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in recent years there has been a growing interest for the vertical structure of the hi disks of spiral galaxies and for the disk - halo connection .
evidence for hi gas flows between disk and halo comes from the detection of large vertical motions in several galaxies viewed close to face - on ( dickey et al .
1990 ; kamphuis 1993 ; schulman & bregman 1994 ) and the connection of this high velocity gas with hi holes and star formation activity in the disk ( kamphuis & sancisi 1993 ) .
more evidence comes from the study of edge - on galaxies like ngc  891 in which the hi has been found to extend up to at least 5 kpc into the halo , where it seems to rotate about 25 km @xmath1 more slowly than in the plane ( swaters et al .
1997 ) . the combination of the results from face - on and edge - on galaxies leads to the picture of effervescent galaxies ( sancisi et al .
1996 ) , consistent with galactic fountains models ( bregman 1980 ; spitzer 1990 ) .    the galaxy studied here , ngc  2403 , has an intermediate inclination ( i=@xmath2 ) .
the consequence is that the measured line - of - sight velocities are a combination of rotational , radial and vertical motions and the column densities are integrated along an oblique line - of - sight .
therefore , the interpretation is less straightforward than in face - on or edge - on galaxies .
however , there is the advantage that information is obtained on both the vertical density structure and the vertical kinematics of the hi for the same object .    for this study
we have used the hi observations obtained by sicking ( 1997 ) with the westerbork radio telescope , which have about a factor of 2 better sensitivity and a higher velocity resolution than those of wevers et al .
1 shows the optical image , the total hi density distribution , the velocity field and the hi position - velocity map along the major axis .
the latter shows that the hi line profiles at any position along the major axis are not symmetrical with respect to the rotation velocities , as they would be if they were determined by random motions only .
instead , they are systematically more extended towards the systemic velocity .
this striking asymmetry is particularly obvious in the lowest contour and extends systematically over almost the whole major axis .
it was already noticeable in the maps produced by wevers et al .
( 1986 ) and by begeman ( 1987 ) and the puzzle presented by those early observations has motivated this study .
the presence of such a ` beard ' is remarkable considering the size of the beam ( see lower left in fig .
1 ) with respect to the size of the galaxy . usually such an asymmetry is seen in edge - on galaxies or in galaxies which are not well resolved . in such cases
the telescope beam ` sees ' not only the emission from a small area on the major axis but also larger areas away from it which have lower line - of - sight velocities and therefore cause the observed asymmetry .
ngc  2403 is neither highly inclined nor poorly resolved .    what is the origin of the ` beard ' ?
it is clear that it can not simply be explained by gas moving perpendicularly away from or towards the disk , because that would produce extensions symmetric with respect to the rotation velocity .
neither can it be the result of deviations from axial symmetry or circular motion .
these would affect the kinematics of the disk and produce visible effects in the velocity field , but not a low density asymmetry as observed .
a likely explanation for the observed asymmetry is that not all of the hi is concentrated in a thin disk , but that part of it is in a vertically extended component . in this case ,
given the inclination of 61 degrees , a line - of - sight to a point on the major axis will also intercept the hi located above and below the plane which has line - of - sight velocities lower than those in the plane .
this will produce a systematic broadening of the hi profiles towards the systemic velocity of the kind seen in fig .
1 . it is this effect that we study here with 3-d models of the density distribution and kinematics of the hi in ngc  2403 .
[ f : lvmodels ]
we consider the possibilities of both a thick hi disk ( as opposed to the usually assumed thin layer ) , and of a two - component structure , with a thin layer and a thicker but less dense one .
this thick layer may be corotating with the thin one or may be rotating more slowly .
both cases are examined .
the reason for considering the slower rotation is that a non - corotating disk and halo have been proposed by swaters et al .
( 1997 ) as the most likely interpretation for the hi observations of the edge - on galaxy ngc  891 .
axial symmetry and circular motions are assumed throughout .
this assumption is supported by the results of schoenmakers et al .
( 1997 ) who found from their harmonic analysis of the hi velocity field of ngc  2403 that non - circular motions are not important in this galaxy .
therefore , we have modelled ngc  2403 with a set of concentric rings , each ring characterized by a radius , a circular velocity , a velocity dispersion and a column density .
centre , systemic velocity , inclination and position angle , scaleheight and vertical density profile were chosen to be the same for all rings .
the values adopted here are , unless specified otherwise , those derived by sicking ( 1997 ) .
the thin component always has a fwhm thickness of 0.5 kpc , the thickness of the thick layer is a free parameter . for the vertical density profile
we have assumed a gaussian distribution .
we have also tried an exponential distribution , but the results do not seem to change significantly . in the case of non - corotation
the circular velocity of the thicker component has been lowered by a fixed amount , for example 25 km @xmath1 , in the flat part of the curve and a proportionally smaller one in the inner parts . for the velocity dispersion
we have used a value of 7 km @xmath1 as derived for the profile widths in the regions of the flat part of the rotation curve .
we have also constructed models with higher velocity dispersions for the thick components , up to 30 km @xmath1 , but the results do not differ significantly .
the two - component models have been constructed by adding two one - component models .
this is obviously an oversimplification as it is more likely that any vertical decrease of density and velocity would be gradual .
the model data cubes have been inspected and analyzed in the same way as the observed cubes . for the comparison of the models and the observations we have used the channel maps and the position - velocity maps along the major and minor axes . here
we present only the position - velocity maps along the major axis and only a small number of models , but we have explored the whole relevant parameter space .    initially , we tried a model with a one - component gas layer .
cuts along the major axis for various thicknesses are shown in the first column of fig .  2 .
the observations are in the top right panel .
it is immediately clear that a thin disk model does not reproduce the observed asymmetry .
a thickness of about 5 kpc ( fwhm ) would be needed to explain it .
it is obvious that such a layer would be unrealistically thick , much thicker than that of our galaxy , which according to dickey and lockman ( 1990 ) has a fwhm of only 220 pc , or that of ngc  891 , for which most of the hi is in an unresolved layer with a fwhm thickness of less than 1 kpc ( swaters et al .
1997 ) .    therefore , we explored the possibility of having , instead of one very thick gaussian disk , a relatively thin disk of high density and in addition a vertically more extended but lower density layer . for this
we have built a model with two components , one thin and one thick , both rotating at the same velocity .
the fwhm of the thick component and the column density ratio between the two components are free parameters .
we found , however , that there is little freedom in the choice of this ratio and we fixed it tentatively at 1:1 . with a lower density for
the thick component only a weak asymmetry would appear .
the best model seems the one with a thick component of fwhm close to 5 kpc ( see fig .  2 )
. hence this model is not significantly different from the one - component model and is equally unrealistic as it requires unreasonable amounts of hi at large distances from the plane .
finally , we released the condition of corotation and explored the effects of a decrease of the rotational velocity with distance to the plane .
for this we have constructed models with a slowly rotating thick component .
again , the fwhm of the thick component and the column density ratio are free parameters . but
here as an additional parameter we have the velocity decrease
. a thin - to - thick disk density ratio of 4:1 was found to give the best comparison with the data . with a higher ratio
the asymmetry would tend to disappear , whereas a lower ratio would not reproduce the observed density contrast between the profile peak and its wings .
for the thick component a fwhm of 1 kpc was adopted . for this thickness the best agreement with the observations is obtained with the 25 km @xmath1 decrease ( see fig .  2 ) .
models with a thick component of larger fwhm than 1 kpc were also tried .
for example , in the lower right of fig .  2 , we show a model that also reproduces the observed asymmetry well , and in which the thick component , still with a 25 km @xmath1 decrease in rotation velocity , has a thickness of 3.5 kpc . for this thickness
the optimal column density ratio of the thin and thick disk is 6:1 .
this illustrates that it is difficult to distinguish between an extended , low density and a less extended , higher density vertical distribution .
from section 3 it is clear that all three types of models can explain the observed asymmetry to some extent .
however , the first two models require unrealistic amounts of hi above the plane .
the third model has a much more realistic vertical distribution , with less than 20% of the gas in the thick component , and it requires that the gas above the plane rotates more slowly than the gas in the disk , by about 25 km @xmath1 .
this model also appears to reproduce the observed position - velocity diagram better than the other models , in particular near the center , where the hi has a narrow and peaked distribution , and at large radii , where low level wings are visible .
note that in the observed position - velocity diagram ( fig .
1 ) the wings near the center extend almost to the systemic velocity .
clearly , such features can not be reproduced in models with corotation , and not even in those with a velocity decrease as high as 35 km @xmath1 .
to explain these extended wings a much larger velocity decrease is needed , probably at least 50 km @xmath1 .
what produces such a thick hi layer and what causes its slower rotation ?
galactic fountain models ( bregman 1980 ; spitzer 1990 ) may provide the framework for an answer . the fountain is formed by hot gas rising from the disk , its energy derived from stellar winds and supernova explosions . in the halo region
the gas cools and condenses into clouds that fall back onto the disk . as the gas moves up ,
the centrally directed gravitational force decreases , and the gas moves outwards . due to conservation of angular momentum the azimuthal velocity decreases .
this decrease will be most pronounced in the central parts of the galaxy , where a fixed radial displacement will result in a larger velocity decrease than in the outer regions .
using thermohydrodynamic models , struck & smith ( 1999 ) have recently shown that a reduced circular velocity above and below the plane is expected to be present in turbulent disks as a result of radial motions driven by star formation activity .
ngc  2403 appears to have sufficient star formation activity to drive a galactic fountain .
this is for instance indicated by its large number of hii regions ( sivan et al .
four of these are exceptionally bright , comparable to the most massive starburst region in the local group , the 30 doradus complex ( drissen et al .
furthermore , thilker et al .
( 1998 ) have found that the surface of ngc  2403 is covered by shells and fragmentary structures which are likely to have formed as a result of star formation activity .
they have also found that these structures are part of a diffuse component of neutral hydrogen extending at least 400 pc from the plane .
the overall picture of ngc  2403 , as suggested by the modelling , is reminiscent of that of ngc  891 . for this galaxy
it was found ( swaters et al .
1997 ) that the thick component has a fwhm of about 4 kpc , and this gas appears to rotate more slowly than the gas in the disk by about 25 km @xmath1 . in the central parts
the velocity decrease was found to be much larger , perhaps up to 100 km @xmath1 .    in conclusion , we have presented evidence that the thin hydrogen disk of ngc  2403 is surrounded by a vertically extended layer of hi , which rotates more slowly than the disk .
the observational picture is very similar to that found for ngc  891 .
these results suggest that a vertically extended , slowly rotating hi layer may be common among spiral galaxies , at least among those with high levels of star formation .
such extended hi layers have , however , very low surface densities and therefore very sensitive observations are needed to detect them .
we thank f.j .  sicking for kindly making available the data and u.j .
schwarz for helpful discussions .
the neutral hydrogen line profiles along the major axis of the nearby spiral galaxy ngc  2403 show a wing towards the systemic velocity . 
 this asymmetry can be explained with the presence of an abnormally thick hi disk ( fwhm @xmath0 5 kpc ) or with a two - component structure : a thin disk and a slowly rotating , thicker ( 1 - 3 kpc ) hi layer . 
 the latter model gives a better representation of the observations . 
 these results throw a new light on the disk - halo connection in spiral galaxies 
 . in particular , the decrease of rotational velocity with height above the plane may be the result of a galactic fountain flow . 
 a vertically extended , slowly rotating hi layer may be common among spiral galaxies with high levels of star formation .