Kupy galaxií – lekce III

1. Kupy galaxií – lekce III Pavel Jáchym

2. Numerical simulations • N-body • tree method • sticky particles • SPH vs. grid codes • genetic algorithms • Applications: ram pressure stripping • ICM - recapitulation • Cluster mass from gravitational lensing Overview

3. Morphological evolution: more spirals at z=0.5 than at z=0 (Dressler 1980) • Morphology-density relation • Fraction of blue galaxies increases with z (Butcher & Oemler effect, 1978) • HI deficiency (Davies & Lewis 1973) • Dynamical perturbations (Rubin et al. 1999) • ... Environmental effects

4. Gravitational interactions • galaxy – cluster • galaxy – galaxy • Ram pressure • galaxy ISM – ICM • cluster galaxies are HI deficient by a factor 2 to 5 compared to field galaxies • Hydrodynamical interactions • viscous stripping • thermal evaporation • ... Interaction of spirals with environment

5. In the hierarchical CDM model, present-day galaxies are built up in a sequence of mergers from originally small objects similar to irregulars • The outcome of a merger between two galaxies depends on the mass-ratio between the two objects, their intrinsic and orbital angular momenta and their gas content • mass-ratio < 1:4 does not change much the structure of the more massive galaxy • mergers between two late-type spirals may create an S0 or an elliptical • mergers between an elliptical and a spiral could produce an elliptical or an S0 galaxy • generally: merger between two galaxies produces a remnant of an earlier type in the Hubble diagram • the orbital angular momentum of the galaxies is absorbed into the angular momentum of the remnant’s halo • the gas quickly moves to the center of the merger remnant; it may feed nuclear BHs • ULIRGs show the final stages of spiral-spiral merger with heavy star-formation taking place Galaxy mergers

6. Possible scenario for spirals transforming into S0’s • infalling spiral galaxies at z=0.5 • triggering star formation • starburst (emission-line galaxies) • gas stripping by intracluster medium • post-starburst galaxies • tidal interactions heat disk • stars fade • S0 galaxies at z=0 • morphological segregation proceeds hierarchically, affecting richer and denser groups earlier. S0’s are only formed after cluster virialization. Evolution of spirals

7. Chandra survey of the Fornax galaxy cluster revealed a vast, swept-back cloud of hot gas near the center of the cluster • the hot gas cloud is moving rapidly through a larger, less dense cloud of gas A note to the formation of clusters

8. typical relative velocity for merging clusters is ~2000 km/s • a cold clump of gas is moving through a warmer medium Shock fronts and cold fronts

9. Clusters • Groups • Ellipticals A sequence …

10. Numerical simulations Gravitational interactions • test particles • direct summation • tree codes • … Hydrodynamical interactions • SPH • finite difference codes

11. Test particles, direct summation, PM method softening parameter Test particles • e.g. Toomre & Toomre (1972) • can be used in combination with other methods Direct method (particle-particle method, PP) • integration of all the N particle’s equations of motion • high computational requirements ~ O(N2) PM method (particle in mesh) • calculating the grav. force field on a grid of regularly spaced points • the acceleration of each particles is obtained by interpolation between nearest points of the grid • PPPM methods …

12. Tree algorithm Lagrangian technique Uses direct summation to compute attraction of close particles Detailed internal structure of distant groups of particles may be ignored • many similar particle – distant-particle interactions are replaced with a single particle-group interaction Particles are organized into a hierarchic structure of groups and cells resembling a tree • - e.g. oct-tree scheme (see Fig.) • alternative AJP method The influence of remote particles is obtained by evaluating the multipole expansion of the group computational cost scales as O(N logN)

13. Tree algorithm, cont. once the tree is completed, information about masses, center-of-mass positions, and multipole moments are appended to each cell the multipole expansion of a cell is used only if "opening" criterion is fulfilled: d > l / θ • d … distance of the cell • l … size of the cell • θ … opening angle the opening criterion follows from comparison of the size of the quadrupole term with the size of the monopole term • higher-order multipoles of the gravitational field decay rapidly with respect to the dominant monopole term • it is possible to approximate the group's potential only by monopole term, or low-order corrections for the group's internal structure can be included as well multipole expansion of the potential:

14. Hydrodynamical calculations Gasdynamics: • continuity equation • Euler equation • energy equation • + eq. of state

15. SPH - methodology Smoothed Particle Hydrodynamics Lagrangian technique an arbitrary physical field A(r) is interpolated as • smoothing kernel function W(r;h) specifies the extent of the interpolation volume, it has a sharp peak about r=0 and satisfies two conditions: in numerical implementation values of A(r) are known only at locations of a selected finite number of particles distributed with number density then number of neighboring particles N is fixed during the calculation

16. SPH – methodology, cont. Πij … artificial viscosity gradient of function density Euler eq. energy eq. EOS

17. Finite-difference method Roediger & Brüggen (2007) Eulerian technique approximates the solutions to differential equations using finite difference equations to approximate derivatives grid-based codes for non-homogeneous systems – adaptive mesh refinement hydrodynamics codes Ram pressure stripping simulation:

18. Intra-cluster medium • optically thin plasma • thermal bremsstrahlung = braking radiation, free-free radiation • radiation by an unbound particle (e-) due to acceleration by another charged particle (ion)‏ • Diffuse emission from a hot ICM is the direct manifestation of the existence of a potential-well within which the gas is in dynamical equilibrium with the cool baryonic matter (galaxies) and the DM • X-ray luminosity is well correlated with the cluster mass and the X-ray emissivity is proportional to the square of the gas density • cluster emission is thus more concentrated than the optical bi-dimensional galaxy distribution ICM – recapitulation

19. X-rays are absorbed by the Earth’s atmosphere • HEAO-1 X-ray Observatory was the first to provide a flux–limited sample of X–ray identified clusters • XMM-Newton & Chandra • we can map the gas distribution in nearby clusters from very deep inside the core, at the scale of a few kpc with Chandra, up to very close to the virial radius with XMM-Newton • We can measure basic cluster properties up to high z~1.3 • morphology from images, • gas density radial profile, • global temperature and gas mass • total mass and entropy can be derived assuming isothermality • X-ray luminosities LX~1043 – 1045 erg/s • clusters are identifiable at large cosmological distances X-ray observations

20. From surveys several global observables can be derived: • X-ray flux (luminosity if z known) • temperature • using scaling relations, these can be related to physical parameters, like mass, … X-ray surveys

21. baryonic matter follows the DM grav. potential well • it is heated by adiabatic compression during the halo mass growth and by shocks induced by supersonic accretion or merger events • gravity dominates the process of gas heating • when assuming that the gas is in hydrostatic eq. with DM and bremsstrahlung dominates the emissivity => • however, from observations: • the luminosity-temperature relation is steeper (α=2.5-3 or even more in groups) • also the relation between the gas mass and T is steeper (α=1.7-2) • this indicates that non-gravitational processes (SN, AGN feedbacks, radiative cooling, winds, etc.) take place during the cluster formation and left an imprint on its X-ray properties Scaling properties

22. typical cluster spectrum • continuum emission dominated by thermal bremsst. • main contribution from H and He • emissivity of the continuum • sensitive to temperature for energies > kT • rather insensitive for energies lower • iron K-line complex at 6.7 eV • intensity of other lines decreases with increasing T • shape of the spectrum determines T • its normalisation then density • ICM is not strictly isothermal – T from an isothermal fit is a „mean“ value • metallicity evolution: ICM

23. cooling timescale • cooling function Λc(T) • tcool = kT / nΛc(T) > 1010 yr (n/10-3 cm-3)-1 (T/108 K)1/2 • in central cluster regions it can be shorter than the age of the Universe • in fairly relaxed clusters, the decrease of the ICM temp. in the central regions has been recognized • cooling flows • supernovae or AGNs as possible feedback mechanisms providing an adequate amount of extra energy to balance overcooling • three ways how an electron can get rid of energy • collisional cooling – very efficient but not for completely ionized ICM • Recombination – probability ~ 1/velocity => unimportant for ICM • free-free interaction = thermal bremsstrahlung Cooling of ICM

24. about 1000 Msol/yr of gas can cool out of the X-Ray halo • this gas could form stars – some cD galaxies show filaments of gas emission and blue colors in the central region • others do not show the lower central temperatures that would be expected if cooling was efficient • presumably, cooling will lead to enhanced accretion of gas onto the black hole in the cD galaxy • it in turn may become active and provide high energy particles to heat the gas • thus, a quasi equilibrium may be established that prevents the gas from ever forming stars • still under debate … Cooling, cont.

25. Mixing via turbulence could counteract cooling towards the outside • Central AGNs can produce relativistic jets which directly inject energy into the ICM and may cause shocks. Jets also inflate bubbles, which rise buoyantly, pushing colder gas upwards out of the core. • Acoustic waves produced by AGN outbursts can also transfer energy to the ICM if it is viscous enough Cooling, cont.

26. Characteristic time-scales Mean free path for the ions and electrons of the ICM • is << cluster size • ICM can be described by fluid dynamics … Timescale for pressure equilibrium • if a region of gas undergoes a compression, how long does it take for the pressure wave to propagate across the cluster? • this is short compared to Hubble time – we can assume that the gas is in pressure eq.

27. Characteristic time-scales, cont. Timescale for cooling • due to thermal emission • longer than a Hubble time • => hot gas stays hot! Crossing time Relaxation time • time-change to equil.

28. From the virial theorem • From X-ray data • hydrostatic equilibrium condition • μ ... mean molecular weight (~0.59 for primordial composition) • distribution of ICM • β ... ratio between the kinetic energy of any tracer of the grav. potential and the thermal energy of the gas • From gravitational lensing Cluster mass estimates

29. clusters act as grav. lenses on more distant galaxies • one of the most important methods for the mass determination of galaxy clusters • the only method working for non-equilibrium systems! • There are two rather different regimes • Strong lensing • background galaxies are strongly distorted • good for massive clusters • Weak lensing • background galaxies only slightly distorted • For a symmetric potential, the galaxies are elongated slightly in the axial direction • This is a "shearing" effect and only reveals the gradient in the potential, not its integrated depth • By measuring thousands of faint galaxy images, the effect is identified statistically. • shape and radial trend of the weak shear and strong lensing effects yield the cluster mass distribution independent of the nature of the mass and therefore allow reliable total mass estimates including the dark matter Mass estimate from gravitational lensing

30. Newtonian deflection angle: • In general relativity: • thin lens approximation: • lens equation: • for β=0: • angular radius of Einstein ring: • critical surface density: • lensing occurs when Σ> Σcrit • convergence: • Jacobian matrix of lens eq.: ˆ α Mass from lensing … complex shear Since κ and γ are derived from the same potential, it is possible to determine the surface mass density.

31. Comparison between the ICM temperatures inferred by the fitting of isothermal profiles to the shear data, and from X-ray measurements. • Comparison between the velocity dispersion found by fitting isothermal profiles to the shear data and those estimated through spectroscopic measurements. Results of lensing