Locating Star Formation Sites Using K-Doublet Formaldehyde Emission

TIP Last Changed: JeffMangum - 30 June 2009

Table of Contents:

To Do

  1. Read background information on molecular excitation, star formation, formaldehyde, etc.
  2. Introduction to data analysis and first look at data to be analyzed.
  3. Step through analysis tasks (such as gaussian fits to all measurements).
    1. Determine best spectral smoothing to apply to all spectra.
    2. Fit baselines to all spectra.
    3. Find best gaussian fits to all spectra. May involve fitting multiple (overlapping) gaussians which are comprised of both emission and absorption components.
    4. Tabulate gaussian fit results, which should include at least the following for each gaussian:
      • Peak intensity (in K)
      • Central velocity (in km/s)
      • FWHM (in km/s)
      • Integrated intensity (in K*km/s)
  4. Compare derived gaussian fit parameters derived from each H2CO transition for similar velocity components within each source. FWHM and central velocity should be very similar.
  5. Form H2CO transition ratios for each source/velocity component integrated intensities using proper statistics. Be sure to apply appropriate Ta-to-Tmb calibration factors. Note, from my analysis of the amplitude calibration measurements in KdoubFormaldehyde:
    • To convert Ta to Ta* use Ta* = (Ta*scale)*Ta. From KdoubFormaldehyde above good average value at each frequency is (Ta*scale) = 1.08 (28.97 GHz) and 1.50 (48.29 GHz).
    • To convert Ta to Tmb use Tmb = (Tmbscale)*Ta. From KdoubFormaldehyde good average value at each frequency is (Tmbscale) = 1.45 (28.97 GHz) and 2.90 (48.29 GHz).
    • The absolute amplitude calibration is reported to be no better than 10-15%, due mainly to temporal drifts in the noise diodes used as absolute amplitude calibration standards.
  6. Study use of line ratios to derive physical conditions. Apply to H2CO measurements using the specific physical structure of the H2CO molecule to this problem.
  7. Analyze dependence of line ratio on density, temperature, and H2CO abundance to understand limitations of line ratio measurements for deriving physical conditions (specifically, density) in star formation regions. Use radiative transfer model (LVG and/or Monte Carlo) in this investigation.
  8. Apply all of the above to the derivation of the spatial density in star formation region sample.
  9. Put derived physical conditions within the context of other measurements of physical conditions in each star formation regions. This will allow for an improved understanding of the physical structure of each star formation region.


All current theories which describe the star formation process predict that an essential ingredient is a dense core which seeds the collapse process. Many star formation regions have been identified through molecular spectral line and dust continuum measurements, and the physical properties of many of these regions have been derived. Due to the non-selective nature of many of the physical probes used to derive these properties, the exact identification of the highest density regions, and thus the regions which are most likely to form stars, have not been identified. For structurally-simple molecular clouds, this density-selective property of the K-doublet transitions allows for a simple and definite identification of the highest densities.

Reference Material

Observations To Be Analyzed

Green Bank Telescope (GBT)

The Green Bank Telescope (GBT) has been used to make single-pointing measurements of the 3(12)-3(13) (28.974805 GHz) and 4(13)-4(14) (48.284547 GHz) K-doublet transitions of H2CO toward a sample of known star formation regions. For both frequencies the correlator was configured using 50 MHz of bandwidth sampled by 16384 channels, which resulted in a spectral resolution of 0.03 and 0.02 km/s at 28.97 and 48.28 GHz, respectively. The primary beam width is 26 and 16 at 28.97 and 48.28 GHz, respectively, offering good spatial resolution to allow identification of the highest density regions.

A summarization of the first-cut results from these measurements is listed in the following table:

H2CO Results Summary
Source H2CO 3(12)-3(13) H2CO 4(13)-4(14)
W3IRS4 -0.060+-0.008 RMS=0.0002
W3OH Emission+Absorption 0.140+-0.013
L1448I3B 0.04+-0.004 RMS=0.04
N1333I4A 0.10+-0.005 0.12+-0.018
N1333I4B 0.05+-0.007 0.090+-0.020
L1551 0.04+-0.004 RMS = 0.02
Orion-KL 4.23+-0.010 1.630+-0.030
OMC2IRS4 0.29+-0.007 0.140+-0.017
Orion-S ... 0.69+-0.02
I05338 0.67+-0.006 0.046+-0.017
NGC2024 ... 0.095+-0.021
NGC2024FIR5 0.21+-0.006 0.150+-0.020
NGC2024FIR6 0.18+-0.009 0.079+-0.018
NGC2071IR 0.209+-0.008 0.175+-0.022
S255N 0.180+-0.005 0.135+-0.009
G34.3 0.172+-0.006 0.119+-0.032
S68N ... 0.090+-0.013
W51M ... 0.200+-0.030
DR21OH 0.247+-0.004 0.255+-0.020
CEPA 0.036+-0.005 0.080+-0.019
N7538-1 0.107+-0.008 0.087+-0.015
N7538-9 0.053+-0.007 0.048+-0.016
3C48 0.62/0.90 0.34/0.25
0319+413 (3C84) ... 2.5/2.3
NGC7027 ... 0.92+-0.04/1.08+-0.04
*For flux cal sources values are continuum Ta in IF0/IF1

The following figures show spectra from each source based on a preliminary analysis. For each spectrum the solid line shows the 3(12)-3(12) transition intensity, while the dashed line shows the 4(13)-4(14) transition intensity.

!H2CO J 3 and J 4 Measurements !H2CO J 3 and J 4 Measurements !H2CO J 3 and J 4 Measurements

Very Large Array (VLA)

The Very Large Array (VLA) was used to image the H2CO 2(11)-2(12) K-doublet transition toward the DR21(OH) star formation region. The 27 antennas of the VLA were in the D-configuration during these observations, which afforded a spatial resolution of approximately 6 arcsec. 128 spectral channels were used to sample the 1.5625 MHz IF bandwidth which, after on-line Hanning smoothing, resulted in a velocity resolution of 0.25 km/s at the line rest frequency of 14.488475 GHz.

The following two figures show some preliminary analyses of these DR21(OH) 2(11)-2(12) emission imaging measurements. The first figure shows the larger-scale distribution of H2CO toward the DR21(OH) region (specifically, the MM1/MM2, DR21OHW, and DR21OHS components. The second figure is a close-up view of the MM1/MM2 region, which contains numerous signposts of star formation including outflow, H2O maser, and CH3OH maser emission.

!H2CO J 2 Toward DR21(OH) !H2CO J 2 Toward DR21(OH)MM1/MM2

Formaldehyde as a High Density Probe

Formaldehyde (H2CO) is a proven tracer of the high density environs of molecular clouds. It is ubiquitous: H2CO is associated with 80% of the HII regions surveyed by Downes etal. (1980), and possesses a large number of observationally accessible transitions from centimeter to far-infrared wavelengths. Because H2CO is a slightly asymmetric rotor molecule, each rotational energy level is split by this asymmetry into two energy levels. Therefore, the energy levels must be designated by a total angular momentum quantum number, J, the projection of J along the symmetry axis for a limiting prolate symmetric top, K_{-1}, and the projection of J along the symmetry axis for a limiting oblate symmetric top, K_{+1}. This splitting leads to two basic types of transitions: the high-frequency \Delta J = 1, \Delta K_{-1}= 0, \Delta K_{+1}=  -1 ``P-branch'' transitions and the lower-frequency \Delta J = 0, \Delta K_{-1}= 0, \Delta K_{+1}= \pm 1 ``Q-branch'' transitions, popularly known as the ``K-doublet'' transitions (see the Figure below). The P-branch transitions are only seen in emission in regions where n(H_2) \geq 10^5 cm^{-3}. The excitation of the K-doublet transitions, though, is not so simple. For n(H_2) \leq 10^5 cm^{-3}, the lower energy states of the 1_{10}\rightarrow 1_{11} through 5_{14}\rightarrow 5_{15} K-doublet transitions become overpopulated due to a collisional selection effect (Evans etal (1975); Garrison etal (1975)). This overpopulation cools the J\leq5 K-doublets to excitation temperatures lower than that of the cosmic microwave background, causing them to appear in absorption. For n(H_2) \geq 10^{5.5} cm^{-3}, this collisional pump is quenched and the J\leq 5 K-doublets are then seen in emission over a wide range of kinetic temperatures and abundances.

!H2CO K-Doublet Prediction

Large Velocity Gradient model prediction of the excitation temperature of the 1_{10}\rightarrow 1_{11} (solid circle), 2_{11}\rightarrow 2_{12} (solid square), 3_{12}\rightarrow 3_{13} (solid star), and 4_{13}\rightarrow 4_{14} (open square) transitions of H_2CO for a typical kinetic temperature and molecular column density over the density range from 10^4 to 10^7 cm^{-3}. When the excitation temperature becomes larger than the cosmic background radiation temperature of 2.78 K, the spectral line goes into emission.

For structurally-simple molecular clouds, this density-selective property of the K-doublet transitions allows for a simple and definite identification of the highest densities. This simple interpretation, though can be made more complicated by the following:

  • Abundance Gradients: Gradients in the abundance of several molecules have been predicted and observed in protostellar environments. Significant gradients in the H_2CO abundance, though, are not observed (Jorgensen etal (2005).
  • Density Gradients: Most models of the density structure of protostars assume a power-law dependence. A typical example of these power-law density models is described by Jorgensen etal (2002), which derive a outer radius (r=10,000 AU) density of approximately 10^5 cm^{-3} for a wide selection of protostellar sources. As this outer radius is very close to the emission excitation point for the H_2CO K-doublet transitions, density gradients in the protostars sampled will likely not significantly complicate the interpretation of the proposed measurements.
  • Temperature Gradients: Models of the physical conditions in protostars tend to predict at most moderate kinetic temperature gradients. Coupled with the fact that the excitation of the K-doublet transitions of H_2CO are only weakly dependent upon temperature, gradients in this physical quantity are likely not to be a source of complication.
Topic revision: r8 - 2009-06-30, JeffMangum
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