wdwarfdate is a Python open source code which derives the Bayesian total age of a white dwarf from an effective temperature and a surface gravity. wdwarfdate runs a chain of models assuming single star evolution and estimate the following parameters and their uncertainties: total age of the object, mass and cooling age of the white dwarf and mass and lifetime of the progenitor star. Checkout the documentation for wdwarfdate here.

To install wdwarfdate please do it from the source in GitHub. This can be done with the following lines:

git clone https://github.com/rkiman/wdwarfdate.git
cd wdwarfdate
python setup.py install

Dependences

To run wdwarfdate the following packages are needed: NumPy, astropy, matplotlib, and SciPy. These can be installed with the following line:

pip install numpy astropy matplotlib scipy 

Getting right to it, let's make and example on how to estimate the ages of a couple of white dwarfs using wdwarfdate. First let's define the effective temperatures and surface gravity for both white dwarfs (Cummings et al. 2018).

import wdwarfdate    # Import the code wdwarfdate
import numpy as np

#Define data for the white dwarfs
teffs = np.array([19250,20250])
teffs_err = np.array([500,850])
loggs = np.array([8.16,8.526])
loggs_err = np.array([0.084,0.126])

To run wdwarfdate we first set up the object WhiteDwarf with the parameters of the models we want to use. The code will explicitly integrate over the prior and the likelihood to perform the normalization, using the grid method. The parameters which are being sampled are the mass of the progenitor star, the cooling age of the white dwarf and the Δm parameter to model the scatter in the initial-to-final mass relation. The limits of the grid will be set automatically but can be set manually in this step too using min_mi and max_mi for the mass, and min_log10_tcool and max_log10_tcool for the cooling age.

WD = wdwarfdate.WhiteDwarf(teffs,teffs_err,loggs,loggs_err,
                           model_wd='DA',feh='p0.00',vvcrit='0.0',
                           model_ifmr = 'Cummings_2018_MIST', 
                           high_perc = 84, low_perc = 16,
                           datatype='Gyr', save_plots=True, 
                           display_plots=True)

Then we run the parameter estimation.

WD.calc_wd_age()

wdwarfdate allows us to select which models we want to use for the white dwarfs: the initial-to-final mass relation, the cooling tracks for DA or non-DA white dwarfs, and the parameters for the stellar evolutionary model of the progenitor star ([Fe/H] and rotation), as shown above. Also with the datatype option we can select the units of the resulting ages. The results of the parameter estimation will be saved in an astropy Table, which is saved in the object WD. To display the results we can do

WD.results

This table will have one row for each teff and logg given and an estimation of the median of the distribution, the difference between the median and the 16th percentile of the distribution, and the difference between the 84th percentile and the median of the distribution for the following parameters:

• ms_age: Main sequence age, or the lifetime of progenitor star.
• cooling_age: Cooling age of the white dwarf.
• total_age: Total age of the white dwarf, which is the sum of the main sequence and the cooling age.
• initial_mass: Initial mass, meaning the mass of the progenitor star.
• final_mass: Final mass, meaning the mass of the white dwarf.

When we run wdwarfdate we can set display_plots=True to display the grid plot with the parameters which were sampled with the code and an extra plot with the distributions of all the parameters, as shown below for the first white dwarf selected above. If we set save_plots=True, these plots will be saved in a folder called results, unless another path is indicated. Below we show the results for the white dwarf with Teff = 19250 and logg = 8.16.

For more explanation and examples checkout the documentation.

If you use wdwarfdate in your research, please cite: Kiman et al. 2022, and the IFMR, cooling models and stellar evolution models you decide to use (See Kiman et al. 2022 or documentation for references.)