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Astrophysical Applications of Scattering in Interstellar and Intracluster Gases

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Astrophysical Applications of Scattering in Interstellar and Intracluster Gases Astrophysical Applications of Scattering in Interstellar and Intracluster Gases Conrad K. Cramphorn Munchen¨ 2004 Astrophysical Applications of Scattering in Interstellar and Intracluster Gases Conrad K. Cramphorn Dissertation an der Fakult¨at fur¨ Physik der Ludwig–Maximilians–Universit¨at Munchen¨ vorgelegt von Conrad K. Cramphorn aus Dundee in Schottland Munchen,¨ den 12. Mai 2004 Erstgutachter: Prof. Dr. Rashid A. Sunyaev Zweitgutachter: Prof. Dr. Ralf Bender Tag der mundlichen¨ Prufung:¨ 24. November 2004 Fur¨ meine Eltern Inhaltsverzeichnis Zusammenfassung (Summary in German) 3 Summary 5 1 Introduction 9 1.1 Diffuse Gas in the Universe ...................... 9 1.2 Supermassive Black Holes in the Centres of Galaxies ........ 11 1.2.1 Sgr A¤ .............................. 13 1.2.2 M31 ............................... 14 1.2.3 M87 ............................... 15 1.3 Relativistic Jets ............................. 16 1.4 Clusters of Galaxies ........................... 17 1.5 The Sunyaev-Zel’dovich Effect ..................... 18 2 The X-ray luminosity of the Galactic centre in the recent past 21 2.1 Introduction ............................... 22 2.2 Method ................................. 25 2.2.1 X-ray Archaeology ....................... 25 2.2.2 GMCs in the Galactic disk ................... 28 2.2.3 Scattered flux .......................... 31 2.3 Limits on the X-ray luminosity of Sgr A¤ from Giant Molecular Clouds 35 2.3.1 Response of a single cloud ................... 36 2.3.2 Response of one field of view .................. 40 2.3.3 Response of all fields of view containing at least one GMC . 43 2.4 Limits on the X-ray luminosity of Sgr A¤ from the interstellar HI distribution ............................... 47 2.5 The Milky Way at extragalactic distances .............. 52 2.5.1 Scattered X-ray surface brightness ............... 53 2.5.2 Scattered X-ray luminosity ................... 58 2.5.3 Fluorescent iron K®-line luminosity .............. 62 2.6 Discussion ................................ 62 1 Inhaltsverzeichnis 3 Constraining the past X-ray luminosity of AGN in clusters of galaxies 65 3.1 Introduction ............................... 66 3.2 Advantage of scattered X-ray lines over the scattered continuum .. 69 3.3 AGN in the centre of a beta-cluster .................. 74 3.3.1 Approximation of isotropic scattering ............. 74 3.3.2 Continuum radiation ...................... 74 3.3.3 Resonance lines ......................... 82 3.4 Numerical simulations ......................... 85 3.4.1 M87 ............................... 85 3.4.2 Cygnus A ............................ 96 3.5 Discussion ................................ 99 4 Scattering in the vicinity of relativistic jets 103 4.1 Introduction ............................... 103 4.2 The model ................................ 106 4.3 Results .................................. 112 4.3.1 Single ejection .......................... 112 4.3.2 Multiple ejections ........................ 121 4.4 Application to M87 ........................... 130 4.4.1 Observations .......................... 130 4.4.2 Constraints on the jet parameters ............... 131 4.5 Discussion ................................ 137 5 A correlation between the SZ decrement and the Thomson depth 139 5.1 Scaling relations for clusters of galaxies ................ 140 5.2 The SZ decrement ........................... 140 5.3 Scaling relation for gas distributed similarly to dark matter ..... 141 5.4 Isothermal gas in a NFW dark matter potential ........... 144 5.5 Clusters with observed SZ decrements ................. 145 5.6 SZ decrement and Thomson depth for simulated clusters ...... 145 5.7 Results .................................. 146 5.8 Discussion ................................ 148 6 Concluding remarks 151 References 156 2 Zusammenfassung Diese Arbeit befaßt sich mit astrophysikalischen Anwendungen von Streuprozessen in diffusen Gasen innerhalb von Galaxien bzw. Galaxienhaufen. Anhand von ak- tuellen Beobachtungsdaten wird versucht, Aussagen uber¨ die zuruckliegende¨ Ent- wicklung der Leuchtkraft von astrophysikalischen Objekten, wie supermassiven schwarzen L¨ochern und relativistischen Jets, zu gewinnen, die innerhalb dieser diffusen Gase Strahlung erzeugen. Die im Rahmen dieser Arbeit relevanten physi- kalischen Eigenschaften dieser Objekte sind in Kapitel 1 zusammengestellt. In Kapitel 2 werden Aussagen uber¨ die R¨ontgenleuchtkraft des supermassiven schwarzen Lochs im Zentrum der Milchstraße, Sgr A¤, w¨ahrend ungef¨ahr der letz- ten einhunderttausend Jahre hergeleitet. Hierzu werden die Ergebnisse großfl¨achi- ger R¨ontgenbeobachtungen entlang der galaktischen Ebene mit den mittels Radio- beobachtungen von Molekulwolken¨ innerhalb der galaktischen Scheibe gewonnenen Ergebnissen kombiniert. In Kapitel 3 wird der Frage nachgegangen, inwieweit sich ¨ahnliche Aussagen uber¨ die in der Vergangenheit liegende R¨ontgenleuchtkraft eines supermassiven schwarzen Lochs gewinnen lassen, das im Zentrum einer elliptischen Galaxie oder eines Galaxienhaufens vorhanden ist. Hierbei wird insbesondere die kontinuierliche Streuung an freien Elektronen sowie die Streuung in Resonanzlinien analytisch als auch numerisch unter Verwendung von Monte-Carlo Methoden untersucht. In Kapitel 4 wird eine anisotrop abstrahlende Strahlungsquelle angenommen, mittels der das von relativistischen Jets erzeugte Strahlungsfeld simuliert wird. Dieses Modell wird auf den relativistischen Jet der aktiven Galaxie M87 ange- wandt, um Aussagen uber¨ den Neigungswinkel dieses Jets relativ zu der Sichtlinie und uber¨ den Lorentzfaktor der in diesem Jet str¨omenden Materie zu gewinnen. In Kapitel 5 wird eine Korrelation zwischen dem durch den Sunyaev-Zel’dovich Effekt hervorgerufenen Intensit¨atsdekrement der kosmischen Hintergrundstrah- lung in Richtung eines Galaxienhaufens und der Thomsondicke des diffusen Gases innerhalb dieses Galaxienhaufens hergeleitet, die im Rahmen von numerischen Si- mulationen der Strukturbildung dunkler Materie aufgefunden worden ist. Kapitel 6 schließt die Arbeit mit einer zusammenfassenden Wurdigung¨ der Er- gebnisse der vorhergehenden Kapitel. 3 Zusammenfassung 4 Summary This thesis studies the question of how observational data can pose non-trivial constraints on the past activity of such diverse astrophysical objects as the centre of the Milky Way, supermassive back holes in the centres of massive elliptical galaxies and of clusters of galaxies and relativistic jets. In order to set the stage for this study, chapter 1 provides a brief summary of the relevant aspects of the different astrophysical objects in question. In the first part of this work, i.e. in chapter 2, I focus on the putative super- massive black hole at the centre of the Milky Way. High resolution observations of the motions of stars in the vicinity of the dynamical centre of our Galaxy are most plausible explained by the presence of such an object with a mass of about 6 2:6 £ 10 M¯. Recent measurements with the Chandra X-ray satellite detect the associated X-ray source Sgr A¤ at a mere 2 £ 1033 erg s¡1, more than ten orders of magnitude below the Eddington luminosity of 3 £ 1044 erg s¡1 for a black hole of such a mass. This relative dimness being remarkable in itself, raises the question of whether Sgr A¤ was equally dim in the recent past. I will address this ques- tion by applying a method which has been successfully applied to giant molecular clouds (GMCs) in the “immediate” vicinity of the Galactic Centre (GC). It has been proposed, that diffuse, hard X-ray emission observed today in the direction of the giant molecular clouds in the central 100 pc of the Galaxy and especially in the direction of a cloud called Sgr B2 is radiation emitted by Sgr A¤ in the past, which has been scattered into our line of sight by the molecular gas present in these 6 clouds. In order for the mass of molecular gas present in Sgr B2 (» 6 £ 10 M¯) to produce the presently observed flux, the X-ray luminosity of Sgr A¤ must have been of the order of 2£1039erg s¡1 about 400 years ago, i.e. six orders of magnitude more luminous than at present. The time delay of 400 years corresponds to the different path lengths for photons, received directly or taking the detour via Sgr B2, which lies at a projected distance of » 120 pc from the GC. The application of the method successfully used in the above described case to constrain the luminosity of Sgr A¤ in the past is not restricted to GMCs close to the GC. In order to provide nontrivial constraints upon the strength of the activity of the GC in the past by means of this method, one requires a scattering material with 5 Summary a sufficient optical depth and an estimate of the scattered flux produced by this material. In the case of our Galaxy two obvious choices which fulfill these criteria are interstellar molecular and atomic hydrogen. CO surveys covering the Galactic 9 plane have shown that about 10 M¯ of H2 reside in GMCs on orbits between the GC and the sun, with a peak mass surface density around a galactocentric radius between 4 and 6 kpc, the so called molecular ring (e.g. Dame (1993)). The time delays, i.e. the difference of the arrival times between the primary and the scattered radiation, for clouds located in the molecular ring, range up to about 40:000 years. The HI phase of the interstellar medium (ISM) is more diffusely distributed than H2. It extends out to about 16 kpc with an approximately constant mass surface ¡2 9 density of about 4 M¯ pc , corresponding to a total mass of the order of 3£10 M¯ (e.g. Dame
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