Weeds, Flowers, Clutter and a New Approach to Removing the Spectroscopic Bottleneck in Millimeter and Submillimeter Astrophysical Spectra - A Discussion Frank C. De Lucia Ivan Medvedev Department of Physics Ohio State University National Radio Astronomical Observatory Charlottesville, VA November 28, 2006 Confessions of a Laboratory Spectroscopist

The Discussion 1. 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 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: H 2 CO, NH 3, 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 % 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 CH 3 OH We need spectrum that is not just complete in frequency, but also in intensity at all temperatures Observed | Calculated

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),..)

Rotational Partition FunctionsAt a given observational frequency: the distance between band heads is the number of K-levels associated with each band head is: the number of M J levels associated with each K - line is: Sum of line strengths/frequency interval - the number of spectral photons available to a multi-channel telescope Because the spectral space occupied by these lines grows as R 2 (the M J factor above adds intensity, but not spectral space) 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 T 1 and T 2, it is possible to calculate spectrum (with intensities) at an arbitrary T 3. For low T 3, a relatively low T 2 improves the accuracy of the calculated spectrum. Collisional cooling provides a general method for achieving this low T 2, 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 $10 9 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 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), 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

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 T 3 without Spectral Assignment

Eliminate Astronomical ‘Weeds’ at T 3 from Laboratory Measurements at T 1 and T 2 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 SO 2

Collisional Cooling for low T 2 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 (T 2 = 300 K) T 1 = 77 K ==>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 Lucia Ivan Medvedev Department of Physics Ohio State University Workshop on Submillimeter and Far-Infrared Laboratory Spectroscopy in Support of Herschel, SOFIA, and ALMA October , 2006 Pasadena, 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 T 1 and T 2 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 T 1 and T 2 lab measurements 2. The lower state energy of the unassigned line Step 2: Solve for the lower state energy of unassigned line Eqn. 1 Eqn. 2

Step 3: Form a ratio between the observed intensities of an assigned and unassigned line at T 1 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 T 3 of the known (assigned) reference line and unassigned line in the molecular cloud Eqn. 3 Eqn. 4

Methyl Formate

Methanol

Comparison of Energy Levels Calculated from Experimental and Quantum Calculations for SO 2

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 voltage power supply Slow wave structure sweeper Aluminum cell: length 6 m; diameter 15 cm Trigger channel /Triangular waveform channel Signal channel BWO Magnet Lens Filament voltage power supply Length ~60 cm Stepper motor Reference channel Lens Stainless steel rails Path of microwave radiation Preamplifier Frequency roll-off preamplifier Reference gas 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 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

CH 3 F 77 K Rotational Temperatures in a Collisional Cooling Cell as a function of K-state: Experiment vs. Theory