Sherpa Part Three (Spectral Measurements)

Over the course of this semester, I have been utilizing the program Sherpa, written in Python, to model Potassium (K) absorption lines and make three specific measurements. Specifically, these measurements are the equivalent width, full width half maximum, and line-to-continuum flux ratio. In this entry, I will show the commands I utilized to make these measurements.

When I use Sherpa, I import it as a python module as such:
>>> from sherpa.astro.ui import *    # All Sherpa functions are found here

If you followed my post on modeling with Sherpa, then I have used 3 separate model components to create my model. These include the power law (pl), the lorentzian (l1) and the gaussian (g1). The power law describes the continuum, and the three together represent the data.

To measure the equivalent width of the K line, I use Sherpa's eqwidth() function. The syntax is:
>>>eqwidth(continuum, continuum+line, lo=lower wl limit, hi=upper wl limit, id=data ID #)
Using my data for a K line whose line goes from 1.252µ to 1.253µ, I measure the eq. width like so:
>>> eqwidth(pl, pl+l1+g1, lo=1.252, hi=1.253, id=1)

The output will be the equivalent width value, in microns. Nice and simple. The hard part was constructing the models and eyeballing the lower/upper limits for the eq. width measurement. All of this I did manually by eye.

The line-to-continuum flux ratio and full width half maximum measurements are harder. They require locating the actual arrays of values for the various models. In order to access the model's x and y values (continuum+lorentzian+gaussian), you do:
>>> modelArrays = get_model_plot(1)     # The 1 is the ID number
# modelArrays.x  --> array of x values
# modelArrays.y  --> array of y values

To access the y values for the continuum only (pl), you have to do:
>>> key = pl._cache.keys()[0]
>>>  cont_yvals = pl._cache[key]
# This may not work if some of the values in pl.__dict__ are not set properly. To be honest, # I'm not fully sure which ones may screw this up, but for me, I have:
>>> pl._NoNewAttributesAfterInit__initialized = True
>>> pl._use_caching = True
# For me, since I use a power law with an exponent of 0, all of the y values are the same. So I can access this value instead by doing:
>>> cont_yval = pl.ampl      # The continuum is a constant value: the amplitude

Armed with the model's x and y value arrays, and the continuum's y value array (or value), we can make the measurements. To calculate the line-to-continuum flux ratio, we must first find the minimum (maximum for emission lines) value of the model, and then compare it with the corresponding continuum flux value:
>>> F_model = numpy.min(modelArrays.y)        # Minimum of the model
>>> min_ind = numpy.where(modelArrays.y == F_model)[0][0]   # min's array index
>>> F_cont = cont_yvals[min_ind]                      # Continuum value
>>> depth = 1.0 - (F_model/F_cont)                  # The line-to-continuum flux ratio!

The full width half maximum was a little tougher. The algorithm I used is as follows:
>>> F_halfmax = (F_cont + F_max) / 2.0            # Flux at the half maximum
>>> indices = numpy.where(modelArrays.y <= F_halfmax)[0]
>>> wls = modelArrays.x[indices]
>>> fwhm = wls[-1] - wls[0]

The problem with this algorithm is that sometimes there are pockets of spectrum that are equal to or lower than the half max, which get into the wls array. For those, I had to go through them manually and fix the wls array.

That's how I measured the equivalent width, line-to-continuum flux ratio, and full width half maximum using Sherpa. If you have any questions or know of a better (or different) way of calculating these values, feel free to leave a comment or email me at danfeldman90@gmail.com

Spectral Line Measurements Visualized

This week I've started looking into making measurements of spectral features using Sherpa  (program in Python). Before doing this, I wanted to understand what these measurements are, visually. These three measurements are Equivalent Width, Full Width Half Maximum (FWHM), and Line-to-Continuum Flux Ratio.

Shown in the figure above is the equivalent width (W) of an absorption line. The idea is you take the total area inside the absorption line, and create a rectangular box of the same area, extending from the continuum to the 0 flux line. The width of this box is the equivalent width. This measurement is used to describe the strength of the line (the higher the value, the stronger the line)!

Shown in the above plot is the Full Width Half Maximum (FWHM) of an emission line (it's the same idea for absorption lines). You get the peak (maximum) value of the emission line, and draw a line at the half point. The width of the spectral feature at this flux value is the FWHM. For an absorption line, it's the half of the minimum value instead of maximum. This measurement is used to describe how broadened the spectral feature is (the higher the value, the more broadened the line)!

Shown above is a sketch I made to illustrate the line-to-continuum flux ratio. In essence, you take the ratio of the flux of the continuum (the example used in the figure is a continuum flux of 1.0) to the flux of the max (or min) value of the feature (in the example, a value of 0.3) and subtracts it from 1. This measurement is used to characterize the depth of the line compared to the continuum (the higher the value, the deeper the line)! In the example above, the value is [1 - (0.3/1)] = 0.7

As illustrated above, these measurements describe a spectral feature. To recap, the equivalent width characterizes the overall strength of the line, the FWHM characterizes the width, or how broadened the line is, and the line-to-continuum flux ratio characterizes the depth of the line! Together, you can discern what the spectral feature may be saying about the physics of the scenario or target you are observing.

-Dan