Spectral Lines

Tools for measuring spectral features with a variety of smoothing and modeling methods.

Methodology

The spectral features are defined in 10 different zones.

Feature name	lambda	Blue lambda_min	Blue lambda_max	Red lambda_min	Red lambda_max
CaIIHK	3945	3504	3687	3887	3990
SiII4000	4128	3830	3963	4034	4150
MgII	4481	4034	4150	4452	4573
Fe4800	4966	4400	4650	5050	5300
SIIW_L	5454	5085	5250	5250	5450
SIIW_R	5640	5250	5450	5500	5681
SIIW	5500	5085	5250	5500	5681
SiII5972	5972	5550	5681	5850	6015
SiII6355	6355	5850	6015	6250	6365
OI7773	8100	7100	7270	7720	8000

5 of these zones have specific subregions used to search for minima, which later define the ejecta velocity measured in these zones:

Feature name	lambda_min	lambda_max
SiII4000	3963	4034
SIIW_L	5200	5350
SIIW_R	5351	5550
SiII5972	5700	5900
SiII6355	6000	6210

The base class (Measure) includes helper functions for moving between wavelength and velocity space (via the relativistic Doppler effect) and gives two options for normalizing a given spectrum:

• norm='SNID' (default) defines a 13-point spline from the entire spectrum and normalizes by this spline (see Blondin & Tonry 2007)
• norm='None' does no normalization

This base class also has methods for finding local extrema once the spectrum is smoothed, using these extrema to define a pseudo-continuum, and finally calculating line velocities and equivalent widths.

Note: The velocity calculation in this code uses the relativistic Doppler equation, unlike most spectral feature measurements (including the SNfactory pipeline).

Every measurement object inherits from the base measurement class and implement particular smoothing methods. The interface is through:

• get_smoothed_feature_spec: This method returns the flux of the feature smoothed by the corresponding smoothing methodology. The wavelengths that the flux model is evaluated at are the same as the input spectrum
• get_interp_feature_spec: same as get_smoothed_feature_spec but interpolated on a finer wavelength grid (determined by the interp_grid parameter)

Smoothing options

Spline (spline.py)

An inverse-Gaussian weighted spline is used to smooth and interpolate the raw spectrum. This is the method presented in Blondin et al. 2006. First, we define a Gaussian window with a width corresponding to the approximate scale of Doppler broadening of the spectral lines at each wavelength. This Gaussian filter is then weighted by the inverse of the variance of the observed spectrum, and then applied to the spectrum signal.

This method requires an accurate variance spectrum to be provided. If the variance is overestimated, the resulting smoothed spectrum will be oversmoothed, which can bias some of the spectral feature measurements.

Savitsky-Golay smoothing (sg.py)

This is the method laid out in Chotard et al. (in prep)., and matches the behavior of the code in the SNfactory pipeline. This method uses a Savitsky-Golay filter with a smoothing window width determined optimally (Appendix A of the paper).

Gaussian and Gaussian doublet (gauss.py and doublet.py)

These use simple maximum likelihood estimation to fit a Gaussian/double Gaussian profile to the zone.

Scripts and notebooks

Each of these scripts makes use of the internal release of the Supernova Factory data (and related IDRTools package). example_plots.py can be easily modified to use other data sets.

• example_plots.py contains functions to make sample plots comparing the different smoothing/normalization methods.
• compare_snf.py calculates all measurements with errors for all at-max spectra in the SNfactory data set and compiles the same measurements in the output of the SNfactory pipeline code.
• debug_plots.ipynb contains some code to visualize the differences between the SNfactory pipeline measurement codes and this code based on the results of compare_snf.py.
• method_comparison.ipynb contains code to directly compare the results of the SNf pipeline measurement to this code.

Installation

1. Clone this repository git clone https://github.com/sam-dixon/spectral_lines.git

2. Create a conda environment. conda env create -f environment.yml

3. Activate this environment conda activate spectral_lines

4. Install pip install .