"Advanced Tools" Example Applications

Here we sketch the likely analysis path for ALMA applications, broken into conrete steps. First we list general common analysis steps and then we look at three specific examples.

Any Simple Spectral Imaging Program

Any imaging program targeting even a single spectral line would need to explore the intensity image in three dimensions to aid in reduction and analysis planning. Not all of these will be useful to all applications. In particular in bright, chemically rich regions many of the basic analysis tools can be expected to break spectacularly.

Data Browsing :

  • handle coordinates, velocities
    • be able to chew on FITS from any major radio/mm/IR observatory
  • examine intensity plane by plane
  • browse spectra as a function of position
    • overlay of Splatalogue line lists (and subsets) with standard constrains (Eu, Aij, freq range etc)
    • overplot LTE representation of species on spectrum
  • collapse cube to examine moments
  • extract basic statistics from (3D) parts of the cube
  • smooth the cube
    • along the frequency axis
    • in the image plane
    • on the fly
  • overplot a 2d contour image
  • extract position-velocity diagrams along x, y, or z
    • extract an arbitrary position velocity diagram (2d map along any projection)
  • overplot other data cubes matching
    (interpolations: nearest, cubic, and full regriding [likely outside viewer]):
    • position
    • frequency axis
    • velocity axis (e.g., to use one line as a prior for another)
    • channel
  • deal with 3-d regions
    • visualize 3-d regions in contour (e.g., source catalog, region assignments)
    • spectra of 3-d regions
    • statistics of 3-d regions

Signal Extraction :

  • Identify regions of the cube with significant emission (i.e., masking capability)
    • simple like everything above 3sigma or an intensity cut
    • more complex approaches based on math and stats, e.g., 3sigma and in 3 consecutive channels
    • still more complex approaches focused on contiguous regions, priors
  • Localized, realistic noise estimates for use in other analysis:
    • estimated from signal free regions
    • spatially variable (important for mosaics, PB-corrected cubes)
    • potential to handle non-Gaussian statistics
  • Search for sources in the cube:
    • identify sources blindly
    • identify sources (or extract spectra for stacking) subject to some priors
      • positions known from imaging at other wavelengths
      • constrained velocity based + line list (based on prior knowledge)
      • needs to have both interactive and run on whole cube capability
    • identify signal in the presence of an astronomical background

Basic Analysis :
  • extract basic spectral information
    • fits to common profiles:
      Gaussian, Voigt, Lorentzian, hermite polynomials, astronomical profiles line (double-horn, P-Cygni)
    • derive line widths/shpaes, intensities, velocity
    • calculate other "spectral statistics" - moment, EW, etc.
  • extract basic spatial information
    • fit size, shape (accounting for beam)
    • gaussian decomposition (AIPS does this in 2D)
    • moment, area
  • identify confidence of detection and derived parameters
    • feed off of realistic statistics above
    • verify confidence via known sources ("false star tests")
  • identify set of plausible lines for each source
    • constrained line lists + frequency
  • compare a data set to a model
    • "forward model" the model to mimic observing with ALMA
    • compare a prediction to a real cube or uv-data

Additional Considerations for the Continuum Case

The 2-d case of many of the above capabilities will be useful. In addition to this robust multifrequency synthesis will be important a concern with fractional bandwidths reaching 10s of % and very steep spectral indices, for for beta=2 dust on the Rayleigh Jeans tail Fnu \propto nu^(-4). Additional continuum specific analysis capabilities could include:

  • Ability to fit polynomial to "psuedo"-continuum data that have been imaged as a spectral cube
  • spectral index and/or curvature fitting

Imaging of a Line-Rich Galactic Region (Hot Core or AGB Star)

Regions where the spectrum is swamped by blended, unidentified lines are the most often-cited example of where analysis tasks will not be ready for ALMA data. The basic problems is to extract maximum physical information from an incredibly complex spectrum. Intermediate steps are identification of lines / species and fitting identified families of lines to extract physical conditions. Both parts can be very complex: the first due to line blending, the many species and transitions involved the second because the convolution of physical conditions and source geometry can be complex even for simple geometries.

Several efforts to attack this problem are now underway in Europe: XCLASS (and a planned successor), CASSIS, WEEDS.

Deep Line Observations of A Cosmological Field

Imagine a large mosaic of any well-studied cosmological field. After imaging, signal identification is the major task. We would definitely want blind source extraction and deriving robust statistics for the detections will be very important. Source identification subject to prior knowledge will also be a major piece of the analysis, given that millions of sources are now known from optical surveys with 10s of thousands of spectroscopic redshifts (to use the COSMOS numbers). Automated source characterization will be important to extract information on a large set of sources and will likely include line profile fitting, measurement of extent/concentration, and cross indexing frequency with possible line identifications. ALFALFA (Giovanelli+ '07, Saintonge '07, Brian K is an expert here) tackled this problem using matched filter techniques in the Fourier domain meshed with by-eye inspection. NRAO continuum surveys (NVSS, Condon+ '98, Schinnerer+ '04) used the AIPS functionality, which meshes region identification (threshold-based masking) with a constrained Gaussian fitter. SExtractor addresses similar issues in the optical domain. All of these approaches seem to work by noise estimation followed by thresholding and then characterization/fitting of regions. Stacking analyses would work by using priors to define 3-D regions and then either searching exclusively over these regions (e.g., with matched filters) or simply extracting spectra. The details would depend on the strength of the prior constraints.

Imaging of a Nearby Galaxy With a Central Starburst or an Extragalactic Star Forming Region

Imagine imaging a nearby galaxy that hosts a central nuclear starburst and an extended star-forming disk. In the disk likely immediate tasks would be signal identification, which might take advantage of prior information (e.g., imaging imaging we image HCN emission and already have a 12CO map or imagine that we know the rotation curve). Along each line of sight with signal, one would want to fit the spectral line in some way --- moments, (multiple) Gaussians, hermite polynomials --- to extract information on the gas kinematics. A likely application is decomposition of a complex, continuous source into distinct regions. These might range from individual clumps or clouds to complex (subjective) structures like bars, spiral arms, "spurs" or feathers," giant molecular associations. Each such source will have a complex, potentially controversial definition. Simple geometric transformations, e.g., to galactocentric coordinates, will be a useful tool in the analysis - particularly in marginally resolved galaxies profiles of the intensity and velocity field will be interesting. Fits to more complex morphological models may like GALFIT may be helpful to understand the morphology.

In the central starburst (or other hotspots) this case is likely to become intermediate between the hot core and disk. Line density will be higher and line identification will be a major task and having a useful subset of lines and relative intensity estimates will be useful analysis aids. The degree to which this approaches the "nightmare" Milky Way hot core case depends on source and integration depth, but it seems clear that at least the most famous bright starbursts (Arp 220, NGC 253, NGC4038/9 - which are all famous partially because of their flux / being the nearest of their type) will quickly approach this case. In the cleaner "many separated lines" case we can imagine wanting to extract subcubes for each spectral line (similar to what IFU teams or those using the 16-line MOPRA correlator do now). Then we can imagine dissecting the starburst in 3D position-position velocity space and wanting to extract spectra / line intensities for each region + line combination. Most of the "disk" analysis above would be interesting to apply to each line+region combination.

-- AdamLeroy - 2011-03-21
Topic revision: r5 - 2011-03-22, ToddHunter
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