Numerical Simulations of the Merging Cluster of Galaxies Cygnus A

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University of Amsterdam

MSc Astronomy & Astrophysics

Track Astronomy & Astrophysics

Master Thesis

Numerical Simulations of the Merging Cluster of

Galaxies Cygnus A

by T. L. R. Halbesma, BSc 6126561 December 2016 54ECTS

Research conducted between September 2015 and August 2016

Supervisors:

Dr. Michael W. Wise Dr. Julius M. F. Donnert

Examiner: Dr. Anna L. Watts

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A B S T R A C T

The nearby Cygnus A galaxy (z = 0.0562) hosts an Active Galactic Nucleus (AGN) that is a thousand times brighter than any other AGN at the same distance and is the brightest extragalactic source of radio emission. This source is the archetype of the FR-II class of classical radio doubles interacting with its environment. At the same time, the galaxy is part of a moderately rich cluster that is about to undergo a major merger between two subclusters about 0.5 Gyr prior to core passage. In this thesis the deepest dataset to date of an AGN interacting with the cluster medium is combined with a numerical representation of the system generated using the state-of-the art proprietary initial conditions code Toy-clusterto simulate the cluster merger. The exposure time at present is already an impres-sive megasecond of Chandra XVP, while the final total combined exposure time will reach 2.2 megasecond within the coming year. Spherically symmetric haloes are sampled using the Hernquist profile, an analytical expression equal to the NFW-profile within a scaling radius. This governs the dark matter content, while the baryonic matter has a fixed baryon fraction of seventeen per cent at the virial radius and is assumed in hydrostatic equilibrium. The β-model then describes the density structure of the hot intracluster medium, and the pre- and post-merger density and temperature profiles are simulated using the massively parallel publicly available TreeSPH code Gadget-2. We investigate the effect of the initial velocity on the line-of-sight integrated two-dimensional post-simulation projected radial profiles obtained using the proprietary map making tool P-Smac2. Our analytical mod-els estimate the total gravitating mass and the concentration parameter of the dark matter halo, both of which can be observationally tested in a weak-lensing study. No such study has been published to date, to our knowledge. Our simulations neglect the AGN-activity, thus provide both the hydrostatic and the merger temperature structure which can be sub-tracted from the measured temperature profiles. The remaining temperature structure then most likely arises as a result of heating the intracluster medium surrounding the central galaxy Cygnus A by the powerful AGN excluded from our numerical models. This system uniquely allows us to study the complicated process of AGN feedback with a spatial res-olution and a level of detail unprecedented in prior studies. For example, the duty cycle and AGN outburst history of the last few hundred mega years could be inferred from the residual temperature maps, which promises exciting results in the foreseeable future.

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T H E S I S O U T L I N E

Hierarchical clustering is the current cosmological paradigm explaining the formation of large-scale structure in the universe. Smaller structures such as stars and galaxies are believed to have formed first, followed by larger structures clumping together in contin-uous merger events. Cluster of galaxies are the largest bound structures in the universe at present. Within this framework, the presence of hot gas in the intracluster medium (ICM) is explained naturally, as is the occurrence of mergers of these objects. X-ray observations of clusters show that the ICM radiates thermal bremsstrahlung, a radiative loss that cools the gas. Order of magnitude timescale arguments show that these radiative losses would cool the core on a timescale significantly shorter than one Hubble time. It thus remains a ques-tion how the cluster sustains the X-ray emission on cosmological timescales as it requires a source of heating. An active galactic nucleus (AGN) or a cluster-cluster merger could inject the required thermal energy and as such reheat the ICM. Clusters of galaxies would then continue to emit the X-rays observed at present.

Cygnus A is a rare astronomical object as it hosts an active galactic nucleus inside its brightest cluster galaxy (BCG) while the Cygnus cluster, at the larger scale, is currently in the early stage of a major merger. More importantly, the source is very powerful, bright and nearby which allows detailed studies of all these physical processes in the same system. It is therefore of no surprise that this object has been subject to numerous studies over the last decades. As of December 2016, querying Simbad for references on Cygnus A yields no less than 1818 publications that mention the source. The Cygnus cluster is an excellent candidate to study the effects of a major merger on the thermal structure of the intracluster medium. Moreover, the relative contribution of the AGN and the merger to (re-)heating the ICM can be studied in the same object.

The optical cD galaxy Cygnus A, when observed at radio frequencies (Figure 7 in sec-tion 2), shows two jets and two lobes associated with the AGN. The collimated outflow results from accretion of the surrounding gas onto a supermassive black hole (SMBH) lo-cated at the galactic center. Simultaneously, the jets sweep up gas surrounding the galaxy, power the two radio lobes starting at a distance of∼30 kpc from the galaxy, and create hot spots at the jet termini. This process is called AGN feedback because the very gas reservoir that powers the system itself is altered as the outflow displaces and heats the gas. The latter

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significantly influences the star formation rate of the host galaxy as well as the properties of the cluster environment. The unique radio signature of Cygnus A make this source the prime example of an active galactic nucleus interacting with its environment (Figure 19 in chapter 3). In fact, Cygnus A is the archetype of the Fanaroff & Riley (1974) type II radio galaxy classification, abbreviated as FR-II.

The relative proximity of Cygnus A at redshift z=0.0562 allows for AGN feedback stud-ies with unprecedented spatial resolution. In addition, the strong radio emission is a thou-sand times brighter than any other source at the same distance, as can be seen in Figure 8. In general, AGN at lower redshifts show lower average radio luminosities. Cygnus A, on the other hand, is the exception that hosts an AGN equivalent in power to an active galactic nucleus at a redshift of z = 1. The high luminosity observed from the radio lobes make Cygnus A the brightest extragalactic radio source in the sky. This combination of proximity and extreme brightness shows the energy transport in the innermost kpc surrounding the SMBH and make Cygnus A the ideal target to study AGN feedback in detail. In a broader context, understanding the fine details and inner workings of AGN feedback is crucial to understand structure formation and evolution in the universe as a whole. Furthermore, AGN feedback affects the growth of the very black hole that powers the AGN in the first place. The study of AGN feedback could further our understanding of how black holes grow and evolve.

In this thesis we focus on the diffuse X-ray emission at the megaparsec scale that origi-nates from the ICM of the Cygnus cluster of galaxies. In particular, we infer initial condi-tions to set up numerical simulacondi-tions of the merger from recent X-ray observacondi-tions, followed by results from the simulations. We are interested in whether or not the merger could re-heat the ICM, and if so where and how much energy is thermalised. Furthermore, we want to compare this energy injection to the amount of energy injected by the AGN to find the relative importance of heating the ICM of both processes. With these goals in mind we investigate the following questions. What are the masses of the two merging subclusters in the Cygnus system? What is the velocity at which both clusters are moving towards each other? How long before core passage is the merger at present?

To address these questions we start with a very general introduction into the current cos-mological paradigm and work our way up to large-scale structure formation in section 1.1. We discuss the distribution of dark matter in clusters of galaxies in section 1.2, followed by the general properties of clusters associated with the X-ray emission in section 1.3. We continue with a summary of the status quo of the literature on observations of Cygnus A in section 2. Note that due to the humongous collection of such publications we have to limit our scope to X-ray observations of the ICM and merger-related publications only, but

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we do include optical studies that are relevant to the merger. However, no literature on the radio source is included in the overview. Next, we discuss how we have used constraints from recent X-ray observations to infer initial conditions to set up numerical simulations of the merging cluster of galaxies in chapter 3. A detailed description of the numerical setup and methods is given in section 4, followed by the simulation results in section 5, discussed in section 6 to come to our conclusions in section 7.

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C O N T E N T S

i literature summary 1 1 introduction 2

1.1 Cosmology: Large-Scale Structure Formation 2 1.2 Structure of Dark Matter Haloes 11

1.3 Clusters of galaxies: X-ray emission from the Intracluster Medium 13 2 observational overview of the cygnus cluster 22

ii initial conditions 41

3 from x-ray constraints to initial conditions 42 3.1 Multi-Wavelength Observational Campaign 42

3.2 X-ray Surface Brightness Maps 43 3.3 Radial Profiles: Number Density 43

3.3.1 Beta-Model Fit 47

3.3.2 From Gas Density to Total Gravitating Mass 51 3.4 Radial Profiles: Temperature 56

iii numerical simulations 59 4 methods 60

4.1 Numerical Hydrodynamics 60

4.2 Toycluster: Stable Initial Conditions 63 4.3 Gadget-2: Massively Parallel TreeSPH 67

4.4 P-Smac2: Line-of-Sight Integrated Observables 69 4.5 Pre- and post-processing 70

5 simulations 71

5.1 Single Cluster Profiles and Numerical Stability 71 5.2 Simulation Runs with Stable Clusters 75

6 discussion 83 7 conclusions 93

a hypergeometrical transformations 106 b code makefiles and runtime parameters 107

References 121

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Part I

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1

I N T R O D U C T I O N

1.1 cosmology: large-scale structure formation

We start with an overview of structure formation in a cosmological context to understand why clusters of galaxies of galaxies emit X-ray emission and why clusters of galaxies are expected to merge with other clusters. Cosmology is the study of the universe as a whole, a field based on the fundamental assumptions that the universe is isotropic and homoge-neous on the largest scales. The current cosmological paradigm is the Lambda Cold Dark Matter (ΛCDM) Big Bang model. This framework emerged from numerous observations at different times on the cosmological timeline, or epochs, that contribute to a consistent model of the universe. The most important observations are the cosmic microwave back-ground radiation (CMBR), the Hubble law, type Ia supernova as a function of redshift z, rotation curves of galaxies and the observation of the bullet cluster, large all-sky surveys of galaxies combined with numerical simulations, and Lyman α line emission in quasars. The concordance of these observations favour (ΛCDM) over alternative models and show that the energy and matter in the universe is split up in roughly seventy per cent dark energy, about twenty-six per cent dark matter, and approximately four per cent baryonic matter. All observed electromagnetic radiation originates from the latter.

Cosmic Microwave Background Radiation and the Big Bang

The universe is thought to have formed in a single event called the Big Bang. Shortly there-after, when the age of the universe was∼10−35 seconds, the small volume of space-time is thought to have undergone a period of rapid expansion called inflation. This concept that is critical to concordance cosmology and fundamentally explains the origin of large-scale structure in the universe. During inflation, quantum fluctuations in the inflaton field in-creased to macroscopic proportions as the universe expanded, which caused ripples in the energy density of the universe (Guth 1981). As the universe expanded, adiabatic cooling

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1.1 cosmology: large-scale structure formation 3

lowered the temperature of the universe reaching the threshold for nucleosynthesis. The light elements present in the universe have formed in this era that lasted from around ten seconds to twenty minutes after the big bang. The state of the universe thereafter can be thought of as a hot primordial soup of free protons, electrons and photons. The plasma was opaque to electromagnetic radiation: photons cannot escape as a result of frequent Thom-son scattering on the abundantly available free electrons and the soup remains ionised. At a certain point in time the temperature in the universe reaches the recombination tem-perature of neutral hydrogen, roughly 3000 K, and the free electrons and protons become bound. The sudden drop in free electrons available for scattering allows the photons to escape. This event is called the epoch of recombination (Peebles 1968; Zel’dovich et al. 1969; Seager et al. 2000). The last time the photons interacted with matter is called the surface of last scattering and blackbody radiation from these photons can be observed at present. Recombination happened around z ∼1100, thus, the original rest frame wavelength of the photons is scattered to microwave wavelengths. These photons were first observed in 1964 - but published a year later - by Penzias & Wilson (1965). This feature, the Cosmic Mi-crowave Background Radiation (CMBR, Figure 1), shows tiny temperature fluctuations of a few hundred µK. The earliest ripples in the cosmic energy density that arose as a result of the inflated quantum fluctuations have translated into small density perturbations to the tightly coupled photon-baryon plasma (Peebles & Yu 1970) which, in turn, resulted in the small temperature variations observed in the CMBR.

Cosmological Redshift and Hubble’s Law

Big Bang theory naturally leads to an expanding universe. An important concept is cosmo-logical is redshift, defined as

z= λobs−λem

λobs , (1.1)

where redshift is an increase in the observed wavelength λobs with respect to the emitted

wavelength λem. Conversely, a decrease is called blueshift. Extragalactic sources are

red-shifted*_{, classically interpreted as a Doppler shift that relates (low) redshifts to a velocity v}

via z _≈ v/c. Redshifted wavelengths correspond to a positive velocity, indicating that ob-jects are moving away from the observer at Earth. This collective movement is interpreted as evidence that space-time itself is indeed expanding which stretches the wavelength of emitted light, or causes the source of emission to move away from us at velocity v.

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Figure 1.: Planck all-sky map showing the universe at the largest scales is isotropic and homogeneous apart from tiny temperature fluctuations of order 100µK. These temperature fluctuations are interpreted as the seeds all large-scale structure currently observed has grown from. Figure adopted from the Planck Collaboration et al. (2015).

Hubble (1929) is the first to observe a linear correlation between the systematic increase in redshift of ‘extragalactic nebulae’ and the distance to these objects. A specific type of stars are Cepheids, variable stars bright enough to be visible in galaxies other than our own. Moreover, these giants show a strong correlation between the intrinsic luminosity and the pulsation period. A measurement of the period and the observed luminosity, thus, effectively is a measure of distance. This method, calibrated on galactic Cepheids using the parallax method, can therefore be used to measure the distance to the host galaxy of Cepheids. The linear relation between redshift and distance D found is

v=cz =H0D , (1.2)

where the Hubble constant H0with units km/s/Mpc is an important cosmological

parame-ter that quantifies the rate of expansion. This observation, the Hubble law, does not depend on direction and shows that the universe is undergoing an isotropic expansion.

Type Ia Supernovae and Dark Energy

Observations show that he rate of expansion increases. Type Ia supernova explosions al-low for distance measurements beyond z = 1. White dwarfs in binary stars can accrete matter until the Chandrasekhar mass is reached. At this point, a runaway process leads

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to the explosion of this fixed mass, thus, a fixed energy is released. Therefore the intrinsic luminosity is known and the distance can be inferred from the observed luminosity. The redshift can be measured if the host galaxy of the supernova is known. Surprisingly, su-pernovae at z > _{0.5 are fainter (Riess et al. 1998; Perlmutter et al. 1999) than expected for} sources at a distance obtained by linear extrapolation of Hubble’s law. This discrepancy is interpreted as accelerated expansion of the universe, and the consequence is that the total mass-energy requires a component that acts opposite to gravity. This is dark energy, and the most straightforward form is the cosmological constant. The first law of thermo-dynamic requires negative pressure in an adiabatically expanding vacuum, which can be thought of as ‘having space-time costs energy’. Albert Einstein was the first to introduce the cosmological constant Λ (although for different reasons), and it is the only mathemati-cal quantity in Friedmann cosmology that causes accelerated expansion of the universe. A more detailed consideration of dark energy is beyond the scope of this thesis. We assume that dark energy contributes to seventy per cent of the energy and matter in the universe, as inferred from type Ia supernovae.

Galaxy Rotation Curves, Bullet Cluster and Dark Matter

We now turn to the matter budget of the universe. The majority of matter is only detected by the gravitational effect it has, whereas all the matter that emits electromagnetic radiation contributes only to a small part of the total gravitating mass. This extra gravitating mass is assumed to originate from hypothesised weakly interacting particles. This form of matter is believed to have a significantly lower cross section for electromagnetic interactions which results in a lack of electromagnetic radiation. As no light is emitted, this form of matter is called dark matter. The concept was introduced by Zwicky (1933) who inferred a signif-icantly higher total gravitating mass in the Coma cluster from virial theorem† than what was expected based on the luminosity of all stars in the cluster. The dark matter hypothe-sis, however, was only accepted by the community decades later when observations of the Andromeda galaxy by Rubin & Ford (1970) showed that the orbital velocity flattens from a certain radius (Figure 2a). Kepler’s harmonic law, on the other hand, dictates an orbital velocity of stars in galaxies inversely proportional the distance of the star to the center of mass squared. This observation is interpreted as strong evidence in favour of the existence of dark matter, but perhaps the most compelling is the merging Bullet cluster (Figure 2b). The galaxy distribution is expected to follow the potential set by the total mass in the clus-ter. Furthermore, the collisional cross section for the individual stars and galaxies is low,

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thus, they are not expected to collide. Optical images of clusters show, as expected, that galaxy mergers are rare events. The hot plasma observed in X-rays, on the other hand, shows clear signs of interplay. The velocity of the ICM decreases through friction while the gas simultaneously heats up. The dark matter distribution can be traced using weak and strong gravitational lensing, and indeed, the dark matter does not appear to feel the gas pressure. In fact, the baryonic gas seems to lag behind the dark halo (Markevitch et al. 2004). At cosmological scales, the dominant longe-range force-term is gravity. As gravity results from mass, gravity is dominated by the ubiquitous dark matter.

(a) The rotation curve of the Andromeda galaxy shows that the orbital velocities of stars at large radii flattens out. From Kepler’s third law it is expected that the curve decreases as 1/r2. The difference can be accounted for by additional gravity from a dark matter halo.

Figure adopted from Rubin & Ford (1970).

104.6◦ 104.7◦

α

0.5 Mpc

(b) X-ray gas of a cluster-cluster merger with weak lensing contour overlay. The bullet shaped gas lags behind the distribution of mass (contours). The gas slows down due to friction, but the dark matter halo (which dominates the total gravitating mass) does not as it does not feel gas pressure.

Figure adopted from Markevitch et al. (2004).

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Hierarchical Clustering and Large-scale Galaxy Redshift Surveys

The small fluctuations of the cosmic energy density observed in the CMBR have grown over time to larger structures ranging from the stars we observe when gazing at the night sky, to a rich morphology of galaxies and clusters of galaxies on larger scales. This growth of structure is driven by gravitational attractions that ultimately push the self-gravitating mass to a point where gas pressure can no longer counter the attractive force. The resulting collapse occurs for structures exceeding a typical length scale that decreases as the universe expands. Larger structures thus form at later times, where clusters of galaxies are the largest modes that have collapsed at present. The resulting large-scale morphology of matter in the universe (Figure 3) is coined ‘Cosmic web’ (Bond et al. 1996). This name originates from the observation of a clumpy filamentary structure that is reminiscent of a rather chaotic spider web. Dark matter dominated potential wells form the backbone of the sheets of structure. As baryonic matter does feel gas pressure it slows down and follows behind the dark matter. The gas condenses and cools down at the bottom of the potential wells where the stars, galaxies and clusters of galaxies are formed. This explains why clusters are typically found at junctions of the cosmic filament where the gravitational potential is the deepest. Moreover, the displacement along the cosmic filament creates ample opportunity for clusters to interact with other clusters in highly energetic merger events. In fact, mergers of clusters are the most energetic events in the universe since the big bang with a typical kinetic energy of order 1063−64 _{erg, and major mergers are likely to occur several times}

during the cluster lifetime with a rate of once every 2−4 Gyr (Edge et al. 1990, 1992). Finally, the constant movement of matter allows larger structures to form in a bottom-up fashion as smaller structures grow hierarchically through the continuous mergers (Press & Schechter 1974). Note that the resulting structure is elongated along the cosmic filament, thus clusters of galaxies are expected to be quasi-spherical.

Large all-sky galaxy surveys clearly show the cosmic web. The most well-known surveys are the galaxy redshift survey of the Center for Astrophysics (CfA; Geller & Huchra 1989), the Sloan Digital Sky Survey (SDSS; York et al. 2000), and the 2-degree Field Galaxy Redshift Survey (2dFGRS; Colless et al. 2001) Interestingly, remarkably similar morphologies are found (Figure 3) in numerical ΛCDM cosmological simulations such as the Milennium Simuation (Springel et al. 2005b) by plugging in the cosmological parameters inferred from the CMBR observations.

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Figure 3.: The Cosmic Web seen in all-sky redshift surveys such as CfA, SDSS, 2dFGRS (blue). Cosmological simulations (red) recreate this geometry at matching limiting magnitudes. The four panels show cone diagrams in which the recession velocity is plotted along the radial direction, and the azimuthal direction shows the right ascension. This shows the distribution of nearby galaxies as if seen from above. Each dot represents a galaxy which clearly shows that matter clumps together. Image adopted from Springel et al. (2006).

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Clusters of Galaxies and Baryonic Matter

Current observations comprise numerous well-known, well-studied clusters of galaxies. Perhaps the best-known rich clusters are Virgo and Coma containing 103−4 of galaxies, while the Cygnus cluster with 118 identified galaxies is relatively unknown as a cluster of galaxies. In general, clusters are made up of several tens to thousands of optically visi-ble galaxies that together with hot intracluster gas‡ _{reside in the dark matter dominated}

potential well§. Clusters of galaxies are the largest gravitationally bound structures in the universe with typical sizes (diameter) in the order of a few megaparsec (1 parsec = 3.09·1016 m) and typical masses of 1014−15 M⊙(1 solar mass = 1.9889·1030 kg). All visible baryonic

matter locked up in the stars and galaxies contributes to∼10% of the baryonic mass in clus-ters of galaxies while the majority of the baryonic matter is found in intracluster medium (ICM). As stated earlier, the dark matter component plays a major role in clusters of galax-ies as it dominates the gravitational potential because dark matter contributes to roughly ninety per cent of the total mass in clusters. The ICM is heated to temperatures of order 107−8K, or typical kT in the range∼2-15 keV (McNamara & Nulsen 2007). The typical tem-perature can be calculated by converting gravitational potential energy to thermal energy as the baryonic matter falls towards the bottom of the potential well. The corresponding virial temperature is roughly equal to Newton’s constant times the mass of the cluster divided by the radius multiplied by the proton mass over the Boltzmann constant. The typical energies are well within the detection range of current X-ray satellites. As the distribution of the hot gas follows the shape of the potential, clusters are ideal testbeds to study the distribution of dark matter in the universe. Moreover, the same potential sets the galaxy distribution and the velocity dispersion along the line of sight of the optically visible galaxies in the cluster. This allows to cross-check results inferred both from optical and from X-ray observations to develop self-consistent models of clusters of galaxies. This makes clusters of galaxies ideal to test and constrain cosmological models.

Evolution of the Universe

The cosmological model in combination with the cosmological parameters allows astronomers to predict the ultimate fate of the universe. The evolution of the universe depends strongly on the density parameter Ωtot = ΩM+Ωr+ΩΛ. The first parameter, the mass density, is

the sum of the baryonic and dark matter, the second being the radiation density, while the

‡ further discussed in section 1.3 § further addressed in section 1.2

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latter constitutes the contribution of the cosmological constant Λ that results in a positive vacuum energy density, thus a negative pressure that results in accelerated expansion of the universe. The mass density can be expressed as the ratio of the true mass density of the universe ρm over the critical density. Equating the gravitational potential energy within a

sphere to the kinetic energy using Hubble’s law for the velocity, and rearranging the terms results in the (classically derived) expression

ρcrit = 3H(z)

2

8πG , (1.3)

where H is the Hubble constant as a function of redshift z. In the classical interpretation this parameter thus determines whether the universe continues to expand or at a certain point in time starts to contract again. The Ωtot > 1 case, which is when the universe is

‘closed’, will ultimately result in a collapse of the universe commonly referred to as the Big Crunch, while the universe is thought of as ‘open’ for Ωtot < 1 because spacetime

under-goes continuous monotonic expansion ad infinitum. For unity the universe is called ‘flat’ and the expansion rate will decline exponentially. Clusters of galaxies provide excellent ob-servational constrains on the mass density parameter. The numerical value can be inferred from observations of the mass distribution, the number density of clusters, and the amount of substructure within clusters of galaxies. Clusters of galaxies can thus be used to probe the evolution of the universe as a whole.

These observations combined with evidence gathered from different epochs on the cos-mological timeline has lead to convincing support for the ΛCDM model. In particular, understanding of the CMBR has contributed greatly to constrain values of the cosmologi-cal parameters. For example, the numericosmologi-cal values are found in the Wilkinson Microwave Anisotropy Probe (WMAP) nine year data release that features the final maps and results (Bennett et al. 2013). The Planck spacecraft is currenly in orbit and is expected to further improve these measurements (Planck Collaboration et al. 2015). Our current best under-standing of the observations shows that the universe is flat as the measured total density Ω_tot _≈ _{1 with the dominant contribution arising from the vacuum energy density. The} typical values, or a generic set of cosmoligical parameters if you will, assumes a Hubble parameter H0 =70 km/s/Mpc, ΩM,0 =0.3, ΩΛ,0 = 0.7. Note that the following quantities

scale with the reduced Hubble parameter h= H0/(100 km/s/Mpc). The X-ray luminosity

scales as Lx ∝ h−2, the core radius (see equation (1.35)) as rc ∝ h−1, and the mass of the

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1.2 structure of dark matter haloes 11

cosmological calculator

A practical use of cosmological theory is that it allows to convert an angle on the sky of an object at given redshift z to a physical distance in kpc. Wright (2006) provides an online cosmological converter that implements the theoretical considerations and allows to input a given set of cosmological parameters and a redshift. This tool has been ported to Python by Schombert (2007). We shamelessly copy-pasted the latter. The cosmological calculator assumes a radiation density that results from blackbody radiation with temperature T0 =

2.72528 K (CMBR) plus three massless neutrino species. The comoving distance divided by the Hubble radius H0/c is denoted as Z given by

Z= 1 Z 1/(1+z) da a _Ω m a + Ω_r a2 +ΩΛa 2_{+ (}₁ −Ω_tot) −1/2 (1.4) where a is the cosmological scale factor normalised at a = 1 in the current epoch. Here da/a can also be written as dz/(1+z)while integrating from 0 to z. Defining

J(x) =          sin √−x /√−x for x <₀ sinh √x /√x for x >₀ 1+x/6+x2/120+...+xn/(2n+1)! for x ≈0 (1.5)

where the three different cases represent an open, closed and flat universe. This gives the formula to convert from seconds of arc to kiloparsec in a flat universe as

1 arcsec= 1 1+z cZ H0 J q |(1−Ω_tot_|Z2 360 2π 3600 1 1000kpc (1.6) Here cZ/H0 is needed to convert back to physical units in Mpc from per unit Hubble

radius, 360/(2π)converts the angle in radians to degrees, 3600 from degrees to arcseconds, and finally we divide by 1000 to convert from Mpc to kpc.

Cygnus A has a redshift of z=0.0562 (Owen et al. 1997), at which one conveniently finds that 1” approximately corresponds to 1 kpc. More precise, 1” ∼ 1.091 using the typical cosmological parameters.

1.2 structure of dark matter haloes

The NFW profile is widely accepted to describe the distribution of dark matter. Navarro et al. (1996) show that this profile spans over two orders of magnitude in radius, and is

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1.2 structure of dark matter haloes 12

valid for a wide range of masses starting at small dwarf galaxies (1012 M⊙) all the way up

to the most massive (1015 _M

⊙) clusters of galaxies. Furthermore, a seemingly inconsistent

picture of typical values for the dark matter core radii is solved by the NFW profile. Specif-ically, arcs observed in gravitational lensing studies show typical core radii of 20−60 kpc (Grossman & Narayan 1988), while X-ray observations show typical values in the range 100−200 kpc (Fabian et al. 1991). This inconsistency is solved naturally when using the NFW-profile. This seminal work provides the basis for any model that includes dark matter, specifically when numerical simulations on the scale of galaxies or clusters of galaxies are in play. The NFW-profile is defined as

ρ(r)∝ 1 r rs 1+ r rs 2 , (1.7)

where rs = r200/cNFW is the scaling radius and cNFW is the concentration parameter. Here

the virial radius r200 is used as the size of the cluster, which is discussed further in

Sec-tion 1.3. Note that the scale radius is the radius over which the profile changes shape. As we will see later on, the X-ray density profile (β-model) has a characteristic core radius rc

such that for r < _r_c _{the density is roughly constant. The baryonic content of the cluster,} thus, has a characteristic radius of clear physical meaning, whereas the scale radius of the NFW-profile has no real physical meaning other than that near this radius the profile is roughly isothermal.

Hernquist (1990) provides an elegant equation similar to the NFW-profile but resulting in analytical solutions when integrated. This formula was originally derived as an analytical alternative for the de Vaucouleurs R1/4 profile for elliptical galaxies.

ρ(r) = M 2π a r(r+a)3 (1.8) MDM(< r) = M r 2 (r+a)2 (1.9) φ(r) = −_rGM₊_a (1.10) ψ(r) = − a GM ·φ(r) = a a+r , (1.11)

The quantity a is a scale length. The mass profile is obtained by integrating the density profile over spherical shells of volume, dV =4πr2dr, from 0 to r and leads to an analytical expression. Note that the quantity M in the mass profile corresponds to a total, finite mass and would be the equivalent of integrating the density profile from 0 to ∞. In this sense, the

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1.3 clusters of galaxies: x-ray emission from the intracluster medium 13

Hernquist profile has a finite total matter mass: the mass profile converges towards to M as r →∞. The potential φ(r)follows by integrating the Poison equation. Dividing out the constants yields a very powerful form, the dimensionless potential ψ(r)that spans a range from 0(r → ∞) to 1(r → 0). Moreover, the distribution function, density of states, pro-jected X-ray surface brightness and the velocity dispersion are all described by elementary functions. Owing to the similarities between the NFW-profile and the de Vaucouleurs R1/4 profile, the Hernquist profile is also an accurate alternative for the NFW-profile to describe dark matter haloes, simply by replacing the total mass M by the total dark matter mass MDM. This analytical expression is first implemented in a numerical routine by Springel

et al. (2005a) to study the effects of feedback from stars and black holes in galaxy mergers. The authors note that the inner shape of the profile is equal to the NFW-profile while the faster decline in the outer part results in a converging mass profile. This can clearly be seen in Figure 4. As stated earlier, the NFW-profile holds for masses ranging from dwarf galaxies to the richest clusters of galaxies. This implies that the Hernquist profile is also a viable solution for numerical simulations of clusters of galaxies.

To force consistency between the NFW-profile and the Hernquist profile (such that ρDM = ρNFW for r <<_r₂₀₀_{), the hernquist scale length is set by the concentration parameter in the} NFW-profile. We adopt the relation from Springel et al. (2005a)

a=rs

q

2[ln(1+cNFW)− cNFW/(1+cNFW)] (1.12)

The similarity between the NFW and the Hernquist profile is illustrated clearly by Fig-ure 4. The solid line shows the NFW-profile, while the dashed line follows the Hernquist profile. The red vertical dashed line indicates the scaling radius rs and clearly shows that

this is the radius over which the profile changes shape. The integrated density, thus, the mass profile is shown in Figure 5. As expected, the NFW-profile increases with radius, and the Hernquist profile converges to a finite value. Both plots are generated for Cygnus A by plugging in the values inferred from the X-ray observation as discussed in chapter 3.

1.3 clusters of galaxies: x-ray emission from the intracluster medium comparing timescales

The intracluster medium (ICM) is ionised given the high temperature of order Tg∼107−8 K.

The assumption of spherical symmetry yields a low typical cluster number density of ne ∼ 10−4−10−2 cm−3 when plugging in the typical cluster mass and radius. More

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accu-1.3 clusters of galaxies: x-ray emission from the intracluster medium 14

Figure 4.: Hernquist versus NFW density profile to show they match at radii smaller than the scaling radius rs,

indicated by the red vertical dashed line. Figure inspired by Springel et al. (2005a), but reproduced with the inferred dark matter properties of Cygnus A.

Figure 5.: Hernquist versus NFW mass profile to show both total cluster masses are within 90 per cent inte-grated up to the virial radius r200, indicated by the red vertical dashed line. This plot shows the

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rately, the ‘hot gas’ is actually (as very eloquently phrased by McNamara & Nulsen (2007)) “an optically thin coronal plasma in ionisation equilibrium”. In this section we summarise

parts of Sarazin (1988) to show this.

The coronal limit of a plasma requires that:

i) The free particles follow the Maxwell-Boltzmann distribution at the kinetic electron temperature Tg because the cooling time and age of the ICM are much larger than the

timescale for Coulomb interactions in the plasma. This determines the excitation and ionization rates of all processes.

ii) The ions are assumed to be in the ground state because in low density environments radiative decay occurs much faster than collisional (de)excitation. Furthermore, three (or more) body collisions are not expected because of the low density.

iii) Stimulated emission is not expected because the radiation field is sufficiently diluted. iv) Radiative transfer is neglected because the plasma is optically thin given the density.

We start with the cooling time. Thermal bremsstrahlung is the dominant emission mech-anism in clusters of galaxies. The cooling time of the plasma is dictated by cooling through radiative losses. We adopt the emissivity, respectively total power per unit volume for free-free emission from Rybicki & Lightman (1979).

ǫνf f ≡ dW dVdtdν =6.8×10 −38_Z2_n eniT−1/2exp(−hν/kT)gf ferg cm−3s−1Hz−1 (1.13) ǫf f ≡ _dVdtdW =1.4×10−27T1/2neniZ2g_{f f}erg cm3s−1 (1.14) ≈3.0×10−27Tg1/2n2perg cm−3 s−1 (1.15)

Here ne is the electron number density, g_{f f} is the Gaunt factor assumed equal 1.1 in the

last equation. Both the charge Z and number density ni are summed over the different ion

species where solar abundances are assumed in the last equation.

Further radiative cooling from line emission is expected when Tg ≤ 3×107K for which

McKee & Cowie (1977) roughly approximate the cooling function as

Λ_≈6.2×10−19T_g−0.6 for 106 <_T_g <₄_×₁₀7_K _(1.16) and the emissivity is given by ǫ = n2pΛ erg cm−3 s−1. For the majority of clusters the

temperature is higher than the threshold such that the line emission contribution can be neglected. Further assuming isobaric cooling results in a cooling timescale given by

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1.3 clusters of galaxies: x-ray emission from the intracluster medium 16 tcool≡ (d ln Tg/dt)−1 =8.5×1010yr n_p 10−3_cm−3 −1 T_g 108_K 1/2 (1.17) We now turn to the typical timescale for Coulomb interactions. A homogeneous plasma with a non-Maxwellian particle distributions will converge to a state in which the velocity distribution does follow an isotropic Maxwellian velocity distribution as a result of elastic collisions. The equilibrium timescale is given by the ratio of the mean free path λeover the

root mean squared electron velocity teq(e, e) ≡λe/<ve>rms. Spitzer (1956) gives the mean

free path before an electron undergoes a collision that alters its energy

λe = 33/2(kTe)2 4π1/2_n ee4ln Λ (1.18) ln Λ=37.8+ln Te 108_K n e 10−3_cm−3 −1/2 , (1.19)

where Te is the electron temperature, ne the electron number density, and Λ the ratio of

largest to smallest impact parameter for the collision, and the expression for the Coulomb logarithm ln Λ is valid for Te≥4×105K. The mean free path for ions is found by plugging

in the ion temperature and number density and dividing by the fourth power of the ion charge while slightly increasing the Coulomb logarithm. Considering all ions are protons and assuming equality in electron, ion, and gas temperature gives

λe =λi _≈23 kpc _T g 108_K 2 ne 10−3_cm−3 −1 , and (1.20) teq(e, e) ≡ _< λe ve >rms = 3m1/2e (kTe)3/2 4π1/2_n ee4ln Λ (1.21) ≈3.3×105yr Te 108_K 3/2 n_e 10−3_cm−3 −1 (1.22) The timescale for protons teq(p, p)ispmp/me·teq(e, e) ≈43·teq(e, e). The electrons and

protons will both follow a different Maxwellian velocity distributions after this time and equipartition takes (mp/me) ·teq(p, e) ≈ 1870·teq(e, e) such that the longest timescale for

Tg ≈108 K and ne≈10−3 cm−3 is teq(p, e) ≈6×108 year.

Finally, the sound crossing time ts for a cluster of diameter D,

ts≈6.6×108yr Tg 108_K −1/2 D Mpc , (1.23)

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is shorter than the age of a cluster estimated as 10 Gyr. If the gravitational potential does not change on timescales shorter than the sound crossing time, and if heating and cooling processes do occur on timescales larger than ts, then it is justified to assume that the cluster

is hydrostatic equilibrium.

Furthermore, ionisation equilibrium holds because the age of the cluster and any other hydrodynamic timescale is larger than the time scales for ionization and recombination (Sarazin 1988). As an added bonus, this also shows that we can use the theoretical frame-work provided by fluid dynamics because we have almost shown that the fluid approxima-tion holds, requiring that:

i) The mean free path σ is much smaller the typical scale length.

ii) The amount of collisions is high enough to sustain the Maxwell velocity distribution, i.e. the fluid should be in local thermal equilibrium (LTE).

The first demand is met as eq. (1.18) gives typical values for the mean free path of order kpc while the diameter of clusters is in the Mpc regime, but we further discuss the size of clusters in the following section. The second requirement has been fulfilled as discussed above.

halo definition

The typical scale length for clusters of galaxies is usually called the virial radius. It is rather arbitrary where a cluster ‘stops’, i.e. what the cluster boundaries are, and for instance at which radius the total mass of a cluster should be quoted. There are three generally accepted definitions of the halo of a cluster of galaxies that we adopted from Duffy et al. (2008).

i) The ‘size’ of a cluster is given by the virial radius r200 such that ρ(< r200 >) =200ρcrit,

for which ρ is the average density assuming spherical symmetry, and ρcrit is the critical

density of the universe at the cluster redshift given in equation. (1.3).

ii) A cluster is delimited by rmean where in the above definition the critical density is

replaced by the mean background density.

iii) Based on the spherical top-hat collapse model, the cluster ‘edge’ is given by ∆ times the critical density, like the first definition but the value of 200 is replaced by ∆ as a function of cosmology and redshift given by Bryan & Norman (1998).

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We adopt definition i) such that when we say ‘virial radius’, we mean r200. The total

gravitating cluster mass M200 is the mass enclosed by the virial radius, according to this

definition. The baryon fraction is a function of radius where bf(r200) equals 17 per cent

(Planelles et al. 2013). Interestingly, this equals the primordial baryon fraction. In this sense the chosen definition of the size of a cluster corresponds to the radius at which one can think of the cluster as ‘blending in’ with the primordial gas in the universe.

virial theorem and hydrostatic equilibrium mass determination

Virial theorem allows to estimate the mass of a cluster of galaxies from optical observations of the galaxies that have a cluster membership, as first used by Zwicky (1933) to infer the mass of clusters of galaxies. It would take a crossing time tcr of roughly 1 Gyr for a cluster

to lose all of its galaxies if they were not gravitationally bound to the cluster. Observations, on the other hand, show relaxed clusters with a regular galaxy distribution that differs significantly from the distributions of galaxies not associated with clusters of galaxies. We can therefore assume that the galaxies are gravitationally bound. The total energy E is the sum of the kinetic energy T and the gravitational potential energy W, or E= T+W < _0, where T= 1 2

∑

_i miv 2 i (1.24) W = −1 2

∑

_i₆₌_j Gmimj rij . (1.25)

Here miis the mass of a galaxy, vithe corresponding velocity, and rijthe distance between

two galaxies. Assuming a stationary cluster distribution and integrating the equation of motion of the galaxies then yields

1 2 dI dt2 =2T+W, where W = −2T, E= −T, and I =

∑

i mir2i. (1.26)

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1.3 clusters of galaxies: x-ray emission from the intracluster medium 19 The above equation states the virial theorem. Defining total cluster mass as the sum over the masses of all galaxies, and the mass weighted velocity dispersion < _v2 _>_≡ _∑

imivi/MVT,

and the gravitational radius RG as

RG≡2M2VT

∑

i6=j mimi rij !−1 (1.27) MVT= RG <_v2> G (1.28)

The above equation is very useful as RG and< v2 > can be inferred from the projected

spatial distribution of galaxies and the radial velocity distribution under the assumption that both quantities are not correlated. This results in an expression for the mass-weighted radial velocity dispersion σ2

r and an equation for the total cluster mass in terms of

observ-ables. σr2 = 1 3 < v 2 _> _(1.29) ⇒ MVT = 3RGσ 2 r G ≈7.0×10 14 σr 1000 km/s 2 RG Mpc (1.30) We now turn to the hydrostatic mass determination. The mass of a cluster of galaxies can be evaluated under the assumption of hydrostatic equilibrium if the temperature and density of the X-ray emitting gas is known. X-ray observations yield both of these quantities as a function of radius. This method requires a stationary gravitational potential, i.e. it does not change on timescales shorter than the sound crossing time. Furthermore, no supersonic motion can be present in the gas, and gravity and gas pressure are the only forces acting on the gas. MHE(<r) = kT (r)r2 µmpG 1 ne dne dr + 1 T dT dr (1.31) Given that the assumptions hold, this method is generally more reliable than mass esti-mates from virial theorem using the galaxies as test particles. While the collisional gas has isotropic velocities, an anisotropic velocity distribution could arise in the collisionless galax-ies that could alter the inferred mass. Moreover, the virial mass is limited to the number of observed galaxies while the statistical significance of the hydrostatic mass increases with observation time. Finally, the hydrostatic method is not very sensitive to the shape of the cluster while the virial mass estimate is.

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spherically symmetric isothermal sphere in hydrostatic equilibrium

We start with the Navier-Stokes equation adopted from Choudhuri (1998, eq. (3.52) on p. 47), assuming the fluid approximation is valid.

∂~_v ∂t + (~v· ∇)~v = − 1 ρ∇p+ ~F+ µ ρ∇ 2_~_v _, _(1.32)

where~_{v is the velocity, t is time,} _∇ _{the differential operator, ρ the density, p the pressure,}

µ the viscosity, and~F the force per unit mass, delivered by gravity in clusters of galaxies. Hydrostatic equilibrium implies v→0 and ∂/∂t→0, leading to the equation

∇p_{= −}ρg_∇φ(r) , (1.33) where p = ρgkTg/µmp, ρg is the gas density, µ the mean molecular weight, mp the proton

mass, and φ(r)the gravitational potential. This equation shows that clusters of galaxies are stable because the magnitude of the gas pressure is equal to the attractive self-gravitating forces. Although ΛCDM demands that general relativity is used to describe gravity on cos-mological scales, Newtonian gravity does suffice for the typical scales for merging clusters of galaxies and we can safely substitute Newtonian gravity for the force term. Movement of clusters is non-relativistic and the gravitational fields are not so strong that a full general relativistic approach is required. Furthermore, we assume spherical symmetry for both the baryonic ICM and for the dark matter halo.

1 ρgas dPgas dr = −G Mtotal(<r) r2 . (1.34)

Here equation (1.34) is the spherically symmetric form of the hydrostatic equation. Fol-lowing Donnert (2014), we adopt the β-model (Cavaliere & Fusco-Femiano 1978) that de-scribes the radial density profile of the intracluster gas. In this model, the slope β is the ratio of the specific kinetic energy of the galaxies to that of the gas. Assuming β = 2/3 (Mastropietro & Burkert 2008) yields an analytical expression for the gas mass by integrat-ing the density profile over volume in spherically symmetric shells of thickness dr. The equations are as follows.

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1.3 clusters of galaxies: x-ray emission from the intracluster medium 21 ρgas(r) =ρ0 1+ r 2 r2 c −3₂β (1.35) β≡ σ 2 r kTg/µmp (1.36) Mgas(<r) = r Z 0 ρgasdV = r Z 0 ρ0 1+r 2 r2 c −3₂·2₃ 4πr2dr =4πr3cρ0 r rc−arctan r rc (1.37) Here r is the radius, and rc is the core radius. Gas within the core radius has an

approx-imately constant central density ρ0 while the density falls off as a power-law with index β

outside the core radius. Note that in this sense the core radius is a quantity with a physical meaning. Should any other value than 2/3 or 1 for β be used, the integration has no analyt-ical solution but can be expressed by the Gaussian hypergeometranalyt-ical function2F1(a, b; c; z)

that can be found in Abramowitz & Stegun (1972, ch. 15).

M(<r) = 4π 3 ρ0·2F1 3 2, 3β 2 ; 5 2;− r2 r2 c (1.38)

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2

O B S E R VAT I O N A L O V E R V I E W O F T H E C Y G N U S C L U S T E R

The Cygnus constellation, denoted by the symbol ‘Cyg’ (Russell 1922), is found on the Northern hemisphere right in the plane of the Milky Way, just below the well-studied Kepler Field. More quantitatively, it is located at a declination of roughly+27◦ <_δ <₊₅₄◦ and a right ascension 19h17m < _α < ₂₁h₄₅m_{. The constellation was named ‘The Swan’ by} ancient Greek astronomers and is featured as early as Ptolemy’s list of constellations. The constellation has stars well visible to the naked eye, such as its brightest star at the tail of the Swan, Deneb (α Cyg, also part of the asterism Summer Triangle together with Vega and Altair), and at the head the optical double Albireo (β Cyg and β2 Cyg). The constellation

hosts interesting deep-sky objects like the Veil nebula, a large bright feature in the X-ray sky caused by a supernova explosion. Other well-known, well-studied X-ray objects found in Cygnus are the (galactic) X-ray binary Cyg X-1, widely accepted as the first (indirect) proof of the existence of black holes, and the microquasar Cyg X-3 where a Wolf-Rayet is found in a binary with a compact object. Figure 6 shows this part of the sky.

Throughout this thesis we use the name Cygnus A for the radio source as well as for its optically visible host galaxy. In addition, the cluster of galaxies is often also named Cygnus A. This indicates that one cannot think of the object Cygnus A as just one source. To avoid confusion we will indicate which source of emission is meant such that the radio source means the active galactic nucleus (AGN), the cD galaxy means the optical galaxy, and the Cygnus cluster or X-ray source means the emission from the intracluster medium. The literature overview in this section does not include the literature on the majority of the radio emission, neither on most of the optical emission, nor the majority of X-ray studies that focus on the emission in the core, unless relevant to our merger study. Seminal publications in the field of radio astronomy are bundled in Sullivan (1982) and contain very interesting early literature on the strong radio source Cygnus A. In addition, proceedings of a four day workshop on Cygnus A by Carilli & Harris (1996), and the comprehensive review by Carilli & Barthel (1996) provide a great source of information on prior observations of Cygnus A as these publications and references therein provide an overview of the study of Cygnus A

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observational overview of the cygnus cluster 23

Figure 6.: Cygnus, the Swan constellation, is found in the plane of the Milky Way on the Northern hemisphere. The green star indicates the location of the Cygnus cluster. Photo courtesy of E. Hanko.

up to mid 1995 in all frequency domains of the electromagnetic spectrum. Our overview does include X-ray observations of the extended source published to date spanning from early Uhuru up to curent-day Chandra observations including the ongoing multi-wavelength campaign of Wise and collaborators.

However, we cannot discuss Cygnus A without at least showing the well-known radio observation. Perhaps most astronomers know Cygnus A as one of the most powerful radio sources in the sky, the brightest extragalactic source, the classical radio double, and the archetype of the FR-II class (Fanaroff & Riley 1974) of radio galaxies (Figure 7). The extreme brightness of the radio source can clearly be seen in Figure 8. Although found at a redshift z=0.562 (Owen et al. 1997), Cygnus A is as bright as a z=1 source, and a thousand times brighter than any other source at the same distance (Stockton & Ridgway 1996; Carilli & Barthel 1996).

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19h57m40s

42s

44s

46s

48s

RA (B1950)

+40°35'24"

36"

48"

36'00"

12"

Dec (B1950)

30 kpc

Figure 7.: JVLA observation at 5 GHz, 0.5” resolution of Cygnus A. The collimated outflow from a central source is visible. The jet injects relativistic electrons, and deposits energy in the medium surrounding the brightest cluster galaxy. The giant radio lobes are clearly visible, and hot spots can be seen albeit slightly misaligned with the direction of the jet. Figure reproduced from Carilli & Barthel (1996).

0.0 0.2 0.4 0.6 0.8 1.0 z 0.0 0.5 1.0 1.5 2.0 2.5 3.0 P178 ( W Hz − 1 ) 1e28 405 348123 20 427.1 295 265 237 268.1 280

Figure 8.: Radio power at 178 MHz taken from the revised third Cambridge catalogue (3CR) (Spinrad et al. 1986) plotted as a function of redshift for z<_{1. Note that the radio power of 3C 405 (Cygnus A) is}

significantly higher than for galaxies at similar (low) redshift. Figure reproduced from Stockton & Ridgway (1996), but we assume H0=70 km/s/Mpc.

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It is of no surprise that the radio emission is detected as early as the first radio observations carried out by radio astronomy pioneer Grote Reber, see (Reber 1944, 1948). On a side note, radio astronomers that do not study Cygnus A might rather dislike the radio source as it so bright it usually ends up in the sidelobes of modern radio telescopes and explicitly has to be filtered out of the correlated data (e.g. Offringa et al. 2012). The optical discovery of the Cygnus cluster follows a few years later by Baade & Minkowski (1954), who report that photographic plates of the same part of sky reveal a few galaxies clustered together at a position corresponding with the location of the radio source. The large, diffuse X-ray emission of the Cygnus cluster that we are particularly interested in is featured in the first catalog of X-ray sources seen by Uhuru (Giacconi et al. 1972).

After each discovery an initial debate sprouted within the community regarding (i) the origin, (ii) emission mechanism, and (iii) the possible, exciting connections between two or three of the sources of unexplained emission. The debate has now mostly settled and consensus has been reached that Cygnus A is indeed the BCG hosting an AGN within a cluster of galaxies. The details, however, are still subject to several major studies. Cygnus A is an excellent target to study AGN feedback, a merging cluster of galaxies, the interplay between both, and the contribution both physical processes have on heating the hot intra cluster medium. The brightness and proximity allow for unprecedented spatial and spec-tral resolution to reveal insight into the detailed workings of AGN Feedback. An even more intriguing feature, however, is not the highly fascinating active galactic nucleus. Rather, we take a specific interest in the cluster of galaxies Cygnus A is part of as it is currently under-going a major, disruptive merger with a subcluster. This is not a well-known observation because the majority of studies focusses on the central region where the AGN feedback can be studied. Furthermore, in order to see the diffuse emission to the North West of Cygnus A, the infalling subcluster, one has to smooth the emission significantly as discussed further in Section 3.2.

A summary of previous X-ray observations presented in Table 1, and an overview of optical studies given in Table 2. Certain references are of particular interest or contain figures that we explicitly adopt in the paragraphs following the tables.

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Table 1.: Overview of the literature on the extended emission in the Cygnus cluster

Observatory Conclusions Reference

Uhuru Detection of extended source with 0.270 square degrees area. Suggested counterpart CygA. Giacconi et al. (1972) Copernicus Confirmation X-ray source has powerful radio galaxy CygA as counterpart. Thermal

bremsstrahlung emission mechanisms suggested.

Longair & Willmore (1974) ANS Misalignment peak of X-ray emission and radio galaxy by 6’ if assumed a point source. On

the other hand, consistent with>_{12’ extended emission as expected from hot cluster gas.}

Brinkman et al. (1977) HEAO-1 Extended∼2’ source with a complex geometry. Fit of isotermal sphere model yields a core

radius of 0.19 Mpc and central density of 0.014 cm−3. A total mass for the galaxy Cygnus A is estimated to be 1014 M⊙.

Fabbiano et al. (1979)

Einstein The X-ray emission is extended, spherically symmetric and centered on the cD galaxy. Feigelson & Schreier (1980) Ariel-V Catalog entry: consistend with prior literature, and detection of iron Kα line. Bell Burnell & Chiappetti (1984) Einstein (2) Cooling flow of 90 M⊙yr−1. Mass-estimate of 1014 M⊙(King approximation) adopting the

HEAO-1 value for the core radius rc = 0.2 Mpc within a source that extends North West

from the central radio source by over 1 Mpc (H0=50 km/s/Mpc).

Arnaud et al. (1984)

Exosat Iron Kα detection. Highly absorbed power-law component associated with nucleus of the radio source. The source extends significantly to the North West, and the central density is 0.02 cm−3_.

Arnaud et al. (1987)

Ginga The X-ray spectrum shows a thermal component with K-shell transition lines and a highly absorbed power-law. The former is consistent with hot intracluster gas, and the latter suggests Cygnus A hosts an obscured quasar.

Ueno et al. (1994)

Table continues on next page

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Table 1.: Overview of the literature on the extended emission in the Cygnus cluster (continued from previous page)

ROSAT HRI The X-ray structure is dominated by the cluster emission centered on the galaxy Cygnus A. A modified King (β-model, equation (1.35)) model yields a core radius of 35_±5 arcsec, central density of 0.07±0.02 and King-model index of β= 0.75±0.25. Note that only the inner 100 kpc is observed.

Carilli et al. (1994)

ROSAT PSPC The X-ray emission is dominated by the thermal emission from the hot ICM, agrees rea-sonably well with spherically symmetric emission within the inner 5 arcsec, and is strongly peaked on the central galaxy. A lower temperature towards the center of the gravitational potential is observed from which a cooling flow of 250 M⊙ yr−1 is induced with a cooling

radius of 180 kpc. A plume extending a bit over 15 arcmim to the North West is reported, and the possibility of a past or ongoing cluster-cluster merger is suggested. Central density is 0.03 cm−3_.

Reynolds & Fabian (1996)

ASCA The merger geometry appears very straightforward. A temperature jump is observed in the region between Cygnus A and the subcluster to the North West. The temperatures measured are T0 ≈ 4±1 K, and postshock T1 ≈8+₋2₁ K, and the estimated merger velocity

is 2000 km/s. NB, the authors assume H0 =50 km/s/Mpc.

Markevitch et al. (1999)

Chandra Part one and two of a series of publications on Cygnus A, the scope of these publications is the emission from the hotspots, respectively, the nucleus. Included for completeness, but outside the scope of our overview.

Wilson et al. (2000) Young et al. (2002) Table continues on next page

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Table 1.: Overview of the literature on the extended emission in the Cygnus cluster (continued from previous page)

Chandra (2) First mention of emission to the North West likely due to another cluster. The mass de-rived from hydrostatic equilbrium (equation (1.31)) within 500 kpc (assuming H0 = 50

km/s/Mpc) is 2×1014 M⊙ respectively 2.8×1014 M⊙ for constant and centrally

decreas-ing temperature profiles, and the total mass from the X-ray emittdecreas-ing gas is 1.1×1013 _M

⊙.

An isothermal β-model is fitted and yields rc ≈18 arcsec and β≈0.51.

Smith et al. (2002)

Suzaku A temperature jump is observed between Cygnus A and the subcluster to the North West. Combined with redshift measures of the iron K line the system appears to have a simple geometry. Both clusters merge at a velocity of 2400−3000 km/s, and the projection angle is estimated as 54◦.

Sarazin et al. (2013)

Chandra (3) Nicely summarises Chandra observations of the central region prior to the Wise (2014) ob-servations. Outside the scope of this overview as it focusses mainly on the central region.

Nulsen et al. (2015) Chandra (4) X-ray observations as part of an ongoing multi-wavelength observational campaign that

provides the dataset used to constrain the initial conditions for the numerical simulations in this thesis.

Wise et al. (in prep)

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Table 2.: Overview of cluster or merger relevant optical studies of Cygnus cluster members

Palomar The 200 inch Palomar telescope shows the brightest member of a cluster of galaxies coin-cides with the location on the sky of the powerful radio galaxy Cygnus A.

Baade & Minkowski (1954) Kitt Peak: Lick Cygnus A lies in the plane of the Milky Way (Figure 6), thus the Galaxy conceals the

majority of the galaxies in the cluster. The authors conclude that the cluster Cygnus is Abell-poor based on the observation of a mere five galaxies. The BCG Cygnus A can be classified as a cD galaxy, and the measured velocity dispersion is 2000±500 km/s.

Spinrad & Stauffer (1982)

Kitt Peak: Steward Velocities of 41 galaxies associated with the cluster are observed. The authors conclude the Abell richness of the cluster is 1 up to 4. A relatively high velocity dispersion of 1581+₋286₁₉₇ is reported, and the dynamical center of the spatial distribution of galaxies appears shifted to the North West, thus CygA is not located at the center of a rich cluster of galaxies. Although statistical evidence supporting two distinct clusters is rather weak, such high velocity dispersions are typically found in clusters with two or more subclusters.

Owen et al. (1997)

Kitt Peak: WIYN Detection of 77 additional galaxies associated with the cluster, combined with temperature structure inferred from X-rays, allows for dynamical modelling. This shows the optical distribution of galaxies and the temperature structure is consistent with a cluster-cluster merger 0.2-0.6 Gyr prior to core passage projected at an angle of 30◦₋45◦.

Ledlow et al. (2005)

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An overview of X-ray observations with different instruments in the first couple of years is shown in Figure 9, where the location of the radio source (3C 405) is marked with a cross. This is compelling evidence suggesting an apparent connection between the radio source and the X-ray emission.

A bit over a decade after the initial Uhuru discovery, consensus has been reached regard-ing the emission mechanism of hot intracluster gas (e.g. Bahcall 1977). For the Cygnus cluster in particular, Arnaud et al. (1984) are the first to write it is safe to assume thermal bremsstrahlung is the main emission mechanism, as suggested earlier by Longair & Will-more (1974). The main evidence for the thermal origin of the X-rays seen in clusters is the presence of iron Kα line emission. This feature is observed in the Cygnus cluster by Bell Burnell & Chiappetti (1984) and Arnaud et al. (1987). In general, models of the emission originating from a spherically symmetric distribution of gas in the gravitational potential of the cluster agree well with the observations (e.g. Cavaliere & Fusco-Femiano 1978). Fab-biano et al. (1979) report similarities of Cygnus A and its larger cluster environment with M87 in the Virgo (Mathews 1978) cluster, and with NGC 1275 in the Perseus cluster (Goren-stein et al. 1978), and therefore fit the extended X-ray flux with an isothermal hydrostatic sphere model following Mathews (1978). This yields first mass estimates of the cluster gas as well as values for the core radius and central density. For the Cygnus cluster this fit yields a total mass of 1014 _M

⊙, a temperature of 6.5 keV, a central number density of 0.014

cm−3 and luminosity of 4.7·1044 ergs s−1 (2−6) keV. The model does require refueling as the cooling time is of order 3 billion years, which is smaller than the Hubble time. One of the major problems in clusters of galaxies at the time was the so-called cooling flow problem.

Although the emission mechanism had been found, the origin of the hot intracluster remained a mystery. Perhaps the gas simply fell into the cluster from a general intercluster medium (Takahara & Ikeuchi 1975), or it might have been expelled by the galaxies (Yahil & Ostriker 1973). The observed metal enrichment of the ICM is clear evidence that part of the material must have been processed through the stars in the galaxies. Another mystery remained, however, the nature of heating and cooling of the gas. The gas is thought to remain as hot as observed by means of shock heating, but at the same time the central regions of clusters have a short cooling timescale so the gas is expected to cool in the absence of a heating mechanism. Clusters of galaxies are assumed to be in hydrostatic equilibrium, thus virial theorem requires an increase in central density as radiative losses actively cool the cores of clusters of galaxies. Alternatively, one can think of this increase in central density as mass flowing from the cluster outskirts to the bottom of the potential well in its center (e.g. Fabian & Nulsen 1977). This ‘flow’ of gas was called the cooling flow

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Figure 9.: Location with detector uncertainties for early observations of the Cygnus cluster: Uhuru (squared box), Copernicus (sphere), ANS and HEAO (MC1, MC2). The radio galaxy is indicated with a cross (3C 405). Figure adopted from Fabbiano et al. (1979)

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Figure 10.: X-ray surface brightness observed with the Einstein satellite. The larger image shows the IPC ob-servation smoothed with a 32” Gaussian, and the inset shows 12” Gaussian smoothed HRI data with a 5 GHz radio contour map of Alexander et al. (1984). This observation clearly shows that the classical radio double is found inside a cluster environment that extends significantly to the North West. Figure adopted from Arnaud et al. (1984).

problem, and it is the main interest of Arnaud et al. (1984). Specifically, the authors aim to find observational evidence for cooling flows.

At this time the central galaxy was considered the archetype of a classical radio double (e.g. Winter et al. 1980), and from photographic and spectroscopic observations Spinrad & Stauffer (1982) find cD galaxy Cygnus A to lie in a poor cluster of galaxies. The authors also note a velocity dispersion of 2000±500km/s, although this study is based on a mere 5 galaxies. This makes Cygnus A rather exceptional as few other classical double radio galaxies are found within a cluster of galaxies. Arnaud et al. (1984) are the first to show a clear image of the large-scale emission smoothed with a 12” Gaussian (Figure 10). However, no significant peak to the North West has been observed yet, but these data do show the emission extends significantly in this direction. The large-scale emissions reaches over a megaparsec from the radio galaxy, which is consistent with observations of other large clusters of galaxies. Using the cooling flow model of Fabian & Nulsen (1977), it is found that the cooling rate is 90 M⊙ per year in the inner 125 kpc region. One should be cautious when