def gaia_spitzer_errors():
""" Visualize the observational errors from Gaia and Spitzer, along with
dispersion and distance scale of Sgr and Orphan.
"""
rcparams = {'lines.linestyle' : '-',
'lines.linewidth' : 1.,
'lines.color' : 'k',
'lines.marker' : None,
'axes.edgecolor' : '#444444',
'axes.facecolor' : '#ffffff'}
sgr_color = '#67A9CF'
orp_color = '#EF8A62'
with rc_context(rc=rcparams):
fig,axes = plt.subplots(1, 2, figsize=(12, 6), sharex=True)
# vertical lines for dwarf satellites
axes[0].vlines([24,65,80,100], 0.001, 100, color='#888888', linestyles='--', zorder=-1)
axes[1].vlines([24,65,80,100], [0.081,0.0465,0.025,0.014], 100, color='#888888', linestyles='--', zorder=-1)
# label the vertical lines
axes[1].text(17.1, 0.075, 'Sgr -', color='#888888', rotation=0)
axes[1].text(29.5, 0.043, 'UMi, Boo -', color='#888888', rotation=0)
axes[1].text(58., 0.023, 'Scl -', color='#888888', rotation=0)
axes[1].text(69.75, 0.013, 'Car -', color='#888888', rotation=0)
# Distance from 1kpc to ~100kpc
D = np.logspace(0., 2., 50)*u.kpc
# Sample metallicities from: http://arxiv.org/pdf/1211.7073v1.pdf
fe_hs = np.random.normal(-1.67, 0.3, size=50)
fe_hs = np.append(fe_hs, np.random.normal(-2.33, 0.3, size=len(fe_hs)//5))
for fe_h in fe_hs:
# Johnson/Cousins (V - I_C) color for RR Lyrae at *minimum*
# Guldenschuh et al. (2005 PASP 117, 721), pg. 725
rrl_V_minus_I = np.random.normal(0.579, 0.006)
# Compute the apparent magnitude as a function of distance
M_V = rrl_M_V(fe_h=fe_h)[0]
m_V = apparent_magnitude(M_V, D)
# Distance error
dp = parallax_error(m_V, rrl_V_minus_I).arcsecond
dD = D.to(u.pc).value**2 * dp * u.pc
# Velocity error
dpm = proper_motion_error(m_V, rrl_V_minus_I)
dVtan = (dpm*D).to(u.km*u.radian/u.s).value
# Plot Gaia distance errors
axes[0].loglog(D.kiloparsec, (dD/D).decompose(), color='k', alpha=0.1)
# Plot tangential velocity errors
axes[1].loglog(D.kiloparsec, dVtan, color='k', alpha=0.1)
# Add spitzer 2% line to distance plot
axes[0].axhline(0.02, linestyle='-', linewidth=3, color='k', alpha=0.75)
# Now add rectangles for Sgr, Orphan
sgr_d = Rectangle((10., 0.15), 60., 0.15,
color=sgr_color, alpha=1., label='Sgr stream range')
axes[0].add_patch(sgr_d)
# From fig. 3 in http://mnras.oxfordjournals.org/content/389/3/1391.full.pdf+html
orp_d = Rectangle((10., 0.03), 35., 0.03,
color=orp_color, alpha=1., label='Orp stream range')
axes[0].add_patch(orp_d)
# Dispersion from Majewski 2004: 10 km/s
sgr_v = Rectangle((10., 10), 60., 1., color=sgr_color, alpha=1.)
axes[1].add_patch(sgr_v)
orp_v = Rectangle((10., 8.), 35., 1., color=orp_color, alpha=1.)
axes[1].add_patch(orp_v)
axes[0].set_ylim(0.003, 10)
axes[0].set_xlim(1, 105)
axes[1].set_ylim(0.01, 100)
#axes[1].set_xlim(10, 100)
axes[0].set_xlabel("Distance [kpc]")
axes[0].set_ylabel("Frac. distance error: $\epsilon_D/D$")
axes[1].set_ylabel("$v_{tan}$ error: $\epsilon_v$ [km/s]")
axes[1].set_xlabel("Distance [kpc]")
axes[0].set_xticklabels(["1", "10", "100"])
axes[0].set_yticklabels(["{:g}".format(yt) for yt in axes[0].get_yticks()])
axes[1].set_yticklabels(["{:g}".format(yt) for yt in axes[1].get_yticks()])
# add Gaia and Spitzer text to plots
axes[0].text(4., 0.125, 'Gaia', fontsize=16, rotation=45, fontweight='normal')
axes[0].text(4., 0.013, 'Spitzer', fontsize=16, color="k", alpha=0.75, fontweight='normal')
axes[1].text(4., 0.06, 'Gaia', fontsize=16, rotation=45, fontweight='normal')
# add legends
axes[0].legend(loc='upper left', fancybox=True)
#axes[1].legend(loc='upper left', fancybox=True)
axes[0].yaxis.tick_left()
axes[1].yaxis.tick_left()
fig.subplots_adjust(hspace=0.1, wspace=0.1)
plt.tight_layout()
plt.savefig(os.path.join(plot_path, "gaia.pdf"))
def fig2(**kwargs):
""" Visualize the observational errors from Gaia and Spitzer, along with
dispersion and distance scale of Sgr and Orphan.
"""
rcparams = {'lines.linestyle' : '-',
'lines.linewidth' : 1.,
'lines.color' : 'k',
'lines.marker' : None,
'axes.facecolor' : '#ffffff',
'xtick.major.size' : 16,
'xtick.major.width' : 1.5,
'xtick.minor.size' : 0,
'ytick.major.size' : 16,
'ytick.major.width' : 1.5,
'ytick.minor.size' : 0}
with rc_context(rc=rcparams):
fig,axes = plt.subplots(2, 1, figsize=(8, 10), sharex=True)
# Distance from 1kpc to ~100kpc
D = np.logspace(0., 2., 50)*u.kpc
# Sample metallicities from: http://arxiv.org/pdf/1211.7073v1.pdf
fe_h = -1.67
# Johnson/Cousins (V - I_C) color for RR Lyrae at *minimum*
# Guldenschuh et al. (2005 PASP 117, 721), pg. 725
rrl_V_minus_I = np.random.normal(0.579, 0.006)
# Compute the apparent magnitude as a function of distance
M_V = rrl_M_V(fe_h=fe_h)[0]
m_V = apparent_magnitude(M_V, D)
# Distance error
dp = parallax_error(m_V, rrl_V_minus_I).to(u.arcsecond).value
dD = D.to(u.pc).value**2 * dp * u.pc
# Velocity error
dpm = proper_motion_error(m_V, rrl_V_minus_I)
dVtan = (dpm*D).to(u.km*u.radian/u.s).value
#dVtan = (D*dpm + dD*1.*u.mas/u.yr).to(u.km*u.radian/u.s).value
# Plot Gaia distance errors
fracDist = (dD/D).decompose().value
fracDist[fracDist > 0.1] = 0.1
axes[0].loglog(D.to(u.kpc).value, fracDist, color='#000000', alpha=1., linewidth=4.)
# Plot tangential velocity errors
axes[1].loglog(D.to(u.kpc).value, dVtan, color='#000000', alpha=1., linewidth=4.)
# Add spitzer 2% line to distance plot
axes[0].axhline(0.02, linestyle='--', linewidth=3, color='k', alpha=0.75)
# Now add rectangles for Sgr, Orphan
sgr_d = Rectangle((10., 0.15), 60., 0.15,
color=sgr_color, alpha=0.75, label='Sgr stream')
axes[0].add_patch(sgr_d)
# From fig. 3 in http://mnras.oxfordjournals.org/content/389/3/1391.full.pdf+html
orp_d = Rectangle((10., 0.03), 35., 0.03,
color=orp_color, alpha=0.75, label='Orp stream')
axes[0].add_patch(orp_d)
# Dispersion from Majewski 2004: 10 km/s
sgr_v = Rectangle((10., 10), 60., 1., alpha=0.75, color=sgr_color)
axes[1].add_patch(sgr_v)
orp_v = Rectangle((10., 8.), 35., 1., alpha=0.75, color=orp_color)
axes[1].add_patch(orp_v)
axes[0].set_ylim(0.003, 1.3)
axes[0].set_xlim(1, 100)
axes[1].set_ylim(0.06, 130)
axes[0].set_yticklabels([])
axes[1].set_yticklabels([])
axes[1].set_xticklabels([])
axes[0].yaxis.tick_left()
axes[0].xaxis.tick_bottom()
axes[1].yaxis.tick_left()
axes[1].xaxis.tick_bottom()
plt.tight_layout()
#fig.subplots_adjust(hspace=0.05)
fig.savefig(os.path.join(plot_path, "fig2.pdf"))