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

Integration of Bootstrap Predictive Quantum Models and Complete Experimental Measurement:

A New Approach to the Spectroscopy Challenge

1. 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)

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

Where are we:

-Astrophysically?

-Spectroscopically?

-Catalogues?

courtesy of J. Cernicharo

1 mm Survey of Orion with IRAM 30-m Telescope

courtesy of J. Cernicharo

U-Lines in the IRAM SurveyAfter 50 years of submillimeter spectroscopy:

>5000 ‘U’ lines

~40% of total

Most attributable to large molecules -Very large number of low lying 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

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

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

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

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

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

Propagation of Uncertainty (T2 = 300 K)

221

213

223

31,

32,

31,

32,

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

)()(

)()(

TTTTTT

TT

TT

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

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

)()(

)()(

TTTTTT

TT

TT

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

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).

Is it possible to recover astronomical molecular concentrations without individually observable lines? 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?

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

Summary and Conclusions 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.

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.

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

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 ChallengesIntensities 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

nal c

hann

el

BWO

Magnet

Lens

Filament voltagepower supply

Length ~60 cm

Steppermotor

Reference channel

Lens

Stainless steel rails

Path of microwaveradiation

Preamplifier

Freq

uenc

y ro

ll-of

fpr

eam

plifi

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 Drift2. 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

Input and Processing Quantum Model ExperimentalMeasure subset of lines of interest Measure all lines of interest

Assign and fit frequencies via bootstrap Frequencies

Does not require intensity measurement Intensities

Does not require Requires

known temperature well defined temperature

known concentration constant concentration