Searching for AGN accretion states with X-ray timing

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Searching for AGN accretion states

with X-ray timing

Stian Huseby

A Thesis presented for the degree of

Master of Astronomy and Astrophysics

Anton Pannekoek Institute for Astronomy

Faculty of Science

University of Amsterdam

The Netherlands

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Searching for AGN accretion states with X-ray timing

Stian Huseby

Submitted for the degree of Master of Astronomy and Astrophysics

December 2018

Abstract

The aim of this project is to investigate whether variability behaviour seen in AGN is consistent with the mass scaling from the same range of variability types seen in BHXRBs in their different scales. This thesis has developed a method to look at the power spectral shapes of AGN and compare these with the corresponding power spectra of BHXRBs using the power colour method. To do this, light curves were extracted from the archives of the Rossi X-ray Timing Explorer(RXTE). These light curves were then analysed using the CARMA module to create a corresponding power spectrum. The power colours were then extracted from these power spectra and plotted in a power colour diagram. This was done using a Monte Carlo approach to ensure that the corresponding errors were normally distributed. These power colours were then compared with corresponding power colours from BHXRBs. This comparison showed that AGN appear to experience the same range of power colours as seen in the different BHXRB variability states. However, there appeared to be a systematic difference between AGN and BHXRBs where the high frequencies of the hard state AGN candidates appears to be suppressed(relative to low frequencies) more than in hard state BHXRBs. This could be due to a different truncation radius in AGN than BHXRBs as the high frequency variations are thought to come from the inner edge of the accretion disc.

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Declaration

The work in this thesis is based on research carried out at the Anton Pannekoek Institute, Department of Physics, The Netherlands. No part of this thesis has been submitted elsewhere for any other degree or qualification and it is all my own work unless referenced to the contrary in the text.

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List of Figures

1.1 Roche-Lobe overflow . . . 3

1.2 Hardness-Intensity Diagram . . . 5

1.3 X-ray spectrum components . . . 7

1.4 Accretion States SED . . . 8

1.5 Example light curves and corresponding power spectra . . . 10

1.6 Binned up light curve MCG -6-30-15 . . . 12

1.7 Pred PSD break . . . 14

1.8 SED of NGC 5548 . . . 15

2.1 Power Colour PSD Spectrum . . . 18

2.2 Power Colour Hue Diagram . . . 19

2.3 Example assessment of CARMA fit. . . 22

2.4 Example Simulated CARMA(5,3) process . . . 24

2.5 Example CARMA AICc values . . . 25

2.6 Example CARMA PSD . . . 26

3.1 Example light curve . . . 32

3.2 Example PSD of NGC 3227 . . . 34

3.3 Example power colour contour plot . . . 35

4.1 Complete PC plot . . . 37

4.2 PSD and Power Colour: 3C 111. . . 41

4.3 PSD and Power Colour: 3C 120. . . 41

4.4 PSD and Power Colour: IC 4329A . . . 42

4.5 PSD and Power Colour: MKN 79 . . . 42

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LIST OF FIGURES vii

4.6 PSD and Power Colour: MKN 110 . . . 43

4.7 PSD and Power Colour: MR 2251-178 . . . 44

4.8 PSD and Power Colour: NGC 3516. . . 44

4.9 PSD and Power Colour: NGC 3783. . . 45

4.10 PSD and Power Colour: NGC 5548 . . . 45

4.12 PSD and Power Colour: ARK 564 . . . 47

4.13 PSD and Power Colour: MCG -6-30-15. . . 47

5.1 PSD CARMA test . . . 54

5.2 Soft state CARMA test . . . 56

5.3 Soft intermediate CARMA test . . . 56

A.1 3C 111 LC. . . 68

A.2 128 s binning section 3C 111 . . . 69

A.4 3C 120 LC. . . 70

A.6 IC 4329A LC . . . 71

A.7 128 s binning section IC 4329A . . . 71

A.8 16 s binning section IC 4329A . . . 72

A.9 MKN 110 LC . . . 72

A.10 128 s binning section MKN 110 . . . 73

A.11 MKN 79 LC. . . 73

A.12 128 s binning section MKN 79. . . 74

A.13 MR 2251-178 LC . . . 74

A.14 128 s binning section MR 2251-178 . . . 75

A.15 NGC 3516 LC. . . 75 December 21, 2018

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A.16 128 s binning section NGC 3516 . . . 76

A.18 NGC 3783 LC. . . 77

A.20 NGC 5548 LC. . . 78

A.22 NGC 7469 LC. . . 79

A.24 NGC 4151 LC. . . 80

A.26 ARK 564 LC . . . 81

A.27 128 s binning section ARK 564 . . . 81

A.28 MGC -6-30-15 LC . . . 82

A.29 128 s binning section MGC -6-30-15 . . . 82

A.30 NGC 3227 LC. . . 83

A.32 NGC 4051 LC. . . 84

A.34 NGC 4593 LC. . . 85

A.36 NGC 4945 LC. . . 86

A.37 1st 128 s binning section NGC 4945 . . . 86

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List of Tables

3.1 Project Sample . . . 29

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CHAPTER

1

Introduction

One solution to Einsteins theory of general relativity(Einstein1916) seemed to indicate that any object that was sufficiently dense would collapse to a point source or singularity as nothing, not even light can escape this sphere. An even more interesting point was that massive stars going through a supernova could achieve this density through core collapse. These black holes have now been observed with a large range of masses. From a few tens of times the mass of the sun, called stellar-mass black holes, up to hundreds of millions of solar masses in the cores of galaxies, including our own Sag A*, called supermassive black holes(SMBH). The stellar-mass black holes can be used as unique laboratories that can give us an insight into the effects of extreme gravitational fields and improve our knowledge of the accretion process. If as with stellar-mass black holes, strong gravity dominates the dynamics of the inner accretion flow around the SMBH an elementary consequence is a mass scale-invariance between a SMBH and a stellar-mass black hole. If this mass scale-invariance can be proven the knowledge acquired from the study of stellar-mass black holes can be adapted to the processes seen in SMBH. To get an idea of how this project will try and prove this in-variance it is essential to first discuss what is known about stellar-mass black holes.

1.1 Black Hole X-Ray Binaries

Most massive stars in our galaxy are in a system consisting of two or more stars(Eggleton and Tokovinin

2008). The most massive star in the system will reach the end of its life first in a supernova explosion. If this star is sufficiently massive and the binary system is not interrupted by the supernova explosion, it could become a X-ray binary system. These are star systems where a neutron star (NS) or black

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hole (BH) accretes matter from a companion star. This can occur if the system allows for either stellar wind accretion from a large companion or Roche-Lobe overflow either because the companion has also reached the end of its life and started to expand(Iben Jr. 1967) or it is located close enough that the primary can siphon gas through its gravitational pull. This accretion process (described in section 1.1.2) gives rise to strong X-ray emission(described in section 1.1.3) that can be observed using modern X-ray observatories such as XMM-Newton or Chandra.

There are in general two types of X-ray binary containing a black hole or neutron star primary, high mass X-ray binaries (HMXB) and low mass X-ray binaries (LMXB). In the high mass systems the secondary object consists of a high mass star (≥ 10M) of type O/B. These systems are in general

young as such massive stars don’t live for much more than a few tens of millions of years. In the low mass binary system the secondary object is a low mass star(≤ 1M) of spectral type K/M(Tauris

and van den Heuvel 2006). There are also intermediate mass X-ray binary systems with the black hole counterparts often called microquasars. However, these systems are rare due to a runaway mass transfer process in their discs causing rapid and violent accretion(see Mirabel and Rodriguez1999for a review). The focus of this project lies with the black hole X-ray binary(BHXRB) systems and there are in general two types of BHXRB. The most common type is the transient BHXRB systems. These systems have a relatively low X-ray luminosity of 1030_{− 10}34 _{erg/s but experience regular outbursts}

where their X-ray luminosities can reach 1036₋₁₀38_{erg/s. The time between these outburst, called the}

quiescent state, can last for months or even years and this behaviour is attributed to a non-continuous accretion flow caused by thermal or viscous instabilities. This type will be discussed in detail below. The second type is called the persistent BHXRB, however in low mass systems these are probably just long lived transients who are currently experiencing a long outburst state. These systems are bright, fairly stable X-ray sources with luminosities matching the outburst stage of the transient systems making them indistinguishable from each other for a short period of time(see e.g. Campana et al.

1998).

1.1.1 Accretion Disc

The accretion process starts when the secondary star either experiences Roche-Lobe overflow(most prominent in LMXB) or mass transfer via stellar winds or from a circumstellar decretion disc(most prominent in HMXB). The Roche-Lobe overflow process arises when the companion star fills its Roche

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1.1. Black Hole X-Ray Binaries 3

lobe, either due to expansion after leaving the main sequence or due to a decrease in orbital separation, causing matter from the outer envelope to cross over the first Lagrange point and start to orbit the compact object instead. A consequence of this process is that the transferred matter has a high specific angular momentum and can thus not accrete directly onto the object causing it to have an elliptical orbit. However, due to the constant stream of matter from the secondary star the stream will interact with itself causing a dissipation of energy via shocks.(Frank, King, and Raine2002; Shakura and Sun-yaev1973). Due to conservation of angular momentum this mass transfer then results in the formation of a disc structure around the compact object as a circular orbit is the lowest energy solution. An example illustration of this situation can be seen in figure1.1. The radial structure of this disc is of-ten described as a geometrically thin(r>>z), optically thick, steady α-disc(Shakura and Sunyaev1973).

Figure 1.1: Artists impression of Roche-Lobe overflow from the companion star(right) into the accretion disc around the compact object. Credit: NASA2018a

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According to the disc instability model an accretion disc is stable when it is either hot enough to fully ionize hydrogen or when it is cool enough that hydrogen stays neutral. In the persistent systems the flow is fast and hot enough to ensure that the fully ionized state stays fairly constant. However, in the transient systems the mass transfer rate is so low that the disc only fills up slowly leaving a largely truncated disc(see e.g Done, Gierli´nski, and Kubota2007; Esin, McClintock, and Narayan1997

for a discussion). The process that follows from this slow build up of mass can best be described by a hardness-intensity diagram as made by the CHAOS project(see fig1.2). If the object starts out in quiescence at the bottom right part of the diagram eventually matter accumulates in the disc and the surface density and temperature starts to rise. This causes the intensity of the object to rise and the object moves from A to B in the diagram. At this stage the accretion flow may produce a region of hot optically thin plasma, often called the corona. It may also exhibit a jet structure originating from above its poles(see e.g. Fender, Belloni, and Gallo2004for a discussion). Eventually the temperature will reach an upper critical value where the hydrogen starts to ionize and due to the high temperature dependence of the opacity in the disc the mass transfer rate increases significantly at a global scale. It is believed that as the surface density and temperature of the disc increases the spectrum softens as the coronal radiation dissipates and the disc radiation increases. This suggests that the object will move from B to C in the diagram and can exhibit superluminal ejection. The system is now thought to have an optically thick disc inner radius with a high accretion rate. As the accretion rate is higher here than what the companion star can provide as fuel the disc starts to empty out, lowering the optically thickness and temperature. There are several paths that the object can take while it is at this stage but it will eventually move down from C to D in the diagram. Eventually the disc empties and the optically thick inner radius of the disc increases causing the corona to reform, hardening the spectrum. This leads the object back to the bottom right of the diagram(D to A), again allowing a potential jet to form.

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Figure 1.2: Top: Hardness-Intensity diagram with a typical hysteresis behaviour as depicted by the CHAOS Project. The letters (A, B, C, D) indicate different time of the outburst and are also reported on the bottom plot(see text for the meaning of the A-B-C-D steps).

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1.1.2 X-Ray Emission Spectrum

The X-ray emission spectrum coming from a BHXRB can be seen as a combination of three compo-nents as depicted in figure1.3. The disc itself radiates a multicolour blackbody spectrum visible all the way up to the X-ray regime due to the high temperatures(up to 107K) at the inner edge(see discussion by e.g. Prendergast and Burbridge1968; Shakura and Sunyaev1973and Shakura and Sunyaev1976). As this blackbody spectrum peaks in the soft X-rays, the outburst stage where this is dominant is called the soft state. The second part of the spectrum is a Comptonized, power law component(see e.g. Remillard and McClintock2006; Lin, Remillard, and Homan 2007) that radiates strongly in the harder X-rays. This part of the spectrum comes from the hot corona(see example in the bottom part of figure1.3). While the exact properties of this region are still under discussion, it appears to originate from a very compact central area(Uttley et al.2011) in the form of a region above(lamp-post model) or around(extended model) the central BH. It is thought that this region is geometrically thick, op-tically thin and very hot(Sunyaev and Truemper1979). Here photons can undergo inverse Compton scattering causing them to be re-emitted at a higher energy resulting in the Comptonized power law component. The seed photons for the scattering process are thought to come from the accretion disc blackbody radiation or from synchrotron emission radiating from i.e. a jet(Markoff, Nowak, and Wilms

2005; Fender, Belloni, and Gallo 2004). This scattered light is re-emitted in all directions, including back to the accretion disc and these photons can then be reflected back to the observer causing the third component of the X-ray spectrum, the reflection. This reflection is also the origin of the promi-nent 6.4 keV Fe K-α line. In between the soft and hard state are several intermediate states where neither the blackbody or the corona are dominating the spectrum(see Belloni2010 for a discussion). Examples of the soft, intermediate and hard accretion state spectra can be seen in figure1.4a, b and c respectively(see Esin, McClintock, and Narayan1997for a more in depth discussion of these states).

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Figure 1.3: Figure describing the different components of the X-ray spectrum of a BHXRB. Top: Shows the different components of the spectrum as: Blue, the blackbody spectrum from the accretion disc. Red, the comptonized power law component coming from the corona. Green, photons originating in the corona reflected off of the accretion disc. Black, the total spectrum. Bottom: Illustration of the physical situation close to the black hole. Colours are the same as the top. The corona is depicted using the extended model. Credit:Gilfanov2010

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Figure 1.4: Spectral energy distributions depicting the different accretion states for black holes. Red line represents the accretion disc, the blue line represents the corona, the purple line represents the reflection from the corona in the disc and the black line is a composition of all curves. a: Depicts the soft state, the spectrum is dominated by the light from the accretion disc. b: Depicts the intermediate state, the corona has formed but is not dominating the spectrum. c: Depicts the hard state, the corona now dominates the spectrum. Credit: P. Uttley

1.1.3 Timing and Variability

Even though energy spectra provide a substantial amount of information on the various components, the rapid variability in the strength of these components is difficult to parametrise. Observations of BHXRBs show this variability on a wide range of time scales(down to less than a millisecond) in all wavelengths. This variability is usually studied in the frequency domain using a power spec-trum(discussed below), which shows the contribution of variations on different time-scales to the total

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variability of the light curve. These power spectra are dominated by a broad band noise component, but at short time-scales the variability is characterized as scale-invariant ”red-noise” producing a power law power spectrum(van der Klis1995). Extensive research has been done on this variability(see e.g. Hasinger and van der Klis1989; Wijnands and van der Klis 1999; Uttley and Mchardy2001; Uttley, McHardy, and Vaughan 2005) revealing a significant difference between a light curve taken while a BHXRB is in the soft accretion state compared to the hard accretion state. In the hard state the light curve shows large amplitude variabilities on long timescales as well as the expected short timescale noise pattern. These long timescale variabilities have much lower amplitudes in the soft accretion state and are though to be connected to the viscous timescale of the accretion flow. This timescale is associated with the propagation of change in the mass accretion rate(Done, Gierli´nski, and Kubota

2007). The short timescale variations on the other hand are not thought to be connected to these large scale changes in the flow, but rather to the dynamic timescale at the inner edge of the disc, down to millisecond scale(Frank, King, and Raine2002). This variability research thus allows us to probe the nature of the innermost region of the accretion flow where the matter may become highly influenced by strong relativistic effects. In figure 1.5 a) a representative example hard and intermediate state light curve can be seen.

To better capture the properties of such a light curve a power spectrum can be created by applying a Fourier transform. This power spectrum or PSD is a representation of the squared variability am-plitude in each frequency bin. The power spectra of BHXRBs always show a broad band noise, with a break/bend at a certain frequency. Additionally BHXRBs can contain quasi-periodic oscillations (QPOs). These are seen as narrow Lorentzian components in the PSD and the study of these are a field of research on its own(see van der Klis2006for an overview). These QPOs were thought to come from standing shocks in the accretion flow or changes in the mass accretion rate(see e.g. Chakrabarti and Molteni1993; Tagger and Pellat1999). However, recent studies show that they most likely have a geometric origin, e.g. due to Lense-Thirring (‘frame dragging’) precession of the inner corona or hot flow.(see e.g. Heil, Uttley, and Klein-Wolt 2015a; Motta et al.2015; van den Eijnden et al.2017).

It has been discovered that the PSD changes along with the accretion state of the BHXRB. In the bottom part of figure 1.5the difference between the hard and intermediate accretion state PSDs can be seen. As it would be expected in the hard state, due to the large amplitude variability on long timescales, the power remains high into the low frequencies. However, Churazov, Gilfanov, and

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Revnivtsev 2001 discovered that in the soft state the accretion disc itself is not very variable. The influence of this on the PSD can be seen as the amplitudes in the soft state are significantly lower than in the hard state. In the intermediate state(second panel in figure1.5) the transition can be seen as the low frequency amplitudes start to diminish leading to a peaked PSD shape. When the BHXRB moves into the soft state this peak flattens out as the disc blackbody radiation starts dominate the spectrum and we are left with a PSD similar to the hard state but at lower amplitudes. Wilkinson and Uttley

2009found that in the hard state the accretion disc itself is intrinsically variable using the covariance spectrum to precisely measure the variable part of the spectrum. This was an important discovery for the X-ray variability research as it was the first clear evidence that the low frequency Lorentzian component in the hard state PSD is produced by disc variability.

Figure 1.5: Figure depicting example light curve and corresponding power spectrum of the hard and intermediate accretion states for comparison. a: Light curves. b: Corresponding power spectra. Credit: P. Uttley

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1.2. Supermassive Black Holes in Active Galaxies 11

1.2 Supermassive Black Holes in Active Galaxies

Even though little is known about the origin of super massive black holes it is generally accepted that there is one located at the centre of each galaxy(Magorrian et al.1998; Gebhardt et al.2000; Ferrarese and Merrit 2000). The observed correlations between properties of SMBH and their host galaxies (Magorrian et al. 1998; Ferrarese and Merrit 2000; Gebhardt et al. 2000; Marconi and Hunt 2003; H¨aring and Rix 2004) suggest that a co-evolution in which the AGN phase may play a central role in regulating gas accretion and star formation in the galaxy. Therefore, understanding how the host galaxy fuels the AGN and how the AGN affects gas accretion is currently one of the most important questions in AGN and galaxy evolution studies.

Early efforts have revealed that the X-ray variability in AGN can, as with BHXRBs, be described as a scale-invariant, red-noise process on time scales of a few hundred seconds up to a few days(McHardy and Czerny 1987; Lawrence et al. 1987). Even though there is a significant difference between the BHXRB and AGN fuel source, the inner region of the accretion disc should thus still be governed by strong gravitational fields. This gave birth to the idea that the processes causing the variability in BHXRBs and AGN may be similar and that any characteristic variability time-scale scales with the central black hole mass.

To be able to test this theory long term observations along with intensive long-looks are needed to define the PSD over the required broad range of frequencies. The Rossi X-ray Timing Explorer(RXTE) had the exact capability to do this. This satellite launched on Dec 30 1995 and was active from Jan 1 1996 RXTE was placed at an altitude of 580 km with an inclination of 23◦resulting in an orbital period of about 90 minutes. It was operational until Jan 5 2012 giving it a lifespan of 16 years. It carried two pointed instruments, the Proportional Counter Array (PCA) and the High Energy X-ray Timing Experiment(HEXTE) for the low and high energy X-rays respectively(NASA 2018b). An example light curve used in this work made by RXTE can be seen in figure1.6below.

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Figure 1.6: Example of a binned up light curve of MCG -6-30-15(this work). The light curve is binned up to 1 ks with a 128s binning section at the days 1621-1689.

Edelson and Nandra 1999 conducted the first systematic broadband PSD study using a series of contemporaneous, evenly sampled RXTE observations of NGC 3516 spanning three decades of tem-poral frequency(4 · 10−8− 7 · 10−4 _{Hz). This yielded the first evidence of a break in the power law}

at ∼ 4 · 10−7 Hz. This was an intriguing similarity to the PSDs of BHXRBs. This break was later confirmed by Uttley, McHardy, and Papadakis2002who also studied three other Seyfert galaxies and found a clear break in two of them(MCG -6-30-15 and NGC 5506) at ∼ 5 · 10−5 Hz. Comparisons of the break frequency with independent measures of black hole mass shows that they scale almost lin-early with mass from the time-scales observed in BHXRBs(Markowitz et al.2003). These similarities raised the possibility that other properties of these sources were similar. For example, do AGN show a similar range of accretion states observed in BHXRBs. McHardy et al.2004 did a comprehensive study of the Seyfert 1 AGN NGC 4051 using > 6.5 years of well sampled observations made by RXTE combined with 100 ks of continuous observation with XMM-Newton. They found that the best fitting model is a gently bending power law similar to the best fit model for Cyg X-1 in its soft accretion state and concluded that NGC 4051 may be an analogue to this state based on the similar slopes above and below the break. These soft state similarities have also been demonstrated with the AGN NGC 3227 and 5506(Uttley and McHardy2005a) while evidence for a doubly bent power law similar to the ones observed in the hard state Cyg X-1 PSDs has been found in the AGN ARK 564(Pounds et al.

2001;Papadakis et al.2002;Markowitz et al.2003) further backing up the possibility that AGN show the same accretion states seen in BHXRBs.

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The idea of mass scaling was thoroughly tested and confirmed on a large sample of PSDs by McHardy et al.2006. They suggested that the break frequency of the PSD was only dependent on the mass and bolometric luminosity of the BH as

logTB= AlogMBH− BlogLbol+ C (1.2.1)

With TB representing the break frequency, MBH representing the mass of the central black hole in

Mand Lbolrepresenting the bolometric luminosity. The predicted break frequency vs observed break

frequency can be seen in figure1.7. Here it is clear that the expected and observed break frequencies in AGN(red and green markers) coincide with a linear fit with the break frequencies from BHXRBs(blue and maroon), albeit with some minor scatter. Their results establish that TB is a powerful tracer of

the innermost accretion processes in both AGN and BHXRBs.

The similarities in the accretion flows become greater when the SED of an AGN is examined as one example made by Mehdipour et al.2015shows(see fig1.8). This SED contains all the same parts as the SED of an XRB including the blackbody radiation, the high energy coronal radiation and the disc reflection spectrum as seen in a hard accretion state BHXRB(see fig1.4). However, the blackbody radiation coming from the disc peaks at a lower energy due to the disc being cooler than its BHXRB counterpart. It has also been suggested that the ratio of 1.4 GHz to optical B-band flux, called radio loudness could be connected to the accretion state of an AGN. Radio loud(ratio larger than 10) galaxies of type low-luminosity AGN or Faranoff-Riley I(FRI) are thought to be in the hard accretion state(see e.g.Meier2001; Maccarone, Gallo, and Fender2003; Falcke, Körding, and Markoff2004; Ho2005and Körding, Jester, and Fender2006) while radio quiet quasars are thought to be in the soft accretion state. Several attempts have been made to find a ”fundamental plane” of black hole activity to confirm this theory(see e.g. Merloni, Heinz, and di Matteo2003; Falcke, Körding, and Markoff2004and Heinz and Sunyaev2003). From this research it is thought that the radio luminosity scales non-linearly with the X-ray luminosity, the mass of the central object and possibly the total accretion rate. However, the uncertainties on this scaling are still large making it hard to prove. In addition, due to interstellar absorption and extinction the AGN accretion disc itself is hard to study.

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Figure 1.7: Plot showing the predicted break time-scales derived in McHardy et al.2006vs observed break time-scales. GRS 1915+105 is shown as a filled maroon star, Cyg X-1 is shown as blue crosses and the red circles are 10 AGN tested in their sample. Also included are NGC 5548, Fairall 9 and NGC 4258 as filled green squares. Credit: McHardy et al.2006

One thing to note when it comes to the PSD of an AGN is that there has so far only been found one case with a reliable detection of a QPO(Gierlinski et al.2008, confirmed by Vaughan2010) in contrary to the BHXRBs where they are observed more often. This is thought to be due to the frequencies where QPOs are seen in XRBs. When they are scaled according to the mass of an AGN they are no longer visible using the current light curves. We should also see the distinct peaked noise component in the PSD but no examples of this has been found so far(Vaughan and Uttley2005).

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If AGN appear to show the same accretion states as seen in BHXRBs the changes we observe in BHXRBs when they transition through the accretion states will not be observed in an AGN as this process could take millions of years. It is therefore necessary to be able to identify these accretion states based on relatively short observation times. Based on the power spectral shape in the different accretion states Heil, Uttley, and Klein-Wolt2015bdeveloped a model independent method of determining the accretion state for any observed XRB purely based on their PSD called power colours.

Figure 1.8: The SED of the AGN NGC 5548 presented by Mehdipour et al. 2015. The SED shows the different components also seen in XRB SEDs such as the low energy bb radiation, the high energy coronal radiation and the reflection spectrum.

To be able to compare AGN to BHXRBs using this method the PSD frequencies would have to be scaled according to the AGN mass creating the need to probe down to 10−8− 10−9 _{Hz. This}

would require several years of observations. At this point in time a decent sample of data has been built up making it possible to start to explore these low frequency regions of the PSD. However, as with any variability research, a large problem is irregular sampling in the data and unfortunately all ground-based or satellite observatories experiences this. It becomes a larger problem when years of data needs to be analysed. In an attempt to solve these problems and quickly determine the accretion state of AGNs this project will develop a method that combines the power colours with the CARMA analysis module developed by Kelly et al.2014.

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The rest of this thesis is built up as follows. Chapter two first describes the power colour method before moving on to give an introduction to the CARMA analysis method used in this project. In chapter three the sample is presented along with the method of obtaining and analysing the data from the RXTE mission. The results of the project is presented in chapter four before they are discussed and the project is concluded in chapter five.

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CHAPTER

2

Methodology

Inspired by the work of Heil, Uttley, and Klein-Wolt2015b, this project will look at the power spectral shapes of AGN and compare these with the ones of BHXRBs using the power colour method. This will be done by adapting a Python module called CARMA made by Kelly et al. 2014. The power colours will be extracted as a contour plot onto a diagram similar to the one made by Heil, Uttley, and Klein-Wolt 2015b to compare their states to the ones found in this project. If successful this will be the first clear evidence from X-ray timing that AGN show the same distinct accretion states as seen in BHXRBs despite the large difference in mass and different fuel source.

2.1 Power Colours

Heil, Uttley, and Klein-Wolt 2015b studied the difference in power spectral shapes between the ac-cretion states of BHXRBs and divided these into 18 different power spectra(see figure 2.1). To be able to qualitatively compare these power spectral shapes they developed a new method that uses the integrated power of four specific frequency bands in the power spectrum to extract the general power spectral shape. To be able to make a fair comparison between AGN and BHXRBs the findings of a 1/M mass scaling in the PSD (McHardy et al.2006) can be used. The assumption is then that the power colour frequency bands can be scaled in the same way. The integrated powers for BHXRBs are then divided with each other as follows: C/A(0.25-2.0 Hz/0.0039-0.031 Hz) results in power colour ratio one(PC1) and B/D(0.031-0.25 Hz/2.0-16.0 Hz) results in power colour ratio two(PC2). These ratios result in the removal of any dependence on power spectral normalization.

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Figure 2.1: Example power spectra for each 20◦range of hue in figure2.2. The numbering is based on power-colour properties as defined by Heil, Uttley, and Klein-Wolt2015band the power spectra move from the hard state(panel 1) to the soft state(panel 18).

When this is done for several BHXRBs while they evolve through the different stages of outburst the result shows a specific curved shape in a so-called power colour diagram(see figure 2.2). In the highly variable hard state the PSD is fairly flat due to the broad nature of the noise resulting in both of the power colour ratios(PC1 and PC2) to be approximately one and the object will be located in the top left corner of the diagram. As the flux increases as the outburst progresses, the strongest variability becomes concentrated in a smaller range of the PSD(panel 2-7 in fig2.1). Due to the more peaked nature of the broad-band noise the BHXRB evolves clockwise along the path in figure 2.2. When the object reaches the hard intermediate state the broad-band noise reaches its most strongly peaked shape, focussed on power colour frequency bands C and D. Due to this strongly peaked noise the object will now be located at the bottom right of the power colour diagram.

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2.1. Power Colours 19

Figure 2.2: Power colour-colour plot for all observations of the transient objects made by Heil, Uttley, and Klein-Wolt2015b. The labels are indicating the 20-degree azimuthal or ‘hue’ regions from which the power spectra given in fig 2.1 were found. The plot is colour-coded for each 20◦ band with the same colours used in fig2.1. Credit: Heil, Uttley, and Klein-Wolt2015b

When the BHXRB enters the soft intermediate state(hues 11-14 in figure 2.2) the peaked noise starts to disappear leaving only a weak low frequency power law noise. In this state the evolution is not monotonic and an object may transition in an out of this state several times before settling in the soft state(hues 15-18 in figure2.2). The time spent in the intermediate soft state on each pass through is relatively short and this can be seen on the number of data points in this region in the figure. Once the BHXRB has entered the soft state its spectrum is dominated by the blackbody radiation from its accretion disc. The PSD flattens out again and even though the strength in variability is much lower than in the hard state it will approach the top left corner of the diagram due to the power colour methods removal of any dependence on power spectral normalization. There is therefore a small overlapping region between the hard and soft accretion states in the power colour diagram created by Heil, Uttley, and Klein-Wolt2015b(hues 18 and 1 in figure2.2). After the XRB has reached the soft state it will eventually start to transition back to the hard state following the same path in the diagram

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as it took to get from the hard to the soft state. The expected luminosity for this transition is based on the luminosity that Cyg X-1 has when it changes from soft to hard accretion state(D to A in figure

1.2), namely 2 % LEdd(Maccarone2003). Where the Eddington luminosity LEdd is calculated based

on the object mass as follows

LEdd= 4πGM mpc σT = 1.25 · 1038 M M erg/s (2.1.1)

2.2 CARMA

Up until this point the standard method used to model a power spectrum has been the PSRESP method developed by Uttley, McHardy, and Papadakis2002. The concept here is to simulate a large number of light curves with a known underlying power spectral shape(based on an estimate from the observed light curve(s)). These light curves are usually made using the method introduced by Timmer and K¨onig 1995, then analysed to determine the shape of the model power spectrum. The found power spectra are then averaged and error bars equal to the RMS spread in simulated power at each frequency bin is assigned to it resulting in a final PSD. This approach is extremely flexible, but can be computationally expensive. This is especially true if there are intervals of fine sampling separated by intervals of sparse sampling, as this requires either generating a very dense light curve at the finest sampling rate, or splitting the light curve into segments and computing their power spectra separately. Therefore a more recent method of acquiring the power spectrum was tested in this project, namely the continuous-time auto regressive moving average(CARMA) algorithm developed by Kelly et al. 2014. This method was developed to estimate variability features of light curves and in particular their power spectral density and will be discussed in detail below.

CARMA builds on the CAR(1) method developed by Kelly, Bechtold, and Siemiginowska 2009, but as this method only had 2 free parameters(bend frequency and normalization) it was not very flexible. In addition CAR(1) could not describe the steep high-frequency power spectra of optical light curves well(Mushotzky et al.2011; Graham et al.2014) indicating that it needed improvement. CARMA creates several higher order derivatives to the stochastic differential equation that defines the CAR(1) processes. Giving many more free parameters such as centroid, width and normalization of each Lorentzian, making it much more flexible than CAR(1). As the calculation of the likelihood function in CARMA scales linearly with the number of data points it makes it a powerful tool to

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2.2. CARMA 21

forecast, interpolate and quantify variability of i.e. light curves but can be adapted to analyse any time series.

Below some of the important mathematical properties of the CARMA(p, q) process such as the definition, PSD and autocovariance function are described. Further details can be found in e.g. Jones

1981, Jones and Ackerson1990, Belcher, Hampton, and Wilson1994and Koen2005. The CARMA(p, q) process with a zero mean is defined to be the solution to the stochastic differential equation:

dp_y(t) dtp + αp−1 dp−1_y(t) dtp−1 + ... + α0y(t) = βq dq_(t) dtq + βq−1 dq−1_(t) dtq−1 + ... + (t) (2.2.2)

Here, (t) is a continuous time white noise process with non-zero mean and variance σ2_{. In addition}

αp and β0 are defined to be 1. The αp−1 to α0parameters are the autoregressive coefficients and the

β1to βq parameters are the moving average coefficients. For this process to be stationary it is required

that p > q and that the roots of the autoregressive polynomial

A(z) =

p

X

k=0

αkzk (2.2.3)

have negative real parts. The final PSD of a stationary CARMA(p, q) process is then defined by the function P (f ) = σ2 Pq j=0βj(2πif )j 2 |Pp k=0αk(2πif )k| 2 (2.2.4)

and the auto-covariance function at lag τ

R(τ ) = σ2 p X k=1 Pq l=0βlrlk Pq l=0βl(−rk)l exp(rkτ ) −2Re(rk)Q p l=1,l6=k(rl− rk)(r∗l − rk) (2.2.5) where Re(.) represents the real part and r∗ is the complex conjugate of r. Since the PSD and the auto-covariance function are a Fourier transform pair the roots of function2.2.3can be connected to the PSD. The auto-covariance function on the other hand is a dampened exponential sinusoidal function and the Fourier transform of this is a Lorentzian function and hence the PSD of the CARMA model can be expressed as a sum of Lorentzian functions as seen in function 2.2.4. This can be seen by applying the simple case of p=1, q=0. The function then becomes

P (f ) = σ2 1 α2

0+ (2πf )2

(2.2.6)

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The PSD of this process is a Lorentzian function centred at zero with a break frequency at α0/(2π).

The quality of the fit can then be assessed by noting that if the Gaussian CARMA model is correct the standardized residuals χi should have a Gaussian white noise distribution. CARMA calculates these

residuals as χi= yi− E(yi|y<i, ˆθ) h V ar(yi|y<i, ˆθ) i1/2 (2.2.7)

where ˆθ is an estimate of θ(model parameters). If there are large deviations from this white noise pattern in the standardized residuals there may be some residual correlation structure that CARMA does not pick up. The square of the residuals χ2_i should also form a white noise sequence under the Gaussian CARMA model. Deviations from this signal non-linear behaviour as they indicate that the variance in the time series is changing through time. These residuals can be seen by using the function ”assess fit()” on the created sample. An example assessment can be seen in figure2.3below.

Figure 2.3: Example CARMA assessment of its own fit onto the light curve of NGC 4051(this work). Top left depicts its light curve fit with the original data points. Top right depicts the residuals and the shape of the errors(should be Gaussian if it is a good fit). Bottom depicts the autocorrelation function of the standardized residuals (left) and its square (right) compared with the 95 % confidence region. This result has no evidence that the model deviates from white noise residuals indicating that CARMA has captured the model of the light curve adequately.

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2.2. CARMA 23

One important note is that the CARMA parameters p and q do not have any specific physical meaning and are more of a model selection process. This should thus not be used to rule out a potential null hypothesis. The commonly chosen order is the one that best predicts additional data in the time series. To find the parameters that best describe the time series, CARMA uses the Akaike Information Criterion(AIC). This criterion is based on the maximum-likelihood estimate of θ and is defined as

AIC(p, q) = 2k − 2logp(y|ˆθmle, p, q) (2.2.8)

where k is the number of parameters of the CARMA(p, q) process and ˆθmleis the maximum-likelihood

estimate of the CARMA parameters θ. The best model is the one that minimizes this AIC. This also automatically penalizes over-fitting with the 2k term. Hence, once the improvement to the log likelihood function does not improve faster than the number of parameters the AIC will begin to worsen. Kelly et al.2014also added in a correction for finite sample size created by Hurvich and Tsai

1989due to the AIC strictly being valid asymptotically. The result is the AICc, defined as

AICc(p, q) = AIC(p, q) +2k(k + 1)

n − k − 1 (2.2.9)

where n is the number of data points in the sample light curve. This puts an even larger constraint on the number of parameters due to the finite number of data points.

The ability of CARMA to account for irregular sampled light curves containing different sized bin-ning, the flexibility of the Lorentzian PSD and its computationally efficient linear scaling makes it an ideal candidate for almost any time series analysis with large amounts of data such as the data used in this project.

As an example of how this process works Kelly et al. 2014presents a test with a simulated a light light curve with realistic errors and sampling pattern using a CARMA(5, 3) process. They simulated three observing seasons of 90 days separated by 180 days with time spacing drawn from a uniform distribution over 1 to 3 days. This simulated light curve including the interpolated and forecasted values with their one σ uncertainties found by CARMA can be seen in figure 2.4. These quantities

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provide a means of simulating realizations of the light curve at these time points, conditional on the measurement light curve(see §3.2 in Kelly et al.2014for more details). Included in this simulation is a strong oscillator mode centred at 1/25 day−1 as this is representative of certain types of variable stars.

Figure 2.4: Simulated light curve from a CARMA(5,3) process irregularly sampled over three ‘observing seasons’. The black line denotes the true values, and the blue dots denote the measured values. Also shown are interpolated and forecasted values, based on the best-fitting CARMA(5,1) process; a CARMA(5,1) model had the minimum AICc value. The solid blue line and cyan region denotes the expected value and 1σ error bands of the interpolated and extrapolated light curve, given the measured light curve. Credit: Kelly et al.2014

The models used to analyse this light curve was p=1,...,7, q=0,..,p-1. For each value of (p, q) a maximum-likelihood estimate was calculated and used to calculate the AICc. These values are shown in figure2.5. The minimum AICc is found for p=5 and q=1 even though the true value is p=5, q=3 indicating that the difference in log-likelihood was not sufficiently large to warrant the inclusion of the two extra parameters included in the original simulation. The MCMC sampler was run with the found p=5 and q=1 using 10 parallel chains for 75k iterations discarding the first 25k as burn-in.

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2.2. CARMA 25

The resulting PSD with a 95% confidence can be seen in figure 2.6below. It is clear that the strong oscillator is found along with a weak oscillatory feature at about 1/5 day−1. However, this oscillator is mostly below the measurement noise level and should thus not be seen as significant. For this project an equal amount of iterations as Kelly et al.2014was used, however the number of parallel chains was reduced to 8 as the laptop used had an Intel i7-4710MQ chipset with 8 cores at 2500 MHz on Ubuntu 16.4. For this setup the process took about 5.1 s per data point in the light curve when CARMA was allowed to choose its own p and q from p=1,..., 6, q=0,...,p-1.

Figure 2.5: The AICc values from the simulated light curve shown in figure 2.4 for CARMA(p, q) models of order p ≤ 7, q < p. The minimum AICc is achieved for a value of p = 5, q = 1, although the AICc curve is fairly flat for p ≥ 3. Credit: Kelly et al.2014

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Figure 2.6: Power spectral density for the light curve shown in figure2.4. The constraints on the PSD are given by a p = 5, q = 1 model. A p = 5, q = 1 model was found to have the minimum AICc and is sufficient to capture the variability characteristics above the measurement noise. Credit: Kelly et al.

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CHAPTER

3

Sample and data reduction

3.1 Sample

The AGN sample was chosen from the public archives of the RXTE mission using two main criteria. The first being that they were not blazars and the second being that they had been observed for more than 4-5 years. This resulted in a total of 21 AGNs covering a large range of masses(∼ 106 _{to a few}

108_M

). In this project only the data from the PCA of RXTE was used as the required energy range

was on the low end (3-15 keV) of the total range (2-250 keV). The PCA consisted of 5 proportional counter units(PCUs) designed to look at bright X-ray sources. However, only data from PCU 2 was used as this was the only PCU to remain active throughout the mission. The lowest standard binning used by RXTE in this project was 16 s and this binning was available for all of the chosen targets. This was later binned up to 1 ks (1024 s) with sections of 128 s, sometimes adding a section of 16 s(see fig1.6for an example binned up light curve). In this sample 17 AGNs had acceptable data and their positions could be constrained in the power colour diagram. The excluded sources: NGC 4258, MKN 766, AKN 120 and NGC 5506 were excluded due to low amounts of data resulting in large errors on the PSD, again resulting in a large scatter in the power colour diagram making it impossible to constrain the contour plots within a reasonable limit. Therefore these objects will not be discussed any further. The sample consists of mainly Seyfert 1 galaxies, including both broad and narrow lined objects plus one Seyfert 2 galaxy(NGC 4945). Further information about the sample, including binned up sections, can be seen in table3.1. However, some sources have been found to show specific interesting properties and these are discussed briefly in the section below.

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3.1.1 Specific Cases

Previous research has revealed that four of the sources in this sample contain powerful radio jets. If the hypothesis that AGN show the same accretion states as BHXRBs is correct and the jet formation in AGN matches what we observe in BHXRBs these luminous jets should correspond to the hard and intermediate hard accretion states. This then offers up an opportunity to double check the results of this project as these objects should lie in these regions in the power colour diagram. The AGN with a confirmed jet in this sample are 3C 111(Linfield and Perley1984) and 3C 120 (Seielstad et al.1979) while the jets observed in NGC 3516(Barbosa et al. 2009) and NGC 4151(Ulvestad et al. 2005) are both much less luminous but could still suggest that these AGN could be in the hard or intermediate hard accretion state.

In addition to the objects with a jet McHardy et al.2004concluded that NGC 4051 most likely is in the soft accretion state based on its PSD as this is a very close match to the PSD of Cyg X-1 in the soft accretion state, having the same slopes above and below the break remaining unchanged for over 4 decades. In addition Uttley and McHardy2005bfound that NGC 3227 shows a soft state PSD despite possessing an intrinsically hard X-ray continuum and apparently low accretion rate. McHardy et al.2007concluded that the AGN ARK 564 is an analogue to Cyg X-1 in the intermediate accretion state based on the shape of its PSD. This gives an indication as to where to expect these objects in the power colour diagram and their expected accretion state may be confirmed based on the results here.

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3.1.

Sam

p

le

29

Name Mass Distance Type** Observed time Binned up Section(s) Radio LBol/LEdd

Log10M z-value s (Days since launch) Loudness(FR/FX)

3C 111 8.254±0.108[1] 0.0485[13] BLRG*** 905344 4053-4115 (128s) 3.06 · 10−3[21] ∼0.025[1] 4726-4805 (16s) 3C 120 7.729±0.21[2] 0.03301[14] Seyfert 1(NLS1) 1773082 4054-4115 (128s) 9.82 · 10−4[21] ∼ 0.316[23] IC 4329A 6.67±0.77[3] 0.016054[15] Seyfert 1 435200 2830-2865 (128s) 2.88 · 10−5[22] ∼ 0.027[24] 2870-2875 (16s) MKN 110 7.225±0.075[4] 0.035291[12] Seyfert 1(NLS1) 1117584 3696-3762 (128s) 1.32 · 10−5_[22] _{∼ 0.125[3]} 8.15±0.25[5] MKN 79 7.70±0.12[2] 0.022189[12] Seyfert 1 1244800 3690-3755 (128s) 1.38 · 10−5[22] ∼ 0.064[23] MR 2251-178 8.28±0.10[6] 0.06398[16] Seyfert 1 523664 4300-4440 (128s) 4.16 · 10−6[22] ∼ 0.23[25] NGC 3516 7.605±0.155[2] 0.008836[12] Seyfert 1 799728 589-595 (128s) 9.19 · 10−6[22] ∼ 0.063[24] 2223-2225 (16s) NGC 3783 7.47±0.08[2] 0.00973[17] Seyfert 1 633632 1959-1981 (128s) 7.37 · 10−6[22] ∼ 0.20[24] NGC 5548 7.825±0.015[2] 0.017175[12] Seyfert 1 916928 2090-2129 (128s) 7.29 · 10−6[22] ∼ 0.015[26] NGC 7469 7.08±0.05[2] 0.016317[12] Seyfert 1 1005056 242-278 (128s) 7.31 · 10−5[22] ∼ 0.126[26] ARK 564 6.535±0.195[7] 0.024684[18] Seyfert 1(NLS1) 264848 1690-1726(16s) 7.82 · 10−7[22] ∼ 0.50[27] MCG -6-30-15 6.80±0.17[8] 0.057[15] Seyfert 1(NLS1) 2010080 1621-1689 (128s) 9.98 · 10−7_[21] _{∼ 0.25[26]} NGC 3227 7.56±0.24[2] 0.003859[12] Seyfert 1(NLS1) 991392 1630-1706 (128s) 3.29 · 10−5[22] ∼ 0.01[24] NGC 4051 6.22±0.14[9] 0.002336[12] Seyfert 1(NLS1) (*) 429-433 (16s) 1.1 · 10−4[22] ∼ 0.30[28] NGC 4151 7.095±0.155[2] 0.003319[12] Seyfert 1 486848 1868-1907 (128s) 2.56 · 10−5[22] ∼ 0.063[29] NGC 4593 6.981±0.095[10] 0.009[19] Seyfert 1 1113472 3700-3768 (128s) 1.58 · 10−6[22] ∼ 0.04[26] NGC 4945 6.125±0.325[11] 0.001878[20] Seyfert 2 1371008 1313-1320 (128s) 4.39 · 10−3[21] ∼ 0.20[24] 2604-2612 (16s)

Table 3.1: Project sample. Radio loudness is based on X-ray flux found during this project and the radio flux found in the given source. (*NGC 4051s data was binned up to one point per obs ID and provided by P. Uttley, thus the total observed time is unknown.)**All broad line unless otherwise noted. ***Seyfert 1 analogue broad line radio galaxy. Sources:[1]Chatterjee et al.2011, [2]Peterson et al.2004, [3]Kaspi et al.1999, [4]Kollatschny

2003, [5]Liu, Feng, and Bai2017, [6]Lira et al.2011, [7]Zhang and Wang2006, [8]McHardy et al.2005, [9]Denney et al.2009, [10]Denney et al.2006, [11]Graham 2008, [12]Vaucouleurs et al. 1991, [13]Krivonos et al. 2015, [14]Michel and Huchra 1988, [15]Kaldare et al. 2003, [16]Bergeron et al.

1983, [17]Theureau et al.1998, [18]Huchra, Vogeley, and Geller1999, [19]Strauss et al.1992, [20]Koribalski et al.2004, [21]White and Becker1992, [22]Condon et al. 1998, [23]Castel´lo-Mor, Netzer, and Kaspi2016, [24]Middleton, Done, and Schurch 2008, [25]Nardini et al.2014, [26]Vasudevan et al.2009, [27]Romano et al.2002, [28]McHardy et al.2004, [29]Vasudevan and Fabian2009

Decem

b

er

21,

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3.2 Data Reduction

The raw data acquired from HEASARCs archive was reduced using HEASARC’s software, ftools v6.23. This software provides tools to extract e.g. a light curve. The first step in the process of extracting a light curve is to make a good time interval or gti file using the maketime command. This command requires a filter file (.xfl file). For this thesis the filter files provided with the raw data were used. The maketime command makes a list of accepted times for the data to be extracted. It does this based on certain parameters set on the satellites observation. In this project the standard GTI criteria for the mission were used. These criteria stated that the object should be at least 10 degrees above the limb of the Earth to make sure that there was no local contamination of the data. To avoid the effects of slewing an offset of maximum 0.01 degrees was recommended to make sure the satellite was relatively motionless at the time of observation. RXTE will have about 10−3 degrees of variations during observations but this does not affect the quality of the data. Further there is an area above South America leading into the Atlantic ocean called the South Atlantic Anomaly(SAA). Here the Earths inner Van Allen belt comes closest to the Earth, dipping down to about 200 km. Due to the low Earth orbit of RXTE (580 km), it passes through this area on each orbit. Large amounts of noise in the data is created at each pass through. This could be avoided by requiring that at least 10 minutes had passed since RXTE was in the SAA. To minimize the electron contamination any time where the parameter ELECTRON2 was higher than 0.1 was also filtered out as recommended when looking at faint objects. Additionally only data from PCU 2 was used in this research as it was the only PCU to remain on at all times throughout the mission.

The second step in the process is to use the saextrct command to extract the light curve. This command, when given the correct input including the gti file and the wanted energy channels, will extract a light curve from the data. Saextr returns a light curve in count rate and this would have to be converted to flux. However, throughout the RXTE mission the energy ranges and the effective area for the channels changed slowly due to a gain drift in the PCA. This separated the data into five epochs (Epoch 1 = launch through 3/21/96; Epoch 2 = 3/21/96 - 4/15/96; Epoch 3 = 4/15/96 - 3/22/99; Epoch 4 = 3/22/99 - 5/12/2000; Epoch 5 = 5/13/00 - end of mission) where the channel ranges had changed enough to require adjustment. The fifth epoch marks the time when PCU 0 lost its propane layer and was the final adjustment of the mission. Since data from the entire mission was used the energy bins had to be adjusted accordingly during the data reduction. To do this a response matrix was needed. This response matrix contains the effective area and energy range of the observing PCU and is gained with the command pcarsp and is represented as two separate files. To ensure that the correct energy per observed photon was used with each observation the matrix was obtained for every five days throughout the mission. The formula used to calculate the flux from the count rate

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3.2. Data Reduction 31

was:

F (erg/cm2s) = C · E · 1.602 · 10

−9

A (3.2.1)

Where C is the count rate, E is the central energy of the bin(in keV) and A is the integrated effective area for the energy bin in question.

The light curves were extracted for each energy bin separately, then converted to flux and finally combined to one light curve. This was then repeated for each individual observation ID in the data and finally concatenated to one light curve. A binning of 16 seconds was used for this final product as this was the highest time resolution of RXTE for these AGN light curves.

The third step is to create a background light curve. This was done using the runpcabackest command. This command required a file describing the background model to be used to calculate the background for a given set of observational parameters and it was acquired from the HEASARC website. This background data could then be entered into the saextr command in the place of the pca data, using the same gti file from the original light curve extraction to get a matching background light curve. This background was then subtracted from the original light curve to arrive at the final light curve.

The light curve was normalized to a mean of 1 and binned up to save on computation time. This binning was set to ∼ 1 ks or 1024 s bins. This would reduce the number of data points by a factor of 64 but would not allow a Nyquist frequency larger than 1/2048. To be able to look at higher frequencies one or more blocks of 128 s binning and in a select few cases one of 16 s binning was kept in the light curve before the analysis was performed by CARMA. In a few cases the short timescale resolution was very low due to relatively short and few long look observations. This resulted in large errors on the regions around and above 10−4 Hz. Due to the highest frequency bands of the power colours being located at about this same frequency this would cause a large error on the resulting power colour. This was compensated for by adding in a section of 16 second binning at a region of higher than average concentration of data points if no other long look was available. This would decrease the size of the error by a greater amount than binning this same section up to 128 s as this helped CARMA to constrain the PSD up to a higher frequency greatly reducing the error on the required intermediate frequencies. However, this was not the reason for the 16 s binning in the two AGN NGC 4051 and ARK 564. These

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two objects were part of the initial test group used to see if the method gave reasonable results and the binning was kept at 16 s as a test to see how well CARMA could work with such a large difference of bin size in one light curve. After this the binning was changed to 128 s to reduce the computation time needed for each object. An example light curve from the AGN NGC 3227 can be seen in figure

3.1below. This final binned up light curve was then analysed with CARMA to get the corresponding power spectrum. The confidence interval on this power spectrum are represented by a 95 % coverage of 50k realisations of the light curves simulated from the distribution of model parameters(αk, βj and

σ in function 2.2.4). The measurement noise level was calculated as 2 ¯∆t ¯σ2

y where ¯∆t and ¯σy2 is the

median time spacing and measurement noise variance, respectively. The median was chosen as the mean would result in a unrealistic large noise level due to the large time gaps in the data influencing

¯

∆t. The corresponding power spectrum to NGC 3227 can be seen in figure3.2 below. The next step to extract the power colour was to adjust the frequencies of the power colour bands according to the mass. This was done by drawing a log-normal distributed number based on the observed mass of the object in question. The frequencies were then adjusted as:

fnew= fold

10 M

(3.2.2)

Figure 3.1: Example 1 ks binned light curve of NGC 3227. The 128 s binned section can be spotted on the days 1630-1706 as a more dense region of data points.

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Where the 10 comes from the stellar mass black hole approximation and the new randomly drawn AGN mass is represented by M(in M). This was then followed by picking a random realization of

the power spectrum created by CARMA to extract the corresponding power colour and integrating according to the frequency bands created by the chosen random mass. Then the appropriate ratios of integrated power were taken to create a point in the power colour diagram as described by Heil, Uttley, and Klein-Wolt2015b(see section 2.1). This was repeated 5000 times to build up a good con-tour plot(see figure 3.3 for the power colour contour of NGC 3227). This contour plot consists of 3 separate levels. The first innermost level represents the peak of the scatter plot containing 5 % of the data points. This number was chosen to create a visible circle for the peak. The second level contains 68 % of the data points, representing an approximate one σ error. Finally the third outermost level contains 95 % of the data points, giving a 95% confidence level. To create the final combined plot the one σ error contour was extracted from each object and represented as a simple two directional error bar based on the length, width and orientation of their power colour contour. As the contours are shaped similarly to an ellipse the short error bar represents the semi-minor axis and the long error bar represents the semi-major axis of the ellipse formed by the contour.

In some cases the mass of the AGN was so large that the frequency bands would extend below the low frequency limit of the PSD created by CARMA. This presented a problem as the integrated power of band A would always be under estimated and as the lowest frequency of the PSD lies with the length of the light curve little could be done to increase this based on the data itself. This problem was solved by extending the PSD down to the required limit with a randomly selected slope drawn from a uniform distribution between 0 and 2.5 for each of the 5000 power colour extractions. These numbers were chosen conservatively based on observed low frequency PSD slopes in BHXRBs. One other thing to note about the PSDs obtained by CARMA during this project is an artefact that sometimes appears close to or at the Nyquist frequency. This caused the PSD to spike up as if there was a QPO at that location. This spike is however connected to the 128 s binning as it was found to disappear in most cases as a sufficiently large portion of 16 s bins was added to the light curve. However, as the highest frequency of the power colour bands was a few 10−5 _{Hz and the spike was located far below}

the measurement noise level this effect did not influence the resulting power colour.

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Figure 3.2: Example power spectrum created by CARMA for NGC 3227 based on the light curve in figure3.1. The high frequency peak is an artefact from the 128 s binning and does not represent a real peak.

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Figure 3.3: Example power colour contour plot extracted from the PSD of NGC 3227 in figure 3.2. The three blue circles represents the peak, one- and two-sigma error. The regions are based on the ones presented by Heil, Uttley, and Klein-Wolt2015b.

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CHAPTER

4

Results

Based on the power colour method presented by Heil, Uttley, and Klein-Wolt2015bas described above (section 2.1) the power colour of 17 different AGN were inferred during this project. The corresponding accretion state found was based on the contour plot of the scatter from the extraction procedure described in section 3.2. In the final power colour plot the extracted power colour is represented by a contour containing three levels. The innermost level represents the peak of the scatter. The second level represents an approximate one sigma error bar containing ∼ 68 % of all data points. The outer level represents a 95 % confidence level. Below the results will be discussed based on their extracted accretion state starting with the hard states, then moving on to the intermediate states and finally the soft states. The individual PSD and power colour contour plot for each object is located at the end of each section and the final power colour plot containing all 17 sources can be seen in figure4.1below. Here each object is represented by a symbol at the peak location and two error bars representing the approximate one σ error contour described at the end of section 3.2.

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4.1. Hard State Candidates 37

Figure 4.1: Complete power colour diagram with all 17 sources. The lines represent an approximate one sigma error bar. Coloured regions are based on the regions presented by Heil, Uttley, and Klein-Wolt

2015b.

4.1 Hard State Candidates

The AGN 3C 111 was expected to be in the hard state based on it having a known jet(Linfield and Perley 1984) and it is clear based on its contour plot that it lies in the correct region on the power colour diagram(see fig4.2). It can also be seen that the error bars appear to be elongated towards a lower PC1 value. This is due to the high mass of 3C 111 (8.254 ± 0.108log10(M), Chatterjee et al.

2011) and how the code extends the PSD below the limit from the time scale of the light curve(see section 3.2 for a description). The PSD of 3C 111 is fairly well constrained but does get noisy at frequencies above ∼ 3 · 10−5 Hz. However, this is also approximately the level of the measurement noise level. This noise is mostly irrelevant for the power colour due to the highest frequency band

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stopping below ∼ 10−5Hz. The resulting contour plot lies slightly above the XRB data points along with some other hard state AGNs. This may be due to a systematic bias in this state for AGN that does not appear in BHXRBs (discussed further in section 5.1).

3C 120 was also expected to be in the hard state due to its one-sided jet(Seielstad et al.1979) and this is again confirmed by its power colour. Even though this AGN also has a fairly large mass of 7.729 ± 0.21 log10(M)(Peterson et al.2004) this was not high enough that the frequency bands from

the power colour extraction went below the limit of the PSD. The errors on this PSD appear large but this error appears to lie mostly in the σ parameter of function 2.2.4meaning that the PSDs created all appear to have similar shapes but at different normalisations. This does in other words not have a large influence on the power colour. The PSD also appears to show a QPO at ∼ 2 · 10−4 Hz but it is located below the measurement noise level and is thus not detected at a significant level. It is also located above the highest frequency of the highest power colour frequency band making it insignificant for the power colour contour.

The fairly low mass(6.67 ± 0.77 log10(M), Kaspi et al. 1999) AGN IC 4329A has no confirmed

jet but is very bright(1.56 · 10−10 keV/s, brightest object of this work). However, it shows a fairly low bolometric luminosity of ∼ 2.7% of Eddington(Middleton, Done, and Schurch2008). The power colour contour plot appears as a part of the possibly biased group. However, due to the low mass the power colour frequency bands extend slightly into the noisy part of the power spectrum creating a larger than average error on power colour band D. This noise was probably caused by the low amount of observation time by RXTE but it can still be constrained to a most likely hard state candidate. The reason for the large elongation on the power colour is more likely connected to the large error in the mass estimation of this AGN creating a large error on the location of the power colour frequency bands.

The AGN MKN 79 has not been studied extensively but it has been found to have a mass of 7.70 ± 0.12 log10(M)(Peterson et al.2004). The PSD of MKN 79 is well constrained all the way up

to the Nyquist frequency where it starts to get a bit noisy and the artefact of the 128s binning shows up as a peak in the spectrum. It also shows a fairly high noise level but the power colour can still be constrained as the power colour frequency bands did not extend significantly below this line. Its power colour contour plot is clearly situated in the hard state region of the diagram.

Searching for AGN accretion states with X-ray timing

Searching for AGN accretion states

with X-ray timing

Stian Huseby

A Thesis presented for the degree of

Master of Astronomy and Astrophysics

Anton Pannekoek Institute for Astronomy

Faculty of Science

University of Amsterdam

The Netherlands

Searching for AGN accretion states with X-ray timing

Stian Huseby

Submitted for the degree of Master of Astronomy and Astrophysics

December 2018

Abstract

Declaration

Contents

List of Figures

List of Tables

CHAPTER

1

Introduction

1.1

Black Hole X-Ray Binaries

1.1.1

Accretion Disc

1.1.2

X-Ray Emission Spectrum

1.1.3

Timing and Variability

1.2

Supermassive Black Holes in Active Galaxies

CHAPTER

2

Methodology

2.1

Power Colours

2.2

CARMA

CHAPTER

3

Sample and data reduction

3.1

Sample

3.1.1

Specific Cases

3.2

Data Reduction

CHAPTER

4

Results

4.1

Hard State Candidates