The magnetic field of the classical T Tauri star V2129 Oph can be modeled approximately by superposing slightly tilted dipole and octupole moments , with polar magnetic field strengths of 0.35 kG and 1.2 kG respectively ( Donati et al . 13 , hereafter D07 ) .
Here we construct a numerical model of V2129 Oph incorporating this result and simulate accretion onto the star using a three-dimensional magnetohydrodynamic code .
Simulations show that the disk is truncated by the dipole component and matter flows towards the star in two funnel streams .
Closer to the star , the flow is redirected by the octupolar component , with some of the matter flowing towards the high-latitude poles , and the rest into the octupolar belts .
The shape and position of the spots differ from those in a pure dipole case , where crescent-shaped spots are observed at the intermediate latitudes .

Simulations show that if the disk is truncated at the distance of r \approx 6.2 R _ { \star } which is comparable with the co-rotation radius , r _ { cor } \approx 6.8 R _ { \star } , then the high-latitude polar spot dominates , but the accretion rate obtained from the simulations ( and from the accompanying theoretical calculations ) is about an order of magnitude lower than the observed one .
The accretion rate matches the observed one if the disk is disrupted much closer to the star , at 3.4 R _ { \star } .
However , in that case the octupolar belt spots strongly dominate .
In the intermediate case of r \approx 4.3 R _ { \star } , the polar spots are sufficiently bright , and the accretion rate is within the error bar of the observed accretion rate , and this model can explain the observations .
However , an even better match has been obtained in experiments with a dipole field twice as strong compared with one suggested by D07 .

The torque on the star from the disk-magnetosphere interaction is small , and the time-scale of spin evolution , 2 \times 10 ^ { 7 } -10 ^ { 9 } years is longer than the 2 \times 10 ^ { 6 } years age of V2129 Oph .
This means that V2129 Oph probably lost most of its angular momentum in the early stages of its evolution , possibly , during the stage when it was fully convective , and had a stronger magnetic field .

The external magnetic flux of the star is strongly influenced by the disk : the field lines connecting the disk and the star inflate and form magnetic towers above and below the disk .
The potential ( vacuum ) approximation is still valid inside the Alfvén ( magnetospheric ) surface where the magnetic stress dominates over the matter stress .