def PlotEccOrbit_aRs(par,t):
"""Function to plot planet orbit in 3D"""
#read in parameters
T0,P,a_Rstar,p,b,c1,c2,e,w,foot,Tgrad,Sec_depth = par
#ensure b and p >= 0
if b<0.: b=-b
if p<0.: p=-p
w *= np.pi / 180.
i = np.arccos(b/a_Rstar)
#make w lie in range 0-2pi
if w >= 2*np.pi:
w -= 2*np.pi #make f lie in range 0-2pi
elif w < 0:
w += 2*np.pi #make f lie in range 0-2pi
#true anomaly of central transit time
f = 1.*np.pi/2. + w
if f >= 2*np.pi:
f -= 2*np.pi #make f lie in range 0-2pi
elif f < 0:
f += 2*np.pi #make f lie in range 0-2pi
if f < np.pi:
E = np.arccos( (np.cos(f) + e) / (e*np.cos(f)+1.) )
M_tr = E - e*np.sin(E)
T_peri = T0 + M_tr * P/(2*np.pi)
if f >= np.pi:
#f = np.pi - f #correct for acos calc
E = np.arccos( (np.cos(f) + e) / (e*np.cos(f)+1.) )
M_tr = E - e*np.sin(E)
#M_tr = 2*np.pi - M_tr
T_peri = T0 - M_tr * P/(2*np.pi)
#calculate mean anomaly
M = (2*np.pi/P) * (t - T_peri)
#get coords
x = PlanetOrbit.get_x(M,a_Rstar,e,w)
y = PlanetOrbit.get_y(M,a_Rstar,e,w,i)
z = PlanetOrbit.get_z(M,a_Rstar,e,w,i)
#make plot
ax = Axes3D(pylab.gcf())
ax.plot(x, y, z, c='k')
ax.scatter(x, y, z, c='r', s=50)
ax.scatter([0],[0],[0],c='y', s=500) #plot star position
ax.scatter([x[0],],[y[0],],[z[0],],c='g', s=100) #plot initial planet position
ax.scatter([x[1],],[y[1],],[z[1],],c='y', s=100) #plot initial planet position
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
range = abs(np.array([x,y,z])).max()
ax.set_xlim3d(-range,range)
ax.set_ylim3d(-range,range)
ax.set_zlim3d(-range,range)
def EccLightCurve_aRs(par,t,plot=False):
"""Lightcurve function for eccentric orbits with aRs parameterisation."""
#read in parameters
T0,P,a_Rstar,p,b,c1,c2,e,w,foot,Tgrad,Sec_depth = par
#ensure b and p >= 0
if b<0.: b=-b
if p<0.: p=-p
w *= np.pi / 180.
i = np.arccos(b/a_Rstar)
#make w lie in range 0-2pi
if w >= 2*np.pi:
w -= 2*np.pi #make f lie in range 0-2pi
elif w < 0:
w += 2*np.pi #make f lie in range 0-2pi
#true anomaly of central transit time
f = 1.*np.pi/2. + w
if f >= 2*np.pi:
f -= 2*np.pi #make f lie in range 0-2pi
elif f < 0:
f += 2*np.pi #make f lie in range 0-2pi
if f < np.pi:
E = np.arccos( (np.cos(f) + e) / (e*np.cos(f)+1.) )
M_tr = E - e*np.sin(E)
T_peri = T0 + M_tr * P/(2*np.pi)
if f >= np.pi:
E = np.arccos( (np.cos(f) + e) / (e*np.cos(f)+1.) )
M_tr = E - e*np.sin(E)
T_peri = T0 - M_tr * P/(2*np.pi)
#calculate mean anomaly
M = (2*np.pi/P) * (t - T_peri)
#calc normalised separation z using PlanetOrbit functions
norm = PlanetOrbit.get_norm(M,a_Rstar,e,w,i)
y_coord = PlanetOrbit.get_y(M,a_Rstar,e,w,i) #get y coord to separate primary and secondary transits
#print "a/R =",a/Rstar
#calculate flux
f = np.ones(norm.size)
#primary transit
index = np.where(y_coord<0) #ie planet closer than star
f[index] = FluxQuad(norm[index],p,c1,c2) * (foot + (t[index] - T0) * 24. * Tgrad) #time in hours for foot and Tgrad!
#secondary transit
index = np.where(y_coord>0) #ie star closer than planet
f[index] = FluxQuad(norm[index],p,0,0) * (foot + (t[index] - T0) * 24. * Tgrad) #time in hours for foot and Tgrad!
f[index] = (f[index]-1.) * Sec_depth/p**2 + 1 #scale the transit depth to secondary depth
f[index] *= (foot + (t[index] - T0)*24. * Tgrad)
if plot:
pylab.plot(t,f,'r-')
pylab.xlabel('Time / days')
pylab.ylabel('Relative Flux')
pylab.ylim(f.min()-(f.max()-f.min())/2.,f.max()+(f.max()-f.min())/2.)
pylab.xlim(t.min(),t.max())
return f
def PlotEccOrbit(par,t):
"""Function to plot planet orbit in 3D"""
#read in parameters
T0,P,Mstar,Mplanet,Rstar,p,i,c1,c2,e,w,foot,Tgrad,Sec_depth = par
#convert units
Rstar *= Cnst.RSun
Mstar *= Cnst.MSun
Mplanet *= Cnst.MJup
i *= np.pi / 180.
w *= np.pi / 180.
#semi-major axis
a = np.power( ( ((P*24.*60.*60./(2*np.pi))**2 * Cnst.G * (Mstar+Mplanet) ) ) , (1./3.) )
#make w lie in range 0-2pi
if w >= 2*np.pi:
w -= 2*np.pi #make f lie in range 0-2pi
elif w < 0:
w += 2*np.pi #make f lie in range 0-2pi
#true anomaly of central transit time
f = 1.*np.pi/2. + w
if f >= 2*np.pi:
f -= 2*np.pi #make f lie in range 0-2pi
elif f < 0:
f += 2*np.pi #make f lie in range 0-2pi
if f < np.pi:
E = np.arccos( (np.cos(f) + e) / (e*np.cos(f)+1.) )
M_tr = E - e*np.sin(E)
T_peri = T0 + M_tr * P/(2*np.pi)
if f >= np.pi:
#f = np.pi - f #correct for acos calc
E = np.arccos( (np.cos(f) + e) / (e*np.cos(f)+1.) )
M_tr = E - e*np.sin(E)
#M_tr = 2*np.pi - M_tr
T_peri = T0 - M_tr * P/(2*np.pi)
#calculate mean anomaly
M = (2*np.pi/P) * (t - T_peri)
#get coords
x = PlanetOrbit.get_x(M,a/Rstar,e,w)
y = PlanetOrbit.get_y(M,a/Rstar,e,w,i)
z = PlanetOrbit.get_z(M,a/Rstar,e,w,i)
#make plot
ax = Axes3D(pylab.gcf())
ax.plot(x, y, z, c='k')
ax.scatter(x, y, z, c='r', s=50)
ax.scatter([0],[0],[0],c='y', s=500) #plot star position
ax.scatter([x[0],],[y[0],],[z[0],],c='g', s=100) #plot initial planet position
ax.scatter([x[1],],[y[1],],[z[1],],c='y', s=100) #plot initial planet position
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
range = abs(np.array([x,y,z])).max()
ax.set_xlim3d(-range,range)
ax.set_ylim3d(-range,range)
ax.set_zlim3d(-range,range)
def EccLightCurve(par,t,plot=False):
"""Lightcurve function for eccentric orbits."""
#read in parameters
T0,P,Mstar,Mplanet,Rstar,p,i,c1,c2,e,w,foot,Tgrad,Sec_depth = par
#convert units
Rstar *= Cnst.RSun
Mstar *= Cnst.MSun
Mplanet *= Cnst.MJup
i *= np.pi / 180.
w *= np.pi / 180.
#make w lie in range 0-2pi
if w >= 2*np.pi:
w -= 2*np.pi #make f lie in range 0-2pi
elif w < 0:
w += 2*np.pi #make f lie in range 0-2pi
#true anomaly of central transit time
f = 1.*np.pi/2. + w
if f >= 2*np.pi:
f -= 2*np.pi #make f lie in range 0-2pi
elif f < 0:
f += 2*np.pi #make f lie in range 0-2pi
if f < np.pi:
E = np.arccos( (np.cos(f) + e) / (e*np.cos(f)+1.) )
M_tr = E - e*np.sin(E)
T_peri = T0 + M_tr * P/(2*np.pi)
if f >= np.pi:
E = np.arccos( (np.cos(f) + e) / (e*np.cos(f)+1.) )
M_tr = E - e*np.sin(E)
T_peri = T0 - M_tr * P/(2*np.pi)
#calculate mean anomaly
M = (2*np.pi/P) * (t - T_peri)
#semi-major axis
a = np.power( ( ((P*24.*60.*60./(2*np.pi))**2 * Cnst.G * (Mstar+Mplanet) ) ) , (1./3.) )
#calc normalised separation z using PlanetOrbit functions
norm = PlanetOrbit.get_norm(M,a/Rstar,e,w,i)
y_coord = PlanetOrbit.get_y(M,a/Rstar,e,w,i) #get y coord to separate primary and secondary transits
#print "a/R =",a/Rstar
#calculate flux
f = np.ones(norm.size)
#primary transit
index = np.where(y_coord<0) #ie planet closer than star
f[index] = FluxQuad(norm[index],p,c1,c2) * (foot + (t[index] - T0) * 24. * Tgrad) #time in hours for foot and Tgrad!
#secondary transit
index = np.where(y_coord>0) #ie star closer than planet
f[index] = FluxQuad(norm[index],p,0,0) * (foot + (t[index] - T0) * 24. * Tgrad) #time in hours for foot and Tgrad!
f[index] = (f[index]-1.) * Sec_depth/p**2 + 1 #scale the transit depth to secondary depth
f[index] *= (foot + (t[index] - T0)*24. * Tgrad)
if plot:
pylab.plot(t,f,'r-')
pylab.xlabel('Time / days')
pylab.ylabel('Relative Flux')
pylab.ylim(f.min()-(f.max()-f.min())/2.,f.max()+(f.max()-f.min())/2.)
pylab.xlim(t.min(),t.max())
#return flux
return f