import numpy as np
from typing import Tuple
from autogalaxy.profiles.light.standard.sersic import Sersic
[docs]
class SersicCore(Sersic):
def __init__(
self,
centre: Tuple[float, float] = (0.0, 0.0),
ell_comps: Tuple[float, float] = (0.0, 0.0),
effective_radius: float = 0.6,
sersic_index: float = 4.0,
radius_break: float = 0.025,
intensity: float = 0.05,
gamma: float = 0.25,
alpha: float = 3.0,
):
"""
The elliptical cored-Sersic light profile.
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.
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).
radius_break
The break radius separating the inner power-law (with logarithmic slope gamma) and outer Sersic function.
intensity
The intensity at the break radius.
gamma
The logarithmic power-law slope of the inner core profiles
alpha
Controls the sharpness of the transition between the inner core / outer Sersic profiles.
"""
super().__init__(
centre=centre,
ell_comps=ell_comps,
intensity=intensity,
effective_radius=effective_radius,
sersic_index=sersic_index,
)
self.radius_break = radius_break
self.intensity = intensity
self.alpha = alpha
self.gamma = gamma
[docs]
def intensity_prime(self, xp=np) -> float:
"""
Overall intensity normalisation in the rescaled cored Sersic light profile.
Like the `intensity` parameter, the units of `intensity_prime` are dimensionless and derived from the data
the light profile's image is compared too, which are expected to be electrons per second.
"""
return (
self._intensity
* (2.0 ** (-self.gamma / self.alpha))
* xp.exp(
self.sersic_constant
* (
((2.0 ** (1.0 / self.alpha)) * self.radius_break)
/ self.effective_radius
)
** (1.0 / self.sersic_index)
)
)
[docs]
def image_2d_via_radii_from(
self, grid_radii: np.ndarray, xp=np, **kwargs
) -> np.ndarray:
"""
Returns the 2D image of the Sersic light profile from a grid of coordinates which are the radial distances of
each coordinate from the its `centre`.
Parameters
----------
grid_radii
The radial distances from the centre of the profile, for each coordinate on the grid.
"""
return xp.multiply(
xp.multiply(
self.intensity_prime(xp),
xp.power(
xp.add(
1,
xp.power(
xp.divide(self.radius_break, grid_radii.array), self.alpha
),
),
(self.gamma / self.alpha),
),
),
xp.exp(
xp.multiply(
-self.sersic_constant,
(
xp.power(
xp.divide(
xp.add(
xp.power(grid_radii.array, self.alpha),
(self.radius_break**self.alpha),
),
(self.effective_radius**self.alpha),
),
(1.0 / (self.alpha * self.sersic_index)),
)
),
)
),
)
[docs]
class SersicCoreSph(SersicCore):
def __init__(
self,
centre: Tuple[float, float] = (0.0, 0.0),
effective_radius: float = 0.6,
sersic_index: float = 4.0,
radius_break: float = 0.01,
intensity: float = 0.05,
gamma: float = 0.25,
alpha: float = 3.0,
):
"""
The elliptical cored-Sersic light profile.
Parameters
----------
centre
The (y,x) arc-second coordinates of the profile centre.
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).
radius_break
The break radius separating the inner power-law (with logarithmic slope gamma) and outer Sersic function.
intensity
The intensity at the break radius.
gamma
The logarithmic power-law slope of the inner core profiles
alpha :
Controls the sharpness of the transition between the inner core / outer Sersic profiles.
"""
super().__init__(
centre=centre,
ell_comps=(0.0, 0.0),
effective_radius=effective_radius,
sersic_index=sersic_index,
radius_break=radius_break,
intensity=intensity,
gamma=gamma,
alpha=alpha,
)
self.radius_break = radius_break
self.intensity = intensity
self.alpha = alpha
self.gamma = gamma