antaress.ANTARESS_analysis.ANTARESS_model_prof module

dispatch_func_prof(line_func)

Line profile model dispatching

Returns the chosen line profile function.

Parameters:

line_func (str) – name of the chosen function

Returns:

func (function) – chosen function

Unorm_Voigt(a, u)

Norm_Voigt(a, u, sigma)

comm_voigt_line(temp_sp, mass_sp, vsini, Vmac, Vmic, wline_rest, delta_line, rv_gas_star, wav_star_tab)

Line model: common Voigt terms

Parameters:

TBD

Returns:

TBD

voigt_abs_line(wline_rest, temp_sp, mass_sp, vsini, Vmac, Vmic, delta_line, rv_gas_star, wav_star_tab, s_vu0_line, logN_sp)

Line model: Voigt absorption line

Calculates stellar or interstellar absorption line as Voigt profile.

Parameters:

TBD

Returns:

TBD

voigt_em_line(wline_rest, temp_sp, mass_sp, vsini, Vmac, Vmic, delta_line, rv_gas_star, wav_star_tab, Ftot_line)

Line model: Voigt emission line

Calculates stellar or telluric emission line as Voigt profile.

Parameters:

TBD

Returns:

TBD

voigt(param, x, args=None)

Line model: Voigt

Calculates Voigt profile, expressed in terms of the Faddeeva function (factorless)

\[V(rv) = Real(w(x))\]

As a function of

\[\begin{split}x &= ((rv-rv_0) + i \gamma)/(\sqrt{2} \sigma) \\ &= (rv-rv_0)/(\sqrt{2} \sigma) + i a \\ &= 2 \sqrt{\ln{2}} (rv-rv_0)/\mathrm{FWHM}_\mathrm{gauss} + i a\end{split}\]

Where a is the damping coefficient

\[\begin{split}a &= \gamma/(\sqrt{2} \sigma) \\ &= 2 \gamma \sqrt{\ln{2}}/\mathrm{FWHM}_\mathrm{gauss} \\ &= \sqrt{\ln{2}} \mathrm{FWHM}_\mathrm{lor}/\mathrm{FWHM}_\mathrm{gauss}\end{split}\]

The \(\mathrm{FWHM}_\mathrm{gauss}\) parameter is that of the Gaussian component (factorless)

\[\begin{split}G(rv) &= \exp(- (rv-rv_0)^2/ ( \mathrm{FWHM}_\mathrm{gauss}/(2 \sqrt{\ln{2}}) )^2 ) \\ &= \exp(- (rv-rv_0)^2/ 2 ( \mathrm{FWHM}_\mathrm{gauss}/(2 \sqrt{2 \ln{2}}) )^2 ) \\ &= \exp(- (rv-rv_0)^2/ 2 \sigma^2 )\end{split}\]

With \(\sigma = \mathrm{FWHM}_\mathrm{gauss}/(2 \sqrt{\ln{2}})\) and \(\mathrm{FWHM}_\mathrm{lor} = 2 \gamma\)

The full-width at half maximum of the Voigt profile approximates as

\[\mathrm{FWHM}_\mathrm{voigt} = 0.5436 \mathrm{FWHM}_\mathrm{lor}+ \sqrt{0.2166 \mathrm{FWHM}_\mathrm{lor}^2 + \mathrm{FWHM}_\mathrm{gauss}^2}\]

From J.J.Olivero and R.L. Longbothum in Empirical fits to the Voigt line width: A brief review, JQSRT 17, P233

Parameters:

TBD

Returns:

TBD

voigt_em(params, x)

Line model: Emission Voigt.

Returns Voigt profile in emission.

Parameters:

• x (array) – Spectral table over which Voigt is computed, in wave number (cm-1)

• params['HWHM'] (float) – HWHM of the Voigt.

• params['gamma'] (float) – Damping coefficient of the Voigt.

• params['center'] (float) – Central value of the Voigt over x.

Returns:

ymodel (array) – Voigt profile.

max_voigt_em(HWHM, gamma)

Line model properties: Emission Voigt maximum.

Returns Voigt profile in emission at line center

Parameters:

• HWHM (float) – HWHM of the Voigt.

• gamma (float) – Damping coefficient of the Voigt.

Returns:

max_prof (array) – Voigt profile maximum.

dvoigt(param, x, args=None)

Line model: Double Voigt

Calculates Double-Voigt profile.

Typically used to model deep stellar line with Voigt-like wings and Gaussian core.

The two profiles parameters are defined through their ratio or difference.

Parameters:

TBD

Returns:

TBD

lor_em(param, x, args=None)

Line model: Emission Lorentzian

Calculates Lorentzian profile in emission.

Parameters:

• x (array) – Spectral grid over which Lorentzian is computed, in wave number (cm-1)

• param['HWHM'] (float) – Half-width at half-maximum.

• param['center'] (float) – Central value of the Lorentzian over x.

Returns:

ymodel (array) – Lorentzian profile.

max_lor_em(HWHM)

Line model properties: Emission Lorentzian maximum.

Returns Lorentzian profile in emission at line center.

Parameters:

HWHM (float) – Lorentzian of the Voigt.

Returns:

max_prof (array) – Maximum of Lorentzian profile.

gauss_intr_prof(param, x, args=None)

Line model: Gaussian

Calculates Gaussian profile.

Parameters:

TBD

Returns:

TBD

gauss_herm_lin(param, x, args=None)

Line model: Skewed Gaussian

Calculates Gaussian profile with hermitian polynom term for skewness/kurtosis.

Parameters:

TBD

Returns:

TBD

gauss_poly(param, x, args=None)

Line model: Sidelobed Gaussian

Calculates Gaussian profile with flat continuum and polynomial for sidelobes.

Parameters:

TBD

Returns:

TBD

dgauss(param, x, args=None)

Line model: Double Gaussian

Calculates Double-Gaussian profile.

Typically used to model sidelobed CCFs, with Gaussian in absorption co-added with a Gaussian in emission at the core.

The Gaussian profiles are centered but their amplitude and width can be fixed or independant. The model is defined as

\[\begin{split}F &= F_\mathrm{cont} + A_\mathrm{core} \exp(f_1) + A_\mathrm{lobe} \exp(f_2) \\ F &= F_\mathrm{cont} + A_\mathrm{core} ( \exp(f_1) - A_\mathrm{l2c} \exp(f_2) )\end{split}\]

We define a contrast parameter as the relative flux between the continuum and the CCF minimum

\[\begin{split}C &= (F_\mathrm{cont} - (F_\mathrm{cont} + A_\mathrm{core} - A_\mathrm{core} A_\mathrm{l2c}) ) / F_\mathrm{cont} \\ C &= -A_\mathrm{core} ( 1 - A_\mathrm{l2c}) / F_\mathrm{cont} \\ A_\mathrm{core} &= -C F_\mathrm{cont}/( 1 - A_\mathrm{l2c}) \\ A_\mathrm{lobe} &= -A_\mathrm{l2c} A_\mathrm{core} = A_\mathrm{l2c} C F_\mathrm{cont}/( 1 - A_\mathrm{l2c})\end{split}\]

Thus the model can be expressed as

\[\begin{split}F &= F_\mathrm{cont} - C F_\mathrm{cont} ( \exp(f_1) - A_\mathrm{l2c} \exp(f_2) )/( 1 - A_\mathrm{l2c}) \\ F &= F_\mathrm{cont} ( 1 - C ( \exp(f_1) - A_\mathrm{l2c} \exp(f_2) )/( 1 - A_\mathrm{l2c}) )\end{split}\]

Parameters:

TBD

Returns:

TBD

ana_abs_star_spec_model(outputs_dic, cen_bins, lines_list, lines_prop, lines_prof, species_prop, star_params, param, p2i, ep_suff)

Analytical spectrum: absorption

Calculates an analytical spectrum of the stellar absorption lines with continuum unity.

The model can be used for the full stellar disk or local regions. See ANTARESS_settings for details about the profiles.

Parameters:

TBD

Returns:

TBD

ana_em_star_spec_model(outputs_dic, cen_bins, dcen_bins, lines_list, lines_prop, lines_prof, species_prop, star_params, param, p2i, ep_suff)

Analytical spectrum: absorption

Calculates an analytical spectrum of the stellar emission lines with continuum unity.

The model can be used for the full stellar disk or local regions. See ANTARESS_settings for details about the profiles.

Parameters:

TBD

Returns:

TBD

prof_cont_model(x_polref, coeff_pol, x)

Line model: continuum

Calculates spectral profile polynomial continuum.

Parameters:

TBD

Returns:

TBD

calc_macro_ker_rt(rv_mac_kernel, param, cos_th, sin_th)

Macroturbulence broadening: anisotropic Gaussian

Calculates broadening kernel for local macroturbulence, based on formulation with anisotropic gaussian (Takeda & UeNo 2017)

Parameters:

TBD

Returns:

TBD

calc_macro_ker_anigauss(rv_mac_kernel, param, cos_th, sin_th)

Macroturbulence broadening: radial-tangential

Calculates broadening kernel for local macroturbulence, based on radial-tangential model (Gray 1975, 2005)

Parameters:

TBD

Returns:

TBD

dopp_width(temp_sp, mass_sp, vsini, Vmac, Vmic, wline)

Doppler broadening

Calculates spectral line broadening from thermal and non-thermal broadening.

Parameters:

TBD

Returns:

None

autom_ranges(data_type_gen, data_dic, inst, vis, gen_dic, coord_dic, star_params, mock_dic, txt_shift='')

Automatic definition of continuum and fit ranges

Defines the velocity or wavelength range(s) for the continuum or the fit of spectral line profiles.

Parameters:

TBD

Returns:

None

calc_linevar_coord_grid(coord, grid)

Line profile coordinate dispatching

Returns the relevant coordinate for calculation of line properties variations.

Parameters:

TBD

Returns:

TBD

calc_polymodu(pol_mode, coeff_pol, x_val)

Line profile coordinate models

Calculates absolute or modulated polynomial

The list of polynomial coefficient ‘coeff_pol’ has been defined in increasing powers, as expected by Polynomial, using input coefficient defined through their power value (see polycoeff_def())

Parameters:

TBD

Returns:

TBD

polycoeff_def(param, coeff_ord2name_polpar)

Line profile coordinate coefficients

Defines polynomial coefficients from the Parameter() format through their power value

Parameters:

TBD

Returns:

TBD

poly_prop_calc(param, fit_coord_grid, coeff_ord2name_polpar, pol_mode)

calc_biss(Fnorm_in, RV_tab_in, RV_min, max_rv_range, dF_grid, resamp_mode, Cspan)

Bissector.

Calculates bissector for a line profile provided in RV space as input.

Parameters:

TBD

Returns:

TBD

gauss_intr_prop(ctrst_intr, FWHM_intr, FWHM_inst)

Intrinsic > Measured Gaussian properties.

Estimates the FWHM and contrast of a measured-like Gaussian profile, defined as the convolution of a Gaussian intrinsic model profile and a Gaussian instrumental response.

The FWHM can be expressed as

\[\begin{split}\mathrm{FWHM} &= \sqrt{\mathrm{FWHM}_\mathrm{intr}^2 + \mathrm{FWHM}_\mathrm{inst}^2 } \\ \mathrm{with}\,\sigma &= \frac{\mathrm{FWHM}}{2 \sqrt{\ln{2}}} = \sqrt{\sigma_\mathrm{intr}^2 + \sigma_\mathrm{inst}^2 }\end{split}\]

The area of the measured convolution profile is equal to the product of the area of the intrinsic and instrumental convolved profiles, providing an analytical expression for the contrast. The instrumental kernel, with area = 1, is expressed as

\[\begin{split}f_\mathrm{kern}(rv) &= \frac{1}{\sqrt{2 \pi} \sigma_\mathrm{inst} } \exp^{ -\frac{rv^2}{2 \sigma_\mathrm{inst}^2} } \\ \mathrm{where}\,\sigma_\mathrm{inst} &= \frac{\mathrm{FWHM}_\mathrm{inst}}{ 2 \sqrt{2 \log{2}} }\end{split}\]

The intrinsic profile, with area = \(\mathrm{A}_\mathrm{intr}\), is expressed as

\[\begin{split}f_\mathrm{intr}(rv) &= \frac{\mathrm{A}_\mathrm{intr}}{\sqrt{2 \pi} \sigma_\mathrm{intr} } \exp^{ -\frac{rv^2}{2 \sigma_\mathrm{intr}^2} } \\ \mathrm{where}\,\sigma_\mathrm{intr} &= \frac{\mathrm{FWHM}_\mathrm{intr}}{ 2 \sqrt{2 \ln{2}} }\end{split}\]

The contrast C of the measured profile relates to its area A as

\[\begin{split}C &= \frac{A}{\sqrt{2 \pi} \sigma } \\ &= \frac{1 \times \mathrm{A}_\mathrm{intr} }{ \sqrt{2 \pi (\sigma_\mathrm{intr}^2 + \sigma_\mathrm{inst}^2 ) }} \\ &= \frac{\mathrm{C}_\mathrm{intr} \sqrt{2 \pi} \sigma_\mathrm{intr} }{\sqrt{2 \pi (\sigma_\mathrm{intr}^2 + \sigma_\mathrm{inst}^2 ) }} \\ &= \frac{\mathrm{C}_\mathrm{intr} \sigma_\mathrm{intr} }{\sqrt{\sigma_\mathrm{intr}^2 + \sigma_\mathrm{inst}^2}} \\ &= \frac{\mathrm{C}_\mathrm{intr} \mathrm{FWHM}_\mathrm{intr} }{\sqrt{\mathrm{FWHM}_\mathrm{intr}^2 + \mathrm{FWHM}_\mathrm{inst}^2}}\end{split}\]

This is only valid for analytical profiles. For numerical profiles, the model is the sum of intrinsic profiles over the planet-occulted surface that may have non-Gaussian shape, and which are further broadened by the local surface rv field. In that case, use cust_mod_true_prop().

Parameters:

TBD

Returns:

TBD

cust_mod_true_prop(param, velccf_HR, args)

Intrinsic > Measured line properties.

Estimates the FWHM and contrast of a measured-like line profile with custom shape. This is done numerically, calculating the model profile at high resolution.

Contrast is counted from the estimated continuum. For double-gaussian profiles, the peaks of the lobes are considered as the closest estimate to the true stellar continuum.

FWHM is calculated by finding the points on the blue side at half-maximum, and on the red side.

Parameters:

TBD

Returns:

TBD

proc_cust_mod_true_prop(merged_chain_proc, args, param_loc)

Wrap-up of cust_mod_true_prop().

Estimates the FWHM and contrast of a measured-like line profile with custom shape, for a sample of properties.

Parameters:

TBD

Returns:

TBD

para_cust_mod_true_prop(func_input, nthreads, n_elem, y_inputs, common_args)

Multithreading routine for proc_cust_mod_true_prop().

Parameters:

• func_input (function) – multi-threaded function

• nthreads (int) – number of threads

• n_elem (int) – number of elements to thread

• y_inputs (list) – threadable function inputs

• common_args (tuple) – common function inputs

Returns:

y_output (None or specific to func_input) – function outputs