Analyzing SED Data in Iris

The SED data file for an object of interest can be downloaded from an astronomical database such as NED or SIMBAD; converted to a supported FITS or VOTable format, if necessary, using the SED Importer tool bundled with Iris; and then loaded into Iris by starting the application and selecting the Read from file option in the File menu. We consider the example ASCII data files 3c273.hut.ascii and 3c273.wuppe.ascii, which contain tables of ultraviolet photometric data observed by the Hopkins Ultraviolet Telescope and Wisconsin Ultraviolet Polarimeter Experiment, respectively.

Iris supports IVOA-compliant VOTable and FITS format SED input files, in addition to files downloaded from the NED photometry archive (e.g., in XML format). If you have a SED file in an unsupported format which you would like to import into Iris - e.g., CSV or ASCII - you may do so by first converting the file to a supported format via the SED Importer tool. The SED Importer tool accepts as 'non-standard' any binary or text-based file that does not conform to the IVOA SED, Spectrum and Photometry Data Model; these include FITS and VOTable files which do not conform to the IVOA standards. The full list of SED Importer features is documented in the Converting SED Data to a Supported Format section of the Iris How-to Guide.

In order to coplot the two separate SED data segments of 3c273 in the Iris display, we load each file into the application using the "File -> Read from File" menu option, and then select the Coplot menu option. This opens the "Spectrograms from Memory" window, where we select both SED segments for plotting, using the Shift or Control key to highlight both:

The Iris Coplot menu allows you to select multiple SED data segments from the tool's memory buffer for simultaneous display in Iris, in order to add and delete segments at will throughout the Iris session.

The Pan option at the bottom of the Iris main display allows you to view the full spectral range covered by all SED data which has been read into the session, beyond the edges of the data segment(s) which is currently displayed.

It is important to note that the coplotting process does not involve combining, coadding, or splicing the spectral data in memory in any way (the Coplot->Process option is unavailable); the raw data from the multiple input spectrograms is completely preserved in the resulting combination, which is why the two spectrograms of 3c273 show in the figure above are offset in the y-direction (flux density) at the same x value (wavelength).

Finally, note that one of the loaded data segments displays in magenta-colored symbols; this indicates that the data have associated zero-value errors. Data points with zero-value errors are ignored in the model fitting in Iris (see the Iris FAQs for details).

By right-clicking on one of the 3c273 SED data segments or points in the Iris display, we can view the metadata for that particular segment or point, including information on the segment type, e.g., "SPECTRUM" or "Photometry Point"; data identification, e.g., the instrument used to obtain the data, in which observing mode, and the bandpass covered by the data; curation information such as the publisher of the data, e.g., "NASA Extragalactic Database", and the rights to the data, whether "PUBLIC" or not; among other details.

In addition to metdata, right-clicking on a data segment also shows the x and y data values comprising that segment, e.g., "SpectralAxis" versus "FluxAxis". The values returned are those which were imported into Iris from NED, or uploaded from a file on your hard disk; i.e., not what is currently plotted in the Iris display in the event that you changed the units of the display.

To simultaneously display the metadata and data values for multiple photometric points, select the Coplot menu option, and then right-click on the appropriate file(s) in the Spectrograms in Memory window which opens).

For our analysis we choose to fit only a subset of one of our loaded segments of 3c273, the ~1370-1830 Angstroms range within the HUT segment (recalling that the WUPPE segment has zero-value errors, and therefore would not be included in the fit had we left it in the fitting range). We set this as the range of data to be fit by selecting the Define Range option in the Fit window. This prompts us to click on the data display twice, once to define the lower endpoint of the data range, and once for the upper endpoint.

We decide to fit our chosen subset of data with a multi-component, 1-D source model consisting of the sum of one polynomial and two Gaussians, to model the observed continuum emission and two emission lines, respectively.

Before defining our model expression, we delete the default power-law component which is automatically added to the list of model components in the Fit window, since we do not wish to include this component in our model expression for fitting (it is not required that we delete this component if we do not wish to fit with it; it may simply be ignored when defining the model expression). Then, we select "Add" to browse the full list of optical and X-ray models available, to find a 1-D polynomial and Gaussian model. From this list, we make three selections: "polynomial1d" once, and "gauss1d" twice, in order to define these as the components with which to build our full model expression. The components will appear with identifiers "c1", "c2", and "c3" in the Fit window.

Having selected our model components, we combine them into the appropriate arithmetic expression in the "Model Expression" field: "c1+c2+c3"; this is the composite model which will be used to fit our specified data range of the HUT SED of 3c273.

Next, we set some starting model parameter values for the fit by selecting the desired model component in the Fit window, and then "Edit". Parameter values may be set in the fields of the editing window which opens, by entering the desired number and then selecting "Return" on your computer keyboard.

For our analysis, we choose to allow all model parameters to vary in the fit except the position (in Angstroms) of the two Gaussian models. Wet set this preference by keeping the "Fit" box checked in the parameter editing window for all model parameters but the 'pos' gauss1d model parameters. Finally, we measure the position (in Angstroms) of each emission line in the Iris main display - aligning the crosshairs of the mouse cursor with the center of each line and reading the associated X-axis value - and set these values in the parameter editing window.

Our final step in the preparation for fitting involves choosing a fit statistic and optimization method appropriate for our analysis. Selecting "Fit" in the Fit window launches a new "Fitted" window containing our statistic and method options.

We see that the fit can be done with a least-squares statistic, or chi-squared (with various methods for estimating the variances used by chi-squared), or with either of two maximum likelihood statistics that are useful when the data have low numbers of counts. We choose to fit with the Least-squares statistic and an optimization method we know to be very robust, Nelder-Mead.

We are now ready to fit the data using our defined data range and model expression, initial model parameters values, and chosen fit statistic and method. Selecing "Start" in the "Fitted" window starts the fitting process.

When the fit completes, we see the fitted model overlaid on the SED data in the Iris main display; a data-to-model residuals plot in dex units ( log₁₀(data/model)); and the following fit statistics returned in the "Fitted" window: the final fit statistic value, the number of data points used in the fit, and the number of degrees of freedom in the fit (the null hypothesis probability value of the fit, and the reduced statistic, are not calculated with least-squares).

Changing the statistic to Cash and switching over to the Confidence tab in the "Fitted" window, we enter "1.6" in the "sigma" field and click "Start" to calculate and display the 90% confidence limits on the best-fit model parameter values resulting from the fit.

Not completely satisfied with this initial fit - as many parameter bounds have been found to lie outside their hard limit boundaries - we adjust the model parameter values to better match the data, thaw the Gaussian position parameters, experiment with different chi-squared fit statistics, and then re-fit. We continue on in this fashion, iterating through the fit - adding or deleting models from the model expression; changing parameter values or ranges; extending or shrinking the fitted data range - until we find a satisfactory model that best describes our 3c273 SED segment. Finally, we opt to write our custom model expression and best-fit parameters to file via the "Save" option in the Iris Fit window, in order to resurrect this particular fit in a future Iris analysis session.

Iris provides many file format options for output, saved SED data; these are: XML (.xml), VOTable (.vot), FITS (.fits), and various image formats (.jpg, .png,. gif,. bmp, .wbmp). To save our 3c273 SED data currently in the Iris main display (excluding model data values) to a FITS format file, for example, we would select the File->Save as FITS menu option, to create file "3c273_hut_wuppe.fits". We can then access our saved SED data in a future session of Iris simply by selecting the File->Read from File option.

When writing output data to a file in Iris, the metadata from the input SED file is copied to the output file. When multiple SED data segments are coplotted in Iris, the output file contains the merged metadata from all input files together.

Our Iris fitting session may be saved separately by being sure to select the "Save" option in the Iris Fit window after we have finalized our fit, and prior to exiting the fitting session with the "Dismiss" button in the Fit window.

This is equivalent to selecting the File->Write to file option, which saves the model to a CDB format file which can be read back into Iris at a later time to restore the fitting session; the File->Read from File menu option may be used for this purpose.

We may also use the File -> Write to text file options to save the spectral model to file in a human-readable text format, either all model components, or only those active in the fit. Example output is shown below:

Mon Sep 26 15:05:15 EDT 2011  Iris 1.0

TARGNAME: 3c273

Fit parameters:
        Final fit statistic:      0.0092142304415961159
        Reduced statistic:        nan
        Probability [Q-value]:    nan
        Degrees of freedom:       884.0
        Data points:              889
        Last function evaluation: 613

Component 1: polynomial
       c0     = 0.01804294 (0.009438135 -0.5074261)                       
   F   c1     = 0.0                                                       
   F   c2     = 0.0                                                       
   F   c3     = 0.0                                                       
   F   c4     = 0.0                                                       
   F   c5     = 0.0                                                       
   F   offset = 0.0                                                       

Component 2: gauss1d
       fwhm = 23.697289   (NaN NaN)                                       
   F   pos  = 1408.0                                                      
       ampl = 0.042726856 (NaN -39918.703)                                

Component 3: gauss1d
       fwhm = 28.892221   (NaN NaN)                                       
   F   pos  = 1788.0                                                      
       ampl = 0.016649174 (NaN NaN)