import numpy as np
from scipy.integrate import quad
from typing import List, Tuple
import autoarray as aa
from autogalaxy.profiles.mass.stellar.sersic import AbstractSersic
from autogalaxy.profiles.mass.stellar.sersic import cse_settings_from
[docs]class SersicRadialGradient(AbstractSersic):
def __init__(
self,
centre: Tuple[float, float] = (0.0, 0.0),
ell_comps: Tuple[float, float] = (0.0, 0.0),
intensity: float = 0.1,
effective_radius: float = 0.6,
sersic_index: float = 0.6,
mass_to_light_ratio: float = 1.0,
mass_to_light_gradient: float = 0.0,
):
"""
Setup a Sersic mass and light profiles.
Parameters
----------
centre
The (y,x) arc-second coordinates of the profile centre.
ell_comps
The first and second ellipticity components of the elliptical coordinate system.
intensity
Overall flux intensity normalisation in the light profiles (electrons per second).
effective_radius
The circular radius containing half the light of this profile.
sersic_index
Controls the concentration of the profile (lower -> less concentrated, higher -> more concentrated).
mass_to_light_ratio
The mass-to-light ratio of the light profile.
mass_to_light_gradient
The mass-to-light radial gradient.
"""
super().__init__(
centre=centre,
ell_comps=ell_comps,
intensity=intensity,
effective_radius=effective_radius,
sersic_index=sersic_index,
mass_to_light_ratio=mass_to_light_ratio,
)
self.mass_to_light_gradient = mass_to_light_gradient
[docs] @aa.grid_dec.grid_2d_to_structure
@aa.grid_dec.transform
@aa.grid_dec.relocate_to_radial_minimum
def deflections_2d_via_integral_from(self, grid: aa.type.Grid2DLike):
"""
Calculate the deflection angles at a given set of arc-second gridded coordinates.
Parameters
----------
grid
The grid of (y,x) arc-second coordinates the deflection angles are computed on.
"""
def calculate_deflection_component(npow, index):
sersic_constant = self.sersic_constant
deflection_grid = self.axis_ratio * grid[:, index]
for i in range(grid.shape[0]):
deflection_grid[i] *= (
self.intensity
* self.mass_to_light_ratio
* quad(
self.deflection_func,
a=0.0,
b=1.0,
args=(
grid[i, 0],
grid[i, 1],
npow,
self.axis_ratio,
self.sersic_index,
self.effective_radius,
self.mass_to_light_gradient,
sersic_constant,
),
)[0]
)
return deflection_grid
deflection_y = calculate_deflection_component(1.0, 0)
deflection_x = calculate_deflection_component(0.0, 1)
return self.rotated_grid_from_reference_frame_from(
np.multiply(1.0, np.vstack((deflection_y, deflection_x)).T)
)
@staticmethod
def deflection_func(
u,
y,
x,
npow,
axis_ratio,
sersic_index,
effective_radius,
mass_to_light_gradient,
sersic_constant,
):
_eta_u = np.sqrt(axis_ratio) * np.sqrt(
(u * ((x**2) + (y**2 / (1 - (1 - axis_ratio**2) * u))))
)
return (
(((axis_ratio * _eta_u) / effective_radius) ** -mass_to_light_gradient)
* np.exp(
-sersic_constant
* (((_eta_u / effective_radius) ** (1.0 / sersic_index)) - 1)
)
/ ((1 - (1 - axis_ratio**2) * u) ** (npow + 0.5))
)
[docs] @aa.grid_dec.grid_2d_to_structure
@aa.grid_dec.transform
@aa.grid_dec.relocate_to_radial_minimum
def convergence_2d_from(self, grid: aa.type.Grid2DLike):
"""Calculate the projected convergence at a given set of arc-second gridded coordinates.
Parameters
----------
grid
The grid of (y,x) arc-second coordinates the convergence is computed on.
"""
return self.convergence_func(self.eccentric_radii_grid_from(grid))
def convergence_func(self, grid_radius: float) -> float:
return (
self.mass_to_light_ratio
* (
((self.axis_ratio * grid_radius) / self.effective_radius)
** -self.mass_to_light_gradient
)
* self.image_2d_via_radii_from(grid_radius)
)
def decompose_convergence_via_mge(self):
radii_min = self.effective_radius / 100.0
radii_max = self.effective_radius * 20.0
def sersic_radial_gradient_2D(r):
return (
self.mass_to_light_ratio
* self.intensity
* (
((self.axis_ratio * r) / self.effective_radius)
** -self.mass_to_light_gradient
)
* np.exp(
-self.sersic_constant
* (((r / self.effective_radius) ** (1.0 / self.sersic_index)) - 1.0)
)
)
return self._decompose_convergence_via_mge(
func=sersic_radial_gradient_2D, radii_min=radii_min, radii_max=radii_max
)
[docs] def decompose_convergence_via_cse(
self, grid_radii: np.ndarray
) -> Tuple[List, List]:
"""
Decompose the convergence of the Sersic profile into singular isothermal elliptical (sie) profiles.
This decomposition uses the standard 2d profile of a Sersic mass profile.
Parameters
----------
func
The function representing the profile that is decomposed into CSEs.
radii_min:
The minimum radius to fit
radii_max:
The maximum radius to fit
total_sies
The number of SIEs used to approximate the input func.
sample_points: int (should be larger than 'total_sies')
The number of data points to fit
Returns
-------
Tuple[List, List]
A list of amplitudes and core radii of every singular isothernal ellipsoids (sie) the mass profile is decomposed
into.
"""
upper_dex, lower_dex, total_cses, sample_points = cse_settings_from(
effective_radius=self.effective_radius,
sersic_index=self.sersic_index,
sersic_constant=self.sersic_constant,
mass_to_light_gradient=self.mass_to_light_gradient,
)
scaled_effective_radius = self.effective_radius / np.sqrt(self.axis_ratio)
radii_min = scaled_effective_radius / 10.0**lower_dex
radii_max = scaled_effective_radius * 10.0**upper_dex
def sersic_radial_gradient_2D(r):
return (
self.mass_to_light_ratio
* self.intensity
* (
((self.axis_ratio * r) / scaled_effective_radius)
** -self.mass_to_light_gradient
)
* np.exp(
-self.sersic_constant
* (
((r / scaled_effective_radius) ** (1.0 / self.sersic_index))
- 1.0
)
)
)
return self._decompose_convergence_via_cse_from(
func=sersic_radial_gradient_2D,
radii_min=radii_min,
radii_max=radii_max,
total_cses=total_cses,
sample_points=sample_points,
)
[docs]class SersicRadialGradientSph(SersicRadialGradient):
def __init__(
self,
centre: Tuple[float, float] = (0.0, 0.0),
intensity: float = 0.1,
effective_radius: float = 0.6,
sersic_index: float = 0.6,
mass_to_light_ratio: float = 1.0,
mass_to_light_gradient: float = 0.0,
):
"""
Setup a Sersic mass and light profiles.
Parameters
----------
centre
The (y,x) arc-second coordinates of the profile centre.
intensity
Overall flux intensity normalisation in the light profiles (electrons per second).
effective_radius
The circular radius containing half the light of this profile.
sersic_index
Controls the concentration of the profile (lower -> less concentrated, higher -> more concentrated).
mass_to_light_ratio
The mass-to-light ratio of the light profile.
mass_to_light_gradient
The mass-to-light radial gradient.
"""
super().__init__(
centre=centre,
ell_comps=(0.0, 0.0),
intensity=intensity,
effective_radius=effective_radius,
sersic_index=sersic_index,
mass_to_light_ratio=mass_to_light_ratio,
mass_to_light_gradient=mass_to_light_gradient,
)