  Aims. We investigate the influence of the Yarkovsky force on the long-term
orbital evolution of Jupiter Trojan asteroids. Methods. Clones of the observed
population with different sizes and different thermal properties were
numerically integrated for 1 Gyr with and without the Yarkovsky effect. The
escape rate of these objects from the Trojan region as well as changes in the
libration amplitude, eccentricity, and inclination were used as a metric of the
strength of the Yarkovsky effect on the Trojan orbits. Results. Objects with
radii $R\leq$1 km are significantly influenced by the Yarkovsky force. The
effect causes a depletion of these objects over timescales of a few hundred
million years. As a consequence, we expect the size-frequency distribution of
small Trojans to show a shallower slope than that of the currently observable
population ($R$ $\gtrsim$ 1 km), with a turning point between $R$ = 100 m and
$R$ = 1 km. The effect of the Yarkovsky acceleration on the orbits of Trojans
depends on the sense of rotation in a complex way. The libration amplitude of
prograde rotators decreases with time while the eccentricity increases.
Retrograde rotators experience the opposite effect, which results in retrograde
rotators being ejected faster from the 1:1 resonance region. Furthermore, for
objects affected by the Yarkovsky force, we find indications that the effect
tends to smooth out the differences in the orbital distribution between the two
clouds.

Earth and Planetary Astrophysics