The sub-module FUSS.isp contains functions used to calculate the Stokes parameters of the Interstellar Polarisation (ISP).

ISP from a depolarised range

Under certain assumptions (e.g. complete depolarisation in line blanketed regions), a range of polarisation can be defined as containing no intrinsic SN polarisation and only ISP.

from_range()

Calculates the Stokes parameters of ISP by averaging q and u within a range defined by the user, either on calling the function or interactively on a plot.

Parameters

• filename_pol (string): Name of the file containing the polarisation data.
• wlmin (optional, int/float): Start wavelength of the range. Default is None. If left as None then a plot will appear showing the data and the range should be selected interactively from the plot.
• wlmax (optional, int/float): End wavelength of the range. Default is None.

Returns

• pisp, Δpisp, qisp, Δqisp, uisp, Δusip

ISP from an emission line

In SNe, the light from emission lines is assumed to be completely depolarised, so the polarisation associated with the emission line is pure ISP. Because there may be underlying SN continuum polarisation mixed in with the emission line polarisation, we need to separate the two to obtain the ISP.

from_emline()

Estimates the ISP from the polarisation and flux associated with an emission line.

Parameters

• filename_pol (string): Name of the file containing the polarisation data.
• filename_spctr (string): Name of the file containing the flux spectrum.
• wlmin (optional, int/float): Lower wavelength cut-off of the data. Default is 4400.
• cont2ranges (optional, Boolean): Whether the continuum should be defined from 2 ranges on either side of the line (True), or from 2 points on either side of the line (False). Default is False.

Returns

• 2 Arrays, first one contains ISP, second contains continuum polarisation, with the Stokes parameters given in the following order: [p, Δp, q, Δq, u, Δu]

Removing the ISP

Constant ISP

const_isp(*args)

Removes ISP that is constant with wavelength.

Parameters

• wlp (1D array): Wavelength bins of the data
• qisp (1D array): Stokes q of the ISP
• qispr (1D array): Error on Stokes q of the ISP
• uisp (1D array): Stokes u of the ISP
• uispr (1D array): Error on Stokes u of the ISP
• q (1D array): Stokes q of the data
• qr (1D array): Error on Stokes q of the data
• u (1D array): Stokes u of the data
• ur (1D array): Error on Stokes u of the data

Returns

• Array containing the ISP corrected stokes parameters: [wlp, new p, new p error, new q, new q error, new u, new u error, new pol angle, new pol angle error]

Linear ISP

linear_isp(*args)

Removes ISP that is linearly dependent on the wavelength, i.e. for which qisp is of the form m*λ + c, where m is the gradient and c the intercept. These two quantities should have errors.

Parameters

• wlp (1D array): Wavelength bins of the data
• gradq (array): The array must be of the form: [gradient of q isp, error on gradient]
• constq (array): The array must be of the form: [intercept of q isp, error on intercept]
• gradu (1D array): The array must be of the form: [gradient of u isp, error on gradient]
• constu (1D array): The array must be of the form: [intercept of u isp, error on intercept]
• q (1D array, optional): Stokes q of the data
• qr (1D array, optional): Error on Stokes q of the data
• u (1D array, optional): Stokes u of the data
• ur (1D array, optional): Error on Stokes u of the data

Returns

• Array containing the ISP corrected stokes parameters: [wlp, new p, new p error, new q, new q error, new u, new u error, new pol angle, new pol angle error]