Eclipsing binaries Learning & Interactive System
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ELISa: A new tool for fast modelling of eclipsing binaries
ELISa
ELISa is a cross-platform python package dedicated to light curves modelling of close eclipsing binaries including surface features such as spots (and pulsations which will be added soon). Current capabilities include:
BinarySystem:class for modelling surfaces of detached, semi-detached and over-contact binariesSingleSystem:class for modelling surfaces of single star light curves with full implementation of spots and pulsationsObserver:class for generating light curves (and in future other observables)Spots:class for generating stellar spot with given longitude, latitude, radius and temperature factorPulsations:class for modelling low amplitude pulsations based on spherical harmonicsFitting methodsprovide capabilities to fit radial velocities curves and light curves via implementaion ofnon-linear least squaresmethod and also viaMarkov Chain Monte Carlomethod.- radial velocity curve modelling in Observer class including
Rossiter-McLaughlineffect, variation due to spots and pulsations
ELISa is currently still under development. Development of the following features is in progress:
- extension of
LCandRVfitting methods using various additional methods and features such as classification of eclipsing binaries vianeural-networksaimed towards automatisation of the inverse problem,
We also plan to implement following features:
- addition of synthetic spectral line modelling
Requirements
ELISa is a python package which requires python v3.6+ and has following dependencies:
REQUIRES UPDATE astropy>=4.0.1.post1 corner>=2.0.1,<=2.1.0 emcee==3.0.1 jsonschema>=3.2.0 matplotlib==3.3.2 numpy>=1.16.2,<=1.19.2 pandas>=0.24.0,<=1.1.2 pypex==0.1.0 pytest==3.2.3 python-dateutil>=2.6.1,<=2.8.1 scipy>=1.0.0,<=1.5.2 tqdm==4.43.0 parameterized>=0.7.4
and potentially also python-tk package or equivalent for matplotlib package to display the figures correctly.
| note: | although python distribution and package versions are specified precisely, that does not mean that the package will not work with higher versions, only that the ELISa was not tested using newer versions. However, we highly recommend sticking with the python distribution and package versions listed above. |
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Installing process
In the case of ELISa, the easiest and safest way to install is to create a python virtual
environment and install all requirements into it. Below is a simple guide, how to do it. Details of installation differ
in dependence on the selected operating system.
Ubuntu [or similar]
First, you have to install Python 3.6 or higher. In the latest stable version Ubuntu 18.04 there is already preinstalled
python 3.6.x. In older versions, you will have to add the repository and install it manually. Several guides
on the internet will help you with installation, e.g. Python_3.6
Install pip3 python package manager if is not already installed on your system, usually by execution of the
command:
apt install -y python3-pip
or you can also use raw python script which provides installation via python:
curl https://bootstrap.pypa.io/get-pip.py | python3.6
Install virtual environment by command:
pip3 install virtualenv
To create a virtual environment, create a directory where the python virtual environment will be stored,
e.g. /<any>/<path>/elisa/venv
and run the following command:
virtualenv /<any>/<path>/elisa/venv --python=python3.6
After few moments your virtual environment is created and ready for use. In the terminal window, activate virtual environment:
. /<any>/<path>/elisa/venv/bin/activate
When the virtual environment is activated, install the elisa package in the latest stable version:
pip install elisa
or you can choose to install the current development version:
pip install git+https://github.com/mikecokina/elisa.git@dev
You will probably also need to install:
apt install -y python3-tk
If you would like to have a look at the jupyter notebooks covering the basic usage of this package, you should install jupyterlab inside the previously created virtual environment:
pip3 install jupyterlab
followed by installation of ipython kernel:
python3 -m pip install ipykernel
Now you should be able to launch jupyter notebooks and run the tutorials stored in <elisa_dir>/jupyter_tutorials/.
Windows
To install python in windows, download the python 3.6.x installation package from the official Python website.
The installation package will create all necessary dependencies except the virtual environment package.
Install virtual environment by execution of following command in the command line:
pip3 install virtualenv
Make sure a correct version of python and pip is used. When done, create a directory where the virtual environment will be stored and run:
virtualenv /<any>/<path>/elisa --python<path>/<to>/python3.6/python.exe
It is common to specify the full path to the python.exe file under Windows, otherwise, It might not work.
Now, when the virtual environment is prepared, run:
. /<any>/<path>/elisa/Scripts/activate
And finally install ELISa:
pip install elisa
How to build API docs
Read this readme file to see detailed instruction how to generate up to date documentation.
Minimal configuration
From version 0.6, ELISa provides a feature to make configuration easier for first time running users. We implemented Settings Manager and Download Manager. When any ELISa script is first time executed and there is missing configuration file a wizzard will walk you through basic configuration (default configuration will be stored in path ~/.elisa/config.ini file). It asks you to supply a directories to store atmospheres and limb darkening files and default atmosphere atlas. It also gives you a chance to automatically download given files without any futher needs to do it manually.
Manual configuration
ELISa requires minimal configuration before the first run provided by the config file. Initially, it is necessary to
download Atmospheres models and Limb-Darkening tables.
Default tables location
By default, the Elisa will search for atmosphere and limb darkening tables in:
- atmospheres: $HOME/.elisa/atmosphere/
- limb darkening: $HOME/.elisa/limb_darkening/
therefore, atmosphere and limb darkening tables stored at those locations will be used by elisa by default.
Custom tables location
Atmosphere models and LD coefficients can be stored on your machine in the directory of your choosing as well. Let's say you want to use Castelli-Kurucz 2004
models stored in the directory /home/user/castelli_kurucz/ck04 and limb darkening models in the directory
/home/user/ld/. You have to create a configuration ini file where
the model and directories will be specified. Now assume that name of our configuration file is elisa_config.ini located
in path /home/user/.elisa/. Then the content of your configuration file should at least look like the following
example:
[support] ld_tables = /home/user/ld castelli_kurucz_04_atm_tables = /home/user/castelli_kurucz/ck04 atlas = ck04
Full content of configuration file with description might be found here: Elisa-Configuration-File
| warning: | atmospheric models and limb darkening tables for this package are stored in industry standard ''.csv'' files. Therefore, their native format is not suitable for Elisa and require conversion to our standard format. Therefore the atmosphere models and LD coefficient tables have been altered to form required by the Elisa. |
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Now, you have to tell ELISa, where to find your configuration file. Environment variable ELISA_CONFIG is used to store a full path to the config file. In UNIX like operation systems it is done by the following command:
export ELISA_CONFIG=/home/user/.elisa/elisa_config.ini
There are plenty ways how to setup environment variable which vary on operation system and also on the tool (IDE)
that you have in use. On Linux, as an example, you can copy the previous command to #HOME/.bashrc (depends on terminal
type). Optionally, you can use the config.ini file located in ELISa_folder/src/elisa/conf/ without
any need for setting an environmental variable.
Now you are all setup and ready to code.
Usage
For in depth tutorials, see directory elisa/jupyter_tutorials.
Physics
See ELISa handbook to see how ELISa models single star and binary systems.
Available passbands
ELISa is currently capable of modelling light curves in the following photometric filters:
bolometric Generic.Bessell.U Generic.Bessell.B Generic.Bessell.V Generic.Bessell.R Generic.Bessell.I SLOAN.SDSS.u SLOAN.SDSS.g SLOAN.SDSS.r SLOAN.SDSS.i SLOAN.SDSS.z Generic.Stromgren.u Generic.Stromgren.v Generic.Stromgren.b Generic.Stromgren.y Kepler GaiaDR2 TESS
Multiprocessing
To speed up the computation of light curves, parallelization of computations has been implemented. Computation of light curve points is separated into smaller batches and each batch is evaluated on a separate CPU core. Parallelization necessarily brings some overhead to process and in some cases might cause even slower behaviour of the application. It is important to choose wisely when using it, especially in the case of circular synchronous orbits which consist of spot-free components where multiprocessing is usually not as effective.
Down below are shown some result of the multiprocessor approach for different binary system types. The absolute time necessary for the calculation of the light curve is highly dependent on the type of the system and hardware. Therefore we have normalized the time axis according to the maximum value in our datasets.
Paralellization benchmark for detached circular synchronous star system.
Paralellization benchmark for detached circular asynchronous star system.
Paralellization benchmark for eccentric synchronous star system.
| note: | outliers in charts are caused by curve symetrization process |
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Building a simple model of a binary system - MWE
ELISa enables fast modelling of binary systems based on parameters supplied in form of a dictionary (or json). Parameters are divided into 'system', 'primary' and 'secondary' parameters. Binary system parameters can either supply masses of the components with mass parameter or system's mass_ratio and semi_major_axis have to be provided instead:
from elisa import BinarySystem
community_params = {
"system": {
"inclination": 86.0,
"period": 10.1,
"argument_of_periastron": 90.0,
"gamma": 0.0,
"eccentricity": 0.0,
"primary_minimum_time": 0.0,
"phase_shift": 0.0,
"semi_major_axis": 10.5, # default unit is solRad
"mass_ratio": 0.5
},
"primary": {
"surface_potential": 7.1,
"synchronicity": 1.0,
"t_eff": "6500.0 K", # parameters can be provided in string representation consistent with astropy unit format
"gravity_darkening": 1.0,
"albedo": 1.0,
"metallicity": 0.0
},
"secondary": {
"surface_potential": 7.1,
"synchronicity": 1.0,
"t_eff": 5000.0,
"gravity_darkening": 1.0,
"albedo": 1.0,
"metallicity": 0.0
}
}
community_binary = BinarySystem.from_json(community_params)
See tutorials 1, 2, 3, 4 for more information about this process.
Calculating light curve
Binary system community_binary can be observed by utilizing a dedicated observer class:
from elisa import Observer
o = Observer(passband=[ # defining passbands at which calculate a light curve
'Generic.Bessell.B',
'Generic.Bessell.V',
'Generic.Bessell.R',
'Generic.Bessell.I'
],
system=community_binary) # specifying the binary system to use in light curve synthesis
# this will create a light curve containing 1200 points
phases, fluxes = o.observe.lc(
from_phase=-0.6,
to_phase=0.6,
phase_step=0.001,
# normalize=True # this will produce observations normalized to 1
)
Visualization of the results
Elisa comes with a substantial graphic library for comfortable visualization of various results. Light curve calculated in the Observer instance o can be visualized:
o.plot.lc()
Solving an inverse problem - general concepts
ELISa provides a built-in capability to infer binary system parameters from observations. Similar to the generating a binary system demonstrated above, the fitting parameters are also supplied in form of a dictionary (json) in the following format:
fit_params = {
'system': {
'mass_ratio': {...},
'eccentricity': {...},
...
},
'primary: {
'surface_potential': {...},
...
},
'secondary': {
'surface_potential': {...},
...
}
'nuisance':{ # used only for MCMC method
'ln_f': {...} # error underestimation factor
}
}
Each model parameter (eg. mass_ratio) is additionally defined in form of a dictionary where the character and behaviour of the variable during the fitting procedure is specified. ELISa recognizes three main types of model variables:
fixed: value of such parameter stays fixed during the whole process. A fixed-parameter can be defined as:
't_eff': { 'value': 5774, 'fixed': True, 'unit': 'K' }variable: such parameter is optimized by the optimizer to provide the best fit to the data. This is an example of the variable parameter expected from the (min, max) interval:
'surface_potential': { 'value': 5.2, # initial value 'fixed': False, 'min': 4.0, 'max': 7.0, 'unit': None # this line is not mandatory (default parameter unit is assumed in its absence) }Additionally, in the case of the MCMC method, the parameter can be sampled from the normal prior distribution. Let's say that we want to take into account the errors of the effective temperature of the component 6300 +- 400 K inferred from color indices:
't_eff': { 'value': 6300, # mean value 'sigma': 400, # standard deviation 'fixed': False, 'min': 3500, 'max': 50000, # normal distribution can be additionally clipped to prevent a sampler from reaching # invalid regions of parameter space 'unit': 'K' }constrained: type of model parameter, which value is dependent on the current value of one or more variable parameters. This feature is very helpful while utilizing parameters such as a sin(i) parameter derived during radial velocity fit inside a light curve fit to constrain a semi-major axis of the system on system's inclination:
'semi_major_axis': { 'value': 16.515, 'constraint': '16.515 / sin(radians(system@inclination))' },
Once the model parameters are defined, we can initialize our optimization tasks that can utilize various optimizing methods. The following example shows initialization of task for the fitting of the light curves:
from elisa.analytics import LCData, LCBinaryAnalyticsTask
# phased and normalized (to 1) light curve observed by the Kepler
kepler_data = LCData.load_from_file(filename='path/to/your/data.dat',
x_unit=None,
y_unit=None
)
task = LCBinaryAnalyticsTask(data={'Kepler': kepler_data}, method='least_squares', expected_morphology='detached')
Observed data are supplied in form of a custom Dataset format for each filter. Optimizer task can for now use least-squares or mcmc method. The least squares method is specialized for the fast determination of a local minimum in the general vicinity of the initial parameters. On the other side the MCMC method is best used as a tool for the determination of the confidence intervals of the model parameters around the solution found by the least squares method. The optimizer in case of light curves requires the 'expected_morphology' of the fitted system with 'detached' and 'over-contact' arguments available.
Subsequently, the fitting procedure can be initiated by the following command:
task.fit(x0=fit_params, *kwargs) task.save_result(param/file/name.json) # storing results into json
where initial parameters are provided and the fitting process can be managed by the additional keyword arguments. The results can be visualised in form of a table:
lst_sqr_task.fit_summary()
which would produce result similar to this:
BINARY SYSTEM Parameter value -1 sigma +1 sigma unit status ------------------------------------------------------------------------------------------------------------------------------ Mass ratio (q=M_2/M_1): 1.08 - - None Fixed Semi major axis (a): 11.53 - - solRad 11.2 / sin(radians(system@inclination)) Inclination (i): 76.26 - - deg Variable Eccentricity (e): 0.03 - - None Variable Argument of periastron (omega): 197.93 - - deg Variable Orbital period (P): 2.47028 - - d Fixed Additional light (l_3): 0.014 - - None Variable Phase shift: 7.378e-05 - - None Variable ------------------------------------------------------------------------------------------------------------------------------ PRIMARY COMPONENT Parameter value -1 sigma +1 sigma unit status ------------------------------------------------------------------------------------------------------------------------------ Mass (M_1): 1.62 - - solMass Derived Surface potential (Omega_1): 5.8397 - - None Variable Critical potential at L_1: 4.0162 - - - Derived Synchronicity (F_1): 1.067 - - None (1 + system@eccentricity)**2 / (1 - system@eccentricity**2)**(3.0/2.0) Polar gravity (log g): 3.888 - - log(cgs) Derived Equivalent radius (R_equiv): 0.21168 - - SMA Derived Periastron radii Polar radius: 0.20899 - - SMA Derived Backward radius: 0.21457 - - SMA Derived Side radius: 0.2113 - - SMA Derived Forward radius: 0.21583 - - SMA Derived Atmospheric parameters Effective temperature (T_eff1): 7022.0 - - K Fixed Bolometric luminosity (L_bol): 13.05 - - L_Sol Derived Gravity darkening factor (G_1): 1.0 - - None Fixed Albedo (A_1): 1.0 - - None Fixed Metallicity (log10(X_Fe/X_H)): 0.0 - - None Fixed ------------------------------------------------------------------------------------------------------------------------------ SECONDARY COMPONENT Parameter value -1 sigma +1 sigma unit status ------------------------------------------------------------------------------------------------------------------------------ Mass (M_2): 1.75 - - solMass Derived Surface potential (Omega_2): 5.7303 - - None Variable Critical potential at L_1: 4.018 - - - Derived Synchronicity (F_2): 1.067 - - None (1 + system@eccentricity)**2 / (1 - system@eccentricity**2)**(3.0/2.0) Polar gravity (log g): 3.857 - - log(cgs) Derived Equivalent radius (R_equiv): 0.22835 - - SMA Derived Periastron radii Polar radius: 0.22512 - - SMA Derived Backward radius: 0.23181 - - SMA Derived Side radius: 0.22802 - - SMA Derived Forward radius: 0.23343 - - SMA Derived Atmospheric parameters Effective temperature (T_eff2): 6793.0 - - K Variable Bolometric luminosity (L_bol): 13.3 - - L_Sol Derived Gravity darkening factor (G_2): 1.0 - - None Fixed Albedo (A_2): 1.0 - - None Fixed Metallicity (log10(X_Fe/X_H)): 0.0 - - None Fixed ------------------------------------------------------------------------------------------------------------------------------
where in the case of the MCMC method, the additional 1 sigma errors would be displayed.
Detailed guides, how to perform a fit of radial velocities or photometric observations including working examples are stored in the Jupyter notebooks 11 and 12. See also notebook 10 that explains handling of ELISa's custom datasets.
