Context : Planets are supposed to form in circumstellar disks .
The additional gravitational potential of a planet perturbs the disk and leads to characteristic structures , i.e .
spiral waves and gaps , in the disk ’ s density profile .

Aims : We perform a large-scale parameter study of the observability of these planet-induced structures in circumstellar disks in the ( sub ) mm wavelength range for the Atacama Large ( Sub ) Millimeter Array ( ALMA ) .

Methods : On the basis of hydrodynamical and magneto-hydrodynamical simulations of star-disk-planet models , we calculated the disk temperature structure and ( sub ) mm images of these systems .
These were used to derive simulated ALMA images .
Because appropriate objects are frequent in the Taurus-Auriga region , we focused on a distance of 140 pc and a declination of \approx 20 ^ { \circ } .
The explored range of star-disk-planet configurations consists of six hydrodynamical simulations ( including magnetic fields and different planet masses ) , nine disk sizes with outer radii ranging from 9 AU to 225 AU , 15 total disk masses in the range between 2.67 \cdot 10 ^ { -7 } M _ { \odot } and 4.10 \cdot 10 ^ { -2 } M _ { \odot } , six different central stars , and two different grain size distributions , resulting in 10 { } 000 disk models .

Results : On almost all scales and in particular down to a scale of a few AU , ALMA is able to trace disk structures induced by planet-disk interaction or by the influence of magnetic fields on the wavelength range between 0.4 and 2.0 mm .
In most cases , the optimum angular resolution is limited by the sensitivity of ALMA .
However , within the range of typical masses of protoplanetary disks ( 0.1 M _ { \odot } – 0.001 M _ { \odot } ) the disk mass has a minor impact on the observability .
It is possible to resolve disks down to 2.67 \cdot 10 ^ { -6 } M _ { \odot } and trace gaps induced by a planet with \frac { M _ { \text } { p } } { M _ { \star } } = 0.001 in disks with 2.67 \cdot 10 ^ { -4 } M _ { \odot } with a signal-to-noise ratio greater than three .
The central star has a major impact on the observability of gaps , as well as the considered maximum grainsize of the dust in the disk .
In general , it is more likely to trace planet-induced gaps in our magnetohydrodynamical disk models , because gaps are wider in the presence of magnetic fields .
We also find that zonal flows resulting from magneto-rotational instability ( MRI ) create gap-like structures in the disk ’ s re-emission radiation , which are observable with ALMA .

Conclusions : Through the unprecedented resolution and sensitivity of ALMA in the ( sub ) mm wavelength range , the expected detailed observations of planet-disk interaction and global disk structures will deepen our understanding of the planet formation and disk evolution process .