How to use the Astrowall to view the 3D shape of Galaxy Clusters

1
How to use the Astrowall to view the 3-D shape of
Galaxy Clusters

• Measuring the Three-Dimensional Shape of Galaxy
  Clusters
• I. Application to a Sample of 25 Clusters E. De
  Filippis et.al., (ApJ 625, 108-120 (May 20,
  2005))
• II. Are Clusters Prolate or Oblate? Sereno
  et.al., (astroph/0602051, accepted to ApJ)
• Presenter Paul Edmon
• 2-9-06
• Journal Club

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Outline

• Why 3-D and how do you get there?
• SZ and X-Ray Surface Brightness
• Shapes and Fitting
• Results and Possible Problems

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Why 3-D?

• 3-D shapes can
• Tell us about the relaxation of the system.
• Tell us about the infall of material
• Tell us if 2 objects are spatially correspondent
  to each other
• Help us understand the density and luminosity
  profiles in an object
• Help us probe cosmology in the case of Galaxy
  Clusters

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2-D to 3-D

• To model you need
• An idea of the scale of the object
• A guess to its morphology
• An idea of its density and light profile
• Trade off
• Always lose information when going to 3-D because
  of the guess
• Guess may be wrong or give an unphysical result
• Degeneracy of solutions

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Method

• Combine the Sunyaev-Zeldovich (SZ) effect data
  with X-ray surface brightness information
• Assume a cosmology
• Simultaneously fit data using an assumed
  morphology, most commonly a triaxial ellipsoid,
  and an orientation for the 3-D shape

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Sunyaev-Zeldovich (SZ) Effect

• In the potential wells of clusters sit plasma
  with electron temperatures around 8-10 keV
• The CMB passes through the cluster and Inverse
  Compton scatters off the plasma electrons
• This causes a distortion in the CMB spectrum

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Sunyaev-Zeldovich (SZ) Effect

• The SZ effect has the form of a temperature
  decrement that looks like this
• The factor f(?,Te) is the frequency shift and
  relativistic corrections

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X-Ray Surface Brightness

• The X-Ray emission in the Cluster is due to
  Bremsstrahlung
• Therefore the surface brightness of the Cluster
  in the X-Ray will be
• Where ?eH is the electron cooling function for
  the ICM in the cluster rest frame

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Shapes

• There are four shapes that are commonly used

Sphere
Oblate
Prolate
Courtesy of Mathworld http//mathworld.wolfram.com
/Ellipsoid.html
Triaxial
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Fitting Parameters

• Assume
• Shape
• Inclination
• Temperature Profile
• Cosmology
• Data
• X-Ray Brightness
• SZ Data
• Strong Lensing if you have it

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Triaxial Fitting

• Assumptions
• Triaxial Ellipsoid with an axis along the LOS
• Isothermal
• Electron Density follows a ß-model where ne0 is
  the central density, and xi is the scaled
  distance along the i-axis
• Cosmology
• H070 km/sec/Mpc
• OM.30
• Flat Universe

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Some Results of Triaxial Fitting

• Graphs
• qmax is the ratio of the semi-major axis to the
  semi minor axis
• eproj is the projected ellipticity on the plane
  of the sky
• P is the prolateness
• Pgt0 Prolate
• Plt0 Oblate
• E is the ellipticity
• EP Prolate
• E-P Oblate
• 25 clusters in all, the gray points are cooling
  flow clusters

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Some Results of Triaxial Fitting

• There are 10 Cooling Flow Clusters
• They are indistinguishable from the other
  clusters
• 18 out of the 25 clusters are likely to be
  prolate which is somewhat expected from some of
  the N-body simulations

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Prolate and Oblate Fitting

• Allow for other inclinations of clusters as
  opposed to assuming that an axis is along the LOS
• Require the cluster to be either Oblate or
  Prolate instead of a general Triaxial Ellipsoid
• Otherwise same method and same 25 clusters

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Prolate vs. Oblate Results

• i is orientation angle
• qint is the same as qmax
• Boxes Prolate
• Triangles Oblate
• Grey Ambiguous
• Statistics
• Prolate 15
• Oblate 4
• Ambiguous 6

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Problems with Method

• SZ data is average over entire cluster. Would
  like higher resolution SZ data for better
  fitting.
• Seems to be bias towards having clusters aligned
  toward our LOS, this is probably due to selection
  effects for X-Ray cluster detection because as
  you have more material lined up along the line of
  sight you will have a brighter source

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Problems with Method

• Would like to relax condition for orientation for
  the case of the Triaxial, also relax the
  isothermal condition
• Method is good for general morphology and for
  finding if the system is relaxed or not, a more
  complicated picture will be needed to see any
  deviations from ellipsoids

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Good Points of Method

• Uses only SZ and X-Ray Brightness data
• Breaks away from a spherical cluster
• Allows us to see the general morphology of a
  cluster
• Can allow us to get a handle on the orientation
  of the cluster
• If you have Strong Lensing you can provide
  constraints to Cosmological Parameters

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Sources

• Measuring the Three-Dimensional Shape of Galaxy
  Clusters
• I. Application to a Sample of 25 Clusters E. De
  Filippis et.al., (ApJ 625, 108-120 (May 20,
  2005))
• II. Are Clusters Prolate or Oblate? Sereno
  et.al., (astroph/0602051, accepted to ApJ)
• Mathworld http//mathworld.wolfram.com/