# Guide to NED Association Search Results

(Latest Revision: 8 May 2009)

The association table identifies one or more sources in the vicinity of the primary object that may be the same object. The NED Team has yet to consider these sources in detail, but are providing here the preliminary positional associations for your information. As time permits, these "possible identifications" will be worked off and these tabular entries will disappear from the interface, to be replaced either by a firm identification between two objects or by a new object in NED.

The table includes

• A sequential data-point number applicable to this list only.
• The name of the associated object.
• The separation in arcseconds from the primary object.
• The position angle in degrees, measured from north through east, with the primary object as the reference point.
• Goodness-of-fit parameters "r" and log "p", defined below.

## Goodness-of-fit Parameters

The dimensionless parameters r and p represent measures of the "goodness of fit" of the positional uncertainty ellipses of an input object and a nearby NED object. Here, x and y are usually RA and Dec, but may represent any coordinate system.

The first parameter is the distance between the two sources in units of the standard deviations of the convolved uncertainties on the principal axes of the error ellipsoid; mathematically, this is the chi-square parameter with two degrees of freedom evaluated for the observed separation and catalog uncertainties, assuming Gaussian errors, and is dimensionless. It is formally defined by

The second parameter, expressed here as a base-10 logarithm, is the expected-error density function evaluated for the observed separation. The expected-error density function is the convolution of the error density functions for the two catalogs involved, assuming Gaussian errors; the density function has units of probability mass per steradian. Its formal definition is

For a given comparison of positions and uncertainty ellipses, it is desirable to minimize r and maximize p. In principle, the acceptable threshold values should be empirically determined for each catalog comparison. In practice, we have found that threshold values do not change substantially among astronomical catalogs. For example, the values adopted for the comparison of the IRAS Faint Source Catalog with NED, rmax = 2.0 and log pmin = 6.0, are generally applicable for most catalogs loaded in NED.

Thus, an association with r < 2.0 or with log p > 6.0 can be taken as a statistically valid position-based identification of those same two objects.