ON THE 511 keV EMISSION OF THE

GALACTIC BULGE WITH FOCUS ON

LOW-MASS X-RAY BINARIES

Timothy R. McClain

Dr. Mark Leising

Dr. Dieter Hartmann

Dr. Jeremy King

AUG 2013

Abstract

The 511 keV emission from the Galactic bulge is known to be caused by the

annihilation of positrons and electrons focused towards the interior of the bulge.

While there is no short supply of electrons in the interstellar medium of the bulge,

the source of positrons has lacked a smoking gun since its detection in the 1970s.

Prantzos et al. (2010) contains a very well constructed break down of the known

positron sources as well as the potential sources, which can range from compact

systems such as pulsars or black holes to massive stars and their eventual supernovae,

and even to exotic dark matter. Utilizing an estimated but robust positron production

rate and a number of systems as predicted by rapid population synthesis models, I

have attempted to synthetically construct the flux profile of the 511 keV line from

the bulge detected by SPI/INTEGRAL and reported on by Weidenspointner et al.

(2008).

ii

Acknowledgements

I would like to thank Drs. Leising, Hartmann, and King for their presence on

my committee and for the guidance in the course of the writing of my thesis. Also

Dr. Rob Izzard of University of Bonn for the use of his population synthesis code, an

integral part of my thesis research. Lastly, I would like to thank Clemson University

for allowing me the opportunity to pursue this degree.

ii

Table of Contents

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . ii

TABLE OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

CHAPTER

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1 The code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3 Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.1 IMF Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.3 Modelling Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 18

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

iii

LIST OF FIGURES

Figure Page

2.1 R is the radius of the gamma-ray emitting disk and σT is the Thomson

cross-section of an electron. . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Spherical scatter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 Gaussian scatter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.4 Bissantz and Gerhard scatter. . . . . . . . . . . . . . . . . . . . . . . 8

2.5 Dehnen and Binney scatter. . . . . . . . . . . . . . . . . . . . . . . . 8

2.6 Double exponential scatter . . . . . . . . . . . . . . . . . . . . . . . . 8

3.1 The flux as measured by SPI/INTEGRAL and the corresponding 511

keV map from Weidenspointer et al. (2008)[1] . . . . . . . . . . . . . 13

3.2 40 systems in a Dehnen & Binney distribution and 135 systems in a

simple gaussian. Dotted line depicts the Weidenspointner model. . . . 14

3.3 2 simple gaussians with 89 and 86 systems. Dotted line depicts the

Weidenspointner model. . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.4 124 systems in a simple gaussian distribution and 51 in a random

spherical model. Dotted line depicts the Weidenspointner model. . . . 16

iv

Chapter 1

Introduction

In the 1970s, the detection of 511 keV emission eminating from the Bulge bewildered

astronomers. Before 1991, the line’s distribution was poorly constrained, but in 1991,

OSSE aboard CGRO clearly resolved a single point source as the origin of the line.

This source was extended over a symmetric bulge and emission from the plane of the

Galaxy (Purcell et al., 1994)[2]. When it was closely inspected, it was found that

the continuum emission closely followed the distribution of positronium annihilation,

which is widely believed to be the dominant mode of annihilation. All models to

describe the annihilation distribution have in common a spheroid component located

in the inner Galaxy and an extended disk component. While OSSE progressed the

field substantially, the origin of the positrons was still uncertain. Early in the 21st

century, many believed the source to be β-decay from unstable isotopes; 26Al, 44Ti,

and 56Co in particular. β-decay does produce a non-negligible contribution to the

observed continuum, however, if a stead state model is to be assumed, decay alone

does not account for the total annihilation rate of 2× 1043e+s−1.

Other non-isotopic sources are thought to be be low-mass X-ray binaries (LMXRBs),

1

pulsars, Sgr A∗, classical novae, γ-ray bursts, hypernovae, and exotic dark matter.

Some of these can be excluded by logical reasoning. Hypernovae can only be pro-

duced by massive stars which would have no major presence in the Bulge due to the

metal-rich environment. The same argument can be made for γ-ray bursts as well.

Sgr A∗ has two modes of producing positrons, via proton-proton collisions and high

energy photons. However, the energy of the photons would result in the production

of positrons of much too high an energy to contribute to the 511 keV emission in the

central bulge, as the resulting positrons would have to travel about the bulge radius

(∼2 kpc) before slowing enough to contribute to the continuum. The same is true for

the p-p collision assuming a magnetic field from Sgr A∗ of B < 0.4mG (Prantzos et

al., 2010)[3]. Pulsars, in all subtypes, produce γ-rays in excess of 30 MeV, which is

well above the continuum energy spectrum.

Exotic dark matter has also been floated to explain the origin of the positrons.

“Exotic” dark matter would have mass ranging from the GeV to TeV. There are

two possibilities utilizing dark matter. The first is assuming “light” dark matter,

by which we mean MeV dark matter, annihilating or decaying. Theoretically, this

would produce positrons with low enough energy to contribute to the continuum. The

second is assuming “heavy” dark matter with mass GeV-TeV de-exciting. This de-

excitation would need to have an energy difference of 1 MeV between initial and final

states. However, annihilation and de-excitation can only aid the continuum given a

cuspy dark matter density profile, whereas decay is ruled out for all profiles (Prantzos

et al., 2010)[3].

LMXRBs then becomes a leading contender for a likely positron source. LMXRBs

are approximately 10 times brighter and more numerous than high-mass X-ray bina-

ries (HMXRBs). The means of positron creation is found either in the pair creation

in the X-ray corona of the compact object, or at the base of the jets in the case

2

of a microquasar. Given the global energy considerations fo XRB luminosities, an

average value of ∼ 1041 e+s−1 for a jet Guessom et al., (2006)([4]). This average value

is confirmed as an upper limit for positron production in XRBs by SPI/INTEGRAL.

While the positron production of a lone LMXRB is much less than the estimated

∼ 1043 e+s−1, if there were on the order of 100 LMXRBs concentrated in the center

of the bulge, they could be the dominant contributer to the 511 keV continuum.

3

Chapter 2

Methods

First and foremost in this endeavor, it is important to identify viable distribution func-

tions which the LMXRBs will be spread across. Also important is to compare these

with a selection of constrained “random” models, for this study, a random spherical

and gaussian models were used. Utilizing the aforementioned random scatter models

as well as the mass models given by a simple double exponential approximation, Bis-

santz & Gerhard, as well as the mass model put forth by Dehnen & Binney (McMillan,

2011[5];Dehnen & Binney, 1998[6]). The radial coordinate for each of these models

was determined by using a rejection method with an initial estimate of 1.5 × Rs. It

was assumed that the angular coordinates had no affect on the distribution and were

therefore chosen randomly. The points were then scattered on an aitoff projection

and fluxes calculated for each pixel with dimensions 2◦ by 1◦. The flux was then de-

termined per steradian with bin size 2◦ by 20◦. This bin size was found to be optimal

for the purposes of this study as it allowed a smoother overall curve across the models

losing any key features.

The 511 keV flux is purely dependent on the positrons available to annihilate.

4

Given that the we see a continuum flux and not a discrete one, a steady state for

positron production was assumed. The value noted as a ‘canonical average’ for XRBs

by Guessoum et al., (2006)[4] is ∼ 1041 e+s−1. This is estimated by the formulation

made by Beloborodov (1999):

Lmaxe+e− =2πmec

3R

σT

Figure 2.1: R is the radius of the gamma-ray emitting disk and σT is the Thomsoncross-section of an electron.

The pairs created form an optically thick envelope and move in equilibrium with

the radiation field with velocity ∼ 0.5c (Belogorodov, 1999[7]). Inferring the mass

of a stellar black hole created by a ≥ 20M� star, the positron production rate is

estimated at ∼ 4× 1041e+s−1.

The number of systems was found using a compound method of determining the

number of high mass stars from a corresponding initial mass function (IMF). A binary

fraction from literature was used to determine the number of those high mass objects

end up in binaries. The flux was determined from the resulting, eventual, black hole

when Roche lobe overflow occurs. The purpose in this methodology is to synthetically

replicate the flux map measured by Weidenspointer et al., (2008)[1].

In this way I intend to target the number of black holes with a low mass, over-

flowing companion which would in turn form an accreting black hole. These systems

would represent the number of low-mass X-ray binaries. Since a distribution cannot

be determined from a population synthesis, I have chosen the above configurations

to test whether the total flux coming from a discrete population of the above forms

can reproduce the observed flux of 511 keV emission by SPI/INTEGRAL.

While a more meaningful and comprehensive study would perform the above with

the estimated number of stars in the Bulge. Due to hardware limitations, the com-

5

putational limit for this study was 107 stars, which totaled ∼ 106M�. As a result,

what follows is a sampling of the Bulge population. However, no qualitative study

involving the binary fraction of the Bulge has been done to date, nor is there avail-

able data on the fraction of those binaries which would have Roche lobe overflow

onto the black hole companion on a timescale which would enable us to detect the

511 keV emission. Additionally, the fraction of systems which manage to stay gravi-

tationally bound post-type II supernova also is unknown. Even the fraction of those

systems which evolve into close enough binaries to have appreciable accretion onto

the compact object is unknown. To this, I shall adopt a ‘Drake’ formalism.

Nabh = Ntot × fbin × fHMB × fRLOF × ... (2.1)

Where fbin is the binary fraction of the Bulge, fHMB is the fraction of those binaries

which have a high mass component of ≥ 20M�, and fRLOF is the fraction of those

systems which enter into a Roche lobe overflow state on a timescale which would

allow it to be detected, and ‘...’ indicates higher order constraints which could be

applied.

From previous sampling and running of the programs, it was found that any

amount of systems over 200 created a flux profile which was too bright to match the

model presented in Weidenspointner et al., (2008)[1]. This points to the constraint

that in a model which could perform this process on 1010M�, the fractional constraints

must be on the order of ∼ 10−8.

6

2.1 The code

The programming code was split into three primary sections. First, IDL was used to

calculate the mass distribution of 107 stars with distribution following the parameters

given by Kroupa (2001)[8]. The minimum mass was set at 0.1M� and the maximum

at 100M� with an adopted α parameter of α = 2.3 for all mass values. Kroupa

(2001)[8] did adopt a value of α = 1.3 for 0.08 ≤ M < 0.5M�; however, since the

intent of this program is to estimate the number of high mass stars, this parameter

difference was not taken into account for the purposes of this research.

A binary fraction originally determined for globular clusters was used since the

density range of GCs is 103−108 ?pc−3. Out of the 107 stars, ∼ 103 qualified as high

mass according to my IMF. From these systems, I had to narrow it down to less than

200. As a result, a binary fraction of 1% was adopted. While this binary fraction was

found for the densest of globular clusters (Fregeau et al., 2009)([9]), a higher fraction

yields flux in excess to what is observed. Performing this whittled the number from

∼ 8000 to 175 systems. This process was iterated 20 times and an average was taken

to alleviate systematic error.

Secondly, C++ was used to calculate the positions of each system given the num-

ber returned from the above. Only spherically symmetric, angular independent mod-

els were considered. IDL was again utilized to map everything to an aitoff projection

and then to calculate and plot fluxes. A positron production rate of ∼ 1041e+s−1

was adopted from Guessom et al., (2006)[4] for each system in the field. The systems

were then selected out based on Galactic longitude for |`| > 10◦. The flux from each

system was calculated for each system using:

F =Ne

4πR2. (2.2)

7

And once the systems were placed within the respective bins, the flux bins were

divided by a factor of∫∫

cos(θ)dθdφ which finalizes the units as γ s−1cm−2sr−1

Thirdly, I attempted to replicate the Weidnespointner, et al., (2008) findings by

adding two or more of the distribution models together to recreate the models used

to fit the data.

Figure 2.2: Spherical scatter. Figure 2.3: Gaussian scatter.

Figure 2.4: Bissantz and Gerhard scat-ter.

Figure 2.5: Dehnen and Binney scat-ter.

Figure 2.6: Double exponential scatter

8

2.2 Models

The models put forth by Bissantz & Gerhard (2.1) and Dehnen & Binney (2.2) have

the following functional forms:

ρb =ρb,0 λ

n

(λ+ x)ne(−x

2) (2.3)

λ = r0rcut

, x = rr0, n = 1.8, r0 = 0.075 kpc, rcut = 2.1 kpc, and ρb,0 = 9.93 1010M�kpc

−3

ρs = ρ0

(m

r0

)−γ (1 +

m

r0

)γ−βe−(

mrt

)2

(2.4)

m =

√R2 +

(zq

)2, r0 = 1 kpc, rt = 1.9 kpc, q = 0.6, and β = γ = 1.8 for the Bulge

The density normalization could not be obtained by observational data, and is

instead determined from least-squared fits, which varied from 0.3 to 1.237M�pc−3

depending on parameters found on Table 3 of Dehnen & Binney, (1998)[6].

Aside from the random scatter models, these two were chosen for their gaussian

behavior and for their spheroidal shape without explicitly being a sphere. The scaling

in the z-direction allows for an oblate sphere which more closely resembles the actual

shape of the Bulge. Despite this, both models appear to be approximately spherically

symmetric. It comes as no surprise that the models should come out roughly the

same as both involve a radial power law, r−a, times a gaussian. However, Bissantz &

Gerhard based their model on a disk with no central hole.

9

2.3 Fitting

Once the number of high mass binary systems was determined and the points were

scattered across the variety of distributions available, the next step was to recreate

the models used by Weidenspointner et al., (2008)[1] to fit the spectrum. Plotting

a variable number of systems ranging from twenty up to the number predicted by

the IMF program, an attempt was made to create a composite model to closely

match what was used. It was clear from inspection of the spherical, and simple

gaussian models that they would supply the bulk of the diffuse sources while Bissantz

& Gerhard and Dehnen& Binney models would be the source of the central peak.

10

Chapter 3

Results and Analysis

3.1 IMF Results

The IMF function returned the predicted number of high mass stars (M ≥ 20M�),

which at the end of their life produce a black hole after core collapse supernova.

Additionally, the program returned the fraction of those which would end up in a

binary state with another star according to the adopted binary fraction. The case of

high mass stars being in a binary system with each other was not included in this

study due to the non-contribution to the 511 keV continuum such a system would

produce. Within the scope of this research, all high mass stars selected to be in a

binary had a companion star of negligible mass. The only important factor the low

mass companion holds is the Roche lobe overflow later on in its evolution. Whether

or not the low mass companion begins its RLOF within the timescale which we can

detect or if it is close enough to the black hole for it to form an accretion disk was not

taken into account based on the vacuum of data on said topics. The IMF function

for the figures shown returned 175 high mass stars in binaries which was determined

11

after the average of 20 iterations of the IMF program was taken.

3.2 Analysis

With 175 high mass binary systems which would eventually evolve into LMXRBs,

the integrated 511 keV flux was either under luminous to observations for far overlu-

minous depending on configuration. This led to the idea that the continuum must be

composed of two or more distributions. For this reason, a composite model was chosen

to replicate the Weidenspointner model. However, of the models, only two managed

to replicate the shape and peak of the overall curve found in Weidenspointer et al.

(2008)[1], those two being Bissantz & Gerhard and Dehnen & Binney. That being

said, they were also far too narrow to fill out the model single-handedly. Add on

top of that the previously mentioned models were grotesquely overluminous when all

175 systems were piled within them. However, a near-nuclear distribution, like the

aforementioned, clearly mirrors what is needed by the observations. This brings up

a further issue, however. The binary fraction of 1% was adopted from the denser of

globular clusters found by Fregeau et al. (2009)[9] and viciously applied to a scenario

for which it was not meant to describe. Thinking in broader terms, the binary frac-

tion used within this study was in essence the combination of constraints within the

fractional portion of the Drake formalism I had adopted.

In this study, 107 stars were used with a total mass of ∼ 106, which is far less than

the mass of the Bulge as determined by basic rotation curves. If the results found

in the course of this research are to at least place a constraint on the population

fractions of the Bulge, then it is clear from what I have presented thus far that the

these fractions for a Bulge population of stars with ∼ 1011 stars containing ∼ 1010M�,

the fractional terms must equate to ∼ 10−9.

12

Figure 3.1: The flux as measured by SPI/INTEGRAL and the corresponding 511keV map from Weidenspointer et al. (2008)[1]

13

Figure 3.2: 40 systems in a Dehnen & Binney distribution and 135 systems in a simplegaussian. Dotted line depicts the Weidenspointner model.

14

Figure 3.3: 2 simple gaussians with 89 and 86 systems. Dotted line depicts theWeidenspointner model.

15

Figure 3.4: 124 systems in a simple gaussian distribution and 51 in a random sphericalmodel. Dotted line depicts the Weidenspointner model.

3.3 Modelling Results

The fitting was performed by comparing each distribution with varying number of

systems against each other. A match was determined by subtracting the maximum

flux from the Weidenspointner model from the maximum flux of the distribution

model. A difference of 10−4 was determined to be a match. Using this method, an

assortment of 600 model fluxes was selected down to just 12. From there they were

eliminated by inspection, and the above figures depict the best fitting of them. The

best fitting model involved 40 systems in a Dehnen & Binney density model and 135

16

systems dispered in a simple gaussian. Comparing this result to the 511 keV map, it

would be expected to find a cluster of positron producers huddled around the nucleus

of the galaxy with others scattered in some spherical manner. What is not expected,

in my opinion, is the fact that as few as 40 of these systems can create the bulk

of the flux that we see emanating from the core of the Galaxy. That being said, if

observations could confirm the existence of a tight cluster of tens of LMXRBs within

100pc of the center of the Galaxy, this would be the smoking gun needed to validate

the key producers of positrons in the Bulge are without doubt LMXRBs.

17

Chapter 4

Summary and Discussion

Within this document lies an approximation. While some may argue a crude one,

the intention was never to find a smoking gun. As it stands, the evidence at hand

points to LMXRBs as a potential major source of positrons. The analysis put forth in

chapter 3 confirms this plausibility; however, there are several constraints. With the

IMF set as Kroupa et al. (2001)[8] describes, and a realistic constraint on the number

of systems which can evolve binaries, determining how many high mass (M ≥ 20M�)

stars end up in binary systems is relatively straight forward to calculate.

There are many other constraints that could be considered, such as the fraction

of low mass companions that survive a type II supernova from their high mass coun-

terpart, number of systems which incur RLOF within a detectable timescale, the

number of binaries which evolve a black hole component and have a small enough

separation that RLOF ends up in an accretion disk. There are undoubtedly more con-

straints which could and should be considered to construct better analytical models

once we have concrete data on those constraints. That being said, the assumptions

and constraints used in the course of this study were based on observational data and

18

literature wherever possible. And from that, we can see that as little as 175 LMXRBs

can account for the total 511 keV flux we see from the Bulge and as little as 40 sys-

tems can reproduce the flux peak which we observe. However, tens of these systems

must reside extremely close to the nucleus of the galaxy, while the remaining ∼ 100

may be scattered in a spherically symmetric way to create the diffuse continuum

Weidenspointner et al., (2008) measured around the nucleus.

That being said, more questions arise. Why is it that approximately one-third of

Bulge LMXRBs are compacted near the nucleus? Is there a model which can predict

this asymmetry? Given that there are ∼ 1011 stars in the Bulge, is it reasonable to

say that only ∼ 100 stellar mass black hole in binaries evolve? If merely 175 systems

can accomodate for the flux we see, what does that say about the other constraints

of the Bulge? These and others can only be answered by more comprehensive studies

designed to target those specific questions with observations to confirm or refute the

hypotheses. The scope of this research was to determine baseline parameters of the

Bulge using more basic assumptions. Models with more complexity could be brought

to bear against this topic, but I believe the likelihood of finding wildly different results

are relatively low.

19

Bibliography

[1] Jean P. Knoedlseder J. von Ballmoos P. Bignami G. Diehl R. Strong A. W. Cordier

B. Schanne S. Winkler C. Weidenspointner G., Skinner G. An asymmetric distri-

bution of positrons in the galactic disk revealed by gamma-rays. Nature, 451:159–

162, 2008.

[2] Ulmer M. P. Purcell W. R., Grabelsky D. A. The distribution of galactic 511 kev

positron annihilation radiation. AIPC, 304:403+, 1994.

[3] Bykov A. M. Diehl R. Ferriere K. Guessoum N. Jean P. Knoedlseder J. Marcowith

A. Moskalenko I.V. Strong A. Weidenspointner G. Prantzos N., Boehm C. The 511

keV emission from positron annihilation in the galaxy. arXiv:1009.4620, [astro-

ph.HE]:1–62, 2010.

[4] Prantzos N. Guessoum N., Jean P. Microquasars as sources of positron annihila-

tion radiation. Astronomy & Astrophysics, 457:753–762, 2006.

[5] Ulmer M. P. 1989 ApJS McMillan S. L., Kowalski M. P. Mass models of the milky

way. MNRAS, 414:2446–2457, 2011.

[6] Binney J. Dehnen W. Mass models of the milky way. MNRAS, 294:429–438, 1998.

20

[7] A. M. Beloborodov. Electron-positron outflows from gamma-ray emitting accre-

tion discs. MNRAS, 305:181–189, 1999.

[8] P. Kroupa. On the variation of the initial mass function. MNRAS, 322:231–246,

2001.

[9] Rasio F. A. Fregeau J. M., Ivanova N. Evolution of the binary fraction in dense

stellar systems. ApJ, 707:1533, 2009.

21