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observations of spiral galaxies indicate that the presence of a central structure called a _ bar _ is a common feature@xcite .
the instability of isolated stellar disks in galactic models leads to bar formation and is characterized by toomre s stability parameter @xmath2@xcite .
the models with @xmath3 are subject to bar formation .
however , we are interested in dynamical effects of non  isolated systems which are found in clusters of galaxies . in this regard
, it has been suggested that the observed bar in many spirals is the result of the gravitational interaction between two or more nearby galaxies .
for instance , nogushi@xcite has found that , during the collision of two galaxies and between the first and the second closest approaches , the disk takes on transient bar shape .
the gravitational interaction between the two galaxies gives rise to perturbations in the orbits of the stars that results in the formation of the bar .
bar formation in the simulations of stellar disks depends upon various simultaneous effects . in the case of collisions ,
these factors are@xcite : rotation curve shape , disk - halo mass ratio , perturbation force and geometry .
however , simulations can suffer from numerical effects such as low spatial and temporal resolution , too few particles representing the system and an approximate force model .
these effects can be drastic : for example , observations show that bars have typically a length scale close to the exponential length of the disk@xcite , while the bar s semi - major axis obtained from numerical models is two to four times longer@xcite .
recent observational data measured in the cosmic microwave background at various angular scales , in supernovae ia , in the 2df galactic survey , and baryon acoustic oscilations , suggest @xcite that the universe is composed of about @xmath4 baryons in the form of gas and stars , @xmath5 dark matter ( dm ) and @xmath6 dark energy , which is a kind of cosmological constant and is responsible for the today accelerated expansion of the universe . in this way
, galaxies are expected to possess these dark components and , in accordance with rotation curves of stars and gas around the centers of spirals , this might be in the form of halos , and must contribute to at least 3 to 10 times the mass of the visible matter of spirals .    regarding to the nature of dm , we know that dm has to be non  baryonic .
this is because nucleosynthesis abundances of light elements are only consistent with the above  mentioned baryonic fraction , and this is not sufficient at all to account for rotational velocities of spirals .
this fact opens up new possibilities for explaining the nature of dm . in this sense , in papers @xcite a model was proposed in which a scalar field ( sf ) couples non - minimally to gravity to produce locally a modified newtonian theory of gravity .
it turns out that the dynamics is now determined by the poisson equation coupled to a klein  gordon equation for the assumed scalar field in the galaxy .
thus , the boson mass of the scalar field modifies the newtonian law of attraction , and the dynamics of dm is different from its newtonian counterpart . in this scalar 
tensor theory potential 
density pairs for various halo density profiles were computed@xcite .    in the present work we use the above - mentioned results to study the collision process of two spirals , each of which possess a disk , bulge and dark halo , in order to estimate the effects of the modified gravity theory on the bar s length and the orbital decay of galaxies .
a numerical treecode was developed by one of us ( marm ) in order to compute the evolution of an @xmath7-body system interacting with the standard gravity plus the interaction of the scalar field@xcite .
we first study dynamical effects on isolated galaxy models for three different interaction scales ( @xmath1 ) .
we found no significant changes in the morphology of models , but we did in the total potential energy .
then , we analyze the formation of a bar during a parabolic collision of two identical galaxies and compare the results obtained in the sf model with three scales of @xmath1 and with a pure newtonian interaction .
a typical scalar  tensor theory is given by the following lagrangian @xmath8 + { \cal l}_m(g_{\mu\nu } ) \ ; , \ ] ] from which we get the gravity and sf equations . here
@xmath9 is the metric , @xmath10 is the lagrangian matter and @xmath11 and @xmath12 are arbitrary functions of the sf .
according to the newtonian approximation , gravity and sf are weak , and the velocities of the stars are non  relativistic .
then , we expect to have small deviations of the sf around the background defined here as @xmath13 .
if we define the perturbation @xmath14 , then the newtonian approximation gives the equations @xcite @xmath15 where @xmath16 .
here we define @xmath17 , the compton wavelength of the effective mass @xmath18 of some elementary particle ( boson ) given through @xmath11 and the potential @xmath12 , and @xmath19 is the amplitude of the perturbed sf , @xmath20 .
the above formalism is valid for any potential that can be expanded in taylor series around @xmath21 .
in what follows we will use @xmath1 instead of @xmath22 .
this mass can have a range of values depending on particular particle physics models .
general solutions of eqs .
( [ rio_eq_psiphibar ] ) can be found in terms of the corresponding green s functions and the new newtonian potential is @xmath23    solutions of these equations for point masses are @xmath24 where @xmath25 with @xmath26 being a source mass .
the total gravitational force on a particle of mass @xmath27 is @xmath28 the potential @xmath29 is the newtonian part and @xmath30 is the sf modification which is of yukawa type .
we use the monte - carlo procedure to construct a galaxy model with a newtonian potential .
a fully self  consistent model in the context of the sf is in preparation .
the initial conditions of the galaxies are constructed following the model described by barnes@xcite . in this model , both the bulge and halo are non - rotating , spherically symmetric and with an isotropic gaussian distribution of velocities characterized by the velocity dispersions @xmath31 and @xmath32 , respectively .
the units are such that the local ( @xmath33 ) gravitational constant is @xmath34 , and the units of mass , longitude and time are @xmath35 m@xmath36 , @xmath37 kpc and @xmath38 myrs , respectively .
the bulge density profile is@xcite @xmath39 and the halo density profile is a dehnen s family member with @xmath40 @xcite @xmath41 the disk density profile is exponential @xcite @xmath42 here @xmath43 , @xmath44 , and @xmath45 are the total mass of the bulge , disk , and halo , respectively .
the scale lengths of the bulge , halo , and disk are @xmath46 , @xmath47 , and @xmath48 , respectively , and @xmath49 is the scale height of the disk .
the mass distributions were truncated at a radius containing @xmath50 of the total mass , since they extend to infinity .
the compound galaxy was sampled with @xmath51 equal mass particles .
the velocity distribution of the disk is given by the schwarzschild distribution function with the velocity dispersions @xmath52 , and @xmath53 given by the equilibrium condition of an infinite gravitating sheet ; @xmath54 is calculated from the epicyclic approximation .
the toomre s parameter of initial disk is @xmath55 , so we have the disk which is marginally stable for axisymmetric perturbations , but not , however , against strong non - axisymmetric ones .
observations suggest that the majority of the interacting galaxies are located on nearly parabolic orbits .
for all the collisions , disks were located in the plane of parabolic orbits , calculated from parameterized equations of the two - body problem , with a pericentric separation @xmath56 , and the time to pericenter @xmath57 .
the direction of rotation of one of the disks ( disk 1 ) was in the same direction as the corresponding orbital - angular - momentum , i.e. , direct motion .
the other disk ( disk 2 ) was in retrograde motion .
the two colliding galaxies are initially identical .
for the time evolution we use a barnes tree code type@xcite modified to include the newtonian contribution of the scalar fields as given by eqs .
( 4)-(8 ) @xcite .
the forces were computed with a tolerance parameter @xmath58 , and including the monopole term only . for the gravitational potential we used the standard plummer model @xmath59 here , @xmath60 is the softening parameter taken in our simulations to be @xmath61 .
the equations of motion were integrated using the second order leap  frog algorithm with a fixed time step @xmath62 . with these parameters
we obtain a good energy conservation ( @xmath63 ) and , also , good angular momentum conservation ( @xmath64 ) for all runs presented here .    to characterize quantitatively the bar amplitude , we consider the distortion parameter defined as@xcite @xmath65 where @xmath66 and @xmath67
the particles that are outside of the spatial region of the original disk can affect the parameter under study .
for instance , if we calculate the distortion parameter using all the particles in the disk , we have in both cases similar evolution curves .
therefore , to avoid the noise , we exclude particles that are outside of the original radius of the disk .
we first study isolated galaxy models with different values of @xmath1 .
we consider four set of simulations followed up to time @xmath68 .
the parameters and results of runs are presented in the table , where @xmath69 and @xmath70 are the initial and mean total energies , and @xmath71 is the relative change of the total energy during the evolution with respect to its initial value .
though the scale of interaction @xmath1 and magnitude of @xmath0 are unknown , we choose their values arbitrarily , such that @xmath1 is equal to the cutoff radius of the disk , bulge and halo for models a1 , a2 and a3 , respectively , and a fixed amplitude of the sf , @xmath72 .
the larger @xmath1 makes weaker the contribution of sf for a fixed galactic size . for @xmath73
one obtains the newtonian case , model a4 .
previous studies of protogalactic interactions under influence of this sf@xcite were made for scales less than those considered here .    [ cols="^,^,^,^,^,^,^ " , ]      + all models show a good energy conservation ( see table ) .
the presence of the sf decreases the total potential energy due to shallower potential well at distances @xmath74 .
the initial models reaccommodate rapidly due to potential modification , i.e. , shifts to a new equilibrium state . at the end of evolution ,
the components of galaxy models with the sf became slightly more extended .
the velocity profiles of the components match the newtonian ones up to @xmath75 .
for @xmath74 there is a slow decay in velocities , since the effective gravitational constant decreases .
the distortion parameter shows a nearly equal noise level of surface density of the disks .
the evolution of the toomre s local stability parameter @xmath2 shows a slow decay from @xmath55 to @xmath76 with mean values presented in the table for each run .
then , we proceed to study the interaction of two equal galaxy models . during the orbital decay
we analyze the bar s strength for different values of @xmath1 .
because the equilibrium galaxy models were constructed with newtonian potential , we relax them up to time @xmath77 with modified sf potential in order to reach a new equilibrium state for a given @xmath1 .
then we place relaxed galaxies on parabolic orbits and let them interact .
the results are as follows .
the first encounter occurs at time @xmath78 .
this is the time of major transfer of orbital angular momentum , and then disk 1 forms a strong bar , while disk 2 is in retrograde motion and develops a very weak bar .
figure 1 ( left ) presents the separation between the centers of mass , @xmath79 , of two galaxies as a function of time .
all runs , except a1 , after several close approaches merge and form a remnant . in the run with model a1 , after the first approach the galaxies separate such a large distance that they will never encounter again .
this is because the weaker gravity is , the more lessable the galaxies are to become bound : at distances larger than @xmath1 the potential diminishes in comparison with the pure newtonian . in the runs a2 and a3
the sf causes just a retardation of the subsequent interactions .
the simulation with model a3 is practically identical to newtonian one .    in order to analyze the bar formation , we consider following only the disk 1 . in figure 1 ( right )
we plot the distortion parameters @xmath80 as a function of time for runs with galaxy models a2 and a4 only . as a consequence of gravity modification
, the galaxies do not approach each other too closely as happens in the newtonian run .
thus , weaker perturbations make the bar shorter .
the run with galaxy model a3 is very similar to the newtonian case .
the bar s phases are displaced due to orbit modification .     for two collision
runs with models a1 and a3.,title="fig:",width=307 ]   for two collision runs with models a1 and a3.,title="fig:",width=307 ]
from simulations of isolated galaxy models with different @xmath1 , we can see that the addition of a non  minimally coupled sf slightly modifies the equilibrium of newtonian model , acting as a small perturbation , and it diminishes the total potential energy for @xmath74 , since the effective gravitational constant decreases in this range .
our results show that the interaction of galaxies with the sf is weaker in comparison with the newtonian case .
we have found that the inclusion of the sf changes the dynamical properties such as the collision time , bar morphology , and in general the remnant properties .
all these changes depend on the pair ( @xmath0 , @xmath1 ) , which on the other hand , can be constrained from observations .
for instance , the duration of interaction can not be larger than the age of the universe , implying constraints on values of @xmath81 , which depends on @xmath82 and @xmath0 .
these constraints can be provided from statistical data on the fraction of observed interacting galaxies .
a wide range of parameters should be investigated and higher resolution have to be used in simulations in order to make predictions for particular interacting models .
further investigations with more particles and self - consistent initial models are under way .
this work was partly supported by sre and conacyt of mxico under contracts u43534-r , sep-2003-c02 - 44917 .
m.  a.  rodriguez - meza , et al . , in _ exact solutions and scalar fields in gravity : recent developments _ , edited by a. macias , et al .
( kluwer academic / plenum publishers , new york , 2001 ) , p. 213 .
arxiv:0907.2466 [ astro-ph.co ] . m.a .
rodrguez - meza and j.l .
cervantes - cota , _ rev .
( serie de conferencias ) _ * 17 * ( 2003 ) 43 .
we study bar formation in galactic disks as a consequence of the collision of two spiral galaxies under the influence of a potential which is obtained from the newtonian limit of a scalar  tensor theory of gravity . 
 we found that dynamical effects depend on parameters ( @xmath0 , @xmath1 ) of the theory . 
 in particular , we observe that the bar is shorter for weaker tidal perturbations , which in turn corresponds to smaller values of @xmath1 used in our numerical experiments .