A STUDY OF Fe Kα SPECTRAL LINES OF THE MAGNETIC

CATACLYSMIC VARIABLE: V1223 Sgr

By

Nwaffiah, Jude Udoka

PG/MSc/10/52660

B Sc. Honors

A project report submitted in partial fulfillment of the requirements for the award

of a Master of Science (M Sc.) Degree

In the

Department of Physics & Astronomy

Faculty of Physical Sciences, University of Nigeria, Nsukka

Supervisor: Dr R. N. C. Eze

May, 2014

Certification

Nwaffiah, Jude Udoka, a post-graduate student in the department of Physics and

Astronomy, with registration number: PG/MSc/10/52660 has satisfactorily

completed the requirements in research work for the degree of Master of Science

(M Sc.) in Astrophysics. The work in this project report is original and has not

been submitted in part or in full for any degree or diploma of this or any other

university.

Dr. R. N. C. Eze Prof. R. U. Osuji

Supervisor Head of Department

External Examiner

Dedication

To my Beloved Late Father

Acknowledgement

I wish to acknowledge the Almighty God for the gift of life and other divine

resources. My heart-felt gratitude goes to my supervisor, Dr. R. N. C. Eze, for his

fatherly kindness, guidance and invaluable pieces of advice given to me. I equally

appreciate Prof. A. E. Chukwude, for all the help he rendered to me especially

when my supervisor travelled to Japan. My gratitude also goes to Dr. Randall, of

Goddard Space Flight Center, USA, for his assistance in the installation of one of

the soft wares used in this work. I acknowledge in a special way, the Suzaku Team,

for making available their archival data and relevant software packages used in this

work. I am indebted to Dr. F. C. Odo, for all his fatherly advice and constructive

criticisms that led to the beauty of this work. Finally, I deeply appreciate my

family and friends for all their assistance, patience and understanding all through.

Thanks and remain blessed.

TABLE OF CONTENTS

CHAPTER ONE

Introduction …………..……………………………………………….. 1

1.1 Magnetic Cataclysmic Variables (mCVs) ……………………… 1

1.1.1 Polars or AM Hercules (AM Her) stars ...........………..….. 2

1.1.2 Intermediate Polars (DQ Her System) ........…………....... 3

1.2 A Brief Review of V1223 Sgr ...…………………………….... 3

1.3 On the Origin and Use of Fe Kα Line in the Study of Astrophysical

Sites ……….………………………………………………...... 4

1.3.1 Line Energy ……………………………………………… 5

1.3.2 Equivalent Width ………….…………………………..… 6

1.3.3 Line Profile ………………………………………………. 7

1.4 The Compact White Dwarf …....................................................... 7

1.5 The Discovery of Compact White Dwarfs ………………..… 8

1.6 Formation of White Dwarfs …………..………………….… 9

1.6.1 Lone White Dwarf …………………………………..….. 9

1.6.2 White Dwarf in a Binary System ………………..… 11

1.7 Accretion Processes ……………………………………………… 11

1.7.1 Physics of Accretion …………………………………….… 11

1.7.2 The Roche Lobe Geometry and Mass Transfer ……….… 14

1.7.3 Mass and Angular Momentum Transfers …….………….. 16

1.8 Uses of Cataclysmic Variables ………………....……………… 23

1.8.1 A Possible Origin of Cosmic Rays ……………………..... 23

1.8.2 A Laboratory for the Study of Gravitational Wave

Emission ………………………………………………………… 24

1.9 Purpose of Study …………………………………………………… 26

CHAPTER TWO

Literature ……………………………………………………………….. 27

CHAPTER THREE

Source of Data and Data Analyses …………………………………...... 30

3.1 Source of Data ………….…………………………………… 30

3.2 Data Analyses and Results ……..………………………..….. 30

CHAPTER FOUR

Discussion of Results ……………………..…………………………… 35

CHAPTER FIVE

Conclusions ……………………………………………………………. 38

Recommendations ……………………………………………………… 39

LIST OF FIGURES

Figure 1.1: Hertzprung-Russell diagram …………………………….…. 10

Figure 1.2: Equipotential surfaces in a typical CV with q =0.2 …….. 15

Figure 1.3: Two stars of masses and orbiting in a plane about their

common center-of-mass X (Adopted from Hellier 2001, p.189) …........ 17

Figure 3.1: Spectrum of V1223Sgr ……………………………………. 32

Figure 3.2: Light curve of V1223 Sgr ……………………………….…. 33

LIST OF TABLE(S)

Table 3.1: Best Fitting Parameters of V1223 Sgr by the Thermal

Bremsstrahlung Model …………………………………………………. 34

Abstract

We present the spectral analysis of a cataclysmic variable, V1223 Sgr, from

Suzaku satellite archive. The Suzaku satellite observations of V1223 Sgr were

made on 13-04-2007 for 42.2 kiloseconds. We resolved the neutral or low-ionized

(6.41keV), He-like (6.70keV), and H-like (7.00keV) iron lines. A thermal

Bremsstrahlung model with full and partial covering absorptions reveal the thermal

origin of the hard X-rays observed from the boundary layer between the white

dwarf and accretion disk. The light curve shows no intrinsic variations during the

observation.

Key words: Magnetic Cataclysmic variables, Accretion, Thermal bremsstrahlung

Recommendations ……………………………………………… 36

References ……………………………………………………… 37

CHAPTER ONE

Introduction

1.1 Magnetic Cataclysmic Variables (mCVs)

Cataclysmic variables (CVs) are semi-detached interacting binary star systems in

which the primary star, which is a white dwarf (WD), accretes matter from its

secondary companion, a low-mass main-sequence star (Warner 1995; Tovmassian

et al. 2001; Galis et al. 2008; Ishida 2008; Aungwerojwit 2011). They manifest

strong mass accretion-related activity from radio up to γ-ray regime, on the time-

scales of seconds to millions of years (Warner 1995; Galis et al. 2008).

X-ray emission in CVs is generally associated with accretion process, which is

capable of shock-heating accreted materials up to high temperatures ~10 −50 . Above the white dwarf surface, in-falling material experiences a shock

before it settles upon the boundary layer of the accretion disk, from which X-rays

are emitted through the process of thermal bremsstrahlung as it cools (Aizu 1973;

Galis et al. 2008). Accreted material from the donor could reach the accretor

through an accretion disk, accretion stream or disk over-flow accretion (Taylor et

al. 1997). The pulse period of the emitted X-rays is the same as the spin period of

the white dwarf owing to the misalignment of the WD spin and the magnetic field

axis (Norton et al. 1999).

The formation of accretion disk is necessitated by the loss of angular momentum of

the in-falling gas from the Roche surface of the secondary star (the inner

Lagrangian point). The gas settles around the WD, forming an accretion disk,

known for its strong line emissions (Penning 1986). The morphology of the

accretion disk is determined by the magnetic field strength of the WD (Mukai et al.

2003). Accretion process can occur in three different modes depending on the

strength of the surface magnetic field of the WD, the accretion rate and the angular

momentum of accreted materials (Bednarek & Pabich 2010). Three basic modes of

accretion exist. These correspond to three different types of accreting white dwarf

systems, namely: polars, intermediate polars and non-magnetic cataclysmic

variables. Since the object of our study (V1223 Sgr) is a magnetic cataclysmic

variable, the two types of mCVs, the polars and intermediate polars, are discussed

briefly in the subsequent subsections.

1.1.1 Polars (AM Her Stars)

These systems contain WDs with magnetic field strengths of 10 MG < B < 200

MG. This high magnetic field is responsible for the large amounts of optical

polarization associated with polars (Penning 1986; Venter 2007), believed to

emanate from an accretion region off the photosphere that forms the accretion spot

(Beuermann et al. 2006). This high magnetic field prevents disk formation. Polars

are intense X-ray emitters (Harrison et al. 2007; Aungwerojwit 2011).

The rotation period of the WD is synchronous with the orbital period of the binary

system ( =). Polars have small binary separation, since ≤ 3hrs

(Chanmugam & Ray 1984). Consequently, polars accrete directly onto one or both

of the magnetic poles of the WD through the field lines.

Unlike most other disk-accreting CVs that produce dwarf nova outbursts, the AM

Her stars have irregular alternating states of low and high luminosity, due to a

change in mass transfer rate (Tovmassian et al. 2001).

1.1.2 Intermediate Polars (DQ Her System)

Intermediate polars show disk accretion (accretion onto a magnetic pole from the

accretion disk). The moderate magnetic field (~10) of the WD truncates the

inner parts of the disk, allowing the accretion flow to stream down towards the

magnetic poles and onto the WD surface (Barlow et al. 2006; Galis et al. 2008).

The rotation period of the WD is asynchronous with the orbital period of the

system, i.e., ( ≠ ) (Chanmugam & Frank 1987). Due to their high

accretion rates, IPs are known to emit harder X- ray spectra, compared to the

polars (Aungwerojwit 2011).

1.2 A Brief Review of V1223 Sgr

V1223 Sgr is a magnetic cataclysmic variable (mCV) of the intermediate polar

(IP) type. The system is a bright X- ray source (4U 1849 -31), in deed, the brightest

IP so far observed (Steiner et al. 1980), located at a distance of about 510 pc. The

position of V1223 Sgr in the equatorial coordinate system is: RA 18h 55m 02.31s;

DEC -31h 09 m 49.5s. Based on the Beuermann et al. (2004), model A, the value

of the magnetic field strength of the WD lies in the range(0.5 − 8) × 10. The

radius and mass of the WD are respectively 4.17 × 10"#$ and 1.17solarmasses (Beuermann et al. 2004).

The accretion rate is about ,- ≈ 10/0123/. This value was obtained from the

observed X-ray luminosity, 45 = 2 × 10789123/(Barlow et al. 2006; Revnivtsev

et al. 2008). The WD orbital period, is 3.37 hrs. (Osborne et al. 1985,

Jablonski & Steiner 1987); while its spin or rotational period = 746 s

(Osborne et al. 1985). The system is known to have prominent long-term

brightness variations, i.e., outburst with duration of about 6hr and amplitude >1

mag (van Amerongen & van Paradijs 1989) and episodes of deep low state that

decrease by several magnitudes (Garnavich & Szkody 1988).

1.3 On the Origin and Use of Fe Kα Line in the Study of

Astrophysical Sites

The emission of the fluorescent low-ionized iron :; line (6.4 keV) is generally due

to the irradiation of iron atoms (cold gas or material) by hard X-rays from the

boundary layer of the accretion disk (Eze 2013). This involves a radiative decay

following inner or outer K-shell photoionization. If the inner K-shell electron is

excited, it jumps to the outer K-shell; while the outer K-shell electron, when

excited, would transit to the L-shell.

The excited level in either case can decay via auto-ionization by ejecting one of

the outer electrons in the valence shell (Kahn et al. 2002). When iron atom or ion

undergoes photoionization due to hard X-ray absorption, one of the two K-shell

electrons would be excited. The decay of this excited electron (i.e., outer K-shell

or L-shell electron) results in the emission of the 6.4 keV :; fluorescence line,

which consists of two components with slight energy difference (6.404 keV and

6.391 keV).

In the case of decay involving excited electron on the L-shell, two possibilities

exist: emission of 6.4 keV :; iron line due to transition of excited electron from

L-shell to K-shell or absorption of the emitted photon by another electron (Auger

electron) ejected from the iron ion (see e.g. Eze 2013).

The study of the Fe :; lines is of great importance. It is one of the main features

that characterize the X-ray spectra of a source, such as mCVs, X-ray binaries and

AGN. This is due to the fact that iron is far more abundant than any other heavy

metal in these sources. Consequently, the Fe fluorescent emission line (6.4 keV) is

a hallmark of accretion driven X-ray sources (Piro 1993). The Fe :; emission line

is a veritable tool used for the study of the geometry, physics and kinematics of

astrophysical sites. The thermal origin of the X-ray emission of some sources like

galaxy clusters was confirmed upon the discovery of the 6.7 keV iron line in their

X-ray spectra (Mitchell et al. 1976; Serlemitsos et al. 1977).

From the analysis of the :; emission spectra, basic physical properties within the

emitting region can be deduced, such as temperatures, densities, excitation

conditions, ionization balance, elemental abundances and electric- and magnetic-

field distributions (Kahn et al. 2002; Jacobs et al. 2004). The parameters that are

usually employed in this study are line energy (<=), equivalent width (<>=),

intensity (?=) and line profile (line width). Here, α stands for the relevant emission

line.

1.3.1 Line Energy

The line energy or line centroid shows how ionized a medium is. The line energy is

a function of the ionization state of the medium in question. It increases slowly

from 6.4 keV in Fe I to 6.45 keV in Fe XVII, and then sharply to 6.7 keV and 7.0

keV in Fe XXV and Fe XXVI respectively. Several authors (e.g. Febian et al. 1989;

Stella 1990 & Matt et al. 1991), among others, pointed out that the line energy

equally depends on Doppler and gravitational shifts, if the accretion disk is that of

a black hole or an AGN. It has been suggested that in a highly ionized medium,

gravitational red-shift could cause the 6.7 keV energy line to be observed as the 6.4

keV line emissions (Hayakawa 1991; Matsuoka et al.1991). In addition to these

effects, Kallman & White (1988) argue that Compton scattering equally

contributes significantly to the line broadening. This in turn depends on the

geometry and optical depth of the medium.

1.3.2 Equivalent Width

Equivalent width is a determinant of the dominant emission process in a given

ionized medium. It depends on the physics of the emitting region. The fluorescent

emission from a photo-ionized medium is of primary importance. Generally, the

equivalent width for photo-ionized plasma, according to Piro (1993) is usually

expressed as:

@AB∆ΩEFG H<I(<)?(<) ?(<=)⁄K

@L ………………………………. (1.1)

where F(E) is the photon spectrum, EO and EPare respectively the iron edge and

line energy; while ∆Ω is the subtended solid angle from the medium to the X-ray

source and PR(E), is the fluorescence efficiency, which is the probability that an

ionizing photon whose energy E > ET produces a fluorescent photon that escapes

from the medium. This energy range has been shown to be solely responsible for

the observed fluorescent Fe line (Piro 1993).

1.3.3 Line Profile

Line profile however, has to do with the broadening or shifting of the spectral

profile of a given line. Some authors attributed this phenomenon to number of

factors. Matt et al. (1991; 1992) believe that line broadening of gravitational and

Doppler origin, would be observed from a compact source due to the bulk motion

of its accretion disk (the medium). They also pointed out that multiple scattering

by free electrons could as well result in Compton broadening, if the width is about

3 keV for kT of 10 keV.

1.4 The Compact White Dwarf

A white dwarf (WD) is a very dense star with mass comparable to that of the Sun

and radius about that of the Earth, i.e, typically ,AU of 0.9 solar mass and WAU of

5 × 10"#$ (Frank et al. 2002), consisting mainly of electron-degenerate matter

(Johnson 2007). Since the nuclear burning processes have ceased, only the thermal

gas pressure cannot prevent the star from collapse under its own gravity. Hence, it

is supported against gravitational collapse by its degenerate electron gas pressure

(Karttunen et al. 2006). The mass of a typical white dwarf is usually less than 1.4

solar masses. A degenerate gas is one in which all available energy levels up to a

limiting momentum, are completely filled. This limiting momentum is called

Fermi momentum. This limiting momentum , according to (Karttunen et al.

2006), as a function of number density of electron n, is given at absolute zero, by:

X = YZ [\F]

[⁄ ^ [⁄ …………………………..………..……. (1.2)

where h is the Planck’s constant.

The consequence of this expression is that a high density of electrons in physical

space implies that they have high momenta and hence they exert a large pressure

which, for non-relativistic electrons, is given as a function of the mass density

_ = `a$bc (see Karttunen et al. 2006). Thus;

X = YdefZ [

\F] [⁄ g h

ifejkd [⁄ ……………………………..… (1.3)

where $a is the electronic mass, $b is the mass of hydrogen and `a is the average

atomic weight per electron. Since white dwarfs are composed mainly of carbon and

oxygen, the value of`a is very close to 2. The nuclei are much more massive than

the electrons and so do not contribute significantly to the pressure. In the extreme

relativistic case, the limiting momentum can be expressed as (Karttunen et al.

2006) X = lYE Z [\F]

[⁄ g hifejk

E [⁄……………………………….... (1.4)

1.5 The Discovery of the Compact White Dwarf

The first discovery of white dwarf was made on 31st January 1783, when William

Herschel, recorded 40 Eridani B, which was discovered in the triple star system of

40 Eridani (Thomas 2011). The term white dwarf was first used by Willem Luyten

in 1922 (Holberg 2005). The best-known example, Sirius B, is the faint companion

of Sirius, the brightest star in the night sky and was first observed in 1844 by

Friedrich Bessel. He inferred that the system is a binary star system consisting of

the visible star and an unseen object.

The white dwarfs of interest in this work, are found in binary systems called

cataclysmic variables CVs, of the intermediate polar (IP) type, which is a semi-

detached close binary, composed of a magnetized ( = 0.1~10,) white dwarf

and a late-type main-sequence Roche-lobe-filling secondary star (Gansicke 1997;

Vojtech et al. 2006; Ishida 2008).

1.6 Formation of White Dwarfs

White dwarfs are formed as the terminal states in the evolution of low-mass stars.

They can be formed by single stars to give lone white dwarfs or may be formed in

binaries. In any given constellation, a white dwarf could exist as a lone star or as a

binary component of a binary star system. Although, there are star systems

consisting of about three, four or five stars, we assume that every white dwarf in

such a system has a nearest neighbor and as such could be seen as a binary

component. Hence, we consider the formation of these two types of white dwarfs.

1.6.1 Lone White Dwarf

If the mass of a main-sequence star is between 0.8 and 3.0 solar masses, then it is a

candidate for becoming a white dwarf. As stars evolve, they burn their elements in

thermonuclear reactions to produce enough energy to counteract the gravitational

pressure of the accreting matter. When all the hydrogen is fused to helium, the star

expands and becomes a red giant. At the core of the star, a phenomenon called the

triple-alpha process occurs, which involves the fusion of helium to carbon and

oxygen. If the mass of the red giant is not enough to generate very high core

temperatures that could trigger off carbon fusion, the outer envelopes would be

blown off. These outer layers form a planetary nebula; while the core becomes a

compact star, consisting mainly of carbon and oxygen (Richmond 2007).

If the mass of the star is less than 1.4 solar masses, known as the Chandrasekhar

limit, then pressure from the degenerate electron gas becomes large enough to

balance the gravitational pressure and the star no longer contracts but stabilizes.

Electron degeneracy pressure is a result of the neighboring electrons vibrating

faster so they do not violate the Pauli Exclusion Principle (Comins & Kaufmann

2000). Their high temperature and low luminosity places them in the bottom left-

hand side of the Hertzprung-Russell diagram (Thomas 2011), as shown in figure

1.1.

Figure 1.1: Hertzprung-Russell diagram (Thomas 2011).

1.6.2 White Dwarf in a Binary System

As the binary system ages, the more massive of the two stars begins to expand, and

eventually becomes a red giant. At this stage, its Roche lobe is filled and it begins

to transfer some of its gas to the other star. As the process continues, a series of

events causes the red giant to lose angular momentum and move in towards the

other star. More gas is still being transferred at this point. The former red giant,

which has lost its outer gaseous envelope, becomes a white dwarf and continues to

move closer to its companion. The newly formed white dwarf begins to accrete

materials from the main sequence star, which forms accretion disk around the

white dwarf. At certain intervals the accretion disk erupts, causing the entire

system to brighten by several magnitudes. This sudden brightening is termed white

dwarf nova.

1.7 Accretion Processes

Processes of accretion in compact astrophysical high energy sources like magnetic

Cataclysmic Variables (mCVs), black hole candidates and Active Galactive Nuclei

(AGN), among others, involve a number of processes. These processes include

Roche lobe over-flow, mass and angular momentum transfers. It is necessary to

first consider the physics of accretion before the accretion processes.

1.7.1 Physics of Accretion

The accretion of matter onto a more or less compact object is a common, but very

important astrophysical process in the universe (Gansicke 1997). The physics of

accretion is very useful in understanding the theories of black holes found at the

center of active galaxies like the nuclei of radio galaxies, BL Lacertae objects,

Seyfert galaxies and quasars; close binaries in which a neutron star or black hole

accretes material from its main-sequence star companion and sites for star

formation. In the thick molecular clouds where stars are formed, some of the

angular momentum of the core must be dispelled so as to initiate star formation

(Lodato 2008). This task is usually achieved by the accretion disk through

processes like turbulence, viscosity and torques.

Among all the compact and binary systems, CVs are most easily accessible to

observation as they are numerous and relatively nearby. Due to their interacting

nature, CVs, then, are the best places to investigate the nature of accretion disks

which are a common phenomenon occurring throughout the Universe. In theory,

the amount of potential energy per unit mass, (<m) obtained through accretion of

material by a compact object of central mass M and radius R, is given by:

ne =op …………………………………........................ (1.5)

where G is the gravitational constant.

For white dwarfs qrs ~6.6 × 10/7

J/kg. The amount of energy is comparable to

that obtained from nuclear energy conversion, (< = $#u) i.e.

H → Fe gives <m~6 × 10/8 J/kg.

In other words, the fusion of hydrogen atoms to helium and subsequently to iron

yields this enormous amount of energy.

The implication is that accretion onto compact sources can approach or exceed

nuclear energy as a power source since compact objects have very deep

gravitational potential wells.

The accretion rate of matter onto the WD surface, (,wxx = 3 × 10/0g23/), can be

estimated from the observed thermal X-ray luminosity (45). Accreted mass ,wxx

and 45 are related to the radius (WAU) and mass (,AU) of the WD, (Frank et al.

2002) by:

z =o|p|

……………………………....…………….. (1.6)

Thus, for typical WAU of 5 × 10"#$ and ,AU of 0.9 solar mass, (Frank et al.

2002), 45 ≈ 7.2 × 10789123/.

Due to the strong magnetic field of rotating WD, the pressure of the accreting

matter is balanced by the pressure of the rotating magnetosphere (Bednarek and

Pabich 2007). Using a simple model of a column of gas impacting the atmosphere

of the WD, a shock formed gives rise to emission of hard X-rays through thermal

bremsstrahlung cooling by free electrons in the hot post-shock region (PSR) with,

~(5 − 60 ). Reflection of the bremsstrahlung photons at the WD surface

also contributes to the hard X-ray spectrum (Galis et al. 2010). V1223 Sgr, like

other IPs is a very luminous hard X-ray source among accreting WDs.

1.7.2 The Roche Geometry and Mass Transfer

The fundamental kinematics of close binary systems, in particular, the CVs are

well described using the Kepler’s third law in the generalized Newtonian

formulation expressed as (Jurua 2005):

~[ = oEF ( +)X ………………………………..… (1.7)

where a, is the binary separation, X is the orbital period, is the mass of the

primary white dwarf while is the mass of the secondary companion.

The gravitational potential of a binary system, written in a frame of reference that

rotates with the binary system is given by (Venter 2007):

Φ(R) = - op3p− o

p3p − ( × p) ……………………..… (1.8)

where p and p are the respective position vectors of the two stars which are

assumed to be point masses, is the angular velocity of the binary, and p is the

radius vector of the center of mass. The shape of the Roche lobes is determined by

a parameter (q), called the mass ratio defined by = ⁄ ; while the size of

the lobes is fixed by the binary separation a. Equation (1.8) defines the critical

equipotential surfaces which limit the radial extent of the components. The

equipotential surfaces in a typical CV with = 0.2 are shown as in figure 1.2.

Figure 1.2: Equipotential surfaces in a typical CV with q =0.2

(Adapted from Gänsicke 2000)

It can be seen that for a specific value of Φ(R), the Roche lobes of the two stars

are in contact at a single point, called the inner Lagrangian point, (z) or the

Critical Roche-Lobe Potential (CRLP), which is a saddle point of Φ(R) i.e. where

the gradient of the effective potential is zero or no force is felt in the co-rotating

frame. Roche lobe is the critical surface where the two equipotentials touch each

other. Of all the Lagrangian points, z is most important in cataclysmic variables,

because the equipotential surface here connects the gravitational spheres of

influence of the two stars (Podsiadlowski 2011). If the secondary star fills its

Roche lobe, which is the case in cataclysmic variables, mass is transferred onto the

Roche lobe of the primary star through the inner Lagrangian point, z; this

scenario, referred to as Roche-Lobe overflow (RLOF) model is believed to be the

best method of transferring mass in semi-detached binary systems (Podsiadlowski

2011).

It is obvious in figure (1.2) that the equipotential surfaces near the centers of the

stars are circular; while the ones in scales comparable to the binary separation are

pear-shaped, e.g. (zE and zd). After leaving z the transferred mass, falls towards

the white dwarf with increasing velocity (Aungwerojwit 2011). In the analysis

above two assumptions were made: first, tidal forces have coerced the two stars

into a circular orbit and second, the mass of each star is concentrated in its center.

1.7.3 Mass and Angular Momentum Transfers

Angular momentum loss is necessary for mass transfer to occur in semi-detached

binary systems like the cataclysmic variable stars. This angular momentum loss

could result from the emission of gravitational radiation through the rotation of the

two components around their center of mass. The generated gravitational waves

remove orbital angular momentum from the binary, which in turn drives mass

transfer from the secondary star to the accreting white dwarf through an accretion

disk (Kraft and Mathews 1962; Littlefair et al. 2006). The gas drifting inward

around the accretion disk can exchange its angular momentum with the gas further

away from the disk due to some mechanisms like disk instabilities. It can as well

be lost through torques, which acts on the gas and dissipative processes like

viscosity acting between gas layers. The outward transport of angular momentum

causes the in-falling materials to be drifted inwards, which triggers off accretion

process.

Let us consider two stars of masses and separated by a distance

~ =~ +~, where, ~ and ~ are the respective distances of and

from their common center-of-mass, as shown in figure (1.3).

Figure 1.3: Two stars of masses and orbiting in a plane about their centre-of-mass X (Adopted from Hellier

2001, p.189).

The gravitational force, F on any of the stars of mass m due to the total mass, M of

the system is given by:

F = oe~ ……..…………………………………………… (1.9)

where G is the gravitational constant; similarly, the centripetal force on m is

expressed as:

F = e~ …………………………………………................…….. (1.10)

Equating equations (1.9) and (1.10) yields an expression for the Keplerian velocity,

ν given as:

= go~ k ⁄

…………………………………..………………….. (1.11)

Using equations (1.7) and (1.11), the orbital period can be expressed as:

X = F~ ………………..………………………..………….. (1.12)

From equation (1.7) the square of the orbital period can be expressed as:

X = EF~[o …………………………………..……………….. (1.13)

Where = +

By definition, angular momentum, J is given by:

J = Ma………………………………………..……………….. (1.14)

The orbital velocity, ν is expressed as:

= F~X ………………………………………………………… (1.15)

2F~ is the orbital circumference. The total orbital angular momentum of the

system then becomes:

= ~ +~ ……………………….……………. (1.16)

Using equation (1.15) in (1.16) yields:

=~ F~X +~ F~

X ……………………………….. (1.17)

Substituting equation (1.11) in equation (1.12) yields:

=go~ k ⁄

~Z~ +~] …………………………….. (1.18)

Since ~ = ~ + ~ and ~ = ~ for a binary system, / and ucan be

expressed respectively as:

~ = ~() ……………………………………..……………. (1.19)

and

~ = ~() …………………………………………………… (1.20)

Using equation (1.19) in equation (1.18), we obtain upon simplification the

expression:

= go~ k

~(~)~ +(~)~ …………...……… (1.21)

Further simplification is achieved by using modified form of equation (1.20) in

equation (1.21) to obtain:

=go~ k

~(~)(~ +~) ……….………………..… (1.22)

The total orbital angular momentum of the binary system therefore becomes:

= go~k

…………………………….…………….. (1.23)

Simplification was achieved using ~ = ~ + ~ and equation (1.19) in equation

(1.22). Differentiating equation (1.23) logarithmically, gives:

Ј-Ј =

-

+ -

+ g~-~ −

-k ………………..……………………. (1.24)

Since mass transfer is conserved, - = −- and - = 0, equation (1.24) reduces

to:

~-~ = -

+ Z3- ]

g − k ……………..………..…………. (1.25)

~- ~⁄ is the rate of change of the binary separation, - ⁄ is the rate of change

of orbital angular momentum and−- ⁄ is the rate of mass transfer from the

secondary star.

It is assumed that angular momentum is also conserved i.e. - = .

Consequently, mass transfer from the secondary star (-- > 0) causes the binary

separation a, to increase i.e. ~- > , because in cataclysmic variables, mass of the

secondary star is less than that of the primary star, i.e. <. In CVs, mass is

transferred from the less massive star to the more massive white dwarf. If mass

transfer is conserved, more material is deposited very close to the centre-of-mass;

while the remaining mass Mu moves to a wider orbit to ensure conservation of the

total angular momentum. The mean radius of the low-mass secondary star’s Roche

lobe obeys the equation (Campbell 1997):

gpz,~ k[ ≈ . ………………………….…………………….. (1.26)

If . ≤ ≤ . \⁄ , where pz, is the Roche Lobe of the secondary star

(Frank et al. 1992, Campbell 1997).

Logarithmic differentiation of equation (1.25) yields:

p- z,pz,

=~-~ + [- 3- ……………………………………………… (1.27)

Recognizing the fact that - = 0 and using the value of ~- ~⁄ from equation (1.25)

in equation (1.27), gives:

p- z,pz,

= - + Z3- ]

g −

k + [- ……………………..…. (1.28)

Further simplification yields:

p- z,pz,

= - + Z3- ]

gd −

k ……………………….……….. (1.29)

Conservation of angular momentum implies that - = and mass transfer from

the secondary star results in the expansion of its Roche lobe (p- z, > 0), which

increases the binary separation. Consequently, mass transfer would stop when the

secondary star is no longer in contact with the Roche lobe (King 1988; Frank et al.

1992).

However, the interest in work is on the scenario whereby sustained and stable mass

transfer is achieved. This demands a gradual decay of the angular momentum of

the binary system which enables the secondary star’s Roche lobe to be continually

in contact with that of the primary star. This ensures further mass transfer from the

secondary star to its companion white dwarf. One can therefore conclude that in

compact binary systems, like the CVs, mass transfer results from the angular

momentum loss from the binary system.

1.8 Uses of Cataclysmic Variables

The study of Cataclysmic Variables is very important in astrophysics as it proffers

plausible solution to some hitherto mysteries of nature, such as the origin of

cosmic rays and gravitational wave emissions. Some of the usefulness of such a

study is discussed in subsequent sections.

1.8.1 A possible Origin of Cosmic-Rays

For more than a century now, since the discovery of cosmic rays (CRs), high

energy astrophysics researchers have not been able to establish the origin of the

cosmic rays. It has been established that particle acceleration of the order of the

knee energy (= 10/. eV) occurs in rotation powered pulsars (RPPs) and super

nova remnants (SNRs) although the total energy density may or may not be

accounted for by them (Koyama et al.1995). CRs above the knee energy are likely

to emanate from extra galactic sources. As in RPPs, a magnetized white dwarf can

achieve rotation-induced voltage given by (Ishida 2008):

= G( × ). ~( ) …………………………………… (1.30)

= × d g X[ k

3 g ¡ok g

p¢lek

[¤ ] …………….. (1.31)

The factor × ¡ is the Lorentz force term which couples the radiation to the

WD’s surface.

Since the voltage generated is as high as 10/ volts, and given the large number of

white dwarfs in the universe, it is reasonable to consider magnetized white dwarfs

as viable origin of the cosmic rays (Ishida 2008). This theoretical value of the

voltage generated by a typical white dwarf falls within the voltage range of

detected cosmic rays of extragalactic origins and this gives credence to the validity

of a WD being considered as a possible source of cosmic rays.

1.8.2 A Laboratory for the Study of Gravitational Wave Emission

Cataclysmic Variables (CVs) are veritable tools for the study of Gravitational

Wave (GW), emission predicted by the theory of General Relativity. Emission of

gravitational wave is believed to trigger off the evolution of short-period

cataclysmic variables, which sustains mass transfer from the low-mass secondary

star to its companion accretor which is a degenerate white dwarf (Rezzolla et al.

2001). In short-period ( < 3ℎ92) binary systems, like the Cataclysmic

Variables, GW is theorized to be emitted through the rotation of the two

components around their center of mass.

Emission of gravitational radiation is believed to be one of the principal

mechanisms that necessitate removal of orbital angular momentum from compact

binary systems (Rezzolla et al. 2001). The theoretical framework employed here is

the classical model of Peters and Mathews (PM) (Barone et al. 1992). This model

assumes the components to be point masses in a slow-moving system with a weak-

field, which implies Keplerian orbits and dominant quadrupole radiation. The GW

luminosity radiated from any binary system (in this case, CVs) is given by (Barone

et al. 1992):

4§A = 2.2¨108 g ee(ee) [⁄ k

©/ª 7⁄

g+- (e) [ergs/sec]……………. (1.32)

Where the e and e are the masses expressed in the units of solar mass, « is

the orbital frequency expressed in hertz (Hz) and ¬ + −(f) are universal functions

which determine the effects of the eccentricity of the system on the two possible

polarizations (+ -).

The search for gravitational radiation is a noble one since its discovery could

reshape the understanding of the universe in the areas of science and technology. It

is possible that gravitational radiation could travel faster than electromagnetic

radiation. If this becomes a reality, different parts of the universe which are

currently inaccessible as a result of the limitations imposed by the speed of light

could be explored. It could also enable a better understanding of the phenomena of

Dark Matter (DM) and Dark Energy (DE) which contain about 95% of the masses

in the universe. In the area of telecommunications, it could as well give rise to the

discovery of a faster and more efficient means of communication.

1.9 Purpose of Study

This research work is aimed at two things, namely:

i) To investigate the possible origin(s) of the hard X-ray emission from V1223 Sgr

ii) To suggest the mechanism(s) for the production of the Fe Kα line in V1223 Sgr.

CHAPTER TWO

Literature Review

Many works have been done on V1223 Sgr, with various interests and intensions

using various satellites and observational approaches. Some of these research

works are briefly discussed below.

Steiner et al. 1980 was the first to optically identify the bright X-ray source

4U1849-31 with V1223 Sgr. Optical brightness variability with a modulation at a

period of 13.2min was observed for the first time in V1223 Sgr.

Warner & Cropper 1984, found the orbital and rotational period of V1223 Sgr to

be: = 3.37ℎ92 and = 0.2207hrs(794.3802) respectively. Brightness

variability was also detected in which the system’s brightness could increase or

decrease by 10 − 20% on time scales of about 100s with excess power in the

0.04 − 0.08¯° frequency range.

Garnavich & Szkody 1988, detected episodes of deep low states (decrease by

several magnitudes in the flux) in the system, V1223 Sgr.

van Amerongen& van Paradijs 1989, discovered, in the optical regime, outbursts

which lasted for about 6-12hrs during revolution 61 (MJD 52743) with a peak flux

about 3 times of the average value.

Barlow et al. 2006 found out that rare IPs and asynchronous polar CVs usually

emit within the 20-100keV energy range, with IPs being more luminous in the soft

γ-ray band than the polars. The light-curve of V1223 Sgr revealed a flaring activity

lasting for about 3.5 hours (MJD=52743) during which the hard X-ray luminosity

was an order of magnitude higher than the average value, i.e. ~ 10789123/. This

observation was the first of its kind for IPs in the high energy bands. The broad-

band spectra of V1223 Sgr were fitted well by a thermal bremsstrahlung model.

Hudec et al. 2008 discovered an X-ray flare in V1223 Sgr, which lasted for about

3.5 hours during revolution 61 (MJD 52743) with a peak flux about 3 times of the

average value as observed earlier (van Amerongen & van Paradijs 1989) in the

optical regime.

Harrison et al. 2010, observed a strong fading burst from V1223 Sgr in the mid-

infrared band, during which the flux decreased by 13 magnitudes. The flux decline

was for the first time linked with transient synchrotron emission and V1223 Sgr

became the third IP known to emit synchrotron radiation. This conclusion was

arrived at due to the similarity between the slopes of V1223 Sgr and AE Aql, one

of the systems that emit synchrotron radiation.

Hayashi et al. 2011 studied the spectra of V1223 Sgr using a multi-temperature

plasma emission model with reflection from a cold matter. The central energy of

the detected fluorescent iron ; emission line was discovered for the first time in

mCVs, to be modulated with the WD rotation.

Galis et al. 2011 observed a possible X-ray flaring activity and a short-term burst

in the optical regime. They observed flux drop both in the optical and 15-40keV

energy band, with lowest value around MJD ~53 650. They argued that disk

instability activities, which are direct consequence of changes in the accretion rate

of the WD, were responsible for the flux drop.

Landi et al. 2012 analyzed the IBIS and BAT spectra of V1223 Sgr in the 20-

100keV energy regime using the thermal bremsstrahlung model fit in XSPEC

v12.7.1 (Dorman & Arnaud 2001). The average post-shock temperature for the

IBIS data is,⟨kT⟩ = 23.2 ± 1keV and ⟨kT⟩ = 19.5 ± 1keV for the BAT data. The

light-curve 0f V1223 Sgr shows evidence of flux variability in both IBIS and BAT

data.

Eze 2013 studied some hard X-ray emitting Symbiotic Stars (hSSs), using Suzaku

satellite. He investigated the formation and origin of the iron K-alpha line

complexes in the sources in order to understand better the geometry of the

emission region.

CHAPTER THREE

Source of Data and Data Analyses

3.1 Source of Data

Observation of V1223 Sgr was done using Suzaku satellite on 13-04-2007 for

42.2kiloseconds. Suzaku is the Japan's fifth X-ray Astronomy mission. Suzaku

was launched on July 10th 2005, to replace the ASTRO-E2 which failed to orbit

during its launch on February 10th 2000. It was developed by the Japanese

Institute of Space and Aeronautical Science (ISAS), a branch of the Japan

Aerospace Agency (JAXA), in association with NASA. The details of its three

instruments have been presented by Petre and Newman (2009) and the associated

references.

The satellite's primary mission is to obtain high spectral resolution data of

astrophysical objects in the energy range of 0.2 - 700keV (soft X-rays to γ-rays),

for guest investigator(s) through the sponsorship of a NASA Guest Observer

Program. After one year from the end of the period of observation, the collected

data are placed in the Suzaku Public Archive for public usage. The V1223 Sgr data

used in this work were retrieved from the Suzaku Public Archive.

3.2 Data Analyses and Results

Our data were analyzed using version 2.0 of the standard Suzaku pipeline products

and HEAsoft version 6.11. A 250" radius was used for the extraction of events for

the XIS detectors for the production of the source spectrum. The same radius was

also used to extract the XIS background spectrum with no apparent sources and

was offset for the source and corner calibrations. The response files: Redistribution

Matrix File and Ancillary Response File were generated for the XIS detectors

using the FTOOLS, xisrmfgen and xissmarfgen respectively. The XIS 0, 2 and 3

are front-illuminated (FI) chips whose features are similar. Consequently, the

spectra of XIS 0 and 3 were merged and referred to as FI. Due to an anomaly, XIS

2 has been out of service since November 9, 2006. XIS1 is a back-illuminated (BI)

chip and its spectral profile is referred to as BI.

The analysis of the HXD PIN detector was done by downloading the non- X-ray

tuned PIN background files and the appropriate response matrix files for the

observation as generated by the Suzaku team. The good time intervals were

merged using the mgtime FTOOLS to obtain a common value for both the PIN

background and source event files. The source and background spectra for the

source were extracted using the xselect filter time file routine. The dead time of the

observed spectra was corrected for using the hxddtcor of the Suzaku FTOOLS.

Exposure time for observation for the derived background spectrum was increased

by a factor 10 to take care of the event rate in the PIN background event file which

was made 10 times higher than the real background for suppression of the Poisson

errors, in accordance with the standard analysis procedure.

Using XSPEC version 12.7.0, the spectrum was modeled using the absorbed

thermal bremsstrahlung model with three Gaussian lines for the three Kα Fe line

emissions. The fitting covers 3-10keV energy range for the XIS BI, about 3-12keV

for the XIS FI and 15-40keV for the HXD PIN. In order to avoid intrinsic

absorption which affects both the XIS FI and BI data below 3keV, this energy

range was not included in the fitting. Also, the energy range above 10keV was not

considered for the XIS BI data since the instrument background is higher relative

to the XIS FI detectors. Figure 3.1 shows the spectrum of v1223 Sgr. Obviously,

the emission lines, low ionized (6.4keV), He-like (6.7keV) and H-like (7.0) iron

lines were resolved clearly in the spectrum.

Figure 3.1: Spectrum of V1223Sgr

The light curve of V1223 Sgr is also shown in figure 3.2. it could be observed from

the figure 3.2 that the light curve of V1223 Sgr shows a deep drop in photon counts

around 4.2 × 1082 − 6.3 × 1082 during the time of observation.

Figure 3.2: Light curve of V1223 Sgr

The parameters of V1223 Sgr were fitted to the thermal Bremsstrahlung model and

the best fitting parameters are presented in table 4.1. The fitting was carried out

using a cross-normalization factor of 1.1 which has been considered to be

satisfactorily acceptable by the Suzaku fitting standard.

Table 3.1: Best Fitting Parameters of V1223 Sgr by the Thermal Bremsstrahlung Model

Parameter Best fit value Unit

¸j¹

. [ ± . le3

¸j«

º ± d le3

» . E ± . [

¼½ d ± [ ¼f

¾l¿^ [E. d ± . [ 3[¹Y^ 3le3

n.E . [\ ± . ¼f

¾.E d. º ± . º 3d¹Y^ 3le3

n|.E \¢3\º f

n.º . º ± . ¼f

¾.º . [ ± . 3d¹Y^ 3le3

n|.º d¢3\\ f

nº. . ¢d ± . ¼f

¾º. \. [ ± . d 3d¹Y^ 3le3

n|º. Ed3E f

The parameters are the hydrogen column density of the full-covering and the partial-covering matter in units of

10uucm3u (NÂR andNÂÃ

), the covering fraction of the partial-covering matter (C), the continuum temperature in keV

(kT), the continuum flux in 1037 photons3/cm3u (FÇÈÉÊË), the center energies of 6.4, 6.7, and 7.0 keV lines in keV

(E.8, E.0and E0.ª), the line fluxes in 103phtons3/cm3u (F.8, F.0and F0.ª), and the corresponding equivalent

width in eV (EW.8, EW.0andEW0.ª).

CHAPTER FOUR

Discussion of Results

From the results of our fits, it was observed that the lower energy range (3-12

keV), of the hard X-ray spectrum of V1223 Sgr can adequately be explained using

a thermal bremsstrahlung model with both a partial-covering matter and full-

covering matter. The model produced a statistically acceptable spectral fit within

this X-ray regime. The statistical acceptability of a spectral fit is determined by the

value of the cross normalization factor used. This agrees very well with the results

of Galis et al. (2008), in which the broad-band spectra (3-100 keV) of V1223 Sgr

fitted well by a thermal bremsstrahlung model, with a post-shock region

temperature, kT of about (20-25 keV). The harder component, the HXD PIN data

also produced a very good spectral fit by the model, although the data points are

fewer compared to that of the XIS FI and BI mirrors.

It was shown in the results that the components of the Fe Kα line-emission were

clearly resolved. These include the low-ionized (6.41 keV), He-like (6.70 keV) and

H-like (7.00 keV) iron lines. The fluorescent Fe line or the neutral Fe Kα line at

6.41 keV indicates that a reflection component is contained in the hard X-ray

spectra of V1223 Sgr. It had been pointed out that a significant portion of this hard

continuum is believed to result from reflection from the WD surface (van

Teeseling et al. 1996; Galis et al. 2011). In addition to the WD surface, the

reflection could also come from the cold gas on or near the WD surface or pre-

shock region (see Yuasa et al. 2010 and Hayashi et al. 2011) as well as the

accretion column. Hayashi et al. (2011), suggest that the reflector is only the WD,

since they got a value for the solid angle,Í F = . ¢d3.º.E, which approximates

to unity. However, it can be argued that other reflector(s) could also be present

given the fact that their fit (reduced chi-squared of 1.12 with 313 degrees of

freedom) was only marginally acceptable. The presence of spectral lines of H- and

He-like ions of Fe is associated with the emission of hard X-rays. It believed that a

portion of this hard X-rays could emanate from the boundary layer of the accretion

disk of the CV of interest, V1223 Sgr.

The results presented in this work also appear to suggest that the thermal

component of the hard X-rays results from the shock-hitting of the accreted

material in a thermal bremsstrahlung cooling at the post-shock region and the

boundary layers of the WD accretion disk. The absorption of this hard X-ray

continuum by the accretion flow and the resultant reflection from the WD surface,

could contribute to the observed iron line emissions (see e.g. Landi et al. 2009).

This hard X-ray irradiates the cold gas around the accretion disk resulting in the

emission of the Kα fluorescence lines of iron (see Eze 2013). This scenario was

equally suggested for the hard X-ray emitting symbiotic stars (see e.g. Luna &

Sokoloski 2007; Eze et al. 2010).

This type of emission line spectrum is compatible with the photo-ionized plasma

model in CVs (Kallman et al. 1993). Mukai et al. (2003), suggested that the

spectra of V1223 Sgr, could entirely be generated using the cooling flow model, if

the lower temperature region is masked by the pre-shock accretion flow.

Consequently, a remnant hard component of the cooling flow is left, which in turn

photo-ionizes the accretion columns above it thereby giving rise to the observed

continuum.

Another important aspect of the results is the light curve of V1223 Sgr generated

using the XIS combined data after background subtraction. Although detailed

timing analysis of the combined spectrum, which could enable in-depth discussion

of all the possible variability in the source is not yet available, the light curve of

V1223 Sgr showed no detectable flaring activity at the time of observation. This

suggests that no significant changes in some observable physical processes, such as

increase in the accretion rate occurred in the system at the time it was observed.

The possibility of short-term bursts, as was observed in the optical band (van

Amerongen and van Paradijs 1989) could not be ruled out.

The apparent decrease in photon counts which could be seen as the intensity

minimum occurred around time Î = 5 × 1082. This time-scale suggests a long-

term amplitude variation, which could be due to a decrease in the mass accretion

rate of the source.

CHAPTER FIVE

Conclusions

We successfully fitted the lower hard X-ray regime (3-12 keV) of the hard X-ray

spectrum of V1223 Sgr obtained from Suzaku satellite data, by a thermal

bremsstrahlung model with a partial- and full- covering matter. This model

produced a statistically acceptable spectral fit, with average spectrum temperature

⟨kT⟩ = 25 ± 3 . The harder X-ray bands (15-40 keV), also produced a very

good spectral fit by the same model, although the data points are fewer in this

region. The implication is that the thermal bremsstrahlung model with both partial-

and full-covering matters is a very good model for fitting the spectra of V1223 Sgr

in the hard X-ray bands.

The presence of Fe line emissions with average continuum temperature of 25 keV

lends credence to the thermal origin of the majority of the detected hard X-rays

from V1223 Sgr, since only a small fraction of the observed spectrum is believed

to be a product of reprocessed hard X-rays from the WD’s surface. In addition, the

observed line emissions suggest that the disk is composed of moderately ionized

plasma, which is very important in understanding the physics of accretion in binary

systems such as symbiotic stars and other compact systems, like black holes and

active galactic nuclei (AGN). Consequently, we infer that any astrophysical

system, in which similar emissions were observed, could certainly have accretion

disk made of moderately ionized plasma.

We associate the low-ionized (6.41 keV) iron line emission with the irradiation of

the cold iron atoms and/or ions around the boundary layer of the inner accretion

disk of the WD, by hard X-rays. The He-like (6.70 keV) and H-like (7.00 keV) iron

spectral lines are believed to result from either the collision of in-falling matter

with WD’s shock waves (collisional excitation) at its boundary layer or

photoionization by hard X-rays, of the accreted matter at the inner rim of the

accretion disk. A combination of the two processes is also possible.

Although, we did not conduct a detailed timing analysis of the reprocessed XIS

data of V1223 Sgr, the deep decline in photon counts (period of almost zero photon

counts) which occurred around time Î = 5 × 1082 could be interpreted as a long-

term amplitude variability considering the time-scales involved. The decline could

be a direct consequence of a decrease in the mass accretion rate of the system.

The light curve showed no detectable flaring activity at the time of observation.

This suggests that no significant changes in some observable physical processes

like increase in the accretion rate occurred in the system during its observation. On

the contrary, we could not rule out the possibility of short-term bursts in the hard

X-ray band of the source since.

Recommendations

We recommend that further work be done on V1223 Sgr, in which in-depth timing

analysis of its spectra could be conducted. This would enable detection of all forms

of flaring activity in the source depending on the sensitivity of the instrument used.

Satellites with higher CCD resolution, like the Astro-H, should be used in the

observation of V1223 Sgr so as to get a better resolution of its emission region(s).

This would better our understanding of the observable processes occurring in the

object in particular, and other astrophysical high energy sources in general.

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