An Experimental Approach to the Prediction of Complete Millimeter and Submillimeter Spectra at Astrophysical Temperatures Ivan Medvedev and Frank C. De Lucia Department of Physics Ohio State University

courtesy of J. Cernicharo U-Lines in the IRAM Survey >5000 ‘U’ lines ~40% of total Baseline often confusion, not noise limited

Large fraction of ‘U’ lines most likely corresponds to isotopologues and vibrational excited states of well known molecules like CH 3 OCH 3, CH 3 OH, methyl formate … To identify lines unambiguously we need to know their frequencies and intensities at the temperature of the observed interstellar region To predict the intensity we need to know the lower state energy and the transition dipole moment matrix element

Traditional Bootstrap Approach to Spectral Assignment 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 Run into lines that are hard to assign or fit (perturbations) Sometimes extend to excited vibrational states, other conformers, etc.

Methyl Formate % of lines are assigned

Non-Bootstrap Approach: Measure every line < 0.01 second of data

BUT! We rarely measure intensities Even if we did, we need to know them over the range of astronomical temperatures 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 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

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

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

Comparison of Line Intensity Calculated from Experimental and Quantum Calculations for SO 2

Propagation of Uncertainty (T 2 = 300 K) T 1 = 77 K ==>It is important to have a low temperature reference

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.

Summary and Conclusions 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 should 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.

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