1. 1
PS451 Final Year Project Literature Survey
Eclipsing Binary Stars
Name: Student
Student No.: 11490688
Class: PHA4
Date: 27th October 2015
Supervisor: Dr. Eamonn Cunningham

2. 2
Declaration
Name: Robert Doyle
Student ID Number: 11490688
Programme: Physics and Astronomy
Module Code: PS451
Assignment Title: Eclipsing Binary Stars
Submission Date: 27th
October 2015
I understand that the University regards breaches of academic integrity and plagiarism as grave and
serious.
I have read and understood the DCU Academic Integrity and Plagiarism Policy. I accept the penalties that
may be imposed should I engage in practice or practices that breach this policy.
I have identified and included the source of all facts,ideas, opinions, viewpoints of others in the
assignment references. Direct quotations, paraphrasing, discussion of ideas from books, journal articles,
internet sources, module text, or any other source whatsoever are acknowledged and the sources cited are
identified in the assignment references.
I declare that this material, which I now submit for assessment,is entirely my own work and has not been
taken from the work of others save and to the extent that such work has been cited and acknowledged
within the text of my work.
I have used the DCU library referencing guidelines (available at:
http://www.library.dcu.ie/LibraryGuides/Citing&ReferencingGuide/player.html) and/or the appropriate
referencing system recommended in the assignment guidelines and/or programme documentation.
By signing this form or by submitting this material online I confirm that this assignment, or any part of it,
has not been previously submitted by me or any other person for assessment on this or any other course of
study.
By signing this form or by submitting material for assessment online I confirm that I have read and
understood DCU Academic Integrity and Plagiarism Policy (available at:
http://www.dcu.ie/registry/examinations/index.shtml).
Name:_________________________
Date:_______________________________________________________________

3. 3
Table of Contents
1 Introduction.............................................................................................................................4
1.1 A Brief History.................................................................................................................4
1.2 Classification of Binary Stars ..........................................................................................4
2 Formation of Binary Stars.......................................................................................................5
2.1 Capture.............................................................................................................................5
2.2 The Binary Fission Hypothesis........................................................................................6
2.3 Fragmentation ..................................................................................................................7
3 The Evolution of Close Binary Stars ......................................................................................8
References................................................................................................................................11

4. 4
1 Introduction
A binary star is a system that contains two stars that orbit about a common centre of mass.
Research over the last couple of centuries has suggested that at least half of all the stars in
the sky are binary or multiple star systems, with two or more stars(1)P180. A recent study has
since challenged this idea stating that the majority of the stars are actually single stars (2).
Studying the orbit of these binary stars allows the calculation of the stars masses. This is
extremely important as the only way to directly calculate a stars mass is by examining its
gravitational interaction with another object (1)P180. Binary stars are not to be mistaken for
optical double stars. They appear to be a pair because of the line of sight but have a large
separation in distance and have no interaction with each other.
1.1 A Brief History
Shortly after the creation of the first telescope, the first visible binary system, Mizar, was
recorded by the Italian astronomer G. B. Riccioli around the year 1650. For the next half a
century there was no surge in binary discoveries. The double stars were originally thought of
as a line of sight coincidence (3). The first eclipsing binary, Algol, was discovered in 1667 by
another Italian astronomer Geminiano Montanari. This was one of the first non-nova variable
stars found. It wasn’t until 1782 that John Goodricke was able to discover the periodicity of
the system (4).
In 1767 John Michell was the first person to propose that double stars were connected to
each other physically. His argument was that the probability of two stars being aligned close
together by chance was much smaller than the recorded pairs (5). William Herschel published
a catalogue of 269 double stars in 1782 and a further 434 two years later. After continuing to
observe the recorded double stars, by 1803 he proved that some of the pairs had a mutual
physical attraction that could not be explained by differential parallaxes. Towards the end of
the 19th century the first spectroscopic binaries were discovered by E.C. Pickering, revealing
that the two components of the Mizar system contained two stars each making it a quadruple
system (3). In 1889 the first eclipsing binary star, Algol, was also confirmed as a
spectroscopic binary (4).
1.2 Classification of Binary Stars
Binary stars are classified by the way they are observed, directly or indirectly. Visual binary
systems are seen as two distinct points of light with a telescope, the most famous being Sirius
which is the brightest star in the night sky (6)P96. Astrometric binary systems only the
brightest companion star can be seen. The path of this star is tracked and it is observed to
deviate back and forth from its straight line path. From this wobble it is inferred that it is
orbiting a companion star (7)P83. Spectroscopic binaries are observed from the Doppler
shifts in their spectral lines. As each star moves towards us the spectral line is blue shifted
and as they move away it is red shifted as the orbit each other. This type of system accounts
for the majority of the known binary stars. Binary systems that orbit each other perpendicular

5. 5
to the line of sight of the observer cannot be found this way as there is no motion in the
direction of the observer and hence no Doppler shift (6)P97.
The type of binary system that I will focus on in this report are eclipsing binaries. The orbital
plane of these systems is approximately aligned with the observer, so that the stars pass in
front of one another periodically. As one of the stars crosses the path of the other, it blocks
some or all of its companions light, dropping the overall brightness of the system (1)P181. A
light curve is a plot of the apparent magnitude of the system as a function of time (8)P84. By
observing the light curve of these systems the two stars are revealed by two dips in light
intensity per phase as seen in figure 1 below. When the secondary star which is the dimmer of
the two, passes in front of its brighter, primary companion a larger fall in light intensity
occurs. Conversely as the secondary moves behind the primary star less of a drop in intensity
is seen as the primary star contains the majority of the light in the system (7).
Figure 1: Demonstration of Eclipsing Binary Light Curve (9)
2 Formation of Binary Stars
There have been many theories for the formation of binary systems and still to this day there
is no one concise answer. In this section I will discuss the four most popular ideas.
2.1 Capture
The first of these is the capture theory which began in 1867 by an Anglo-Irish physicist, G.J.
Stoney. He suggested that the two companion stars were originally single stars, independent
of each other. As they approached one another they were forced to revolve around the other
about a common centre of gravity (10). This theory has been disregarded in its simplest form
as a source of energy dissipation is needed to restrain the two stars together (11)P361. There
are three separate cases in which the formation of binary stars can occur from the capture
theory.

6. 6
The first is the presence of a third-body. The energy lost from the two stars relative orbit is
transferred to the third star as kinetic energy, pushing this star out of the system leaving the
other two behind gravitationally bound (12). The three-body capture model is a rare
occurrence that has a higher chance of occurring in an area of high stellar density such as a
centre of a globular cluster. This creates massive binary systems that are very wide apart
(11)P361.
The second capture process is tidal dissipation through two-body dissipation. These two-body
interactions occur more often than the previously mentioned three-body interactions. For this
process to happen the two bodies must be extremely close to dissipate enough energy to bind
the system (13)P361. The excitation of the tides in the stars converts the orbital energy into
heat. In cases were the tides are not significant enough because the distance is not close
enough, many counters are needed to dissipate enough energy (12).
The third and finally case occurs from an interaction with the gaseous disks of a rotating
protostar or the gas of a newly forming cluster (14)P231. A protostar being an early phase of
the formation of a star that forms by the gas of giant molecular cloud contracting (7). If two
protostar disks have a close interaction the gaseous can cause dissipation through processes
that include gas or gravitational drag, tidal forces, shock heating and radiation. Binary stars
formed in this way would have separations limited to the size of the protostellar disks,
roughly 10 – 100 AU (Astronomical Units) (11)P363.
As these three processes depend on many variables and must occur in areas of high stellar
density clusters, the capture method cannot be the dominant process in the creation of the
majority of binaries (12).
2.2 The Binary Fission Hypothesis
The theory that the fission of rapidly rotating protostars being a process for creating binary
star systems has been around for more than a century and at one point was thought to be the
most likely candidate (15). The idea of fission takes place as the star is accumulating material
during the protostar phase or after disk accretion is done and it is contracting towards the
main sequence. The conservation of angular momentum means that as it is contracting the
star must increase its spin (14)P232. The star is then thought to become rotationally unstable
as the ratio of rational to gravitational energy T/|W| becomes higher. As this ratio increases
the glass cloud will prefer to evolve into an ellipsoidal shape and become progressively
distorted (16). As it becomes more distorted it forms a bar shape and then continues to form a
barbell shape. A star is formed with the accumulated mass at the each end of the barbell,
creating a contact binary. As the stars move to the main sequence they become detached (17).
Numerical simulations have ruled this method out as the gravitational torque and spiral arms
of the system are able to eject the mass and angular momentum. This result is still fission as
there is break up of material. This ejected mass creates a disk around stellar remnant which is
a non-axisymmetric bar like structure (18).

7. 7
2.3 Fragmentation
The current leading theory for the formation of binary stars occurs by fragmentation during
the collapse of a molecular cloud to create a protostar. There are two phases of a protostar
collapse. The first being an early optically thin isothermal phase followed by an adiabatic
phase which is optically thick. The conditions of the isothermal phase are much more
favourable for fragmentation to occur (14)P234. As Fragmentation is a relatively new theory,
less than 50 years old, there are a number of different ideas on how it works. For this review I
will discuss two types, one being more promising than the other.
The first being that the fragmentation is induced by the rotating collapse of material from the
infalling envelope (12). In this case, during the collapse the density perturbation of the
spherical envelope increases. A large, flattened asymmetric structure with two density peaks
is formed from the rotation. The angular momentum of the infalling influences the separation
of the peaks creating either wide binary systems of about 1000 AU separation or close binary
systems with less than half that distance (19).
The second suggestion is fragmentation of a gravitationally unstable disk. This theory
suggests that the disks of a protostar subject to a strong enough gravitational instability may
fragment to create one or more companions (20). The angular momentum of the infallling
envelope forms a massive disk. The gravity of this disk enables fragmentation to happen at
large radii, creating binary components. These fragments would be in the same equatorial
plane as the original star and would share a common angular momentum vector.
This second method is deemed to be the more likely fragmentation mechanism for creating
binary stars after recent research J.J Tobin et al (19). By using observations from the Very
Larger Array (VLA) and the Combined Array for Research in Millimeter-wave Astronomy
(CARMA) they discovered an apparent circumbinary disk around two protostars in the source
L1165-SMM1 which can be seen in figure 2. They also found two protostars with secondary
sources located nearly orthogonal to the outflow direction, which is expected if they formed
in the disk and the outflow is perpendicular to the equatorial plane. These findings along with
other recent data makes disk fragmentation the strongest theory on the creation of close
binary stars.
Figure 2 – Images of L1165-SMM1 at 7.3 mm at resolutions of 0″.3 (left), 0″.1 (centre) and 0″.07 (right) (19)

8. 8
3 The Evolution of Close Binary Stars
In the majority of binary systems the two stars are sufficiently far away so that they have only
a negligible effect on one another. These stars evolve independently as if they were single
stars with only a slight force of gravity keeping them together (1)P653. In this section I will
discuss the more complex case of close binary stars. Binary stars that are close enough can
alter the structure of one another. The surface of the smaller star can be distorted by its bigger
companion via the gravitational force being stronger at its near side than its far side creating a
pear like shape, this is called a tidal effect. This distortion of a star causes a loss of internal
energy. As the star rotates, different material is shifted into the swelled area and these
material create friction by rubbing against each other. This causes a loss of orbital and
rotational energy resulting in the orbits circularising and the stars always facing the same side
as one another. At this point the spins are synchronized (7)P209. The distorted star could also
lose some of its outer layer to its companion if the force is strong enough (1)P653.
3.1 Roche Lobes
Now with the orbits circularised the Roche approximation can be used. The equipotential
surface lines in the orbital plane of two stars of mass M1 and M2 are shown in Figure 3 below
(21). There are five points in the figure called Lagrangian points marked L1, L2, L3, L4, and
L5. At these points the effective gravitational force of the system is at zero. The L1 point,
called the inner Lagrangian point, lies between the two stars at the intersection mark of the
critical surfaces marked in bold in the image (7). The two sides of the intersection are called
Roche lobes. If a star fills its Roche lobe it will start transferring material to its companion
(21).
Figure 3 – Surfaces of constant effective potential (21).

9. 9
3.2 Evolutionary of Binary Stars
The evolution of binary stars can be divided into three classes which are detached, semi-
detached and contact binaries. In detached binaries both stars are fully within their Roche
lobes and interact with each other only through tidal effects. When one of the stars exactly
fills its Roche lobe the system is said to be a semi-detached binary. Finally a contact binary is
created when both stars fill their Roche lobes and create a common envelope (7).
The most common way that a star fills its Roche lobe is when it evolves off the main
sequence and expands as a red giant. If both stars are on the main sequence the primary star,
which is the most massive of the pair, will evolve quicker than the secondary star. If the
radius of the red giant exceeds the Roche lobe radius the star will begin to transfer mass to its
companion, this is called a Roche lobe overflow (22). As the primary star loses mass its
Roche lobe radius decreases and the companions Roche lobe increases as it gains mass (7).
The star losing the mass is called the donor and the other is called the accretor. The
transferring matter must lose energy as it enters through the L1 point for it to fall on the
accretor. This energy is lost from the matter heating up and dissipating energy by radiating
heat (13)P187.
A common envelope can occur in two ways during the mass transfer. If the radius of the
donor star continues to grow, expanding past the Roche lobe its envelope will encompass the
companion star. Another way is if the material is transferred at a much greater rate than the
companion can accrete, the matter will build up. This accumulation of matter will increase
until the accretors Roche lobe is filled as well as the donors creating the common envelope.
The orbital motion of the of the accretor and the core of the donor can eject the common
envelope (13).
Figure 4 – Three stages of evolution. Detached (Top), Semi-detached (middle), Contact (bottom) (23).

10. 10
Once the common envelope is gone what remains is a stellar remnant, most likely a white
dwarf, from the donor and the secondary star. When this secondary star evolves off the main
sequence it is possible that it will become a red giant also and fill its Roche lobe (7). The
formation of an accretion disk is expected when the angular momentum of the material that is
flowing towards a star is too high to actually fall on it. The more compact the star the better
chance of this occurring. This means that as the companion star transfers its material to the
stellar remnant it will most likely create an accretion disk around it (11).

11. 11
References
1. Carroll BW, Ostlie DA. An Introduction to Modern Astrophysics. Second Edi.
Addison-Wesley; 2007.
2. Lada CJ. Stellar multiplicity and the imf: most stars are single. Astrophys J.
2006;650(March):L63–6.
3. Niemela V s. A Short History and other Stories of Binary Stars. Rev Mex Astron y
Astrofísica. 2001;11(June):23–6.
4. Price A. American Association of Variable Star Observers [Internet]. Available from:
https://www.aavso.org/vsots_betaper
5. Michell J. An Inquiry into the Probable Parallax, and Magnitude of the Fixed Stars,
from the Quantity of Light Which They Afford us, and the Particular Circumstances of
Their Situation. Philos Trans. 1767;57:234–64.
6. Green SF, Jones MH. An Introduction to the Sun and Stars. 2003.
7. Kutner ML. Astronomy A Physical Perspective. Second. 2003.
8. Binney J, Merrifield M. Galactic Astronomy. 1998.
9. Light Curve Picture [Internet]. Available from:
http://pages.uoregon.edu/jimbrau/BrauImNew/Chap17/FG17_21.jpg
10. Zinnecker H, Mathieu RD. The Formation of Binary Stars. In.
11. Sahade J, McCluskey Jr. GE, Kondo Y. The Realm of Interracting Binary Stars.
Kluwer Academic Publishers; 1993.
12. Tohline J ~E. The Origin of Binary Stars. Annu Rev Astron Astrophys. 2002;40:349–
85.
13. Benacquista M. An Introduction to the Evolution of Single and Binary Stars. Springer;
2012.
14. Bodenheimer PH. Principles of Star Formation. Principles of Star Formation: Springer;
2011.

12. 12
15. Bonnell I a., Bate MR. The Formation of Close Binary Systems. Mon Not R Astron
Soc [Internet]. 1994;271:999–1004. Available from:
http://adsabs.harvard.edu/abs/1994MNRAS.271..999B
16. Tohline JE, Cazes JE, Cohl HS. The Formation of Common-Envelope, Pre-Main-
Sequence Binary Stars [Internet]. Available from:
http://www.phys.lsu.edu/astro/nap98/bf.final.html
17. Brainerd JJ. Theories of the Birth Of Binary Stars [Internet]. Available from:
http://www.astrophysicsspectator.com/topics/stars/BinaryStarBirth.html
18. Durisen RH, Gingold RA, Tohline JE, Boss AP. Dynamic fission instabilities in
rapidly rotating N = 3/2 polytropes - A comparison of results from finite-difference
and smoothed particle hydrodynamics codes. Astrophys J. 1986;305:281–308.
19. Tobin JJ, Chandler CJ, Wilner DJ, Looney LW, Loinard L, Chiang H-F, et al. VLA
and CARMA Observations of Protostars in the Cepheus Clouds: Sub-arcsecond Proto-
binaries Formed via Disk Fragmentation. Astrophys J [Internet]. 2013;779(2):93.
Available from: http://stacks.iop.org/0004-
637X/779/i=2/a=93?key=crossref.16db6ff832a9ca36cdc3da0e8389347cnpapers3://pu
blication/doi/10.1088/0004-637X/779/2/93
20. Offner SSR, Kratter KM, Matzner CD, Krumholz MR, Klein RI. The Formation of
Low-Mass Binary Star Systems Via Turbulent Fragmentation. Astrophys J [Internet].
2010;725(2):1485–94. Available from: http://stacks.iop.org/0004-
637X/725/i=2/a=1485?key=crossref.9fd96275c951e2bc4784e8df0e3ea8f4
21. Iben, Jr I, Livio M. Common Envelopes In Binary Star Evolution. Astron Soc Pacific.
1993;105(694):1373–406.
22. Hurley JR, Tout C a., Pols OR. Evolution of binary stars and the effect of tides on
binary populations. Mon Not R Astron Soc. 2002;329(4):897–926.
23. Available from: http://usercontent1.hubimg.com/6869686_f260.jpg

13. 13