The question to explore is the following: given Kepler observations, how many events of the following type are we likely to observe as single eclipse events?

EBs
BEBs
HEBs

More specifically, given a period and depth range, how many of each do I predict?



In [6]:

    
from keputils import kicutils as kicu
stars = kicu.DATA # This is Q17 stellar table.

OK, first, let's calculate the number of expected EBs. That is, assign each Kepler target star a binary companion according to the Raghavan (2010) distribution, and see what the eclipsing population looks like. Let's use tools from vespa to make this happen.



In [8]:

    
stars = stars.query('mass > 0') #require there to be a mass.
len(stars)









    Out[8]:





196469



In [9]:

    
from vespa.stars import Raghavan_BinaryPopulation

binpop = Raghavan_BinaryPopulation(M=stars.mass)









    



WARNING:root:progressbar not imported



In [18]:

    
binpop.stars.columns









    Out[18]:





Index([u'H_mag', u'H_mag_A', u'J_mag', u'J_mag_A', u'K_mag', u'K_mag_A',
       u'Kepler_mag', u'Kepler_mag_A', u'Teff_A', u'age_A', u'g_mag',
       u'g_mag_A', u'i_mag', u'i_mag_A', u'logL_A', u'logg_A', u'mass_A',
       u'r_mag', u'r_mag_A', u'radius_A', u'z_mag', u'z_mag_A', u'H_mag_B',
       u'J_mag_B', u'K_mag_B', u'Kepler_mag_B', u'Teff_B', u'age_B',
       u'g_mag_B', u'i_mag_B', u'logL_B', u'logg_B', u'mass_B', u'r_mag_B',
       u'radius_B', u'z_mag_B', u'q', u'distance', u'distmod'],
      dtype='object')



In [30]:

    
%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np

# e.g., 
plt.hist(np.log10(binpop.orbpop.P.value), histtype='step', lw=3);
plt.figure()
plt.hist(binpop.orbpop.ecc, histtype='step', lw=3);
plt.figure()
binpop.orbpop.scatterplot(ms=0.05, rmax=1000);









    












    












    





<matplotlib.figure.Figure at 0x10c41bc50>



In [51]:

    
# Determine eclipse probabilities

import astropy.units as u

ecl_prob = ((binpop.stars.radius_A.values + binpop.stars.radius_B.values)*u.Rsun / binpop.orbpop.semimajor).decompose()



In [52]:

    
sum(ecl_prob > 1) # These will need to be ignored later. 
ok = ecl_prob < 1



In [54]:

    
# Rough estimate of numbers of systems with eclipsing orientation
ecl_prob[ok].sum()









    Out[54]:





$4078.11 \; \mathrm{}$



In [65]:

    
# OK, how many that have periods less than 1 years?
kep_ok = (ok & (binpop.orbpop.P < 3*u.yr))
ecl_prob[kep_ok].sum()









    Out[65]:





$3553.61 \; \mathrm{}$



In [59]:

    
# And, including binary fraction
fB = 0.4
fB * ecl_prob[kep_ok].sum()









    Out[59]:





$1421.44 \; \mathrm{}$

This is actually a bit low compared to the Kepler EB catalog haul of 2878 EBs. However, keep in mind that this is only looking at binaries, not considering triple systems that tend to have much closer pairs. So to my eye this is actually a pretty believable number. (Also note that this does not take eccentricity into account.) How many of these would have periods from 5 to 15 years?



In [72]:

    
minP = 5*u.yr; maxP = 15*u.yr
kep_long = ok & (binpop.orbpop.P > minP) & (binpop.orbpop.P < maxP)
fB * ecl_prob[kep_long].sum()









    Out[72]:





$72.7025 \; \mathrm{}$

This seems like a lot. Now keep in mind this is just the number with eclipsing geometry, not the number that would actually show up within the Kepler data, taking the window function into account. A quick hack at this would be that the probability for an eclipse to be within the Kepler window would be 4yr / P.



In [73]:

    
in_window = np.clip(4*u.yr / binpop.orbpop.P, 0, 1).decompose()

fB*(ecl_prob[kep_long] * in_window[kep_long]).sum()









    Out[73]:





$36.6332 \; \mathrm{}$

OK, better, but this still seems like a lot. Perhaps I'm doing something wrong here? Accounting properly for eccentricity in the transit probability will only make this number larger. Of course, only a fraction of these would be plausibly planetary-like signals, but still, this seems like an overestimate, though not crazy.



In [ ]: