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PS451 Final Year Project Literature Survey

Eclipsing Binary Stars

Name: Student

Student No.: 11490688

Class: PHA4

Date: 27th October 2015

Supervisor: Dr. Eamonn Cunningham

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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.

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Name:_________________________

Date:_______________________________________________________________

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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

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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

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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.

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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).

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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)

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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).

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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).

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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).

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