Equivalent Radius

Setup

Let's first make sure we have the latest version of PHOEBE 2.1 installed. (You can comment out this line if you don't use pip for your installation or don't want to update to the latest release).



In [ ]:

    
!pip install -I "phoebe>=2.1,<2.2"

As always, let's do imports and initialize a logger and a new Bundle. See Building a System for more details.



In [1]:

    
%matplotlib inline



In [2]:

    
import phoebe
from phoebe import u # units
import numpy as np
import matplotlib.pyplot as plt

logger = phoebe.logger()

b = phoebe.default_binary()

Now let's add a mesh dataset at a few different times so that we can see how the potentials affect the surfaces of the stars.



In [3]:

    
b.add_dataset('mesh', times=np.linspace(0,1,11), dataset='mesh01')









    Out[3]:





<ParameterSet: 4 parameters | contexts: compute, dataset>

Relevant Parameters

The 'requiv' parameter defines the stellar surface to have a constant volume of 4./3 pi requiv^3.



In [4]:

    
print b['requiv@component']









    



ParameterSet: 2 parameters
        requiv@primary@component: 1.0 solRad
      requiv@secondary@component: 1.0 solRad

Critical Potentials and System Checks

Additionally, for each detached component, there is an requiv_max Parameter which shows the critical value at which the Roche surface will overflow. Setting requiv to a larger value will fail system checks and raise a warning.



In [5]:

    
print b['requiv_max@primary@component']









    



Parameter: requiv_max@primary@component
                       Qualifier: requiv_max
                     Description: Critical (maximum) value of the equivalent radius for the given morphology
                           Value: 2.01327517654 solRad
                  Constrained by: q@binary@component, syncpar@primary@component, ecc@binary@component, sma@binary@component, incl@primary@component, long_an@primary@component, incl@binary@component, long_an@binary@component
                      Constrains: None
                      Related to: q@binary@component, syncpar@primary@component, ecc@binary@component, sma@binary@component, incl@primary@component, long_an@primary@component, incl@binary@component, long_an@binary@component



In [6]:

    
print b['requiv_max@primary@constraint']









    



Constrains (qualifier): requiv_max
Expression in SI (value): requiv_L1({q@binary@component}, {syncpar@primary@component}, {ecc@binary@component}, {sma@binary@component}, {incl@primary@component}, {long_an@primary@component}, {incl@binary@component}, {long_an@binary@component}, 1)
Current Result (result): 2.01327517654 solRad



In [8]:

    
b.set_value('requiv@primary@component', 3)









    



Wed, 17 Oct 2018 14:45 PARAMETERS   WARNING primary is overflowing at periastron (requiv=3.0, requiv_max=2.01327517654)  If not addressed, this warning will continue to be raised and will throw an error at run_compute.



In [ ]:

At this time, if you were to call run_compute, an error would be thrown. An error isn't immediately thrown when setting requiv, however, since the overflow can be recitified by changing any of the other relevant parameters. For instance, let's change sma to be large enough to account for this value of rpole and you'll see that the error does not occur again.



In [10]:

    
b.set_value('sma@binary@component', 10)









    



Wed, 17 Oct 2018 14:45 PARAMETERS   WARNING primary is overflowing at periastron (requiv=3.0, requiv_max=1.89931620428)  If not addressed, this warning will continue to be raised and will throw an error at run_compute.
Wed, 17 Oct 2018 14:45 PARAMETERS   WARNING primary is overflowing at periastron (requiv=3.0, requiv_max=1.89931620428)  If not addressed, this warning will continue to be raised and will throw an error at run_compute.
Wed, 17 Oct 2018 14:45 PARAMETERS   WARNING primary is overflowing at periastron (requiv=3.0, requiv_max=1.89931620428)  If not addressed, this warning will continue to be raised and will throw an error at run_compute.

These logger warnings are handy when running phoebe interactively, but in a script its also handy to be able to check whether the system is currently computable /before/ running run_compute.

This can be done by calling run_checks which returns a boolean (whether the system passes all checks) and a message (a string describing the first failed check).



In [13]:

    
passed, message = b.run_checks()
print passed, message









    



False primary is overflowing at periastron (requiv=3.0, requiv_max=1.89931620428)



In [14]:

    
b.set_value('sma@binary@component', 5)









    



Wed, 17 Oct 2018 14:46 PARAMETERS   WARNING primary is overflowing at periastron (requiv=3.0, requiv_max=1.89931620428)  If not addressed, this warning will continue to be raised and will throw an error at run_compute.
Wed, 17 Oct 2018 14:46 PARAMETERS   WARNING primary is overflowing at periastron (requiv=3.0, requiv_max=1.89931620428)  If not addressed, this warning will continue to be raised and will throw an error at run_compute.
Wed, 17 Oct 2018 14:46 PARAMETERS   WARNING primary is overflowing at periastron (requiv=3.0, requiv_max=1.89931620428)  If not addressed, this warning will continue to be raised and will throw an error at run_compute.
Wed, 17 Oct 2018 14:46 PARAMETERS   WARNING primary is overflowing at periastron (requiv=3.0, requiv_max=1.89931620428)  If not addressed, this warning will continue to be raised and will throw an error at run_compute.
Wed, 17 Oct 2018 14:46 PARAMETERS   WARNING primary is overflowing at periastron (requiv=3.0, requiv_max=1.89931620428)  If not addressed, this warning will continue to be raised and will throw an error at run_compute.
Wed, 17 Oct 2018 14:46 PARAMETERS   WARNING primary is overflowing at periastron (requiv=3.0, requiv_max=1.89931620428)  If not addressed, this warning will continue to be raised and will throw an error at run_compute.
Wed, 17 Oct 2018 14:46 PARAMETERS   WARNING primary is overflowing at periastron (requiv=3.0, requiv_max=1.89931620428)  If not addressed, this warning will continue to be raised and will throw an error at run_compute.
Wed, 17 Oct 2018 14:46 PARAMETERS   WARNING primary is overflowing at periastron (requiv=3.0, requiv_max=1.89931620428)  If not addressed, this warning will continue to be raised and will throw an error at run_compute.



In [15]:

    
passed, message = b.run_checks()
print passed, message









    



False primary is overflowing at periastron (requiv=3.0, requiv_max=1.89931620428)

Semi-Detached and Contact Systems

Semi-detached systems are implemented by constraining the value of requiv to be the same as requiv_max by appyling the 'semidetached' constraint on the 'primary' component. For more information see the critical radii: semidetached systems tutorial.

Contact systems are implemented by constraining the value of requiv both stars to correspond to the potential of the contact envelope. For more information see the critical radii: contact systems tutorial.