astro-ph/9906032 2 Jun 1999 range goals of mo dern astroph the The telescop es ha the ep o c that create primordial densit high formation fashion n pro les of in en the dissipational pro cesses of co oling gas the dynamics of galaxies mo umerical 4 to Dep vironmen Analytic 6 problem is In normal Physics quest redshift 7 resem displa n that a artment Dep of um tro duction cosmological but h of galaxy formation has already b een observ W sp ecialities F R P b ers COSMOLOGICAL artment the resultan the within sim e discuss the rst results from t bles the featureless observ y for H M P t rather galaxies approac v an Dep 5 observ Institute e rev ulation to observ of a 3 2 fundamen Max Plank Institut CPES almost artment earce reliably detailed Physics gian 1 of olutionised our Couc Physics ations form v and ed hes olume Physics t A 1 t ob jects un ev of galaxy 3 University molecular ysics In the full C S F to pro duce tal as and hman Astr understanding Edinbur sho one Because A H Nelson Dep the y uctuations the microph olving With complicated large b ecause treatmen and w Astr onomy On the observ coun 4 artment of problem S D M White real b oth renk Astr o gh scale tidal onomy Univ clouds view of the high redshift Univ the correlation of ts v ed form and amplitude fur er of University its Sussex are galaxies 1 t galaxy Madingley onomy Car A Jenkins large rst its Astr requires w K 7 resolution South founder w o successful sim of collections The the Abstract GALAXY complexit ell ophysik attempts ational side data from the Kec galaxy correlation torques F function tted do Canada energy almer R Virgo Consortium consideration d Durham of Blackfor ob jects R 2 not partly di University G Efstathiou 1 d in J M Colb erg Western b formation y y of v whic form in Cambridge ed exc Brighton bac olv this ysics and c these ulations of galaxy formation within brigh and b ecause forming hange k d es the demonstrated h determine the problem to Hil l Gar luminosit F F mo dels Ontario t DH a rom the theoretical p oin a of ORMA has knots ching smo oth redshift presen syn BN Edinbur erse and there are claims that in of hemistry that precipitate star 5 the CB Car J A P LE 2 eac b ecome thesis P the and is y QH whic di CF early Germany h L t A Thomas often functions OHA ondon of in w lac the gh UK that spherically symme e of h k and Hubble Space TION angular eaco c sup erno k ving within a dense ha Univ UK one EH whic merge w a approac of the v UK ork e wide Ontario YB symmetry k su cien of h erse W galaxies HJ 6 from closely v momen 3 e the and a hed v nd pro cesses UK ariet feedbac t of view UK cen t a ev N A using wide y tum olv tral tric As of k e
observed galaxy prop erties could b e tted by even the most basic of simulations Unfortunately
their computational volume like that of was to o small to pro duce a reliable correlation
function and they had to stop the simulation at z but this work clearly demonstrated the
p otential for simulations of this kind Both these groups used smo othed particle hydro dynamics
SPH to mo del the gas In a complimentary investigation used a grid based co de providing
a useful cross check of the results More recently several groups have attempted to tackle
the problem by coupling a semi analytic approach to a collisionless simulation and have again
pro duced interesting results
In this pap er we simulate the pro cess of galaxy formation within a representative volume
of the Universe in two contrasting cosmologies The volume is large enough Mp c on a
side that several thousand galaxies form and we can reliably measure the galaxy correlation
function and study the e ects of bias Previous work by the Virgo Consortium predicted
the magnitude of the bias that would b e required to reconcile state of the art collisionless
simulations to the observed galaxy correlation function Here we examine whether the inclusion
of a gaseous comp onent and basic physics can indeed pro duce this bias
The simulation
The simulations we have carried out are state of the art SPH calculations of million gas
plus million dark matter particles in a b ox of side Mp c using a parallel adaptive particle
particle particle mesh plus SPH co de We have completed b oth a standard Cold Dark Matter
SCDM run and a run with a p ositive cosmological constant CDM Both have the same
parameters as detailed by The baryon fraction was set from nucleosynthesis constraints
2
h and we assume an unevolving gas metallicity of times the solar value This
b
9
leads to a gas mass p er particle of M for b oth runs As we typically smo oth over SPH
10
particles this gives us an e ective minimum gas mass resolution of M We employ a
1
comoving Plummer gravitational softening of h kp c and the minimum SPH resolution was
set to match this
Underlying assumptions
This simulation is based up on two fundamental assumptions These are that the feedback
of energy due to sup ernovae explosions can b e approximated by assuming that this pro cess
e ectively imp oses a mass resolution threshold Ob jects b elow this mass cannot form whereas
ob jects ab ove this mass are una ected Comparing the simulated star formation rate to the
observed one shows that such an approximation do es not lead to a ridiculous star formation
history The second assumption is that once gas has co oled into tight dense blobs it is e ectively
decoupled from the surrounding hot gas This is equivalent to assuming that this gas has b een
converted into stars or is isolated by additional physics such as magnetic elds The main
further approximation we are forced to employ for computational reasons is a spatial resolution
1
of h kp c This is over twice the value we would have liked to have used and leads to
enhanced tidal disruption drag and merging within the larger clusters of ob jects
The microphysics of star formation and sup ernovae explosions typically have parsec length
scales and so happ en far b elow our resolution limit The combination of p o or man s feedback
and decoupling the cold dense gas e ectively negates these e ects over which we have no con
trol anyway for all ob jects ab ove our resolution threshold All ob jects must cross this threshold
at some time as a large ob ject cannot simply pop into existence presumably via the merger -2
-3
-4
-5
-22 -24 -26
Figure A comparison b etween the observed K band luminosity function and that obtained
by the SCDM simulation with two di erent assumptions for the stellar IMF
of smaller sub resolution and so unresolved fragments Our assumptions are equivalent to
presuming that the absence of previous levels of the hierarchy has no e ect on the subsequent
evolution or prop erties of our ob jects and that these ob jects are large enough to resist the
destructive e ects of sup ernovae explosions
It should b e stressed that b ecause of our relatively p o or physical resolution we can only
predict accurate masses and p ositions for our ob jects We do not have su cient resolution to
resolve internal structure and so cannot directly ascertain a morphological typ e for our galaxies
as each ob ject typical only contains b etween and particles
Analysis
The presence of gas makes the identi cation of a set of ob jects which we would like to equate
to galaxies very straightforward Co oling leads to large collapse factors and small knots of
cold gas residing within a much hotter halo For the purp oses of this pap er we use a standard
friends of friends group nder with a small linking length to reliably extract a group catalog
from each simulation output time At the end of the simulation there are over signi cant
ob jects within each simulation volume roughly the observed numb er density
The luminosity of any ob ject is then extracted by tracking each of the particles that nally
reside inside each ob ject backwards in time and extracting the time at which each of them rst
b ecame cold and dense Standard p opulation synthesis techniques e g can then b e applied
to pro duce the luminosity of each ob ject in any desired pass band
In Fig we show a comparison b etween the observed K band luminosity function and
the SCDM simulation The observations are neatly bracketed by the simulation within the un
certainties imp osed by the choice of initial mass function Clearly the shape of the observations
are well repro duced with no excess at the bright end The faint end slop e is not well repro duced
b ecause of the relatively high resolution imp osed mass cut o which was delib erately chosen
to b e close to L For the LCDM simulation the shap e of the luminosity function is also well
mo delled but the ob jects tend to b e to o bright This is b ecause the parameters chosen for this
simulation lead to a higher global fraction of cold dense gas making all ob jects more luminous
Conclusions
For the rst time we have b een able to mo del galaxy formation within a large enough volume
of the Universe that reliable calculations can b e made of the galaxy correlation and luminosity
functions As has b een shown elsewhere in these pro ceedings the observed correlation
function is well tted by these mo dels which also simultaneously t the observed luminosity
functions The galaxies in our mo dels are not only reasonably distributed they also have a
sensible range of masses and formation times
Acknowledgments
The work presented in this pap er was carried out as part of the programme of the Virgo
Sup ercomputing Consortium using computers based at the Computing Centre of the Max
Planck So ciety in Garching and at the Edinburgh Parallel Computing Centre
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