antaress.ANTARESS_launch.ANTARESS_systems module#
- get_system_params()[source]#
Planetary system properties.
Returns dictionary with properties of planetary systems. Format with minimum required properties is
>>> all_system_params={ 'star_name':{ 'star':{ 'sysvel': val, 'Rstar': val, 'istar': val, 'veq': val }, 'planet_b':{ 'period': val, 'TCenter': val, 'ecc': val, 'omega_deg': val, 'inclination': val, 'lambda_proj': val, 'aRs': val, 'Kstar': val }, }, }
Additional planets can be associated with a given system. Required and optional properties are defined as follows.
Star properties
sysvel [km/s] : systemic radial velocity
relative velocity between the stellar and solar system barycenters
this value is used for first-order definitions and does not need to be extremely accurate
veq [km/s] : equatorial rotational velocity
veq_spots [km/s] : equatorial rotational velocity of active regions categorized as spots (contrast < 1)
veq_faculae [km/s] : equatorial rotational velocity of active regions categorized as faculae (contrast >=1)
istar [deg] : stellar inclination
angle counted from the LOS toward the stellar spin axis
defined in [ 0 ; 180 ] deg
dstar [pc]: distance Sun-star
Mstar [Msun] : stellar mass
only used if Kstar is not defined
Rstar [Rsun]: stellar radius
used to calculate the planet orbital rv in the star rest frame
used as Req if the star’s oblateness is accounted for
alpha_rot, beta_rot [] : differential rotation coefficients
differential rotation is defined as \(\Omega = \Omega_\mathrm{eq} (1-\alpha_\mathrm{rot} y_\mathrm{lat}^2-\beta_\mathrm{rot} y_\mathrm{lat}^4)\)
the pipeline checks that \(\alpha_\mathrm{rot}+\beta_\mathrm{rot}<1\) (assuming that the star rotates in the same direction at all latitudes)
defined in percentage of rotation rate
alpha_rot_spots, beta_rot_spots [] : differential rotation coefficients of active regions categorized as spots (contrast < 1)
alpha_rot_faculae, beta_rot_faculae [] : differential rotation coefficients of active regions categorized as faculae (contrast >= 1)
ci [km/s] : coefficients of the \(\mu\)-dependent convective blueshift velocity polynomial
convective blueshift is defined as \(\mathrm{rv}_\mathrm{cb} = \sum_{i}{c_i \mu^i}\)
\(c_0\) is degenerate with higher-order coefficients and defined independently
V [] : stellar magnitude
assumed to correspond to the achromatic band of the transit light curve
only used in plots to estimate errors on surface rv
f_GD [] : stellar oblateness
defined as \((R_\mathrm{eq}-R_\mathrm{pole})/R_\mathrm{eq}\)
Tpole [K] : stellar temperature at pole
used to account for gravity-darkening
used as effective temperature for stellar atmosphere grid and mask generation
beta_GD [K] : gravity-darkening coefficient
A_R, ksi_R, (A_T, ksi_T) : radial–tangential macroturbulence properties eta_R, (eta_T) : anisotropic faussian macroturbulence properties
only used if macroturbulence is activated, for analytical intrinsic profiles
set _T parameters equal to _R for isotropic macroturbulence
logg [log(cgs)] : surface gravity of the star
only used for the stellar atmosphere grid
vmic and vmac [km/s] : micro and macroturbulence
only used for the stellar atmosphere grid
Tcenter [bjd] : reference time for null stellar phase
set to 2400000 if undefined
Planet properties
period [days] : orbital period
TCenter [bjd] : epoch of transit center
calculated from Tperi if unknown, and orbit is eccentric
Tperi [bjd] : epoch of periastron
TLength [days] : duration of transit
only used to estimate the range of the phase table in the light curve plot
ecc [] : orbital eccentricity
omega_deg [deg] : argument of periastron
inclination [deg] : orbital inclination
counted from the LOS to the normal of the orbital plane
defined in [ 0 ; 90 ] deg
lambda_proj [deg] : sky-projected obliquity
angle counted from the sky-projected stellar spin axis (or rather, from the axis \(Y_{\star \mathrm{sky}}\), which corresponds to the projection of \(Y_{\star}\) when \(i_{\star} = i_{\star \mathrm{in}}\) in [ 0 ; 180 ]) toward the sky-projected normal to the orbital plane
defined in [ -180 ; 180 ] deg
Kstar [m/s] : rv semi-amplitude induced by the planet on the star
Msini [Mjup] : Mpl*sin(inclination)
only used to calculate Kstar if undefined
aRs [Rs] : semi-major axis
Notes
this is a note about degeneracies on a planetary system orbital architecture. See the definition of the axis systems in Bourrier+2024 (ANTARESS I).
we distinguish between the values given as input here for \(i_\mathrm{p,in}\) ([0;90]), \(\lambda_\mathrm{in}\) (x+[0;360]), and \(i_{\star \mathrm{in}}\) ([0;180]) and the true angles that can take any value between 0 and 360. Note that the angle ranges could be inverted between \(\lambda\) and \(i_{\star}\). The reason is that degeneracies prevent distinguishing some of the true angle values, except in specific cases.
the true 3D spin-orbit angle is defined as \(\psi = \arccos(\sin(i_{\star}) \cos(\lambda) \sin(i_p) + \cos(i_{\star}) \cos(i_p))\).
with solid body rotation, any \(i_{\star}\) is equivalent, and there is a degeneracy between
\((i_\mathrm{p},\lambda) = (i_\mathrm{p,in},\lambda_\mathrm{in})\) associated with \(\omega = \lambda_\mathrm{in}\)
\((i_\mathrm{p},\lambda) = (\pi-i_\mathrm{p,in},-\lambda_\mathrm{in})\) associated with \(\omega = -\lambda_\mathrm{in}\)
Both solutions yield the same \(x_{\star \mathrm{sky}}\) coordinate. \(\omega\) is the longitude of the ascending node of the planetary orbit (taking the ascending node of the stellar equatorial plane as reference).
if the absolute value of \(\sin(i_{\star})\) is known, via the combination of \(P_\mathrm{eq}\) and \(v_\mathrm{eq} \sin(i_{\star})\), then the following configurations are degenerate. The coordinate probed by the velocity field is \(x_{\star \mathrm{sky}} \sin(i_{\star})\). The other coordinate probed is \(|\sin(i_{\star})|\). Only combinations of angles that conserve both quantities are allowed.
\((i_\mathrm{p},\lambda,i_{\star}) = (i_\mathrm{p,in} , \lambda_\mathrm{in} , i_{\star \mathrm{in}})\)
default \(x_{\star \mathrm{sky}},y_{\star \mathrm{sky}},y_{\star}\).
default \(x_{\star \mathrm{sky}} \sin(i_{\star \mathrm{in}})\) and \(|\sin(i_{\star \mathrm{in}})|\).
default \(\psi = \psi_\mathrm{in}\).
\((i_\mathrm{p},\lambda,i_{\star}) = (i_\mathrm{p,in} , \pi+\lambda_\mathrm{in} , -i_{\star \mathrm{in}})\)
same as 1. rotated around the LOS: yields \(-x_{\star \mathrm{sky}},-y_{\star \mathrm{sky}},y_{\star},\psi_\mathrm{in}\)
\((i_\mathrm{p},\lambda,i_{\star}) = (-i_\mathrm{p,in} , \pi+\lambda_\mathrm{in} , \pi+i_{\star \mathrm{in}})\)
same as 1. rotated around the LOS: yields \(-x_{\star \mathrm{sky}},-y_{\star \mathrm{sky}},y_{\star},\pi-\psi_\mathrm{in}\)
\((i_\mathrm{p},\lambda,i_{\star}) = (\pi-i_\mathrm{p,in} , -\lambda_\mathrm{in} , \pi-i_{\star \mathrm{in}})\)
yields \(x_{\star \mathrm{sky}},-y_{\star \mathrm{sky}}, -y_{\star},\psi_\mathrm{in}\)
\((i_\mathrm{p},\lambda,i_{\star}) = (\pi+i_\mathrm{p,in} , -\lambda_\mathrm{in} , i_{\star \mathrm{in}})\)
yields \(x_{\star \mathrm{sky}},-y_{\star \mathrm{sky}}, -y_{\star},\pi-\psi_\mathrm{in}\)
\((i_\mathrm{p},\lambda,i_{\star}) = (\pi-i_\mathrm{p,in} , \pi-\lambda_\mathrm{in} , \pi+i_{\star \mathrm{in}})\)
same as 2. rotated around the LOS: yields \(-x_{\star \mathrm{sky}},y_{\star \mathrm{sky}},-y_{\star},\psi_\mathrm{in}\)
\((i_\mathrm{p},\lambda,i_{\star}) = (\pi+i_\mathrm{p,in} , \pi-\lambda_\mathrm{in} , -i_{\star \mathrm{in}})\)
same as 2. rotated around the LOS: yields \(-x_{\star \mathrm{sky}},y_{\star \mathrm{sky}},-y_{\star},\pi-\psi_\mathrm{in}\)
\((i_\mathrm{p},\lambda,i_{\star}) = (i_\mathrm{p,in} , \lambda_\mathrm{in} , \pi-i_{\star \mathrm{in}})\)
yields \(x_{\star \mathrm{sky}},y_{\star \mathrm{sky}}, y_{\star,2} = \sin(i_{\star \mathrm{in}}) y_{\star \mathrm{sky}} - \cos(i_{\star \mathrm{in}}) \sin(i_\mathrm{p,in}), \psi_2 = \arccos(\sin(i_{\star \mathrm{in}}) \cos(\lambda_\mathrm{in}) \sin(i_\mathrm{p,in}) - \cos(i_{\star \mathrm{in}}) \cos(i_\mathrm{p,in}))\), where \((y_{\star,2},\psi_2)\) are associated with another possible system configuration that cannot be related to \((y_{\star},\psi)\)
\((i_\mathrm{p},\lambda,i_{\star}) = (i_\mathrm{p,in} , \pi+\lambda_\mathrm{in} , \pi+i_{\star \mathrm{in}})\)
same as 3. rotated around the LOS: yields \(-x_{\star \mathrm{sky}},-y_{\star \mathrm{sky}},y_{\star,2},\psi_2\)
\((i_\mathrm{p},\lambda,i_{\star}) = (-i_\mathrm{p,in} , \pi+\lambda_\mathrm{in} , -i_{\star \mathrm{in}})\)
same as 3. rotated around the LOS: yields \(-x_{\star \mathrm{sky}},-y_{\star \mathrm{sky}},y_{\star,2},\pi - \psi_2\)
\((i_\mathrm{p},\lambda,i_{\star}) = (\pi-i_\mathrm{p,in} , -\lambda_\mathrm{in} , i_{\star \mathrm{in}})\)
yields \(x_{\star \mathrm{sky}},-y_{\star \mathrm{sky}},-y_{\star,2},\psi_2\)
\((i_\mathrm{p},\lambda,i_{\star}) = (\pi+i_\mathrm{p,in} , -\lambda_\mathrm{in} , \pi-i_{\star \mathrm{in}})\)
yields \(x_{\star \mathrm{sky}},-y_{\star \mathrm{sky}},-y_{\star,2},\pi-\psi_2\)
\((i_\mathrm{p},\lambda,i_{\star}) = (\pi-i_\mathrm{p,in} , \pi-\lambda_\mathrm{in} , -i_{\star \mathrm{in}})\)
same as 4. rotated around the LOS: yields \(-x_{\star \mathrm{sky}},y_{\star \mathrm{sky}},-y_{\star,2},\psi_2\)
\((i_\mathrm{p},\lambda,i_{\star}) = (\pi+i_\mathrm{p,in} , \pi-\lambda_\mathrm{in} , \pi+i_{\star \mathrm{in}})\)
same as 4. rotated around the LOS: yields \(-x_{\star \mathrm{sky}},y_{\star \mathrm{sky}},-y_{\star,2},\pi-\psi_2\)
These degenerate configurations thus yields two possible values for \(\psi\), equivalent to maintaining the same sky-projected angle and orbital inclination, and considering a Northern configuration (\(i_{\star}=i_{\star \mathrm{in}}\) ; \(\Psi=\arccos(\sin(i_{\star \mathrm{in}}) \cos(\lambda_\mathrm{in}) \sin(i_\mathrm{p,in}) + \cos(i_{\star \mathrm{in}}) \cos(i_\mathrm{p,in}))\)) and a Southern configuration (\(i_{\star}=\pi-i_{\star \mathrm{in}}\) ; \(\Psi=\arccos(\sin(i_{\star \mathrm{in}}) \cos(\lambda_\mathrm{in}) \sin(i_\mathrm{p,in}) - \cos(i_{\star \mathrm{in}}) \cos(i_\mathrm{p,in}))\)) which are equiprobable.
if the absolute stellar latitude is constrained (eg with differential rotation), then there is a degeneracy between two configurations, which yield the same \(\psi\). The coordinate probed by the velocity field is \(x_{\star \mathrm{sky}} \sin(i_{\star})\). The other coordinate probed is \(y_{\star}^2\) Only combinations of angles that conserve both quantities are allowed. Fewer configurations than in the previous case are allowed since \(|y_{\star}|\) is more constraining than \(|\sin(i_{\star})|\).
\((i_\mathrm{p},\lambda,i_{\star}) = (i_\mathrm{p,in} , \lambda_\mathrm{in} , i_{\star \mathrm{in}})\)
conserves \(x_{\star \mathrm{sky}} \sin(i_{\star})\) and \(y_{\star}^2\).
yields \(\psi = \psi_\mathrm{in}\).
\((i_\mathrm{p},\lambda,i_{\star}) = (i_\mathrm{p,in} , \pi+\lambda_\mathrm{in},-i_{\star \mathrm{in}})\)
conserves \(-x_{\star \mathrm{sky}} \sin(-i_{\star})\) and \(y_{\star}^2\).
yields \(\psi = \psi_\mathrm{in}\).
this configuration is the same as 1., rotating the whole system by \(\pi\) around the LOS (ie, yielding \(x_{\star \mathrm{sky}} = -x_{\star \mathrm{sky}}\) and \(y_{\star \mathrm{sky}} = -y_{\star \mathrm{sky}}\) in the sky-projected frame).
\((i_\mathrm{p},\lambda,i_{\star}) = (\pi-i_\mathrm{p,in},-\lambda_\mathrm{in} , \pi-i_{\star \mathrm{in}})\)
conserves \(x_{\star \mathrm{sky}} \sin(i_{\star})\) and \((-y_{\star})^2\).
yields \(\psi = \psi_\mathrm{in}\)
\((i_\mathrm{p},\lambda,i_{\star}) = (\pi-i_\mathrm{p,in},\pi-\lambda_\mathrm{in} , \pi+i_{\star \mathrm{in}})\)
conserves \(-x_{\star \mathrm{sky}} (-\sin(i_{\star}))\) and \((-y_{\star})^2\).
yields \(\psi = \psi_\mathrm{in}\).
this configuration is the same as 2., rotating the whole system by \(\pi\) around the LOS (ie, yielding \(x_{\star \mathrm{sky}} = -x_{\star \mathrm{sky}}\) and \(y_{\star \mathrm{sky}} = y_{\star \mathrm{sky}}\) in the sky-projected frame)
\((i_\mathrm{p},\lambda,i_{\star}) = (-i_\mathrm{p,in} , \lambda_\mathrm{in} , \pi-i_{\star \mathrm{in}})\)
conserves \(x_{\star \mathrm{sky}} \sin(i_{\star})\) and \(y_{\star}^2\).
yields \(\psi = \pi - \psi_\mathrm{in}\).
\((i_\mathrm{p},\lambda,i_{\star}) = (-i_\mathrm{p,in} , \pi+\lambda_\mathrm{in}, \pi+i_{\star \mathrm{in}})\)
conserves \(-x_{\star \mathrm{sky}} (-\sin(i_{\star}))\) and \(y_{\star}^2\).
this configuration is the same as 3., rotating the whole system by \(\pi\) around the LOS (ie, yielding \(x_{\star \mathrm{sky}} = -x_{\star \mathrm{sky}}\) and \(y_{\star \mathrm{sky}} = -y_{\star \mathrm{sky}}\) in the sky-projected frame).
yields \(\psi = \pi - \psi_\mathrm{in}\).
but this configuration is not authorized for a transiting planet (it would yield the transit behind the star). Note that if several planets are constrained, only combinations of 1. together, or 2. together, are possible since they must share the same \(i_{\star}\)
- Parameters:
None
- Returns:
all_system_params (dict) – dictionary with planetary system properties