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using a large cosmological dark matter simulation , box ; see e.g. @xcite for details . ]
we look at the evolution of the haloes identified at @xmath0 by tracking their properties through their most - massive progenitors at each simulation output time @xmath1 .
we call the change in the properties of a halo between timesteps ( e.g. from @xmath2 ) an _ event _ , and we consider the distribution of events for all the selected particles ( i.e. @xmath3 ) , and have sufficiently large @xmath4 that its orientation is not subject to discreteness bias : @xmath5 ( see @xcite ) . ] haloes in the @xmath6 timesteps from @xmath7 .
in particular , we compute the fractional halo mass change @xmath8 , and the angular momentum direction change @xmath9 , in terms of the halo mass @xmath10 and specific angular momentum vector @xmath11 .
we show the distribution of events in terms of @xmath12 and @xmath13 in the left panel of fig .
[ f : spinflips ] , and their cumulative distributions in the middle and right panels .
these show that major mergers are much more likely to than minor mergers to coincide with spin direction changes of more than a given angle , @xmath14
. however , most events with significant direction change are _ minor _ mergers , not major .    , for major mergers ( @xmath15 ) and minor mergers or accretion ( @xmath16 ) .
right : cumulative fraction of events with @xmath17 , for events where the spin direction changes by more than @xmath18.,title="fig : " ] , for major mergers ( @xmath15 ) and minor mergers or accretion ( @xmath16 ) .
right : cumulative fraction of events with @xmath17 , for events where the spin direction changes by more than @xmath18.,title="fig : " ] , for major mergers ( @xmath15 ) and minor mergers or accretion ( @xmath16 ) .
right : cumulative fraction of events with @xmath17 , for events where the spin direction changes by more than @xmath18.,title="fig : " ]
we use a high - resolution simulation of galaxy formation in a single halo ( see @xcite for details ) , to study the evolving relationship between halo and galaxy spin in more detail , over many hundreds of output times . in fig .
[ f : mainresults ] , we plot the evolution of the angular momentum magnitudes and directions of the total halo dark matter , inner halo dark matter ( @xmath19 ) , and the stellar component of the central disc galaxy . without a merger occurring , the halo flips @xmath20 at @xmath21 ( although its orientation is poorly defined at this point ) .
the galaxy also flips by about @xmath22 , but over a longer timescale .
afterwards , the galaxy and halo are well aligned . in this case , the disc survives , and the `` flip '' events are too slow to be seen by the analysis used in the previous section for the hms simulation . in future work
, we shall relate the timescales for spin flips to the masses and other properties of haloes and their progenitors , and characterise the frequency of these disturbing non - merger events .
semi - analytic models of galaxy formation typically form the spheroidal components of galaxies ( `` bulges '' ) , solely through galactic major mergers . however , it is possible that non - merger events ( e.g. a `` fly - by '' by a smaller halo ) can perturb a galaxy  halo system sufficiently to form a bulge . 
 we present a preliminary investigation into the frequency of major changes in halo and galaxy spin direction , which could be signatures of such events .     
 address = argelander - institut fr astronomie , universitt bonn , auf dem hgel 71 , d-53121 bonn , germany ,