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Small-Scale Structure Is It a Valid Motivation?

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Small-Scale Structure Is It a Valid Motivation? Small-scale Structure Is it a valid motivation? Jakub Scholtz IPPP (Durham) Small Scale Structure Problems <—> All the reasons why “CDM is not it” How did we get here? We are gravitationally sensitive to something sourcing T • <latexit sha1_base64="055AcnSYYRkGsBe2aYAe7vH1peg=">AAAB8XicbVDLSgNBEOz1GeMr6tHLYBA8hV0R9Bj04jFCXphdwuxkNhkyM7vMQwhL/sKLB0W8+jfe/BsnyR40saChqOqmuyvOONPG97+9tfWNza3t0k55d2//4LBydNzWqVWEtkjKU9WNsaacSdoyzHDazRTFIua0E4/vZn7niSrNUtk0k4xGAg8lSxjBxkmPzX4eChtKO+1Xqn7NnwOtkqAgVSjQ6Fe+wkFKrKDSEI617gV+ZqIcK8MIp9NyaDXNMBnjIe05KrGgOsrnF0/RuVMGKEmVK2nQXP09kWOh9UTErlNgM9LL3kz8z+tZk9xEOZOZNVSSxaLEcmRSNHsfDZiixPCJI5go5m5FZIQVJsaFVHYhBMsvr5L2ZS3wa8HDVbV+W8RRglM4gwsI4BrqcA8NaAEBCc/wCm+e9l68d+9j0brmFTMn8Afe5w/beZEG</latexit> µ⌫ —> we are fairly certain that DM exists. • An exception is MOND, which has issues of its own. However, the MOND community has been instrumental in pointing out some of the discrepancies with CDM. • But how do we verify the picture? —> NBODY simulations (disclaimer: I have never run a serious body simulation) 2WalterDehnen,JustinI.Read:N-body SimulationsN-body simulations of gravitational dynamics have reached over 106 particles [6], while collisionless calculations can now reach more than 109 particles [7–10]. This disparity reflects the difference in complexity of these rather dissimilar N-body problems. The significant increase in N in the last decade was driven by the usage of parallel computers. In this review, we discuss the state-of-the art software algo- Takerithms N and dark hardware matter improvements particles, that have driven this dra- • matic increase in N. We consider the very different challenges optionallyposed by collisional add ( 2) baryon versus collisionless gas ((which3) systems, and we attempt to give a§ fair critique of the methods§ employed, haspointing to be out wheretreated there is di roomfferently for improvement, and dis- cussing some interesting future research directions. Our focus becauseis primarily onit gravity;is far we from do not consider linear the ) important and role that the other fundamental forces play4. Since our goal is to numericallyelucidate the numerics, solve we will for only their touch uponmotion. the many in- teresting and important results that have come out of N-body modelling over the past 50 years. We must therefore apologise in advance for all that is missed out in this brief review. We do • Thisnot haveimplies space to discussa limit modelling in resolution gas physics and its many complications. Nor will we discuss the art of setting up initial (finiteconditions N), for butN-body we simulations. also have to regulateThere are the already IR several singularitiesN-body reviews and books in the literature. Aarseth [25] and Heggie & Hut [26] give excellent (softening).reviews of the N-body problem, focusing mainly on collisional N-body simulations. Hockney & Eastwood [27] cover many aspects of particle-based simulations, focusing on collisionless Fig. 1. The increase in particle number over the past applications. Trenti & Hut [28] give a general overview of the 50 years for selected collisional (red, [4–6, 11–16] taken N-body problem, covering both the collisional and collision- from [17]) and collisionless (blue, [3, 7–9, 18–24]) N-body The whole code has to be checked (year−y0)/2 • less regimes. Our review takes a somewhat different approach simulations. The line shows the scaling N = N02 forto theseconvergence previous works. We (changing attempt to review numerical tech- expected from Moore’s law if the costs scale ∝ N. niques for both collisional and collisionless N-body simula- unphysicaltions, focusing on parameters the very latest techniques, does and not with a view to assessing interesting future research directions. As much as possible, we present the key equations and describe the methodology at a level[1105.1082] where we hope the reader will changebe able to obtainphysics a relatively on deep relevant understanding scales) of the algorithms and their hidden gremlins. This paper is organised as follows. In 2, we review numerical methods for collisional N-body simulations: the astrophysical ( 2.1) and numerical foundations§ ( 2.2) with special treatment of the time integration ( 2.3), recent hardware-driven§ developments ( 2.4); and give a critique§ of the current state of the art ( 2.5), summarise§ alternatives to N-body methods ( 2.6), as well§ as present a (brief and biased) overview over past and§ recent astrophysical results with an outlook for the§ future ( 2.7). In 3, we review numerical methods for collisionless simulations: the astrophysical ( 3.1) and numerical foundations§ ( 3.2),§ the basis of cosmological N-body simulations ( 3.3), force softening ( 3.4) and the§ various force solvers ( 3.5), recent§ developments and challenges ( 3.6), and a very§ brief overview of astrophysical§ results ( 3.7). 4 describes§ methods for validation of N-body simulations,§ and in 5 we present our conclusions and outlook§ for the§ future of the field. § 2N-bodymethodsforcollisionalsystems Collisional systems are dynamically old such that tdyn is short compared to their age. This applies mainly to massive star clusters, and for this reason we will mostly refer to the N-body particles in this section as stars within a star cluster. Such clusters typically orbit deep within the potential of a host galaxy – like our own Milky Way – such that their dynamics is affected by the tidal field of their host. Over many dynamical times, the accumulated effect of many small encounters between stars significantly affects the evolution of collisional systems. Relaxation-driven equipartition of energy causes heavier stars to sink towards the centre, while low-mass stars are pushed to the outskirts, where they are susceptible to being skimmed off by Galactic 4 Many stellar systems contain significant amounts of gas, which in addition to gravity also interact electromagnetically. This gives rise to a large number of complicated effects from radiative cooling and the formation of stars (inside of which the strong and weak interactions become important, too), to active galactic nuclei and outflows driven by radiative heating. While for most gravitational systems these non-gravitational effectsplayanimportantroleonlyforbriefperiodsoftheirlifetime, their understanding and appropriate modelling is at the forefrontofmanycontemporarychallengesinastrophysics.Thisis,however, beyond the scope of this paper. Subgrid Physics • Some physics is not known from first principles. Such as: star formation details, supernova feedback parameters. • Or if it is known at certain scale (at the level of the molecular clouds), but the simulation cannot reach a resolution that can probe those scales. • These processes can still have a important role and need to be included. • Resolution: do it by hand. Ff a particular region reaches a low enough temperature and high enough density the code inserts stars by hand. If a star is old enough, the code turns into supernova and deposits some amount energy into the surrounding gas. • This subgrid physics has to be validated: you sacrifice some output (such as stellar mass distribution), in order to set the unknown parameters correctly. Possible small scale discrepancies • Missing Satellites • Too-big-to-fail Probably not a problem • Cores in Dwarf galaxies Maybe a problem a problem • Diversity of Rotation Curves • Planes of galaxy satellites Missing Satellites and Too- big-to-fail • Pure LCDM simulations made APOSTLE [1511.01098] predictions on number of satellites as a The APOSTLE [1611.00005] simulations 7 functionfrom each of of their the two DM main galaxies mass. per volume (labelled “primary” and “secondary” in order of halo mass), as well as within 2 Mpc from the LG barycentre, which includes • Thisboth number central and does satellite galaxies. not match the +10 The primary and secondary galaxies have 20 6 and observed number of satellites (in− the 18+8 satellites more massive than M =105M inside 300 observational5 footprint). ⇤ kpc,− respectively, where the errors indicate the scatter equiv- alent to 1σ about the median values. This is in good agree- ment with the observed number of MW and M31 satellites. However,Within 2 Mpc once of the LGthe barycentre, baryons there are were60 galaxies • ⇠ with M > 105M presently known; our simulations pro- included,⇤ this is significantly improved. +20 duce 90 15.Themodestnumberofluminousgalaxiesisin stark contrast− to the very large number of dark matter halos found within the same volume, indicated by the grey shaded • Tidalarea stripping in Fig. 3. While is feedback also from likely supernovae responsible and stellar winds regulates star formation in those halos where a dwarf [1707.03898]galaxy has formed, reionisation has left most of the low mass halos completely dark. The observed stellar mass function of the LG and those of the MW and M31 satellites are within However,the 1 σ scatter see of the[1807.07093] average stellar mass function in our • resimulations over most of the stellar mass range. The rela- tive scatter is larger for the satellite galaxies, reflecting the Figure 4. Cumulative number of halos as a function of maximum circular velocity, v ,averagedover12Apostle volumes at res- larger relative sampling error, and the fact that the relative max olution level L2. The four bottom curves correspond to satellite variation in single-halo mass among the di↵erent Apostle halos within 300 kpc of each of the two main galaxies; the top volumes is larger than that of the total LG mass. two curves to all
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