Kupy galaxi

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Kupy galaxií lekce III

• Pavel Jáchym

2
Overview

• 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

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Environmental effects

• Morphological evolution more spirals at z0.5
  than at z0 (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)
• ...

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Interaction of spirals with environment

• 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
• ...

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Galaxy mergers

• 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 lt 14 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
  remnants 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

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Evolution of spirals

• Possible scenario for spirals transforming into
  S0s
• infalling spiral galaxies at z0.5
• triggering star formation
• starburst (emission-line galaxies)
• gas stripping by intracluster medium
• post-starburst galaxies
• tidal interactions heat disk
• stars fade
• S0 galaxies at z0
• morphological segregation proceeds
  hierarchically, affecting richer and denser
  groups earlier. S0s are only formed after
  cluster virialization.

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A note to the formation of clusters

• 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

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Shock fronts and cold fronts

• typical relative velocity for merging clusters is
  2000 km/s
• a cold clump of gas is moving through a warmer
  medium

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A sequence

• Clusters
• Groups
• Ellipticals

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Numerical simulations

• Gravitational interactions
• test particles
• direct summation
• tree codes
• Hydrodynamical interactions
• SPH
• finite difference codes

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Test particles, direct summation, PM method

• 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 particles 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

softening parameter
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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)

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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 gt l / ?
• d distance of the cell
• l size of the cell
• ? 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

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Hydrodynamical calculations

• Gasdynamics
• continuity equation
• Euler equation
• energy equation
• eq. of state

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SPH - methodology

• Smoothed Particle Hydrodynamics
• Lagrangian technique
• an arbitrary physical field A(r) is interpolated
  as
• smoothing kernel function W(rh) specifies the
  extent of the interpolation volume, it has a
  sharp peak about r0 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

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SPH methodology, cont.

• gradient of function
• density
• Euler eq.
• energy eq.
• EOS

?ij artificial viscosity
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Finite-difference method

• 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

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ICM recapitulation

• 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

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X-ray observations

• X-rays are absorbed by the Earths atmosphere
• HEAO-1 X-ray Observatory was the first to provide
  a fluxlimited sample of Xray 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 z1.3
• morphology from images,
• gas density radial profile,
• global temperature and gas mass
• total mass and entropy can be derived assuming
  isothermality
• X-ray luminosities LX1043 1045 erg/s
• clusters are identifiable at large cosmological
  distances

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X-ray surveys

• 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,

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Scaling properties

• 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
• gt
• however, from observations
• the luminosity-temperature relation is steeper
  (a2.5-3 or even more in groups)
• also the relation between the gas mass and T is
  steeper (a1.7-2)
• 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

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ICM

• typical cluster spectrum
• continuum emission dominated by thermal bremsst.
• main contribution from H and He
• emissivity of the continuum
• sensitive to temperature for energies gt 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

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Cooling of ICM

• cooling timescale
• cooling function ?c(T)
• tcool kT / n?c(T) gt 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 gt
  unimportant for ICM
• free-free interaction thermal bremsstrahlung

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Cooling, cont.

• 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

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Cooling, cont.

• 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

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Characteristic time-scales

• Mean free path for the ions and electrons of the
  ICM
• is ltlt 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.

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Characteristic time-scales, cont.

• Timescale for cooling
• due to thermal emission
• longer than a Hubble time
• gt hot gas stays hot!
• Crossing time
• Relaxation time
• time-change to equil.

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Cluster mass estimates

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

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Mass estimate from gravitational lensing

• 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

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Mass from lensing

• Newtonian deflection angle
• In general relativity
• thin lens approximation
• lens equation
• for ß0
• angular radius of Einstein ring
• critical surface density
• lensing occurs when Sgt Scrit
• convergence
• Jacobian matrix of lens eq.

ˆ
a
complex shear
Since ? and ? are derived from the same
potential, it is possible to determine the
surface mass density.
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Results of lensing

• 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.