antaress.ANTARESS_analysis.ANTARESS_model_prof module

gen_fit_prof(param_in, x_tab, args=None)

Generic profile fit function

Function called by minimization algorithms, returning the chosen model profile after applyying (if requested) convolution, spectral conversion and resampling.

The profile model function must return several arguments (or a list of one) with the model as first argument. The profile is calculated over a continuous table to allow for convolution and use of covariance matrix (fitted pixels are accounted for directly in the minimization routine).

Parameters:

TBD

Returns:

TBD

dispatch_func_prof(func_name)

Line profile model dispatching

Returns the chosen line profile function.

Parameters:

func_name (str) – name of the chosen function

Returns:

func (function) – chosen function

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

gauss_intr_prof(param, rv_tab, 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, RV, args=None)

Line model: Sidelobed Gaussian

Calculates Gaussian profile with flat continuum and polynomial for sidelobes.

Parameters:

TBD

Returns:

TBD

dgauss(param, rv_tab, args=None)

Line model: Double Gaussian

Calculates Double-Gaussian profile, 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

pol_cont(cen_bins_ref, args, param)

Line polynomial continuum

Calculates polynomial modulated around 1.

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

calc_linevar_coord_grid(dim, 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