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Paper text:
the hot gas in clusters is often called the intracluster medium ( icm ) .
the typical temperature and density of the icm are @xmath010  kev and @xmath1 , respectively @xcite .
while most galaxies are moving at transonic velocities ( @xmath2 ) @xcite , the galaxies that fall into a cluster from the outside have a mach number of @xmath33 @xcite .
so far , the interaction between disk galaxies and the surrounding icm has been considered mostly in terms of ` ram - pressure stripping ' @xcite .
the disk of a disk galaxy is composed of stars and gas filling the disk .
the latter is called interstellar medium ( ism ) , and is cold and dense ( @xmath4  k and @xmath5 ) compared with the icm .
the ism prevents the penetration of the galaxy by the icm .
if the ram - pressure force of the icm ( @xmath6 per unit area ) becomes larger than the gravitational restoring force of the galaxy , the ism is stripped away from the galaxy @xcite .
once the ism is stripped , the icm flows through the stellar disk of the galaxy without much resistance .
many numerical simulations have been performed to study this ram - pressure stripping @xcite .
another possible interaction between the icm and ism may be aerodynamic effects on a galaxy by the flow around the galaxy . in this paper ,
i discuss a few cases where the aerodynamic forces could operate on the galaxy motion , assuming that a disk galaxy is a thin solid disk for simplicity . since the aerodynamic effects are available only when the disk ism is not completely removed , i discuss only the cases where numerical simulations showed that the ram - pressure does not remove the ism completely .
ram - pressure stripping is ineffective when the attack angle of a galaxy is small , and/or when the galaxy velocity is small .
i consider the former in section  [ sec : lift ] and the latter in section  [ sec : drag ] .
i consider a disk galaxy that falls into a cluster from the outside .
the galaxy should have an almost radial orbit and should be affected by aerodynamical forces when it passes the central region of the cluster .
suppose that a galaxy is moving in the icm with a velocity of @xmath7 ( fig .
[ fig : flow ] ) .
the angle of attack , @xmath8 , is defined as the angle between the disk and the traveling direction of the galaxy . if @xmath8 is much smaller than @xmath9 ,
ram - pressure stripping is not strong ; the ism of the galaxy is not completely removed and makes the surface of the disk .
the icm flows on both sides of the ( remaining ) ism disk .
it is assumed that the ism disk is thin and its radius is @xmath10 . if @xmath11 , the lift force on the disk is given by @xmath12 where @xmath13 is the area of the disk @xcite .
the lift force is not sensitive to the form of the disk cross - section @xcite .
although this equation is for an infinitely long airfoil , the correction for a finite long one is small .
the influence of the wing ends is limited to the inside of the mach cones with the apexes at the wing ends and the angle of @xmath14 ( fig .  [ fig : foil ] ) .
for a disk , its portions included in the cones are small .    for a luminous disk galaxy ,
the radius of the ism disk is @xmath15  kpc if ram - pressure stripping can be ignored totally .
considering the ram - pressure stripping , @xmath16  kpc is taken here @xcite . for the central region of a rich cluster similar to the coma cluster , the icm temperature and density are @xmath17  kev and @xmath18 , respectively .
thus , for a disk galaxy passing through the central region with @xmath19 , the lift force is @xmath20^{-1/2}\ : .
\label{eq : lift}\end{aligned}\ ] ] as a result , the galaxy gains extra velocity perpendicular to its original direction of travel , @xmath21 , where @xmath22 ( @xmath23 ) is the galaxy mass , and @xmath24 ( @xmath25  yr ) is the time for the galaxy to cross the central region of the cluster .
since this is much smaller than the velocity dispersions of galaxies in rich clusters ( @xmath26 ) , it can be ignored .
it is to be noted that since @xmath8 must be small enough to avoid ram - pressure stripping @xcite and large enough to lift the galaxy ( @xmath27 ) , the fraction of galaxies affected by the lift force ( @xmath28 ) is very limited .
after the galaxy reaches the apocenter far away from the cluster center , it falls back into the cluster again .
however , it is unlikely for the galaxy to have an attack angle of @xmath29 again .
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for a poor cluster with a temperature of @xmath30  kev , ram - pressure stripping is almost ineffective for most galaxies regardless of the attack angle @xmath8 , because the velocity of the galaxies and thus the ram - pressure on them are small . as a result , the radius of a ism disk is large , and the drag force on a galaxy would be important especially when @xmath31 . for spherical galaxies , the drag force has been studied , although its influence on galaxy motion has not been discussed @xcite . for a given radius ,
the drag force on a disk perpendicular to wind ( @xmath32 ) is much larger than that on a sphere @xcite .
therefore , it is worthwhile to revisit the problem for disk galaxies .
the drag force is given by @xmath33 where @xmath34 is the drag coefficient .
for a disk of @xmath32 , the coefficient is @xmath35 , while for a sphere with the same radius , the coefficient is @xmath360.47 depending on the reynolds number @xcite .
the values of @xmath34 are for incompressible fluids ( @xmath37 ) ; they rise by a few tens percent at @xmath380.8 @xcite .
i consider a disk galaxy ( @xmath39 and @xmath32 ) orbiting well - inside a poor cluster with a temperature of @xmath40  kev and a density of @xmath41 .
since the galaxy is orbiting inside the cluster and the drag force is not as sensitive to the attack angle as the lift force , the galaxy is constantly affected by the drag force from the icm .
assuming that @xmath42 , the drag force is @xmath43 considering weak ram - pressure pressure stripping , the disk radius was assumed to be @xmath44  kpc @xcite .
after @xmath45  gyr , which is the typical age of poor clusters , the galaxy velocity decreases by @xmath46 and the deviation from the orbit that the galaxy would have been in if it were not for the icm is @xmath47  mpc , which is comparable to the size of poor clusters ( @xmath48  mpc ) . note that although ram - pressure may distort the ism disk , it is unlikely that the disk becomes as round as a sphere .
thus , the drag coefficient , @xmath34 , is at least larger than 0.20.47 .
i have shown that while the lift force on disk galaxies can be ignored , the drag force could not be ignored for face - on disk galaxies in poor clusters .
equations  ( [ eq : lift ] ) and  ( [ eq : drag ] ) show that the strengths of the lift and drag forces are sensitive to the radius of the ism disk , @xmath10 . in the above estimates ,
gas supply from stars in the galaxy was not considered . if the gas ejected from the stars is added to the ism
, @xmath10 should become larger @xcite .
it is likely that active disk galaxies , in which large amount of gas is being released from the stars , have much larger @xmath10 and are more affected by the aerodynamic forces .
it is also to be noted that if the velocity or pressure distribution of the icm around a disk galaxy is measured , the aerodynamic forces can be constrained .
the observations of stripped ism will be useful to obtain the velocity field around a disk galaxy @xcite .
x - ray observations will tell us the pressure distribution around a galaxy @xcite .
the models presented here are very simple . in an actual galaxy
, the situation would be rather delicate .
one example is how the lift or drag would operate on the collisionless stars and dark matter particles , as required to alter the orbit of the whole galaxy .
the connecting force is gravity .
if the gas disk is lifted or dragged off the stellar disk , and the center of the dark matter halo , then both will pull back on the gas disk .
this would communicate the lift or drag force to all components .
too much separation , and the restoring gravity force will be weakened and the gas will be stripped , too little and nothing will happen . in order to study the process quantitatively , numerical simulations would be required .
disk galaxies in a cluster of galaxies are moving in hot gas filling the cluster . 
 generally , they are moving at transonic or supersonic velocities . 
 if ram - pressure stripping is insufficient to destroy the gas disk , the galaxies should be affected by the wind of the surrounding hot gas similar to an airfoil . in this paper , 
 i consider whether the aerodynamic interaction can be strong enough to force a disk galaxy to deviate from the orbit that it would have been in . 
 i find that while the lift force is not effective , the drag force could affect face - on disk galaxies in poor clusters on long timescales .