Everywhere¶
Instances of Everywhere
represents the global photosphere.

class
xpsi.Everywhere.
Everywhere
(time_invariant, bounds=None, values=None, sqrt_num_cells=64, num_rays=200, num_leaves=100, num_phases=None, phases=None, custom=None, image_order_limit=None, _integrator_toggle=False)[source]¶ Bases:
xpsi.ParameterSubspace.ParameterSubspace
The photospheric radiation field represented by a global mesh.
An instance of this class cannot be used in conjuction with hot region objects nor with an elsewhere instance.
The local comoving radiation field properties are not assumed to be azimuthally invariant, so a timedependent signal can be generated upon integration over the image.
However, if you want to generate a timedependent signal, you need to customise the parameters that control the radiation field w.r.t. surface local comoving frames. By default a single temperature parameter is defined which is globally invariant and thus the radiation field is azimuthally invariant and the image subtended on a distant observer’s sky is phaseinvariant.
Parameters:  time_invariant (bool) – See above. Is the radiation field azimuthally invariant, thus generating a phaseinvariant signal? Although the default configuration is simple and azimuthally invariant, we do not provide a default value for this argument to force the user to verify their intentions.
 bounds (dict) – If
custom is None
, these bounds are supplied for instantiation of a temperature parameter. The parameter name'temperature'
must be a key in the dictionary unless the parameter is fixed or derived. If a bound isNone
that bound is set equal to a strict hardcoded bound. We note that the bounds for parameters used in the atmosphere model should be restricted (by the user) to be within the tabulated values, in case a numerical atmosphere extension is used.  values (dict) – Either the fixed value of the temperature, a callable if the
temperature is derived, or a value upon initialisation if the
temperature is free. The dictionary must have a key with name
'temperature'
if it is fixed or derived.  sqrt_num_cells (int) – Number of cells in both colatitude and azimuth which form a regular mesh on the surface. Must be an even number such that half of the cells are exactly in one hemisphere. The total number of cells is the square of this argument value. The mesh suffers from squeezing in the polar regions, leading to a high degree of noncongruence in cell shape over the surface.
 num_rays (int) – Number of rays to trace (integrate) at each colatitude, distributed in angle subtended between ray tangent 4vector and radial outward unit vector w.r.t a local orthonormal tetrad.
 num_leaves (int) – Number of stellar rotation phases to rotate a moving mesh through during signal integration.
 num_phases (int) – Number of phases to resolve the signal at if the signal is time dependent.
 ndarray[m] – Array of phases to resolve a timedependent signal at.
 custom (iterable) – Iterable over
Parameter
instances. If you supply custom parameter definitions, you need to overwrite the_compute_cellParamVecs()
method to implement your custom behaviour.  image_order_limit (int) – The highestorder image to sum over. A value of one means primary
images only (deflections \(<\pi\)) whilst a value of two means
primary and secondary images (deflections \(<2pi\)) where visible,
and so on. If
None
(the default), there is no hard limit. In this case the limit is determined quasinaturally for each mesh element, meaning that images will be summed over until higher order images are not visible or the visibility limit is truncated due to lack of numerical precision (e.g. for rays that orbit very close to the Schwarzschild photon sphere three times or more). Higherorder images generally contribute less and less due to geometric projection effects (higherorder images become more tangential), and the images of elements get squeezed in solid angle at the stellar limb. In principle, effects such as relativistic beaming can counter this effect to a degree for certain sourcereceiver configurations, by increasing brightness whilst solid angle decreases, and thus the flux contribution relative to that from a primary image can be greater than suggested simply by geometric project effects. Nevertheless, inclusion of these images is more computationally expensive. If, when iterating through image orders, an image is not visible because the deflection required is greater than the highest deflection permitted at a given colatitude on a surface (accounting for the surface tilt due to rotation), then the iteration over image orders terminates.  _integrator_toggle (bool) – For testing purposes, toggle the integrator for timedependent signals.
If left as the default (
False
) the generalpurpose integrator is called. If toggled, an integrator is called that assumes the surface radiation field is azimuthally invariant, which combined with the default global mesh (i.e., no subclassing) results in a timeinvariant signal.
 Required parameter names:
 temperature (if no custom specification)

_compute_cellParamVecs
()[source]¶ Precompute photospheric source radiation field parameter vectors cellbycell. Free model parameters and derived (fixed) variables can be transformed into local comoving radiation field variables.
Subclass and overwrite with custom functionality if you desire.

_compute_rays
(st, photosphere, threads)[source]¶ Trace (integrate) a set of rays.
These rays represent a null mapping from photosphere to a point at some effective infinity.
Parameters:  st – Instance of
Spacetime
.  threads (int) – Number of
OpenMP
threads for ray integration.
 st – Instance of

_construct_cellMesh
(st, threads)[source]¶ Call a lowlevel routine to construct a mesh representation.
Parameters:  st – Instance of
Spacetime
.  threads (int) – Number of
OpenMP
threads for mesh construction.
 st – Instance of

integrate
(st, energies, threads, atmosphere)[source]¶ Integrate over the photospheric radiation field.
Parameters:  st – Instance of
Spacetime
.  energies – A onedimensional
numpy.ndarray
of energies in keV.  threads (int) – Number of
OpenMP
threads the integrator is permitted to spawn.
 st – Instance of

num_cells
¶ Get the total number of cells in the mesh.

num_rays
¶ Get the number of rays integrated per colatitude.

phases_in_cycles
¶ Get the phases (in cycles) the pulse is interpolated at.

set_phases
(num_leaves, num_phases=None, phases=None)[source]¶ Construct the set of interpolation phases and foliation leaves.
Parameters:  num_leaves (int) – Number of leaves mesh motion is discretised into.
 num_phases (int) – Number of phases in a discrete representation of the specific flux
pulses on the interval \([0,1]\). If
None
, the number of phases interpolated at is set equal to the number of leaves.  phases – If not
None
, anumpy.ndarray
of phases for a discrete representation of the specific flux pulses on the interval \([0,1]\). IfNone
(default), thenum_phases
argument is utilised.

sqrt_num_cells
¶ Get the number of cell colatitudes.