It has recently been proposed that radio emission from magnetars can be evaluated using a “ fundamental plane ” in parameter space between pulsar voltage gap and ratio of X-ray luminosity L _ { \mathrm { x } } to rotational energy loss rate \dot { E } .
In particular , radio emission from magnetars will occur if L _ { \mathrm { x } } / \dot { E } < 1 and the voltage gap is large , and there is no radio emission if L _ { \mathrm { x } } / \dot { E } > 1 .
Here we clarify several issues regarding this fundamental plane , including demonstrating that the fundamental plane is not uniquely defined .
We also show that , if magnetars and all other pulsars are different manifestations of a unified picture of neutron stars , then pulsar radio activity ( inactivity ) appears to be determined by the ratio L _ { \mathrm { x } } / \dot { E } \lesssim 1 ( L _ { \mathrm { x } } / \dot { E } \gtrsim 1 ) , although observational bias and uncertainty in the ratio for some sources may still invalidate this conclusion .
Finally , we comment on the use of other pulsar parameters that are constructed from the three observables : spin period P , period derivative \dot { P } , and L _ { \mathrm { x } } .