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Initializing PSG


The easiest way to prepare the parameters for a spectral synthesis is by loading a configuration template. These templates are actually pre-saved configuration text files that are read by the radiative transfer modules when requesting an on-demand calculation. Actually, the full purpose of the online web-interface is to edit a configuration file. This file can be saved and downloaded for future operations. Every user is identified by a cookie and their IP address, and has a unique configuration file associated to this ID.
 
By selecting a template, and clicking on "Load Template", the user replaces the actual configuration file by that of the template. Several templates targeting the main objects in the solar system are available. One can then modify the parameters of the run by clicking on the "change" buttons, and one can also upload a previous parameter file by selecting "Upload config-file".
 
Once the configuration of the parameters is ready, one can start the calculation by pressing "Generate Spectra". This will first verify the geometric parameters and pre-calculate geometric and atmospheric parameters. These will be fed together with the input configuration file to the radiative transfer modules for analysis. The output of these modules are actually text files (tables with a header), that are read by the graphics module to produce spectral plots.
 
Types of parameters
 Planetary target  Viewing geometry
 Atmosphere: molecular abundances  Atmospheric scattering aerosols
 Surface properties  Instrument / telescope

 

Defining the object


PSG incorporates a 3D (three-dimensional) orbital calculator for most bodies in the Solar system, and all confirmed exoplanets. This information is used to calculate all possible geometry parameters needed when computing spectroscopic fluxes. The astronomical data is based on pre-computed ephemerides tables that provide orbital information from 1960 to 2050 with a precision of 1 minute.
 
In the "Target and geometry parameters" section, select the object, define date/time (UT) and press "Ephemeris" to load and calculate orbital parameters. This operation will fill the fields in this section by interpolating from high-precision pre-computed ephemeris tables.
 
JPL-Horizons: for bodies not defined in the object list (and for dates outside of the 1960-2050 range), PSG connects to the JPL-Horizons server and extracts orbital parameters for that object. For small bodies with no sun/obs-lat/lon, PSG defines them based on the ecliptic angles. The object-name provided should be unique, or JPL will require providing a specific JPL-Horizons record number (additional information).
 
For exoplanets, PSG performs the numerical integration of the orbit by extracting orbital parameters from the NASA Exoplanet Archive. PSG will search for specific ephemeris by clicking on these buttons: T) next primary transit; S) next secondary transit; P) next planet-star periapse. The name of the object should be compatible with that of the archive (see current list). Due to the uncertainty and degeneracies in the derivation of the orbital parameters for exoplanets, PSG assumes the following: a) the longitude of ascending node (Ω) is assumed to be π; b) the planets are tidally locked, and the star sub-solar lat/lon are set to the center of the planet; and c) the phase identifies the true anomaly with respect to that of the secondary transit, with a phase of 180 corresponding to the primary transit.
 
Orbital parameters
Orbital parameters: In order to compute spectroscopic fluxes, one needs to establish the location of the object relative to its host-star, and the location of the observer relative to the object. The sub-observer parameters define the nadir position of the observer, while, the offsets, distance and velocity establish the lateral displacements (x/y), vertical altitude (z) and (dz/dt) parameters respectively.

 

Orbital and spectroscopic velocities


When performing high-resolution spectroscopic simulations, a detailed and accurate description of the different velocities is of paramount importance. In PSG, these parameters are specifically captured via three fields: OBJECT-OBS-VELOCITY, OBJECT-STAR-VELOCITY and GEOMETRY-ROTATION. Each sub-component of the sources sampled by the field-of-view (FOV) will have a particular Doppler shift associated to the object's rotation and orbital parameters. As summarized in the figure below, the stellar fluxes will have a Doppler shift that integrates the full system velocity and that of the star as being affected by the planet. This "tug" of the star by the orbiting planets is now of the prime methods used to characterize the properties of exoplanets.
 
The integration of all these Doppler effects is particularly relevant when employing the cross-correlation method in exoplanetary research. This method compares residual planetary spectra at different phases with a synthetic set of templates shifted following the orbital motion of the planet (and all the associated Doppler shifts). This is the prime method to characterize exoplanets using ground-based observatories, since telluric signatures are static spectroscopically, yet the planetary signatures shift by km/s across the planetary orbit.
 
Orbital parameters
Orbital velocities and Doppler shifts: The motion of the planets across their orbit introduces spectroscopic shifts on the planetary and stellar fluxes. This motion also perturbs or "tugs" the host-star, introducing a Doppler shift on the stellar signatures. In PSG, all these effects are taken into account when synthesizing spectra, and described via three fields: OBJECT-OBS-VELOCITY, OBJECT-STAR-VELOCITY and GEOMETRY-ROTATION. This figure describes how these three fields (calculated by PSG's Geometry module) encode the Doppler information of the motions for the whole system.

 

Types of stellar-hosts


PSG includes the possibility to integrate stellar templates by adopting the Kurucz 2005 stellar templates (0.15-300 μm), which is complemented at short wavelengths (<0.4 μm; X-ray, EUV, FUV) with the MUSCLES Treasurey Survey (France et al. 2016). When considering the G-type template, the spectrum is complemented with the ACE solar spectrum (2-14 μm) in the infrared and with the LISIRD template (<0.4 μm) in the UV. PSG picks the template based on the stellar type and temperature, and all fluxes are scaled to the actual effective stellar temperature of the star. The stellar information is used to compute reflected stellar/solar fluxes, and also to compute the total observable exoplanet fluxes, when the (exo)planet and star are within the field-of-view (FOV).
 
To download the fluxes shown below click on the following links: Sun (G2V, 5778K), HD85512 (K6Vk, 4305K), HD40307 (K2.5V, 4783K), HD97658 (K1V C, 5156K), V-EPS-ERI (K2V B, 5162K), GJ551 (M5.5V, 2800K), GJ1214 (M4.5V, 2935K), GJ876 (M3.5V, 3062K), GJ436 (M3V B, 3281K), GJ581 (M3V C, 3295K), GJ667C (M1.5V, 3327K), GJ176 (M2.5V, 3416K), GJ832 (M2/3V, 3816K), The fluxes are in units of spectral radiance in [W/m2/um/sr], and in order to compute the actual spectral irradiance [W/m2/um] received by the planet one needs to multiply by the solid angle encompassed by star as seen from the planet (Ω = 6.807E−5 ⋅ (Rstar/Dstar)2 [sr]), where Rstar is the star size with respect to our Sun [1.0 for Sun], and Dstar is the distance to the star in AU [1.0 for Earth].
 
Stellar templates
Stellar templates: PSG allows to integrate a broad range of stellar templates, with the UV templates shown in this figure. The UV templates (<0.4 μm) are based on the MUSCLES Treasurey Survey (France et al. 2016), with the UV solar template derived from the LISIRD tool (LASP). The templates at longer wavelengths (i.e., 0.15-300 μm, optical, IR and radio) are based on the Kurucz 2005 spectral templates, which is complemented with the ACE solar spectrum (2-14 μm) for the G-type.

 

Types of geometries


Once the locations of the object relative to its host-star and that of the observer relative to the object, one needs to define the observing geometry. PSG allows to define for different observing geometries: observatory, nadir, limb, solar/stellar occultation and from-surface (looking-up).
 
To compute incidence/emission angles, PSG employs a hybrid approach in which the geometry module computes fluxes and geometry parameters (e.g., emission:αi and incidence:βi angles) across the sampled FOV/disk employing a grid of 140 × 140 points (19,600 sets of geometry values). The point-by-point fluxes are computed employing a Lambertian model, and are then used to determine the contribution function (wi) for each of these points to the total flux. The effective emission angle (α) and incidence angle (β) are then calculated as the flux weighted value across the FOV, α = cos−1(sum(wi • cos(αi)) and β = cos−1(sum(wi • cos(βi)). The same procedure is used to compute the effective sub-solar and sub-observer latitudes and longitudes. PSG allows for sub-sampling of the disk, see more details here.
 
Observatory Nadir Limb Stellar Looking Up
Observatory: in this configuration the observer is located above the sub-obs location, and lateral displacements (x/y) are entered as offsets. Nadir: in this configuration the observer is located above the sub-obs location, and only the distance (z) and angle relative to this point are defined. Of relevance to orbiters. Limb: in this configuration the observation is performed tangentially to the surface towards empty space. The sub-obs point defines the shortest distance to the surface. Solar/stellar occultation: in this configuration the observation is performed tangentially to the surface towards the sun or a star. The sub-obs point defines the shortest distance to the surface. Looking up: in this configuration, the observer is located on the planet's surface and observe upwards. Of relevance for computing telluric radiances / transmittances.

 

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