def eqPM2galPM(ra, dec, mu_ra, mu_dec):
"""
Description: Given coordinates and proper motion in the equatorial J2000.0 system,
return proper motions in the galactic coordinate system
"""
# we need galactic coordinates
gl, gb = eq2gal(ra, dec)
## angle phi between the NCP and the NGP (eqs.1-11)
# but first, the equatorial coordinates of the NGP (J2000, from Wikipedia)
alpha0 = 192.85948
delta0 = 27.12825
sinphi = np.sin(np.radians(90 - dec)) * np.sin(
np.radians(ra - alpha0)) / np.sin(np.radians(90 - gb))
aux1 = np.cos(np.radians(90 - delta0)) * np.sin(np.radians(90 - dec))
cosphi = (aux1 -
np.sin(np.radians(90 - delta0)) * np.cos(np.radians(90 - dec)) *
np.cos(np.radians(ra - alpha0))) / np.sin(np.radians(90 - gb))
# rotation: eq.1-10
mu_gl = mu_ra * cosphi + mu_dec * sinphi
mu_gb = -mu_ra * sinphi + mu_dec * cosphi
return mu_gl, mu_gb
def load_PS1_data(lc_filename):
# load cleaned PS1 data and correct magnitude errors
lc_ps = np.genfromtxt(lc_filename, usecols=(1, 2, 3, 6, 8, 17), names='mag_err, ra, dec, filter, mjd_obs, ucalmag', dtype='f8, f8, f8, |S5, f8, f8')
lc_ps['mag_err'] = np.sqrt((1.3*lc_ps['mag_err'])**2 + 0.015**2)
# correct PS1 light curves for extinction
gl, gb = eq2gal(lc_ps['ra'][0], lc_ps['dec'][0])
EBV = getval(gl, gb)
for band, c in zip(['g', 'r', 'i', 'z', 'y'], [3.172, 2.271, 1.682, 1.322, 1.087]):
lc_ps['ucalmag'][lc_ps['filter'] == band] -= c*EBV
# light curve data used in fitting
lc_data = [lc_ps['mjd_obs'][lc_ps['filter'] == 'g'], lc_ps['ucalmag'][lc_ps['filter'] == 'g'], lc_ps['mag_err'][lc_ps['filter'] == 'g'], lc_ps['mjd_obs'][lc_ps['filter'] == 'r'], lc_ps['ucalmag'][lc_ps['filter'] == 'r'], lc_ps['mag_err'][lc_ps['filter'] == 'r'], lc_ps['mjd_obs'][lc_ps['filter'] == 'i'], lc_ps['ucalmag'][lc_ps['filter'] == 'i'], lc_ps['mag_err'][lc_ps['filter'] == 'i'], lc_ps['mjd_obs'][lc_ps['filter'] == 'z'], lc_ps['ucalmag'][lc_ps['filter'] == 'z'], lc_ps['mag_err'][lc_ps['filter'] == 'z']]
return lc_data
def load_data(P_ref=0.52854, FeH_ref=-1.4):
# load Table 2 of Dambis et al. (2013)
dambis = getdata('Dambis_2013_Table2.fits')
# load Table 1 of Klein & Bloom (2013)
tbl = np.genfromtxt(
'rrl_fit_table1.txt',
names=
'name, type, blazhko, period, log10(P_f/P_0), FeH, prior_mu, prior_mu_err, SF_ebv, SF_ebv_err, m_U_obs, m_U_obs_err, m_B_obs, m_B_obs_err, m_hipp_obs, m_hipp_obs_err, m_V_obs, m_V_obs_err, m_R_obs, m_R_obs_err, m_I_obs, m_I_obs_err, m_z_obs, m_z_obs_err, m_J_obs, m_J_obs_err, m_H_obs, m_H_obs_err, m_K_obs, m_K_obs_err, m_W1_obs, m_W1_obs_err, m_W2_obs, m_W2_obs_err, m_W3_obs, m_W3_obs_err, post_mu, post_mu_err',
dtype=
'|S10, |S5, bool, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8, f8',
skip_header=1)
tbl = append_fields(tbl,
names=('ra', 'dec', 'gl', 'gb', 'EBV', 'FeHErr',
'par_obs', 'sigma_par'),
data=(np.zeros(tbl.size), np.zeros(tbl.size),
np.zeros(tbl.size), np.zeros(tbl.size),
np.zeros(tbl.size), np.zeros(tbl.size) + 0.15,
np.zeros(tbl.size), np.zeros(tbl.size)),
usemask=False,
asrecarray=False)
# uncertainty in [Fe/H] is 0.15 dex (Note 8 in Table 1 of Fernley et al. 1998)
# remove spaces from Table 2 names
for i, name in enumerate(dambis['Name']):
dambis['Name'][i] = name.replace(' ', '')
if dambis['Name'][i][0:2] == 'V0':
dambis['Name'][i] = name.replace('V0', 'V').replace(' ', '')
# match Table 2 and Table 1 to get positions of RR Lyrae stars
for i, name in enumerate(tbl['name']):
ind = np.where(name == dambis['Name'])[0]
if ind.size > 0:
tbl['ra'][i] = dambis['RAJ2000'][ind[0]]
tbl['dec'][i] = dambis['DEJ2000'][ind[0]]
else:
print "Object %s has no data!" % name
# add galactic coordinates
gl, gb = eq2gal(tbl['ra'], tbl['dec'])
tbl['gl'] = gl
tbl['gb'] = gb
# add extinction
tbl['EBV'] = getval(tbl['gl'], tbl['gb'])
# add TGAS parallaxes
tgas = np.genfromtxt('tgas_match.txt', names=True)
# back out TGAS uncertainty corrections
tgas['parallax_error'] = np.sqrt(tgas['parallax_error']**2 - 0.2**2) / 1.4
h = esutil.htm.HTM(10)
m1, m2, d12 = h.match(tbl['ra'],
tbl['dec'],
tgas['ra'],
tgas['dec'],
5 / 3600.,
maxmatch=1)
tbl['par_obs'][m1] = tgas['parallax'][m2] / 1000.
tbl['sigma_par'][m1] = tgas['parallax_error'][m2] / 1000.
tbl['ra'][m1] = tgas['ra'][m2]
tbl['dec'][m1] = tgas['dec'][m2]
# eliminate objects without TGAS parallaxes
tbl = tbl[tbl['sigma_par'] <> 0]
# define the PLRs (Table 2 of Klein & Bloom 2013)
klein2014_table2 = np.genfromtxt('%s/Klein_et_al_2014_Table2.csv' %
work_dir,
delimiter=',',
names=True,
dtype='|S10,f8,f8,f8,f8,f8,f8,f8,f8')
bands = klein2014_table2['band']
alphas = klein2014_table2['alpha']
betas = klein2014_table2['beta']
gammas = np.array([
0.5, 0.4, 0.3, 0.3, 0.18, 0.18, 0.18, 0.18, 0.18, 0.18, 0.1, 0.1, 0.1
])
#alphas[9] = -2.326 # K-band slope from Braga et al. (2015)
alphas[9] = -2.38 # +- 0.04, from Sollima et al. (2006)
gammas[9] = 0.09 # +- 0.14, from Sollima et al. (2006)
#ax = (alphas[9]+0.04*np.random.randn(1000))*np.log10(P_ref) + (gammas[9] + 0.14*np.random.randn(1000))*FeH_ref -1.04 + 0.13*np.random.randn(1000)
betas[9] = -0.50 # np.mean(ax)
alphas[10] = -2.381 # +- 0.097, from Dambis et al. (2014)
gammas[10] = 0.106 # +- 0.023, from Dambis et al. (2014)
#ax = (alphas[10]+0.097*np.random.randn(1000))*np.log10(P_ref) + (gammas[10] + 0.023*np.random.randn(1000))*FeH_ref - 1.135 + 0.077*np.random.randn(1000)
betas[10] = -0.62
alphas[11] = -2.269 # +- 0.127, from Dambis et al. (2014)
gammas[11] = 0.117 # +- 0.023, from Dambis et al. (2014)
#ax = (alphas[11]+0.127*np.random.randn(1000))*np.log10(P_ref) + (gammas[11] + 0.023*np.random.randn(1000))*FeH_ref - 1.088 + 0.077*np.random.randn(1000)
betas[11] = -0.62
# set scatter in all PLRs to 0.001 mag to measure the uncertainty in recovered parameters
sigma_PLRs = np.zeros(bands.size) + 0.001
#sigma_PLRs = klein2014_table2['sig_intrinsic']
#ext_coeffs = np.array([4.334, 3.626, 3.0, 2.742, 2.169, 1.505, 1.263, 0.709, 0.449, 0.302, 0.2, 0.1, 0.05])
ext_coeffs = calculate_ext_coeffs(
0
) * 0.96710433795664874 # A_band = C_band * E(g-r), following Schlafly et al. (2016); multiply by 0.96710433795664874 to get A_band = C_band * E(B-V)
# uncertainty in extinction coefficients assuming sigma(x) = 0.02 or sigma(RV) = 0.18 and Schlafly et al. (2016) extinction curve
ext_coeffs_unc = np.array([
0.14, 0.14, 0.14, 0.14, 0.14, 0.13, 0.12, 0.07, 0.04, 0.03, 0.01,
0.001, 0.05
])
obs_mags = np.zeros((tbl.size, bands.size))
obs_magErrs = np.zeros((tbl.size, bands.size))
Nstars = obs_mags.shape[0]
Nbands = obs_mags.shape[1]
for b, ext_coeff in enumerate(ext_coeffs):
obs_mags[:, b] = tbl['m_%s_obs' % bands[b]]
obs_magErrs[:, b] = tbl['m_%s_obs_err' % bands[b]]
log10P_fP_0 = tbl['log10P_fP_0']
EBV = tbl['EBV']
# RIJHK: Table 2 of Braga et al. (2015)
# alphas: R = -0.847 +- 0.177, I = -1.137 +- 0.144, J = -1.793 +- 0.109, H = -2.408 +- 0.082, K = -2.326 +- 0.074
# W1, W2, W3: Eqs. 2-7 of Klein et al. (2014)
# DM of M4 is 11.4 (Neeley et al. 2015)
# Gaussian priors on betas, alphas, gammas, and sigma_PLRs from Table 2 of Klein et al. (2013)
alpha_mean = klein2014_table2['alpha']
alpha_sig = klein2014_table2['alpha_sig']
#alpha_mean[9] = -2.326 # from Braga et al. (2015)
#alpha_sig[9] = 0.074 # from Braga et al. (2015)
alpha_mean[9] = -2.38 # from Sollima et al. (2006)
alpha_sig[9] = 0.04 # from Sollima et al. (2006)
alpha_mean[10] = -2.381 # from Dambis et al. (2014)
alpha_sig[10] = 0.097 # from Dambis et al. (2014)
alpha_mean[11] = -2.269 # from Dambis et al. (2014)
alpha_sig[11] = 0.127 # from Dambis et al. (2014)
beta_mean = klein2014_table2['beta']
beta_sig = klein2014_table2['beta_sig']
beta_mean[9] = -0.50
beta_sig[9] = 0.23
beta_mean[10] = -0.62
beta_sig[10] = 0.09
beta_mean[11] = -0.62
beta_sig[11] = 0.09
gamma_mean = gammas
gamma_sig = gammas * 0 + 0.14
gamma_mean[10] = 0.106 # from Dambis et al. (2014)
gamma_sig[10] = 0.023 # from Dambis et al. (2014)
gamma_mean[11] = 0.117 # from Dambis et al. (2014)
gamma_sig[11] = 0.023 # from Dambis et al. (2014)
#sigma_PLR_mean = klein2014_table2['sig_intrinsic']
#sigma_PLR_sig = klein2014_table2['sig_intrinsic_sig']
sigma_PLR_mean = np.zeros(bands.size) + 0.001
sigma_PLR_sig = np.zeros(bands.size) + 0.0001
# hard limits on PLR parameters, mean +- 7*sigma
alphas_lower_limit = []
alphas_upper_limit = []
for alpha, sig in zip(alpha_mean, alpha_sig):
alphas_lower_limit.append(alpha - 7 * sig)
alphas_upper_limit.append(alpha + 7 * sig)
alphas_lower_limit = np.array(alphas_lower_limit)
alphas_upper_limit = np.array(alphas_upper_limit)
betas_lower_limit = []
betas_upper_limit = []
for beta, sig in zip(beta_mean, beta_sig):
betas_lower_limit.append(beta - 7 * sig)
betas_upper_limit.append(beta + 7 * sig)
betas_lower_limit = np.array(betas_lower_limit)
betas_upper_limit = np.array(betas_upper_limit)
# use broad priors for the W1 and W2 bands
alphas_upper_limit[10:12] = 2
alphas_lower_limit[10:12] = -5
betas_upper_limit[10:12] = 0
betas_lower_limit[10:12] = -4
# use broad priors for the Hipparcos band
alphas_upper_limit[2] = 2
alphas_lower_limit[2] = -5
betas_upper_limit[2] = 2
betas_lower_limit[2] = -2
# this prior is not used right now
sig_PLR_lower_limit = []
sig_PLR_upper_limit = []
for sig_PLR, sig in zip(sigma_PLR_mean, sigma_PLR_sig):
sig_PLR_lower_limit.append(sig_PLR - 5 * sig)
sig_PLR_upper_limit.append(sig_PLR + 5 * sig)
sig_PLR_lower_limit = np.array(sig_PLR_lower_limit)
sig_PLR_lower_limit = np.where(sig_PLR_lower_limit <= 0, 0.00001,
sig_PLR_lower_limit)
sig_PLR_upper_limit = np.array(sig_PLR_upper_limit)
# dump all important data
dat = {}
dat['scenario'] = 'real'
dat['name'] = tbl['name']
dat['ra'] = tbl['ra']
dat['dec'] = tbl['dec']
dat['P_ref'] = P_ref
dat['type'] = tbl['type']
dat['blazhko'] = tbl['blazhko']
dat['FeH_ref'] = FeH_ref
dat['obs_mags'] = obs_mags
dat['obs_magErrs'] = obs_magErrs
dat['par_obs'] = tbl['par_obs']
dat['sigma_par'] = tbl['sigma_par']
dat['log10P_fP_0'] = log10P_fP_0
dat['EBV'] = EBV
dat['FeH'] = tbl['FeH']
dat['FeHErr'] = tbl['FeHErr']
dat['alphas_lower_limit'] = alphas_lower_limit
dat['alphas_upper_limit'] = alphas_upper_limit
dat['betas_lower_limit'] = betas_lower_limit
dat['betas_upper_limit'] = betas_upper_limit
dat['sig_PLR_lower_limit'] = sig_PLR_lower_limit
dat['sig_PLR_upper_limit'] = sig_PLR_upper_limit
dat['alpha_mean'] = alpha_mean
dat['alpha_sig'] = alpha_sig
dat['beta_mean'] = beta_mean
dat['beta_sig'] = beta_sig
dat['gamma_mean'] = gamma_mean
dat['gamma_sig'] = gamma_sig
dat['sigma_PLR_mean'] = sigma_PLR_mean
dat['sigma_PLR_sig'] = sigma_PLR_sig
dat['ext_coeffs'] = ext_coeffs
dat['ext_coeffs_unc'] = ext_coeffs_unc
with gzip.open('TGAS_data.pklz', 'wb') as f:
cPickle.dump(dat, f)
return dat