sgn(T1)

l u, u sgn(T2 )

l u, a sgn(T1)

l u, a sgn(T2 )

1/ T3 1/ T1

1/ T1 1/ T2

==>It is important to have a low temperature reference

Model Integration for Accuracy and Surety Combined Model

Quantum Model Experimental Model

Line Frequencies Calculated Measured

some lines all lines, interpolated all 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

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

A Time Efficient Experimental Approach to Catalogues for Astrophysics

Frank C. De LuciaIvan Medvedev

Department of PhysicsOhio State University

Workshop on Submillimeter and Far-Infrared Laboratory Spectroscopy in Support of Herschel, SOFIA, and ALMA

October 19 - 20, 2006Pasadena, CA

What Could Go Wrong?(In ‘Proposal Speak’: What are the challenges?)

Spectroscopically?

Accuracy of the spectroscopic intensities? Need to be as good as the S/N of astronomical spectrum Need chemical stability and low temperature reference for good intensities

Astronomically (Flowers application)? Vibrational temperatures not same as Rotational temperatures Low lying vibrational states relax more rapidly - for some species there is considerable mixing How homogeneous is the astronomical region? Large arrays help a lot

How good is the intensity calibration of the telescope? As we calibrate in lab, fit to known dense spectrum to calibrate telescope Even though not a linear problem, many of the ‘errors’ and inhomogeneities will cancel as well

Experimental Challenges

Intensities

Basic calibration scheme (e. g. mode steering relative to chopper)

Standing waves that impact effective path length - variation scale will be on order of 100 MHz

Saturation: detectors - molecules - Beers Law

Linewidths: impact on modulation schemes, integrated vs peak absorption

Efficient cooling and well defined temperatures

Model Integration for calibration and checks

Consider two lines, one assigned and one unknown at two temperatures T1 and T2

Step 1: With Eqn. 1 for both the known and unknown line, we have two equations and two unknowns:

1. The number density and partition function ratio for the T1 and T2 lab measurements

2. The lower state energy of the unassigned line

Step 2: Solve for the lower state energy of unassigned line

E l,u sgn k

(1/T1 1/T2)ln

1

C

l u,n (T1)

l u,n (T2)

E l,a sgn

k

(1/T1 1/T2)ln

l u,u sgn (T1)

l u,u sgn (T2)

l u,a sgn (T1)

l u,a sgn (T2)

Eqn. 1

Eqn. 2

Step 3: Form a ratio between the observed intensities of an assigned and unassigned line at T1

Step 4: Combining with the lower state energy for the unassigned line from the previous Eqn. 2, provides the matrix element of the unassigned line

Step 5: To predict ratios at T3 of the known (assigned) reference line and unassigned line in the molecular cloud

Eqn. 3

Eqn. 4

l u,u sgn (T1)

l u,a sgn (T1)

u sgn (1 e h u sgn / kT1 )

a sgn (1 e h a sgn / kT1 )

u sgn,l u

2gl,u sgn

a sgn,l u

2gl,a sgn

e (E l ,u sgn E l ,a sgn ) / kT1

l u,u sgn (T3)

l u,a sgn (T3)

u sgn (1 e h u sgn / kT3 )

a sgn (1 e h a sgn / kT3 )

u sgn,l u

2gl,u sgn

a sgn,l u

2gl,a sgn

e (E l ,u sgn E l ,a sgn ) / kT3

Methyl Formate

Methanol

Comparison of Energy Levels Calculated from Experimental and

Quantum Calculations for SO2

Spectra Calculated at 100 K and 200 K from Measurements at 423 K and 293 K

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

Measure Every Line

FASSST Attributes

1. Can record 10000-100000 resolution elements/sec Freezes Source Frequency Drift

2. Can record entire spectrum in a few seconds

Freezes Chemistry Changes

3. ‘Locally’ intensity measurement is flat to ~1%

A basis for intensity measurement

But to be astronomically ‘complete,’ we need intensities at other, typically lower temperatures

CH3F 77 K Rotational Temperatures in a Collisional Cooling Cell as a function of

K-state: Experiment vs. Theory