From (Cohn et al. 2010) we get some estimate of mass and with the function from @[casares_mass_2016]

The inner bright CVs

According to (Cohn et al. 2010):

The fairly high R-band flux indicates that the secondaries are relatively massive, \(\approx 0.5-0.7 \, M_{\odot}\)._

The inferred mass range for the bright CVs (\(1.5 \pm 0.2 M_{\odot})\) is consistent with a system made up of a heavy WD (\(\approx 0.9 M_{\odot})i\) with a MS secondary of mass \(\approx 0.6 M_{\odot}\).

From table 2 the inferered mass for these CVs is: \(1.46 \pm 0.22 M_{\odot}.\)

The CVs:

q is the mass ratio of the companion star to the compact object.

U21

cv21 = {"name":"U21", "fwhm":"20.93", "dp":str(6568.749-6556.928), "flux":getflux('U21')}`

U23

cv23 = {"name":"U23", "fwhm":"24.97", "dp":str(6569.895-6555.707), "flux":getflux('U23')}

U10

cv10 = {"name":"U10", "fwhm":"37.27", "dp":str(abs(6551.823-6572.753)), "flux":getflux('U10')}

The plot:

With the formula from (Casares 2016) and the estimation of the mass from (Cohn et al. 2010):

def f(q):
    return (0.49*(1+q)**(-1))/(0.6+q**(2/3.)*np.log(1+q**(-1/3.)))


def ratiodp(q,alpha,beta):
    return 3**(1/3.)*(1+q)**(2/3.)*beta*np.sqrt(alpha*f(q))

xdata = np.arange(0.001,0.8, 0.01)
ydata = ratiodp(xdata,0.42, 0.83)
plt.plot(xdata, ydata)
plt.ylim(0.5,0.7)


maxrat = .7/(1.5-.7)
minrat = .5/(1.5-.5)
ypoints = [ (float(cv21['eqw'])/float(cv21['fwhm'])),(float(cv23['eqw'])/float(cv23['fwhm'])), (float(cv10['eqw'])/float(cv10['fwhm']))   ]
xpoints=[.6/.9 for i in range(3)]
plt.errorbar(xpoints, ypoints, xerr=(maxrat-minrat)/2., fmt='o')

Second try. Getting mass from relation:

def find_nearest(array,value):                                                 
        idx = (np.abs(array-value)).argmin()
        return idx
def f(q):
    return (0.49*(1+q)**(-1))/(0.6+q**(2/3.)*np.log(1+q**(-1/3.)))


def ratiodp(q,alpha,beta):
    return 3**(1/3.)*(1+q)**(2/3.)*beta*np.sqrt(alpha*f(q))

xdata = np.arange(0.001,0.8, 0.01)
ydata = ratiodp(xdata,0.42, 0.83)
xpoints=[xdata[find_nearest(ydata,i)] for i in ypoints] 

Flux

To compare to (Cohn et al. 2010) they say:

Photometric calibration to the VEGAMAG system from (Strickler et al. 2009)

And in (Strickler et al. 2009) they say as explain in (Sirianni et al. 2005)

VEGAMAG system

VEGAMAG system makes use of Vega (a Lyr) as the standard star.

There is a very cool package for python called: pysynphot 0.9.7

Examples can be found here.

Something worth mentioning is this two new units for me. The FLAM and FNU

• flam is ergs \(s^{-1} cm^{-2} \mathring{A}^{-1}\)
• fnu is ergs \(s^{-1} cm^{-2} Hz^{-1}\)

To import the spectra with the units:

from astropy.io import ascii
import matplotlib.pyplot as plt
import pysynphot
tab = ascii.read('U23spectra.txt', names=['wave', 'flux']) 
wave = tab['wave']  # First column
flux = tab['flux']*10**(-20)  # Second column
sp = pysynphot.ArraySpectrum(wave=wave, flux=flux, waveunits='angstrom', fluxunits='flam')
#To see Vega spectrum
pysynphot.Vega.flux
pysynphot.Vega.fluxunits
pysynphot.Vega.wave

Had to sownload the filters fro Hubble from http://www.stsci.edu/hst/observatory/crds/throughput.html

Then do this http://ssb.stsci.edu/pysynphot/docs/

Now it is in my bashrc

For the filter bp_acs = S.ObsBandpass('acs,wfc1,f625w')

There is wfc 1 and 2

TO get observation do:

import numpy as np
def find_nearest(array,value):
    idx = (np.abs(array-value)).argmin()
    return idx
import pysynphot as S
bp_acs = S.ObsBandpass('acs,wfc1,f625w')
obstar=S.Observation(sp, bp_acs, force='taper')
obvega=S.Observation(S.Vega, bp_acs, force='taper')
#Taper the spectrum by adding zeros to each end.
plt.plot(obstar.wave, obstar.flux, color='blue')
plt.plot(obvega.wave, obvega.flux, color='red')
plt.show()

6 outer and faiter

No H\(\alpha\) only He 1.