Skip to content

Latest commit

 

History

History
36 lines (24 loc) · 2.86 KB

conventions.md

File metadata and controls

36 lines (24 loc) · 2.86 KB

COOLEST conventions

The standard relies on a set of fixed conventions, that are implicitly assumed by all lens models stored in the COOLEST format.

Units

  • Width, height, angular positions and length (e.g. radii) are all given in arcseconds.
  • Position angles and orientations are given in degrees, by default in the interval $(-90^\circ, +90^\circ]$. This typically holds true for profiles with 180° symmetry such as elliptical profiles and external shear. Otherwise, it is explicitly mentioned in the profile definition.
  • data and model images (e.g., including pixelated light profiles) are assumed to be given in electrons per second. If these units are evidently not suitable to the type of data (e.g., radio wavelenghts), the alternative units must be specified in the 'meta' section of the template.

Coordinates system

  • The origin of the coordinate system in which all quantities are defined is fixed by a single absolute J2000 coordinate, given in 0h:0m:0.0s (right ascension) and 0d:0m:0.0s (declination) format. Any dependence on a specific field-of-view should be subtracted out.
  • Quantities are expressed in a cartesian coordinate system $(x, y)$, the $x$ axis positively increasing to the right, the $y$ axis positively increasing upwards. Since coordinates are then always aligned with the image axes, this is a more intuitive description compared to (RA, Dec).
  • Position angles and orientations (usually denoted $\phi$) are measured counter-clockwise from the positive $y$ axis. Thus it is similar to the frequently used "East-of-North" convention.

drawing

Notations

  • Cartesian coordinates are given $(x,y)$, polar coordinates are $(r,\phi)$. If required, the radial vector (in polar coordinates) is $\boldsymbol{r}$.
  • Parameters and quantities representing radii are given in angular units (i.e. arcsec) and thus it is better suited to note them "$\theta$" (instead of "$r$"). This includes the Einstein radius ($\theta_{\rm E}$) and the effective radius ($\theta_{\rm eff}$), for instance. However, fpr some profiles are systematically defined with "$r$" in the literature (e.g., NFW), the common notations are followed.
  • Notations for recurrent lensing quantities:
    • $\psi$: lens potential;
    • $\boldsymbol{\alpha}$: deflection field;
    • $\kappa$: surface mass density or convergence;
    • $\boldsymbol{\gamma}$: shear field;
    • $\mu$: magnification.

Ellipticity parametrization

For elliptical profiles, any characteristic radius (e.g., Einstein radius, half-light radius) is given along the intermediate axis, as the product average of the semi-major and semi-minor axis, i.e. $r_{\rm inter} = \sqrt{a,b}$. The relation between intermediate-axis and major-axis is $r_{\rm inter} = \sqrt{q}, a$, where $q = b/a$ is the axis ratio of the ellipse.