COSMOLOGICAL GALAXY FORMATION 13 1 1 2 3 F R Pearce C S Frenk A Jenkins J M Colb erg P A Thomas 4 2 5 6 H M P Couchman S D M White G Efstathiou J A Peaco ck 7 A H Nelson The Virgo Consortium 1 Physics Department South Rd Durham DH LE UK 2 MaxPlankInstitut fur Astrophysik Garching Germany 3 CPES University of Sussex Falmer Brighton BN QH UK 4 Department of Physics and Astronomy Univ of Western Ontario London Ontario NA K Canada 5 Institute of Astronomy Madingley Rd Cambridge CB OHA UK 6 Physics Department Edinburgh University Blackford Hil l Edinburgh EH HJ UK 7 Department of Physics and Astronomy Cardi University Cardi CF YB UK Abstract We discuss the rst results from two successful simulations of galaxy formation within a cosmological volume With over large ob jects forming in each we have sucient numb ers to reliably pro duce b oth galaxy correlation and luminosity functions We nd that the observed galaxy counts are well tted by these mo dels and that the galaxies display an almost unevolving correlation function back to a redshift of which closely resembles the featureless observed form and amplitude Intro duction astro-ph/9906032 2 Jun 1999 The quest for a detailed understanding of galaxy formation has b ecome one of the central goals of mo dern astrophysics On the observational side data from the Keck and Hubble Space telescop es have revolutionised our view of the high redshift Universe and there are claims that the ep o ch of galaxy formation has already b een observed From the theoretical p oint of view the problem is fundamental b ecause its resolution involves the synthesis of work from a wide range of sp ecialities A full treatment requires consideration of the early Universe pro cesses that create primordial density uctuations the microphysics and chemistry that precipitate star formation within giant molecular clouds the energy exchange present in sup ernova feedback the dissipational pro cesses of co oling gas the dynamics of galaxies moving within a dense environment and the large scale tidal torques which determine the angular momentum proles of the resultant ob jects Analytic approaches to the problem founder partly b ecause of the lack of symmetry As high redshift observations show real galaxies do not form in a smo oth spherically symmetric fashion but rather form as complicated collections of bright knots which merge and evolve into normal galaxies Because of its complexity this problem is often approached using numerical simulation In one of the rst attempts demonstrated the a wide variety of 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 crosscheck of the results More recently several groups have attempted to tackle the problem by coupling a semianalytic 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 eects of bias Previous work by the Virgo Consortium predicted the magnitude of the bias that would b e required to reconcile stateoftheart 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 stateoftheart SPH calculations of million gas plus million dark matter particles in a b ox of side Mp c using a parallel adaptive particle particle particlemesh 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 eective 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 eectively imp oses a mass resolution threshold Ob jects b elow this mass cannot form whereas ob jects ab ove this mass are unaected 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 eectively 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 mans feedback and decoupling the cold dense gas eectively negates these eects 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 Kband luminosity function and that obtained by the SCDM simulation with two dierent assumptions for the stellar IMF of smaller subresolution and so unresolved fragments Our assumptions are equivalent to presuming that the absence of previous levels of the hierarchy has no eect on the subsequent evolution or prop erties of our ob jects and that these ob jects are large enough to resist the destructive eects 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 sucient 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 identication 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 friendsoffriends 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 signicant 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 eg 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 Kband 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 cuto 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 References Baugh C M Cole S Frenk C S Lacey C G ApJ Bruzual G Charlot S ApJ Cen R Ostriker J ApJ Evrard A E Summers F J