Plotting error box

[lmichel]

The API plotting catalogues could be enable to plot individual error boxes for any plotted source.

The API could look like ( just an example, not a requirement)

aladin.plotCatalogue(cat_url, ra_col, dec_col,  error_columns=[err_columns]);

error_columns is an array which dimension denotes the type of error:

• err_columns=[pos_err]: plots a circle with the value of the column pos_err as radius.
• err_columns=[pos_ra, pos_dec]: plots a vertical ellipse with the value of the column pos_ra and pos_dec as axes.
• err_columns=[major_axis, minor_axis, angle]: plots an ellipse with major_axis and minor_axis as axes oriented following angle from the east of the North (convention)

[fxpineau]

@tboch and @bmatthieu3 asked me to comment this issue.
I think that one should pass the explicit type of error in addition to its parameters, e.g.:

• RadialError(r=e_RADEC, enclosed_proba=0.39347) in which:
  • r is the radius of the cone containing the real (unknown) position with a probability equals to enclosed_proba; for the enclosed_proba default value (0.39347, i.e. 39.347%), r correspond to the sigma of the Rayleigh distribution
  • enclosed_proba the probability the cone of radius r has to contain the real position; common values are 0.68269 (the 1-dimentional 1-sigma), 0.90 and 0.95.
• SymmetricError(sigma=e_RADEC): the parameter on both axis of a symmetric 2-dimentional Gaussian
• ? CovEllipse(sigma_ra=e_RA,sigma_dec=e_DEC, covariance=0.0): parameters of a 2-dimentional Gaussian provided as an ellipse with a covariance parameter, in which:
  • sigma_ra: error on the RA*cos(Dec) quantity, usually simply called RA error
  • sigma_dec: error on the Dec quantity
  • covariance: covariance factor, default value equals 0
• CorEllipse(sigma_ra=e_RA,sigma_dec=e_DEC, correlation=0.0): parameters of a 2-dimentional Gaussian provided as an ellipse with a correlation parameter, so that it equals CovEllipse(sigma_ra, sigma_dec, covariance=correlation * sigma_ra * sigma_dec), and in which:
  • sigma_ra: error on the RA*cos(Dec) quantity, usually simply called RA error
  • sigma_dec: error on the Dec quantity
  • correlation: correlation factor, default value equals 0
• CoSigmaEllipse(sigma_ra=e_RA,sigma_dec=e_DEC, cosig=0.0) parameters of a 2-dimentional Gaussian provided as an ellipse with a correlation parameter, so that it equals CovEllipse(sigma_ra,sigma_dec, covariance=cosig * |cosig|), see sigradec in the AllWISE doc.
• OrientedEllipse(smaj, smin, pa) parameters of a 2-dimentional Gaussian provided by its 1-sigma ellipse, in which:
  • smaj: semi-major axis
  • smin: simi-minor axis
  • pa: position angle, east-of-north convention (like in @lmichel comment)

For each error, one could add an extra parameter ellipse_enclosed_probability with a default value set to 0.39347 and which would be the integral of the probability of the 2-dimentional Gaussian enclosed in the drawn ellipse. This parameter will thus influence the size of the ellipses which are displayed.

I can provide you with Rust code making the various conversions from/to ellipse/symmetric error/covariance matrix/...

For more details, see section 4.2 of this paper.