We test whether the population of “ extreme ” trans-Neptunian objects ( eTNOs ) detected in the Y4 Dark Energy Survey ( DES ) data exhibit azimuthal asymmetries which might be evidence of gravitational perturbations from an unseen super-Earth in a distant orbit .
By rotating the orbits of the detected eTNOs , we construct a synthetic population which , when subject to the DES selection function , reproduces the detected distribution of eTNOs in the orbital elements a,e, and i as well as absolute magnitude H , but has uniform distributions in mean anomaly M , longitude of ascending node \Omega, and argument of perihelion \omega . We then compare the detected distributions in each of \Omega, \omega, and \varpi \equiv \Omega + \omega to those expected from the isotropic population , using Kuiper ’ s variant of the Kolmogorov-Smirnov test .
The three angles are tested for each of 4 definitions of the eTNO population , choosing among a > ( 150 , 250 ) AU and perihelion q > ( 30 , 37 ) AU .
These choices yield 3–7 eTNOs in the DES Y4 sample .
Among the twelve total tests , two have the likelihood of drawing the observed angles from the isotropic population at p < 0.05. The 3 detections at a > 250 ,q > 37 AU , and the 4 detections at a > 250 ,q > 30 AU , have \Omega distribution with p = 0.03 of coming from the isotropic construction , but this is not strong evidence of anisotropy given the 12 different tests .
The DES data taken on their own are thus consistent with azimuthal isotropy and do not require a “ Planet 9 ” hypothesis .
The limited sky coverage and object count mean , however , that the DES data by no means falsify this hypothesis .