def sigK_LHS1140(N=1e3, P=24.73712, T0=2456915.6997):
'''From Dittmann et al 2017'''
# get time-series
#bjd, rv, erv = np.loadtxt('Nrv_tests/LHS1140old.dat').T
bjd, rv, erv = np.loadtxt('Nrv_tests/LHS1140.dat').T
Pc, T0c, Kc = 3.777931, 2458226.343169 + .5, 2.35
kepc = get_rv1((Pc, T0c, 0, Kc, 0, 0), bjd)
rv -= kepc
# sample parameter posteriors approximating the PDFs as Gaussian
N = int(N)
Krvs = _random_normal_draws(4.85, .55, N, positive=True)
As = _random_normal_draws(2.7, .81, N, positive=True) # 9,5
ls = _random_normal_draws(49.8, 38, N, positive=True)
Gs = _random_normal_draws(1.44, .2, N, positive=True)
Ps = _random_normal_draws(132.9, 10, N,
positive=True) # median of posterior
ss = _random_normal_draws(2.7, .3, N, positive=True) # 3,1
# Monte-Carlo computation of sigKs
sigKs = np.zeros(N)
for i in range(N):
print float(i) / N
theta = P, T0, Krvs[i], As[i], ls[i], Gs[i], Ps[i], ss[i]
sigKs[i] = compute_sigmaK_GP(theta, bjd, rv, erv)
print sigKs[i]
# save output
_save_draws('LHS1140', Krvs, As, ls, Gs, Ps, ss, sigKs)
def sigK_Kep78(N=1e3, P=.35500744, T0=2454953.95995):
'''From Grunblatt et al 2015'''
# get time-series
bjd, rv, erv = np.loadtxt('Nrv_tests/Kepler78_HARPSN.dat').T
# sample parameter posteriors approximating the PDFs as Gaussian
N = int(N)
Krvs = _random_normal_draws(1.86, .25, N, positive=True)
As = _random_normal_draws(5.6, 1.7, N, positive=True)
ls = _random_normal_draws(26.1 / np.sqrt(2),
15 / np.sqrt(2),
N,
positive=True)
Gs = _random_normal_draws(1 / np.sqrt(2 * .28**2),
1 / np.sqrt(2 * .28**2) / 5.6,
N,
positive=True)
Ps = _random_normal_draws(13.26, .12, N, positive=True)
ss = _random_normal_draws(1.1, .5, N, positive=True)
# Monte-Carlo computation of sigKs
sigKs = np.zeros(N)
for i in range(N):
theta = P, T0, Krvs[i], As[i], ls[i], Gs[i], Ps[i], ss[i]
sigKs[i] = compute_sigmaK_GP(theta, bjd, rv, erv)
sigKs[i] *= np.sqrt(
109. / 193
) # correct for lack of HIRES RVs to compare to measured sigK = 0.25 m/s
# save output
_save_draws('Kep78HARPSN', Krvs, As, ls, Gs, Ps, ss, sigKs)
def sigK_CoRoT7(N=1e3, P=.85359165, T0=2454398.0769):
'''From Haywood et al 2015'''
# get time-series
bjd, rv, erv = np.loadtxt('Nrv_tests/CoRoT7.dat').T
kepc = get_rv1((3.7, 2455953.54, 0, 6.01, 0, 0), bjd)
rv -= kepc
# sample parameter posteriors approximating the PDFs as Gaussian
N = int(N)
Krvs = _random_normal_draws(3.42, .66, N, positive=True)
As = _random_normal_draws(7, 2, N, positive=True)
ls = _random_normal_draws(20.6, 2.5, N, positive=True)
Gs = _random_normal_draws(1, .1, N, positive=True)
Ps = _random_normal_draws(23.81, .03, N, positive=True)
rmsRVrot, rmsRVconv, rmsRVtot = .46, 1.82, 3.92 # FF' contributions
ss = _random_normal_draws(np.sqrt(rmsRVtot**2 - rmsRVrot**2 -
rmsRVconv**2),
0,
N,
positive=True)
# Monte-Carlo computation of sigKs
sigKs = np.zeros(N)
for i in range(N):
theta = P, T0, Krvs[i], As[i], ls[i], Gs[i], Ps[i], ss[i]
sigKs[i] = compute_sigmaK_GP(theta, bjd, rv, erv)
# save output
_save_draws('CoRoT7', Krvs, As, ls, Gs, Ps, ss, sigKs)
def sigK_Kep21(N=1e3, P=2.78578, T0=2456798.7188):
'''From Lopez-Morales et al 2016'''
# get time-series
bjd, rv, erv = np.loadtxt('Nrv_tests/Kepler21_HARPSN.dat').T
# sample parameter posteriors approximating the PDFs as Gaussian
N = int(N)
Krvs = _random_normal_draws(2.12, .66, N, positive=True)
As = _random_normal_draws(6.7, 1.4, N, positive=True)
ls = _random_normal_draws(24.04 / np.sqrt(2),
.09 / np.sqrt(2),
N,
positive=True)
Gs = _random_normal_draws(1 / .42, .12 / .42, N, positive=True)
Ps = _random_normal_draws(12.6, .02, N, positive=True)
rmsinst, rmsgran = unp.uarray(.9, .1), unp.uarray(1.76, .04)
s = unp.sqrt(rmsinst**2 + rmsgran**2)
ss = _random_normal_draws(float(unp.nominal_values(s)),
float(unp.std_devs(s)),
N,
positive=True)
# Monte-Carlo computation of sigKs
sigKs = np.zeros(N)
for i in range(N):
theta = P, T0, Krvs[i], As[i], ls[i], Gs[i], Ps[i], ss[i]
sigKs[i] = compute_sigmaK_GP(theta, bjd, rv, erv)
# save output
_save_draws('Kep21HARPSN', Krvs, As, ls, Gs, Ps, ss, sigKs)
def compute_nRV_GP(GPtheta, keptheta, sigRV_phot, sigK_target, duration=100):
assert len(GPtheta) == 5
assert len(keptheta) == 2
a, l, G, Pgp, s = GPtheta
P, K = keptheta
# search for target sigma by iterating over Nrv coarsely
Nrvs = np.arange(10, 1001, 90)
sigKs = np.zeros(Nrvs.size)
for i in range(Nrvs.size):
# get rv activity model
gp = george.GP(a*(george.kernels.ExpSquaredKernel(l) + \
george.kernels.ExpSine2Kernel(G,Pgp)))
t = _uniform_window_function(duration, Nrvs[i])
erv = np.repeat(sigRV_phot, t.size)
gp.compute(t, np.sqrt(erv**2 + s**2))
rv_act = gp.sample(t)
# get planet model
rv_kep = -K*np.sin(2*np.pi*foldAt(t, P))
# get total rv signal with noise
rv = rv_act + rv_kep + np.random.randn(t.size) * sigRV_phot
# compute sigK
theta = P, 0, K, a, l, G, Pgp, s
sigKs[i] = compute_sigmaK_GP(theta, t, rv, erv)
# fit powerlaw in log space to estimate Nrv for the target sigK
g = np.isfinite(sigKs)
p = np.poly1d(np.polyfit(np.log(sigKs[g]), np.log(Nrvs[g]), 1))
Nrv = np.exp(p(np.log(sigK_target)))
return Nrv
def compare_WFs(N):
'''Compute a set of sigKs using a GP with the K2-18 HARPS WF and a uniform
WF to test the sensitivity of sigK on the assumed WF.'''
GPtheta, keptheta, sig_phot = set_thetas()
a, l, G, Pgp, s = GPtheta
P, K = keptheta
sigK_target = K / 3.
N = int(N)
sigKs_uni, sigKs_harps = np.zeros(N), np.zeros(N)
for i in range(N):
print float(i) / N
gp = george.GP(a*(george.kernels.ExpSquaredKernel(l) + \
george.kernels.ExpSine2Kernel(G,Pgp)))
t1 = get_uniform_WF()
t2 = get_true_WF()
assert t1.size == t2.size
erv = np.repeat(sig_phot, t1.size)
gp.compute(t1, np.sqrt(erv**2 + s**2))
rv_act1 = gp.sample(t1)
gp.compute(t2, np.sqrt(erv**2 + s**2))
rv_act2 = gp.sample(t2)
# get planet model
rv_kep1 = -K*np.sin(2*np.pi*foldAt(t1, P))
rv_kep2 = -K*np.sin(2*np.pi*foldAt(t2, P))
# get total rv signal with noise
rv1 = rv_act1 + rv_kep1 + np.random.randn(t1.size) * sig_phot
rv2 = rv_act2 + rv_kep2 + np.random.randn(t1.size) * sig_phot
# compute sigK
theta = P, 0, K, a, l, G, Pgp, s
sigKs_uni[i] = compute_sigmaK_GP(theta, t1, rv1, erv)
sigKs_harps[i] = compute_sigmaK_GP(theta, t2, rv2, erv)
return sigKs_uni, sigKs_harps
def sigK_K218(N=1e3, P=32.93963, T0=2457264.39157):
'''From Cloutier et al 2017'''
# get time-series
bjd, rv, erv = np.loadtxt('Nrv_tests/K218.dat').T
kepc = get_rv1((8.962, 2457264.55, 0, 4.63, 0, 0), bjd)
rv -= kepc
# sample parameter posteriors approximating the PDFs as Gaussian
N = int(N)
Krvs = _random_normal_draws(3.18, .71, N, positive=True)
As = _random_normal_draws(.67, 1.8, N, positive=True)
ls = _random_normal_draws(64.49, 15, N, positive=True)
Gs = _random_normal_draws(1.2, .45, N, positive=True)
Ps = _random_normal_draws(38.6, .9, N, positive=True)
ss = _random_normal_draws(.25, .4, N, positive=True)
# Monte-Carlo computation of sigKs
sigKs = np.zeros(N)
for i in range(N):
theta = P, T0, Krvs[i], As[i], ls[i], Gs[i], Ps[i], ss[i]
sigKs[i] = compute_sigmaK_GP(theta, bjd, rv, erv)
# save output
_save_draws('K218', Krvs, As, ls, Gs, Ps, ss, sigKs)
def compute_nRV_GP(GPtheta,
keptheta,
sig_phot,
sigK_target,
fname='',
duration=100):
'''
Compute nRV for TESS planets including a GP activity model (i.e. non-white
noise model.
'''
assert len(GPtheta) == 5
assert len(keptheta) == 2
a, l, G, Pgp, s = GPtheta
P, K = keptheta
# search for target sigma by iterating over Nrv coarsely at first
Nrvs = np.arange(10, 1001, 90)
sigKs = np.zeros(Nrvs.size)
for i in range(Nrvs.size):
# get rv activity model
gp = george.GP(a*(george.kernels.ExpSquaredKernel(l) + \
george.kernels.ExpSine2Kernel(G,Pgp)))
t = _uniform_window_function(duration, Nrvs[i])
erv = np.repeat(sig_phot, t.size)
gp.compute(t, np.sqrt(erv**2 + s**2))
rv_act = gp.sample(t)
##if rv_act.std() > 0:
## rv_act *= a / rv_act.std()
# get planet model
rv_kep = -K * np.sin(2 * np.pi * foldAt(t, P))
# get total rv signal with noise
rv = rv_act + rv_kep + np.random.randn(t.size) * sig_phot
# compute sigK
theta = P, 0, K, a, l, G, Pgp, s
sigKs[i] = compute_sigmaK_GP(theta, t, rv, erv)
# fit powerlaw to Nrv vs sigK
##g = np.isfinite(sigKs)
##alpha0 = np.polyfit(np.log10(sigKs[g]), np.log10(Nrvs[g]), 1)[0]
##A0 = Nrvs.max() / sigKs[g].min()**alpha0
##bounds = [-np.inf,-np.inf,0], [np.inf]*3
##popt,_ = curve_fit(powerlawfunc, sigKs[g], Nrvs[g], p0=[A0, alpha0, 0],
## bounds=bounds)
##Nrv1 = float(powerlawfunc(sigK_target, *popt))
# fit power in log space
g = np.isfinite(sigKs)
p = np.poly1d(np.polyfit(np.log(sigKs[g]), np.log(Nrvs[g]), 1))
Nrv = np.exp(p(np.log(sigK_target)))
# save diagnostic plot
if fname != '':
label = fname.split('/')[-1].split('.')[0]
starnum = label.split('_')[0].split('t')[-1]
try:
os.mkdir('plots/star%s' % starnum)
except OSError:
pass
sigKs_temp = np.logspace(np.log10(sigKs.min()), np.log10(sigKs.max()),
100)
# dont plot!!
#plt.scatter(sigKs, Nrvs), plt.plot(sigKs_temp, np.exp(p(np.log(sigKs_temp))), '-')
#plt.xlabel('sigK (m/s)'), plt.ylabel('nRV'), plt.xscale('log'), plt.yscale('log')
#plt.savefig('plots/star%s/%s.png'%(starnum, label)), plt.close('all')
np.savetxt('plots/star%s/%s_datapoints.dat' % (starnum, label),
np.array([sigKs, Nrvs]).T,
fmt='%.5e',
delimiter='\t')
np.savetxt('plots/star%s/%s_fit.dat' % (starnum, label),
np.array([sigKs_temp,
np.exp(p(np.log(sigKs_temp)))]).T,
fmt='%.5e',
delimiter='\t')
return Nrv