Modelling the evolution of density perturbations in the intracluster medium 1
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Ashmeet Singh , Prateek Sharma 1
Department of Physics, Indian Institute of Technology Roorkee, India 2 Department of Physics, Indian Institute of Science, Bangalore, India Results and Correlations
The ICM tcool/tff Profiles
We focus on blob ‘runaways’ so it forms cold gas with δ ∼ 104. ’Multi Phase Flag’ (mp) an indicator: +1 ; Positive Runaway (our focus in the paper) mp = 0 (3) ; No Runaway and/or Brunt V¨ ais¨al¨ a Oscillations −1 ; Negative Runaway (δ → −1)
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We extend the Cold Feedback Model of ICM heating (Pizzolato and Soker 2005) (PS05) where overdense blobs of gas cool faster and feed the AGN to trigger winds and/or jets to reheat the ICM. We find a regime of ICM parameters, where runaway cooling occurs for arbitrarily small amplitudes. We include the influence of a spherical gravitational field where it is easier for runaway cooling to occur.
Stage Setup - The Story of the ICM and the Blob The 1-D model of the ICM. (Radial coordinate r, Cooling Function Λ(T ) and electron and ion number densities ne and nH ). An overdense blob in the ICM has been studied by PS05 as a non-linear perturbation, (the primed terms correspond to blob parameters). the evolution is an interplay of gravity, thermodynamics and Brunt-V¨ais¨al¨ a oscillations.
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10 10 Distance from Cluster Center (r) [kpc]
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Modeling the Geometric Compression • Radial component of gravity will compress the blob, enclosed in a cone with half-angle η = sin−1(a/r). • With perfect compression, blob follows the instantaneous cone boundary and gets compressed, keeping η constant; r˙ a˙ = . a geom r
(1)
and compresses each blob to a point - Not Physically Plausible, but a start guess! Figure 4: Schematic blob evolution under the Mixing Length Hypothesis • The Mixing Length Hypothesis - Turbulence and viscosity due to the ICM, blob retains its spherical shape only upto a characteristic length. The blob looses spherical shape, mixes with the ICM, compression becomes much less important. • As the ICM mass encountered Mencr ∼ Mblob, blob looses its spherical shape and gets mixed with the ICM. a˙ Mencr Mencr a˙ a˙ + . (2) = exp −β 1 − exp −β a total a geom M a PS05 M • β encodes the “strength” of the mixing length hypothesis. Given a blob mass, β decides the extent till which geometric compression be important, following which PS05 is dominant.
Figure 2: Summary of the 1D ICM Model (left) and the blob evolution (right)
• We find, in addition to McCourt et al. 2012 and Sharma et al. 2012, a critical tcool/tff , geometry sensitive, below which multiphase gas is formed for any initial arbitrary value of δ , however small. The critical value for cartesian profiles is ∼ 1.5 (agreement with McCourt et al. 2012). 1
Runaway to cold temperatures
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Runaway to cold temperatures
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0.8 Multi Phase Flag (mp)
• Some heating mechanism to explain the lack of the CF in the ICM. (Binney and Tabor 1995).
Fiducial ICM Profile
Multi Phase Flag (mp)
• Observations by Chandra and XMM-Newton show a dramatic lack of the CF and equivalent cold plasma.
Useful implications for the evolution of the overdense perturbations as shown by McCourt et al. 2012 and Sharma et al. 2012. A plot of tcool/tff for 9 clusters used in our study. Different regimes of the parameter dictate the fate of the blob as an interplay of thermodynamics and gravity and is sensitive to the geometry of the cluster.
tcool / tff
• An expected subsonic inflow in the ICM due to differential cooling - The Cooling Flow(CF) (Fabian 1994) and presence of cold gas.
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Figure 5: MP Flag vs. tcool/tff for Cartesian (left) and Spherical (right) geometry. • In spherical geometry, cold gas is seen for less effective cooling,( tcool is longer). Sharma et al. 2012 find the critical value to be ∼ 10. • Clusters with K0 > 30 keVcm2, have tcool/tff > 10 for all r and cold gas is not seen at all. (Sharma et al. 2012) - Our results are compliant! −1
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Compression Strength Parameter β
Introduction
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Core Entropy K0 (keV cm )
Figure 6: Scatter of β with ICM profiles • β is ascertained using profile independent results Sharma et al. 2012 and is found to be insensitive to ICM profiles. • For tcool/tff larger than the critical value, a threshold value of initial δ is needed to form cold gas, depending of the blob release parameters. 1
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