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this paper tries to understand whether concentrations of emission in observations of position - velocity space represent real clumps of gas in molecular clouds ; whether the properties inferred for the observed objects describe the actual clouds ; and what we can say about the mechanisms that drive interstellar turbulence by observing molecular clouds with different tracers . several papers have tried to address these points before . @xcite show that , in a galactic disk model , gas complexes in a longitude - velocity diagram do not necessarily correspond to real complexes . more recently , based on numerical simulations , @xcite showed that observed clumps frequently come from the superposition of several physically disconnected regions in the line of sight at the same radial velocity ( see also @xcite , ) but not necessarily at the same three - dimensional velocity . moreover , the morphology seen in observed position - position - velocity maps seems to be more representative of the spatial distribution of the velocity field in the line of sight than of the distribution of the density field , as has been shown in 3d numerical simulations by @xcite . similarly , @xcite shown that only the velocity field is responsible for the structure existing in the channel maps of observational data cubes . if observed structures do not match actual structures , it is valid to ask whether statistical properties of observed clouds , such as the @xcite relationships , are still valid for actual clouds . as @xcite mentions , they may instead be artifacts of the observations . in fact , @xcite argues that the mean density - size relationship is an artifact of the limited dynamical range of the observations ( see also @xcite . ) @xcite used two - dimensional simulations of the diffuse interstellar medium to suggest that there is no relationship between mean density and size of physical clouds ( defined as a connected set of pixels in their simulations ) , but that there is a relationship , although with strong scatter , between the velocity dispersion and size , a result confirmed by @xcite . although as we mentioned , several papers have studied the same questions as the present paper , they addressed them only partially , studying for example only objects in physical space @xcite , or in observational space @xcite ; or giving physical arguments to explain the observed @xcite relationships ( e.g. , @xcite itself ; @xcite ; @xcite ) . in the present paper we use three - dimensional numerical models of molecular clouds to directly compare structures in simulated observations to the actual physical structures that produce them . our goals are : to give observational predictions about the nature of the sources of the turbulence ; to disentangle what observed properties are representative of the true physical entities ; and what are more likely to just be the result of superposition of multiple structures along the line of sight . another way of asking this is , what are the differences between the observational space and the physical space ? the plan of the paper is as follows : in  [ simulationssec ] we describe the numerical models used here , and the methods used to define clumps and to generate simulated observations from model density and velocity cubes . in [ role ] we study the role of the luminosity @xmath0 , wavenumber @xmath1 and initial magnetic field @xmath2 in the production of density fluctuations , and give observational criteria to infer the properties of the sources of turbulence . we discuss the superposition effects , and analyze the relative importance of the parameters of the simulations in the superposition effects (  [ superposition ] ) . section  [ larsonsec ] studies larson s relations ( mean density vs.  size , velocity dispersion vs.  size and mass spectrum ) and discusses the importance of each one of them , by comparing physical and observational space , and  [ summary ] draws the main conclusions . in the present work we analyze driven , supersonic , hydro- and magnetohydrodynamical ( mhd ) models described by @xcite . details of the models and forcing can be found there . here we just mention that the models are solutions of the mass , momentum and induction equations using zeus-3d @xcite at a resolution of @xmath3 and @xmath4 zones . they include periodic boundary conditions in each direction and an isothermal equation of state , implying that the simulations are scale free . they are forced at a characteristic scale given by the wavenumber @xmath1 and at a constant energy injection rate @xmath0 , with an initial magnetic field intensity @xmath2 . table [ simulations ] shows the parameters of those simulations . the first column shows the name of the run , following the notation in @xcite of the alfvn velocity to the sound speed , with x representing 10 . ] in columns 2 , 3 and 4 we show the driving luminosity , wavenumber and initial intensity of the magnetic field intensities . column 5 shows the value of the root mean square of the density fluctuations @xmath5^{1/2}.\ ] ]    these simulations were performed to model the interior structure of molecular clouds , at scales of 0.01 - 1  pc , densities of @xmath6  cm3 , and temperatures of @xmath7  k. under these conditions , the isothermal equation of state is a reasonable approximation to the full thermodynamics of the cloud . other works focussing on larger scales ( 10 - 1000  pc ) have explicitly included heating and cooling , a star formation scheme , and so forth @xcite , but these are not necessary to study the scales we are concerned with . a bigger omission in our simulations is the lack of self - gravity , which will play a role in the production of dense cores @xcite . nevertheless , we find the non - self - gravitating simulations useful to study superposition effects , and their consequences in the statistical properties observed for clumps . even more , since our results are consistent with other works that include self - gravity , we conclude that its lack in our simulations is not relevant for the conclusions stressed here . a similar conclusion has recently been reached by @xcite , who studied wavelet transforms of self - gravitating mhd turbulence and found that the overall structure was decoupled from that of the densest cores . we analyze the numerical data first by analyzing the physical variables such as density , velocity , and magnetic fields themselves , and second by simulating observations of the models . in previous work @xcite we represented the line profiles of the simulations as histograms of the velocity weighted by density . however , those line profiles did not include the effect of temperature in broadening the profiles , and did not account for optical depth effects . therefore we calculate the radiative transfer here , assuming local thermodynamic equilibrium ( lte ) for the population of the molecular energy levels , which is a sufficiently good approximation to study qualitatively the effects of projection and superposition ( velocity crowding ) of structure in the cloud . in order to model differences when observing the same region with different tracers , we took into account that at low densities the molecules will be underexcited . to do this we made the very simple assumption that the lines are excited only if the density is above 650  cm3 for the @xmath8co(1 - 0 ) transition , 6200  cm3 for @xmath8co(2 - 1 ) , and 1.8@xmath94 for cs(1 - 0 ) @xcite . in other words , we assume lte if the local density is larger or equal to these density thresholds for each transition .    because the simulations are scale - free , the units of density , temperature and length are arbitrary , but the included physics is adequate to represent the behavior of molecular gas with length scales between thousands of astronomical units for the densest cores , up to several parsecs . for the construction of the @xmath8co(1 - 0 ) , ( 2 - 1 ) and cs(1 - 0 ) line profiles , we adopted solar abundances ; and typical scales for the density and length of @xmath10  cm3 and @xmath11  pc , respectively . since the simulations are isothermal , we choose the temperature equal to 10  k. these choices produce regions that are mostly optically thin in both @xmath8co  and cs .    in the production of line profiles , we fixed the number of velocity channels at 32 . this choice results in a velocity resolution of 0.06  km  s@xmath12  for the less energetic simulations , and of 0.2  km  s@xmath12  for the more energetic cases . these resolutions are comparable to the velocity resolution of typical observations of molecular clouds at fcrao which is 0.08  km  s@xmath12 , or in large - scale surveys like the full galactic co survey by @xcite which reaches resolutions as high as 0.26  km  s@xmath12 .    since we know the detailed density and velocity distribution , and assume a constant temperature , in order to determine the emission from any given molecular transition we just have to integrate the corresponding transfer equation , @xmath13 where @xmath14 is the intensity ; @xmath15 is the source function , which we assume to be a blackbody at @xmath16  k ; @xmath17 is the distance along the ray ; and @xmath18 is the mass absorption coefficient of the line , and has units of [ @xmath19 gr@xmath12 ] . in order to integrate equation ( [ transfer ] ) along the line of sight we solve , in practice , the following equations : @xmath21 and @xmath22 where @xmath23 represents the background intensity and @xmath24 is the total optical depth of the cloud , and @xmath25 is the local mass density . since the models have constant elements of volume ( zones ) , the integration over @xmath26 becomes a summation with constant step equal to the zone size . the absorption coefficient @xmath18 is _ = a_ij c^28 ^ 2 g_ig_j ( v ) [ kappa ] where @xmath27 is the einstein coefficient for the @xmath28 transition if the density is larger than the threshold density for excitation , and zero if the density is smaller ; @xmath29 and @xmath30 are the statistical weights of the upper and lower states respectively ; @xmath31 is the numerical density of molecules in the lower state ; and @xmath32 is the line profile , which is assumed to be thermal . these last two parameters take the form n_j = g_j q^-1 , and ( v)=c(m_mol2kt)^1/2 ( -m_mol ( v - v_0)^22kt ) , where @xmath33 is the mean molecular mass of the gas ( assumed to be 2.5 times the mass of the hydrogen atom ) , @xmath34 is the mass of the emitting molecule , @xmath35 is its molecular abundance relative to the hydrogen ( assumed to be solar ) , @xmath36 is the partition function , and @xmath37 is the velocity of the zone , which is known . the molecular parameters are given in table  [ molecules ]      in order to represent and compare the physical and observational spaces in two - dimensional plots we integrate over one of the dimensions . in particular , when we integrate in the @xmath38 direction the physical space , the corresponding observational cube is integrated in the @xmath39 direction . this will allow us to compare , whether a clump in a position - velocity diagram has a counterpart in the position - position diagram . then , when we label a plot as @xmath40 or @xmath41 , we show the column density field integrated in the @xmath42 direction , after zeroing all those points where the density is smaller than the density threshold ( see table [ molecules ] . ) the corresponding observational plot will be @xmath43 or @xmath44 respectively , and then represents the simulated observation of the @xmath45 map as seen by an observer located at the left of the plot , assuming @xmath8co(1 - 0 ) or @xmath8co(2 - 1 ) emission as described above . the first problem that appears when we study the properties of clouds and clumps is how to define them . for instance , if we are interested in studying large complexes and their substructure , we define a complex as a connected set of points with intensity above an arbitrary threshold @xcite . when we work in physical space , the `` intensity '' is the actual density . if we work in the observational space , the `` intensity '' is the brightness temperature . if instead , we are interested in studying individual clumps , we define a clump as a connected set of points below a local maximum following the intensity _ only _ downwards until the threshold is reached . this scheme has been implemented by @xcite in a code called clumpfind . a single large cloud with internal structure in the first scheme may be counted as several smaller clumps in the second scheme . other schemes are also used . for example , one can assume that clumps have a gaussian distribution of intensity @xcite , so that a clump defined as single by clumpfind  can be decomposed into several gaussian substructures .    in the present work we will use clumpfindfor simplicity . differences between methods will be discussed in future contributions , but it is worth noting that , as @xcite has shown , these methods can not identify clumps larger than a few resolution elements . we analyze how the parameters of the simulations ( driving strength and wavelength , magnetic field strength ) affect the structure in both observational and physical space . in particular , we attempt to give observational criteria to help determine the equivalent parameters of the physical mechanism driving the observed turbulence . we begin by comparing models with the same driving wavenumber and magnetic field , but different driving strengths . in table  [ simulations ] we see that the larger the driving strength @xmath0 , the larger the density fluctuations . this occurs because the rms mach number in the simulations depends on the driving strength and the wavenumber as @xmath46 @xcite , and the density contrast across an isothermal shock depends on the mach number as @xmath47 . figure  [ maps_l ] shows maps of both the physical column density and the observed emission for two hydrodynamical models with the same wavenumber ( @xmath48 ) , but driving strength different by a factor of 100 : model ha8 ( @xmath49 ) and model he8 ( @xmath50 ) . the main difference between these extreme cases is that ha8 has larger column densities of low - density tracers , and lower column densities of high - density tracers . another clear difference is that in high - density tracers ha8 shows well - separated , roundish cores , while he8 shows a more filamentary structure with few compact cores . these differences can be understood as follows . when the turbulence is weakly driven ( ha8 ) , density fluctuations are small . there will be few regions with density below the density threshold for the low density tracer ( @xmath8co(1 - 0 ) ) , so most of the cube will emit in that line , but conversely only a few places will have densities higher than the threshold for the high - density tracer ( @xmath8co(2 - 1 ) ) , so only a small column density is seen in that line . conversely , for strong driving ( he8 ) , the fluctuations around the mean are larger , and more regions will have densities either below the threshold for @xmath8co(1 - 0 ) or above the threshold for @xmath8co(2 - 1 ) , so that the mean column density for @xmath8co(1 - 0 ) is lower , but the mean column density for @xmath8co(2 - 1 ) is larger . stronger driving leads not just to higher densities , but more extreme fluctuations , as indicated by a greater fraction of material at both high and low densities . since structures in the simulations are produced by the convergence of turbulent flows , the smaller the driving wavenumber , the larger the dominant structures . we can see this effect in figure  [ maps_k ] , where we show four maps for hc2 and four maps for hc8 , both with the same driving strength ( @xmath51 ) , but different wavenumber ( @xmath52 and  8 respectively ) . from these plots we can see that the density structure is more homogeneously distributed in the case of high wavenumbers ( hc8 ) , in both physical and observational spaces . on larger scales , this suggests that _ large molecular clouds might be the result of turbulence driven at large scales in the diffuse interstellar gas ( see , e.g. , @xcite ) , and not the agglomeration of small clouds by the action of the self - gravity _ , as in some models of molecular clouds ( e.g. , @xcite )    the effect of magnetic fields in our models is consistent with previous work using simulations of the diffuse interstellar medium by @xcite , who showed that weak magnetic fields decrease the size of the density fluctuations compared to the hydrodynamic case . for intermediate magnetic fields , the density fluctuations may increase above the hydrodynamic and weak field cases , and finally , for very strong magnetic fields , the density fluctuations decrease again . ( the actual diagnostic they used , as shown in their fig . 8 , is the star formation rate as a function of the magnetic field strength ; but in their scheme the star formation rate depends directly on the size of the density fluctuations ) .    in figure  [ magnetic ] we demonstrate this behavior . the simulations used have intermediate driving strength ( @xmath51 ) and wavenumber ( @xmath53 ) , and three different initial magnetic field strengths of @xmath54 ( hc4 ) , @xmath55 ( mc41 ) , @xmath56 ( mc45 ) . we can understand the dependence of the density fluctuations on the magnetic field strength as follows : weak magnetic fields are strongly tangled by the flow , so that they have a nearly isotropic magnetic pressure that prevents compressions and large density fluctuations , while stronger fields have an anisotropic magnetic pressure that allows larger compressions along the mean field lines , and thus larger density fluctuations . magnetic fields do not noticeably affect the structure of the maps unless they are strong enough to introduce some anisotropy . for example , in figure  [ maps_b_10 ] we show @xmath8co(1 - 0 ) maps of three different simulations , integrated parallel ( @xmath39 ) , and perpendicular ( @xmath38 ) to the initial field direction . from bottom to top , the relative importance of the magnetic field compared to the luminosity of the simulation increases . we show : me21 ( large driving strength , small wavenumber and small magnetic field ) ; ma81 ( low driving strength , large wavenumber and small magnetic field ) ; and ma4x ( small driving strength , intermediate wavenumber and large magnetic field ) . only the strong field case ma4x ( top panels ) shows a morphology different than the hydrodynamic case . in this case , a marked anisotropy is visible , with the projection perpendicular to the magnetic field ( upper left panel ) , showing low - density structures aligned mainly in the direction of the field lines while the projection along the field line ( upper right panel ) presents regular structures , with no preferred direction . interestingly , in a higher density tracer , there is no clear morphological difference between projections along or perpendicular to the initial field ( see fig  [ maps_b_21 ] . ) the maximum values of the column density are similar in both physical and observational projections for small magnetic field intensity . nevertheless , in the strong - field case ( ma4x , see upper panels in fig . [ maps_b_10 ] and  [ maps_b_21 ] ) the column density integrated perpendicular to the mean field ( right panels ) is higher than the column density integrated parallel to it ( left panels ) , as can be seen in the grayscale bars . this effect can be explained in the same way as that shown in figure  [ magnetic ] : strong magnetic fields only allow compressions parallel to the field . therefore , when we observe along the magnetic field lines we do not see high column density contrasts , while when we observe perpendicular to the field lines , we see higher contrasts in the compressions along the field lines . as a summary , _ strong fields can produce anisotropy and compressed structures perpendicular to the field lines , but weaker fields merely reduce the maximum density contrast somewhat . _      velocity crowding contributes substantially to the generation of clumps in observational space , so observed clumps frequently contain emission from physically separated regions @xcite . we demonstrate this effect using a typical mhd simulation : mc41 . we choose this run because it has intermediate values of driving strength ( @xmath51 ) and wavenumber ( @xmath53 ) , and it clearly shows the effects of superposition . figure  [ map_mc41 ] shows physical and observed maps for @xmath8co(1 - 0 ) and ( 2 - 1 ) . we see that clumps in real space ( letters a , b , and c in panel @xmath57 ) do not necessarily have a counterpart in observational space . clumps in observational space , on the other hand , ( letter d in panel @xmath58 ) do not necessarily come from isolated regions in real space , but have contributions from many different regions along the same line of sight . in figure  [ map_mc41 ] we plot dotted lines that show the places where the emission of a physical clump lies in observational space , and where the emission from an observational clump is generated in physical space . for reference , we use the same lines in the @xmath8co(1 - 0 ) map as in the @xmath8co(2 - 1 ) map . for the same data set we made another set of maps using higher density tracers . figure  [ mc41_cs10 ] shows the emission of cs(1 - 0 ) . the same lines are shown as in figure  [ map_mc41 ] , to indicate the location of the large @xmath8co(1 - 0 ) core . in this case , the illusory observational clump d has almost disappeared , and the physical clump a is observed more clearly in its observational counterpart . we also note that the position that we would attribute to the cores in different tracers is slightly different . in order to quantify the effects of superposition , we now compute the typical number @xmath59 of physically disconnected regions that contribute to the emission of a single observed clump . to do so , we developed an algorithm that brackets each observed clump in position and velocity and calculates the number of connected regions in physical space within the bracketed region in phase space .    in figure [ subclumps]_a _ we show the influence of driving strength and wavenumber on the amount of superposition . we find that high - density tracers behave differently than low - density tracers . in the case of a high - density tracer such as cs , @xmath60  23 , and is almost constant for different driving strengths and wavenumbers . on the other hand , in the case of a low - density tracer such as @xmath8co , which emits from most of the cube , superposition increases with driving wavenumber . this is a natural consequence of the way we forced the models , since short - wavelength driving produces multiple physical regions at the same velocity . there is also a marginal tendency for strongly - driven models to exhibit more superposition than weakly - driven ones . this occurs because the greater velocity dispersion in the strongly - driven model produces clumps with greater internal velocity dispersion that more easily overlap . we conclude that higher - density tracers will better disentangle velocity crowding , as is shown by the results using cs(1 - 0 ) , though still by no means completely .    in figure [ subclumps]_b _ we show the relative influence of the magnetic field by examining @xmath59 as a function of the ratio of the driving strength to the initial magnetic field strength @xmath61 . we find that the amount of superposition is a bit larger when we observe along the mean field direction ( @xmath39 ) than when we observe perpendicular to it . the effect is small , but present , and it is a consequence of the greater compressions parallel to the field lines producing more condensed clumps with smaller cross - sections for superposition when observed perpendicular to the field lines . a final word concerning superposition is in order : although it is true that high spatial resolution helps to segregate large clouds into their clumps , high velocity resolution does not necessarily help to disentangle superposition . it only helps if there is a monotonic velocity gradient along the line of sight , such that two clumps with similar velocities merge at low velocity resolution , and can be separated at higher velocity resolution . if clumps are produced in regions of converging flow in a larger turbulent region , however , as is likely the case in real clouds , then the velocity gradients will not be monotonic , and physically disconnected regions will often share the same line - of - sight velocity , so increasing velocity resolution will not help .    as a summary , we conclude that velocity crowding is likely to always occur , implying that cores in observational space are not single entities in real space , and that it is larger for low - density tracers , large driving wavenumbers , and when we look along the mean field lines . if observed clumps have contributions from multiple physical regions , it is important to understand whether the relationships reported for observed clumps in molecular clouds have anything to do with the properties of the actual physical clumps . @xcite studied the dependence on size of the mean density , velocity dispersion , and mass spectrum of the clouds in a sample of observational data taken from the literature . he found    @xmath62    @xmath63    and    @xmath64    the most commonly quoted values in the literature are @xmath65 , @xmath66 , and @xmath67 . in particular , values of @xmath68 and @xmath69 have been attributed to virial equilibrium @xcite . however , there is some discrepancy in the values reported @xcite , especially for high latitude clouds , where the velocity dispersion - size relationship has been questioned @xcite . @xcite himself already suggested that the relationships he identified might be due to the limitations of the observations , but it was @xcite who first demonstrated that the observed mean density - size relationship could be due to observational effects , and that the observed and physical properties such as radius or volumetric density may be quite different . @xcite showed that co and extinction saturate at roughly the same column density , which forms the upper envelope of the mean density - size relationship . he also discussed how the surveys are biased due to the limitations of instrumental sensitivity and saturation . @xcite reproduced the mass spectrum , as well as the velocity dispersion - size relationship ( although with large scatter ) for clumps in physical space , using two - dimensional models . they reported the lack of a mean density - size relationship , confirming numerically the analysis by kegel ( 1989 , see also the discussions in @xcite and @xcite ) in the sense that there are clouds with small sizes and low column density that will be undetected in observational surveys . more recently , @xcite reported a slope close to @xmath70 for the mean density - size relationship derived from simulated observations of their models , and a very flat correlation between velocity dispersion and size ( @xmath71 ) . as they mentioned , both results are a consequence of their clump finding method ( based on what they call regions of contrast ) , which samples the entire line of sight . none of these studies attempting to explain the origin of the @xcite relationships have compared simulated observations to the actual physical density and velocity distributions for the same numerical model . we now do that , using the three - dimensional simulations of molecular clouds that we have described above . we must first define the size of a clump , both in observational and in physical space . for clumps drawn from simulated observations we take the circular radius , defined as @xmath72 , where @xmath73 is the projected area of the clump on the plane of the sky , for comparison with wgb94 . for physical clumps we take the geometric radius , defined as @xmath74 . other definitions are equally valid , but can lead to differences of a factor up to half an order of magnitude when comparing different size definitions , and differences of as much as a factor of 100 when calculating mean densities by dividing the total mass by the size .    finally , since the results discussed in the present section do not appear to depend on the parameters of the runs we analyze or ( in the magnetic case ) on the projection with respect to the mean magnetic field , we only present results for run hc8 - 256 ( see table  [ simulations ] ) , an available high - resolution run ( @xmath4 zones ) . we search for clumps in physical space using clumpfind , considering only regions with a density larger than 650  cm3 , the critical density for @xmath8co(1 - 0 ) emission . the results do seem to depend on the clumpfinding scheme used and on its parameters . for example , the number and size of the clumps found in clumpfinddepends on the level of refinement used in clumpfind : at high refinement , large clumps can be split into multiple smaller clumps , changing not only the slope of the mass spectrum , but also the dynamical range of size in the scaling relations .      in fig .  [ rhomeanfig ] ( upper panel ) , we show the mean density - size relationship for clumps in three - dimensional physical space . we note three points about this figure . first , the relation between mean density and size given by equation  ( [ rhomean ] ) is not seen at all , confirming the results of vbr97 from two - dimensional models . second , there is a minimum density below which there are no clumps identified . this minimum is just given by the density threshold we used in clumpfind . third , even though the simulations exhibit a large dynamical range in density ( @xmath75 ) , the dynamical range in the mean density - size relationship is small , because in constructing such a plot we choose the clumps around the local density maxima .    in the middle and lower panels of fig . [ rhomeanfig ] we show the mean density - size relationship for clumps in simulated observational maps of the same run , integrated along the @xmath38 axis . the middle panel is the one obtained by using cs(1 - 0 ) , and the lower panel is the relationship obtained by using @xmath8co(1 - 0 ) . the observed clumps do exhibit approximately the relationship given by @xcite , despite the lack of correlation exhibited by the physical clumps in this model . we conclude from this demonstration that the observed density - size relationship ( eq .  [ [ rhomean ] ] ) is an observational artifact . two mechanisms have been suggested to explain density - size relationship with slope @xmath76 in observations . first , it might be due to the selection effect described by @xcite : only clouds with intensity exceeding the noise threshold determined by the instrumentation will be detected , effectively setting a column density cutoff , rather than the physical density cutoff imposed in the physical density - size relationship . a constant column density cutoff produces a cutoff with slope @xmath70 in the mean density - size plane ( middle and lower panels ) , just as the constant physical density cutoff in physical space produces a flat cutoff . second , it might be due to the limited dynamical range of the observations @xcite . to understand this , lets consider the simulations : if we had clumps with constant column density @xmath77 , we would infer a mean density @xmath78 , giving exactly a slope of @xmath70 . in the simulation analyzed here we do not have a constant column density , but the column density varies by only a factor of 30 ( see burkert &  mac low 2001 ) , far less than the variation in physical density . even worse , from this narrow distribution , the selected clumps have an even narrower column density distribution : on the one hand , as we already mentioned , there is a column density cutoff given by the minimum intensity used in clumpfind ; on the other hand , even the emission of the brightest clump does not come from the whole line of sight , and its column density is not the largest column density available in the simulation . the end result is that selected clumps naturally end up with column density constant to within an order of magnitude , consistent with the observed scatter in the middle and lower panels of fig . [ rhomeanfig ] . similar arguments can be applied to the observational data . for example , when observing emission lines from molecules , there is a limited dynamical range in density available in which any particular tracer can be excited : it will not be excited at too low density , and it will become optically thick at too high a density @xcite . at iras wavelengths , @xcite claim constant column densities in iras observations of dust , where the dynamical range of the data should have allowed detection of any significant variations . however , @xcite showed that for iras observations , only the external layers of the clouds are heated by the diffuse uv radiation , so that the emission at 60 and 100  @xmath79 m actually comes from surface layers that are indeed expected to have nearly constant column density .    finally , we point out that deviations from the mean density - size relationship have also been found in observations @xcite , suggesting that with sufficient care , the trap of apparently constant column density can be overcome .      in figure  [ deltavfig ] we show the velocity dispersion - size relationship for clumps in physical and observational space . in the case of physical space ( upper panel ) the typical velocity dispersion is of order of 0.2  km  s@xmath12 , a value that coincides with the value of the fluctuations of the overall velocity field for the run analyzed here ( hc8 - 256 ) . the slope fit to the data is 0.3  @xmath80  0.38 , smaller than the value of 1/2 suggested for compressible turbulent behavior ( see , e.g. , vbr97 ) , but with a strong scatter . in fact , in order to reduce substantially the uncertainty in the determination of the slope , we should have at least two orders of magnitude of dynamical range in sizes if the scatter is about one order of magnitude , as it is the case . but with clumpfind , it is difficult to have a large dynamical range ( see , e.g. , upper right panel of fig 7 in @xcite ) , since a reasonable refinement of the intensity contouring makes large clumps split up into several pieces @xcite .    on the other hand , when we analyze observational data as in fig  [ deltavfig ] ( lower panel ) , additional problems play a role . we now have the possibility that substantial superposition is occurring , in particular for low - density tracers . if this is so , the velocity dispersion of a single observed clump will reflect the velocity dispersion of several , physically disconnected regions in the same line of sight . this will also help to produce both large mean values of @xmath81 ( 0.8  km  s@xmath12 , compared to the 0.2  km  s@xmath12corresponding to the mean velocity fluctuations in the simulation ) and low values of the slope in the velocity dispersion - size relationship ( fig . [ deltavfig ] , lower panel ) . in contrast , for high density tracers ( cs(1 - 0 ) , fig.[deltavfig ] , middle panel ) , we obtain a steeper relationship ( 0.46 ) , and the mean velocity dispersion drops back to @xmath82  km  s@xmath12 . three reasons why this occurs are : in the case of high density tracers there is weaker superposition as shown in fig . [ subclumps ] ; clumps are substantially smaller than in the low - density case , giving smaller velocity dispersion ; and the sizes span about one and a half orders of magnitude , favoring disentanglement between the scatter and the actual trend . now we turn to the clump mass spectrum . before showing the mass spectra for the simulations , we have to think about the nature of the turbulent density structure and how clumpfind  ( or any other clumpfinding algorithm ) works . for instance , in a driven turbulent medium , such as the simulations we examine here , we expect density fluctuations at all scales above the dissipation scale . it is not at all clear when to stop counting substructure inside structure . in other words , should we look for all the stones in the small hills in every single mountain of the mountain chain , or only count the larger mountains ? if only the larger mountains , how do we define a lower limit ? intuitively , we might think that the dependence of clump numbers on clumpfind  parameters would be reduced in regions where clumps are well defined and reasonably isolated , as in an isolated star - formation region where cores have suffered some amount of collapse . to show that this is _ not _ the case , we show in figure  [ mapa_hc8 ] a contour map of a slice through the center of model hc8 . we use five and ten isocontours between an arbitrary density threshold of @xmath83 and the maximum density @xmath84 . as we can see , the density structures seem to be well - separated and reasonably well defined . in figure  [ closeup_hc8 ] we present an enlargement of the lower - right corner of figure  [ mapa_hc8 ] , again using five and ten isocontours . we see that , even for the same density threshold , by changing the number of isocontours we find five more peaks ( see right panel in fig .  [ closeup_hc8 ] ) that will result in five new clumps in clumpfind . this happens in just a small region containing what we would think of as well - defined structures , at a single slice in @xmath39 . but in practice , we have 3d structures , so that every structure is far more complicated than apparent at first glance . even without considering whether observational and physical clumps are the same or not , the mass spectrum appears to be more an artifact of the manner in which we count clumps than an actual physical characterization of the structure , unless we count them exhaustively all the way down to the numerical or physical dissipation scales below which there is no longer well - defined structure . we note also that in the case of self - gravitating simulations the result is the same ( ossenkopf et al . 2001 ) , and that similar results will hold for observations : at low resolution the structures look soft , but once we increase the resolution and the sensitivity , structure emerges inside the structure , as is clear from figure  4 in dame et al . .    preliminary work by @xcite shows that , by setting the density threshold in physical space to the average density , a large enough number of contour levels gives a log - normal mass spectrum , independently of the number of contours used . we compute the mass distribution using this prescription for run hc8 smoothed at a resolution of @xmath85 for physical space , and @xmath86 velocity channels for observational space in order to avoid excessive computation time and memory usage by clumpfind . the results are shown in fig . [ masspec ] . the upper panel corresponds to physical space , and the lower panel corresponds to observational space , where instead of density , we used intensity contouring . the results are clear : for large number of isocontours the shape of the mass spectrum converges . good agreement is observed in the large - mass end of the distribution , although slower convergence is observed at the low - mass end . convergence to a factor of two for the full spectrum appears to be reached for 64 or more contours .    in fig . [ lognormal ] we compare the mass spectrum calculated in physical space ( bold line ) to that from observational space ( thin line ) using 512 isocontours . the dotted parabola shows a log - normal fit that reproduces fairly well the large - mass end of the spectra . such log - normal behavior of the observed spectrum might explain observations obtained for dense cores in the last few years . in particular , @xcite found a power - law mass spectrum with slope of @xmath87 for star - forming cores in serpens , substantially larger than the standard @xmath88 value . moreover , @xcite found a change in slope at low mass : the less massive cores exhibit slope of @xmath88 , considerably shallower than the @xmath89 slope found for the more massive cores . finally , we note that in these works , the mass spectrum was obtained using dust continuum observations with high signal - to - noise ratios . for present - day molecular - line observations , typical signal - to - noise ratios of 10 or less do not allow small contour separation , since contouring at less than the signal - to - noise ratio is meaningless @xcite . mass spectra derived from such observations are likely to be far from physical ( fig . [ masspec ] ) . we analyze a set of three - dimensional mhd numerical simulations at intermediate ( @xmath3 zones ) and higher ( @xmath4 zones ) resolution described by @xcite , in which the parameters driving strength ( @xmath0 ) , driving wavenumber ( @xmath1 ) , and initial magnetic field ( @xmath2 ) are varied . we show that :    * density fluctuations are primarily controlled by the driving luminosity : the larger the luminosity , the larger the fluctuations seen in the maps . morphology of the density structure , on the other hand , is primarily controlled by the driving wavelength : the larger the driving wavelength , the larger the structures seen in the maps , and vice - versa . * the magnetic field only produces detectable effects in our simulated molecular line observations if the fields are strong and in the plane of the sky , and the structure is observed in low density tracers . when observing magnetized clouds , it is slightly easier to obtain larger column densities if the field is in the plane of the sky than if it is perpendicular to it . * simulated observational maps of the models show strong superposition of structures along the line of sight . this implies that single clumps in observational space are frequently the superposition of multiple clumps in physical space . the apparent properties of observed clumps are poorly related to the physical properties of their constituent objects if strong superposition occurs . * we explore the effect of the simulation parameters on the generation of strong velocity crowding , finding that large driving strength and large wavenumber tend to favor velocity crowding . so far , the only more - or - less reliable method to ensure there is no substantial superposition of clumps is to use high - density ( close to the maximum density ) tracers . nevertheless , even in those situations superposition can occur . * larson s ( 1981 ) mean - density to size relationship does not exist in physical space , but does occur in our simulated observations . it appears to be an observational artifact , whose explanation we discuss . * larson s velocity - dispersion to size relationship is reproduced in both physical clumps and simulated observations , though with substantial scatter in the slope . more dynamical range in the simulations would probably help , although our clumps already span an order of magnitude in size with half an order of magnitude in scatter . * the mass spectra converge to a particular shape only when we use large number of contours ( above 32 for the high mass end , but above 64 for the whole spectrum ) , corresponding to an extraordinarily large signal - to - noise ratio in the observations . rather than a single power law , they seem to follow a log - normal distribution . ballesteros - paredes , j.  & vzquez - semadeni , e.  1997 , in star formation near and far , eds . holt & l.g . aip conference series 393 , 81 ballesteros - paredes , j. , vzquez - semadeni , e. , & scalo , j.  1999 , , 515 , 286                                                                  sheth , k. , vogel , s. n. , wilson , c. d. , and dame , t. m. 2000 , in `` the interstellar medium in m31 and m33 '' , proceedings 232 . we - heraeus seminar , 22 - 25 may 2000 , bad honnef , germany . edited by elly m. berkhuijsen , rainer beck , and rene a. m. walterbos . ( shaker : aachen ) 2000 , p. 37 . vazquez - semadeni , e. , ostriker , e.  c. , passot , t. , gammie , c.  f. , & stone , j.  m.  in 2000 , protostars and planets iv , eds mannings , v. , boss , a.p . , russell , s. s. ( tucson : university of arizona press ) , p. 3 williams , j. p. , de geus , e. j. , &  blitz , l. 1994 . , 428 , 693        rrrrr ma81 & 0.1 & 8 & 0.1 & 0.68 + mc81 & 1 & 8 & 0.1 & 1.21 + mc85 & 1 & 8 & 0.5 & 1.56 + mc45 & 1 & 4 & 0.5 & 1.83 + ma4x & 0.1 & 4 & 1 & 1.27 + mc4x & 1 & 4 & 1 & 2.21 + mc41 & 1 & 4 & 0.1 & 1.35 + me21 & 10 & 2 & 0.1 & 2.32 + hc4 & 1 & 4 & 0 & 1.97 + hc8 & 1 & 8 & 0 & 1.40 + hc8 - 256 & 1 & 8 & 0 & 2.00 + ha8 & 0.1 & 8 & 0 & .71 + hb8 & 0.3 & 8 & 0 & 1.05 + hd8 & 3 & 8 & 0 & 1.82 + he8 & 10 & 8 & 0 & 1.97 + he4 & 10 & 4 & 0 & 2.39 + hc2 & 1 & 2 & 0 & 2.21 + he2 & 10 & 2 & 0 & 2.50    r c c c r r c @xmath8co(1 - 0 ) & @xmath90 & @xmath91 & 0.112 & 1.43 @xmath92 & 650 cm3 & 1,2 + @xmath8co(2 - 1 ) & @xmath93 & @xmath94 & 0.112 & 1.43@xmath95 & 6200 cm3 & 1,2 + cs(1 - 0 ) & @xmath96 & @xmath97 & 1.957 & 1.0 @xmath98 & 18000 cm3 & 1,2 +
we examine the question of how well the physical properties of clumps in turbulent molecular clouds can be determined by measurements of observed clump structures . to do this , 
 we compare simulated observations of three - dimensional numerical models of isothermal , magnetized , supersonic turbulence to the actual physical structure of the models . 
 we begin by determining how changing the parameters of the turbulence changes the structure of the simulations . 
 stronger driving produces greater density fluctuations , and longer wavelength driving produces larger structures . 
 magnetic fields have a less pronounced effect on structure , and one that is not monotonic with field strength . 
 aligned structures are seen only with low - density tracers , and when the intensity of the field is large . comparing different regions with the same tracers ( or conversely 
 , the same region with different tracers ) can give information about the physical conditions of the region . 
 in particular , different density tracers can help determine the size of the density fluctuations and thus the strength of the driving . 
 nevertheless , velocity superposition of multiple physical clumps can fully obscure the physical properties of those clumps , and short wavelength ( compared to the size of the region under analysis ) driving worsens this effect . 
 we then compare larson s relationships and mass spectra in physical and observational space for the same structure dataset . 
 we confirm previous claims that the mean density - size relationship is an observational artifact due to limited dynamical range in column density : it is the inevitable consequence presence of a lower cutoff in column density . the velocity dispersion - size relationship , on the other hand , 
 is reproduced in both physical and observed clumps , although with substantial scatter in the derived slope , consistent with observations . 
 finally , we compute the mass spectra for the models and compare them to mass spectra derived from simulated observations of the models . 
 we show that , when we look for clumps with high enough resolution , they both converge to the same shape . 
 this shape appears to be log - normal , however , rather than the power - law function usually used in the literature .