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Example Case: AU Mic Spectral Line Fitting

This document describes the AstroGrid example case of finding the measuring the variable strength of the Lyman-alpha line for the flare star, AU Mic. The example case demonstrates how to find the spectra using AstroScope and then send it to SPLAT-VO. It then demonstrates how to normalise the spectra and fit a Gaussian to the Lyman-alpha spectral line.

1   The Example Case

AU Mic is a cool, main sequence, red dwarf that also belongs to a group of variable stars called "flare stars". These flare stars undergo unpredictable but significant increases in brightness which can last from several minutes to several hours and, the flare activity may be observed in the strength of the Lyman-alpha (1216 Angstrom) spectral line [GURZADYN1977].

The aim of this example case will be to use the Astroscope to find spectra of AU Mic. A selection of these spectra will be transferred to the SPLAT, the spectra will be normalised and the strength of the Lyman-alpha line will be measured by fitting a Gaussian profile.

2   AstroScope

2.1   Launching AstroScope

Since AstroScope is a component of the Workbench, the first step is to start the Workbench; information on how to start the Workbench can be found here. Once the Workbench has started, click on the "AstroScope" button to launch the AstroScope component (see the figure below, the AstroScope button has been highlighted with a red circle).

The AstroGrid Workbench with the AstroScope button highlighted.

If you are unfamiliar with the Astroscope, please read the overview (available here) before continuing with this example case.

2.2   Searching for Spectra

The first step in using the AstroScope to search for spectra is to enter the name of the target in the "Position or Object Name" box (in this case one would enter "AU Mic"); upon pressing enter, the AstroScope retrieves the RA and Dec of the target. For the purposes of this exercise we do not want to search for catalogues and images so the relevant boxes on the search panel are unticked. Upon clicking the "Search" button, the AstroScope will search for spectra based on the RA, Dec and search radius provided; depending on what resources on are available at the time, your view will appear similar to the figure below. It is worth noting that placing the cursor over a particular node will display information about that resource; in the image below the cursor (not visible) has been placed over "Hubble Space Telescope".

AstroScope with the results of searching for AU Mic (spectra only).

For this example case, we will focus on retrieving a particular set of spectra taken with the Hubble Space Telescope. Clicking on the "Hubble Space Telescope" node changes the focus of AstroGrid onto that particular search result and moves it to the centre of the search window (see the figure below).

AstroScope search results for AU Mic with focus on HST results.

The data set we are interested in is labelled "0.000458" and clicking on this node, again changes the focus of AstroGrid, but now reveals the available spectra; holding the cursor over any of the spectrum-nodes will display information about that individual spectrum.

2.3   Selecting the Spectra

The search reveals 13 spectra belonging to this data set. We can select all 13 spectra by double-clicking the central node, which turns all the selected spectrum nodes yellow (see the figure below). We can now either save these spectra to the local disk (by clicking the save button) or send the data directly to SPLAT; the method by which the spectra is sent from the AstroScope to SPLAT-VO is explained in the next section.

AstroScope search results for AU Mic.  A group of HST spectra have been selected.

3   SPLAT (Spectral Line Analysis Tool)

3.1   Launching SPLAT

SPLAT is a "graphical tool for displaying, comparing, modifying and analysing astronomical spectra " (from the SPLAT Home Page). For this example case we need to run the Virtual Observatory enabled version of SPLAT (or SPLAT-VO); the Java Web start version (please read this for more information about Java Webstart) can be launched from this page. As with all Java Web start applications, when you first launch SPLAT you may be asked whether you wish to run the application (see the figure below). To speed up launching the application in the future, click the "Always trust content from this publisher" tick box and then click on the "Run" button.

The digital signature message from JAVA with respect to SPLAT-VO.

If you are not familiar with SPLAT, please read the SPLAT walkthrough before continuing.

3.2   Sending the Spectra to SPLAT

After SPLAT has finished loading, it should automatically connect with PLASTIC on the Workbench; you may see a message similar to astrogridplastic temporarily appear on your screen. You should also see a new button appear in the "Process" section of the AstroScope window, labelled "View Spectra in Splat-vo" (see the figure below). With the desired spectra already selected, click this button to send the spectra to SPLAT.

A cropped screen capture of the AstroScope interface showing the button used to send spectra to SPLAT-VO.

The "Global list of spectra" in the main SPLAT-VO window should now list the spectra that you sent to it from the AstroScope; the figure below shows what one should expect.

The main window of SPLAT-VO showing the spectra that it has received from AstroScope.

3.3   Plotting the Spectra

Having sent the spectra from AstroScope to SPLAT-VO, we may wish to plot them to see what they look like; we are going to plot three spectra from the set on top of each other. Select the first, middle and last spectra on the "Global list of spectra" by clicking on them while holding down the control key. Then click on "View" on the menu bar and select "Display/Add to plot" from the drop down menu; this should open up a new window with a plot of all three spectra, similar to the figure below.

The SPLAT-VO plotting window showing three spectra of AU Mic.

Close this plotting window once you have finished with it, it will not be required for the following steps.

3.4   Normalising A Spectrum

The normalisation of a spectrum in SPLAT-VO (and the subsequent fitting of a Gaussian Profile) will be demonstrated for one spectrum (the first one on the "Global list of spectra) and, it can repeated relatively simply for all subsequent spectra.

Click on the spectrum in the main window (to select it) and select the "Display in new plots" option under the "View" menu. This will open a new window, similar to the figure shown above, but just showing the single selected spectrum. To normalise the spectrum one must fit a low order polynomial function to the continuum. Click on "Analysis" on the menu and select "Fit polynomial" from the list that appears. A new window should open that will look similar to the figure shown below.

The SPLAT-VO window used to fit a polynomial to a spectrum.

The following is a step-by-step guide of how to use the "Fit polynomial" interface to normalise the spectrum. The step numbers correspond to the numbers on the figure shown above.

  1. By default, a 0 order polynomial (corresponding to a straight line with no gradient) will be fit to the data points that you later specify. Change this to a first order polynomial (a straight line with a variable gradient by selecting "1" from the drop-down list that appears when the down-arrow button next to "Degree of polynomial" is pressed.

  2. We wish to divide the original spectrum by the polynomial fit to the continuum to obtain a normalised spectrum. Click the tick box next to "Divide spectrum by fit" to ensure that this is done automatically.

  3. One of the most important parts of the fitting process is defining the regions with which to fit. For this example case we will define the continuum fitting regions as being either side of the Lyman-alpha peak. To add a continuum region, first click the "Add" button which will change the window focus to the plotting window and the cursor will change to a cross-hair. Draw a rectangle across a continuum region to the left of the Lyman-alpha peak by clicking and holding the mouse button at the left edge of the region, moving the mouse to the right edge of the area and releasing the mouse button; the height of the boxed region is not important but the width is. Once the mouse button is released, a green vertical band will appear on the spectrum, indicating the selected range and the focus will return to the "Fit polynomial" window. Additionally, the upper and lower limits appear in the "Coordinate ranges" section of the window. Repeat the process for selecting a continuum region on the other side of the Lyman-alpha line. The figure below shows a section of the plot window, where one continuum region has already been selected and another is in the process of being selected. Note: It is possible to edit the continuum region manually by double-clicking either the upper or lower boundary value, editing it to the required value, and pressing enter to accept the changes.

    The SPLAT-VO plotting window showing continuum regions being selected.
  4. With the two continuum regions defined, it is simply now a case of clicking the "Fit (replace)" button. We choose to use the "Fit (Replace)" function rather then the standard "Fit" function because it automatically displays the normalised spectrum in the plotting window (the coefficients of the fit can be found in the "Fit status" section of the "Fit polynomial window"); the figure below shows the normalised spectrum that one might expect. Note also that there will now be two additional spectra in the "Global list of spectra" (on the main window), one spectrum called "Polynomial fit" which is the actual polynomial generated from the fitting process and, a spectrum called "Ratio (AU Mic) by (Polynomial Fit)", which is the normalised spectrum.

    The normalised spectrum.
  5. The "Fit polynomial" window is no longer needed and it should be closed by clicking the "Close" button.

3.5   Fitting a Gaussian Profile

For this final section of the example case, we will be using another spectrum analysis function which is linked to the "Plot window". While ensuring the the plot window is showing the normalised spectrum, select the "Fit lines" option from the "Analysis" drop down menu, this will open the "Measure spectral lines" window (see the figure below).

The SPLAT-VO window used to measure or fit spectral lines.

The following is a step-by-step guide of how to fit a Gaussian profile to the Lyman-alpha line; it is important to note that a Gaussian profile may not be the best profile shape to fit the spectral line but, it is used here for demonstrative purposes. The step numbers correspond to the blue numbers on the figure above.

  1. By default, the "Measure spectral lines" feature of SPLAT-VO performs a "Quick" fit to a defined region, which simply performs an analysis of intensities in the selected region and the chosen background to estimate such values as the line centre and equivalent width. However, the function also has the ability to perform Gaussian, Lorentzian or Voigt fits to profiles. Each profile fitting function is selected using the tick box next to the name. For this example, ensure that "Gaussian" has a tick next to it.
  2. The function can fit a continuum to the spectral line or it can assume a constant value. Since the spectrum has already been normalised, we want it to assume a constant value of 1.0. Click in the box next to "Constant" and enter a value of 1.0 in the "Background value" text field.
  3. As with normalising the spectrum, it is necessary to define the region over which to fit the profile. This is performed in a similar way to selecting the continuum regions shown in the last section. Click the "Add" button and focus will change to the plot window. Click and drag a region across the Lyman-Alpha profile. Upon letting go of the mouse button, the selected region will become yellow and focus will return to the "Measure spectral lines" window; the selected coordinate ranges appear in the "Coordinate range:" table.
  4. Click on the "Fit" button to fit the profile given the parameters provided. The results will appear in the "Spectral fitting results:" table and the best fit Gaussian profile will be plotted over the top of the real spectrum (see the figure below); the black dashed line is the "Quick" fit to the profile.
  5. Clicking on the "Quick" tab in the "Spectral fitting results" section displays the quick fit coefficients (such as peak strength, line centre and equivalent width) of the profile.
  6. Clicking on the "Gaussian" tab displays the results of fitting a Gaussian profile to the Lyman-Alpha line.
  7. After recording the values, close the window by clicking on the "Close" button.
The SPLAT-VO plotting window showing the results of fitting a Gaussian to the Lyman-alpha line.

Repeat the procedure for each valid spectrum (i.e. suitable quality and covering the correct wavelength range) in the "Global list of spectra".

4   The Results

The following table shows the time, centre and flux of the 11 HST spectra of AU Mic retrieved through AstroScope and analysed in SPLAT-VOT (2 were removed due to covering the wrong wavelength range); they have been sorted into chronological order. If you decide to repeat the experiment, use the table as a rough guide to the values that you should obtain (your own values may differ slightly). Note that we observe little change in the line centre fit to the Lyman-alpha line but, we do observe considerable variability in the strength of the line over a relatively short period (several hours in the case of the last 7 spectra).

Time (MJD) Centre (Angstrom) Flux
48501.76 1215.87 223.35
48502.09 1215.80 273.93
48502.15 1215.79 329.41
48502.22 1215.77 255.90
48874.36 1215.81 341.53
48874.43 1215.82 313.73
48874.50 1215.83 221.64
48874.57 1215.83 155.96
48874.65 1215.85 304.51
48874.70 1215.85 302.05
48874.77 1215.85 233.16
[GURZADYN1977]Gurzadyn, G. A.: 1977, Ap&SS 52, 51 (abstract)