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# Binary Stars and their Mechanisms Quiz

### Don't be put off by the title of this quiz! You'll be surprised how much you know and how interesting it is to learn. Good luck!

A multiple-choice quiz by pagea. Estimated time: 5 mins.

Author
pagea
Time
5 mins
Type
Multiple Choice
Quiz #
362,816
Updated
Dec 03 21
# Qns
10
Difficulty
Average
Avg Score
7 / 10
Plays
2156
This quiz has 2 formats: you can play it as a or as shown below.
Scroll down to the bottom for the answer key.
1. In a binary star (or in fact a binary system between any two astronomical bodies), both stars orbit the centre of mass. When looking at the gravitational interaction of binary stars we are interested in which points, where (theoretically) a particle of negligible mass could be placed and stay in the same position relative to the two stars? Hint: They were named after an Italian mathematician and astronomer. Hint

Lagrangian points
Cartesian points
Eulerian points
Hilbertian points

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2. As well as looking at Lagrangian points, astronomers also consider so called 'equipotential lines'; these are imaginary lines in a binary system showing lines of equal potential energy. The shape of these lines depends only on which factor, often denoted by 'q'? Hint

Binary separation or distance between the stars
How long the two stars have been in orbit
Weather conditions
Mass ratio between the two stars

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3. There are many different types of stars that can evolve in a binary star system. Can we say that if one star is bigger than another then it will definitely be heavier?

Yes
No

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4. The two stars found in a binary system are given names depending on their mass. The heavier star is generally called the 'primary', while the lighter star is given what name? Hint

Partner
Pal
Companion
Friend

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5. Many astronomers study mass transfer between the two stars in a binary system. This largely depends on whether or not one or both of the stars is 'Roche lobe filling', but what is a Roche lobe? Hint

A protrusion on the larger of the two stars
The radius around a star within which material is gravitationally bound
The radius at which one star is able to touch the other star
The distance between the smaller star and earth

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6. Focusing on mass transfer between the two stars, there are three main types of binary system. They are detached, semi-detached and which third type, in which both stars are Roche lobe filling? Hint: Forget types of house. Hint

Contact binaries
Junction binaries
Terraced binaries
Unity binaries

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7. What is the dramatic name given to a system containing a white dwarf and a main sequence donor star? Hint

Armageddon binary
Cataclysmic variable
Destruction variable
Catastrophic binary

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8. One of the features of binary stars most useful to astronomers is their brightness. Some systems see a significant drop in brightness once in every period, why would this be? Hint

A satellite reflected some of the light
A nearby black hole took some of the light
The stars are eclipsing
The rate of accretion had increased

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9. Which quantity, expressed as the product of a body's moment of inertia and its angular velocity, needs to be conserved while material falls from one star onto another? Hint

Binary separation
Rotational velocity
Angular momentum
Luminous intensity

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10. The way in which binary stars develop over time is dependent on many factors, particularly the initial masses of the two stars. In a system with two main sequence stars, one of 5 solar masses and one of 0.5 solar masses, which star will evolve from the main sequence first, and possibly accrete from the other in the future? Will it be the heavier or lighter star?

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Quiz Answer Key and Fun Facts
1. In a binary star (or in fact a binary system between any two astronomical bodies), both stars orbit the centre of mass. When looking at the gravitational interaction of binary stars we are interested in which points, where (theoretically) a particle of negligible mass could be placed and stay in the same position relative to the two stars? Hint: They were named after an Italian mathematician and astronomer.

There are five Lagrangian points in a two body star system, the most important of which is L1, the Lagrangian point found between the two objects. This is the point through which mass transfer will occur (see later questions!). The theory of Lagrangian points is often used by astronomers, particular for placing satellites into space. The second Lagrangian point, L2, is found behind the smaller object in the binary system (relative to the larger object). This means that in the binary system of the Earth and the Sun, scientists can place satellite telescopes on the 'dark side' of the Earth in order to image deep space and they will stay there thanks to the balance in gravitational energies.

Despite Leonhard Euler discovering the first three points, they were named for Joseph Louis Lagrange who discovered the final two.
2. As well as looking at Lagrangian points, astronomers also consider so called 'equipotential lines'; these are imaginary lines in a binary system showing lines of equal potential energy. The shape of these lines depends only on which factor, often denoted by 'q'?

Answer: Mass ratio between the two stars

Equipotential lines can take on all kinds of weird and wonderful shapes, determined by the ratio of masses between the two stars. This is interesting as it tells us that the shape of the equipotential lines in a system where the stars are 0.3 and 0.6 solar masses will be the same as the much larger system where they are 5 and 10 solar masses.

The equipotential line that passes through the inner Lagrangian point L1 can be a figure of eight around the two stars, with the larger lobe around the heavier star. Further out from the system, the equipotential lines are just large circles around both stars.
3. There are many different types of stars that can evolve in a binary star system. Can we say that if one star is bigger than another then it will definitely be heavier?

This is not true at all! It completely depends where the stars are in their life cycle. If they were both main sequence stars, such as our Sun, then it is highly probable that the larger star is heavier. However, if one of the stars has evolved from the main sequence, then the situation may be different.

It is thought that a typical neutron star has a mass of around 1.4 solar masses while having a radius of a mere 10km!
4. The two stars found in a binary system are given names depending on their mass. The heavier star is generally called the 'primary', while the lighter star is given what name?

When describing binary stars, astronomers write 'A' after the name of the system to denote the primary, and 'B' for the companion, or secondary star. One of the most famous binaries is the Sirius system. Sirius A is generally accepted as the brightest star in the night sky, located only 8.6 light years from our solar system.

It is impossible to view Sirius B with the naked eye as it is a white dwarf, far less luminous that the main sequence Sirius A.
5. Many astronomers study mass transfer between the two stars in a binary system. This largely depends on whether or not one or both of the stars is 'Roche lobe filling', but what is a Roche lobe?

Answer: The radius around a star within which material is gravitationally bound

The Roche lobe denotes the radius within which material remains gravitationally bound to the star. Outside of the Roche lobe the material can be lost. This is particularly prevalent in a binary star system when there is another star on standby ready to eat up the material that the Roche lobe filling star loses.

The standard shape for a Roche lobe is a teardrop pointing towards the inner Lagrangian point L1. This is where mass transfer will occur if the star is Roche lobe filling.
6. Focusing on mass transfer between the two stars, there are three main types of binary system. They are detached, semi-detached and which third type, in which both stars are Roche lobe filling? Hint: Forget types of house.

In a detached binary, neither of the stars are Roche lobe filling and thus very little mass transfer occurs. However, there may be small amounts from stellar winds. In a semi-detached binary, one of the stars, often called the 'donor' star fills its Roche lobe and mass transfers through the inner Lagrangian point.

The process of mass falling from one object onto another is known as 'accretion'. In a contact binary both stars are Roche lobe filling and so can touch at the Lagrangian point. A contact binary can lead to the merging of two stars.
7. What is the dramatic name given to a system containing a white dwarf and a main sequence donor star?

Cataclysmic variable stars are widely studied as they can periodically increase and decrease in brightness. These changes in brightness were originally called 'novae' meaning 'new star', and although it is now known that this is not the case, the name has stuck.

These systems are quite dramatic; the gravity of the white dwarf can distort the companion star into a Roche lobe filling teardrop shape. The material that transfers from the donor to the white dwarf often forms an accretion disc around the dwarf.

It is believed that the periodic 'novae' occur as a result of instabilities in the disc.
8. One of the features of binary stars most useful to astronomers is their brightness. Some systems see a significant drop in brightness once in every period, why would this be?

Eclipsing binaries are relatively rare as they require the binary to be in the same plane as our line of sight from earth. However, when this does happen, a telescope will pick up significantly less light as one star moves in front of the other. There are several other reasons why one may observe minor changes in the brightness of a binary system. One of these is 'ellipsoidal modulation'.

This effect occurs when the companion star has become distorted by the gravity of the primary and thus is no longer spherical.

As it will have a roughly ellipsoid shape the system will appear brighter when viewed sideways on (it will have a larger cross section).
9. Which quantity, expressed as the product of a body's moment of inertia and its angular velocity, needs to be conserved while material falls from one star onto another?

The need for the conservation of angular momentum has provided astronomers with a headache for many years. If material fell directly from the donor star onto the accreting star then angular momentum would not be conserved. This helps to explain the formation of accretion discs but the actual theories as to what occur within the accretion disc are far more complicated. I won't go into detail here but I encourage you to research if you're interested!

Angular momentum is somewhat analogous to linear momentum, expressed as the velocity vector of an object multiplied by the mass of the object.
10. The way in which binary stars develop over time is dependent on many factors, particularly the initial masses of the two stars. In a system with two main sequence stars, one of 5 solar masses and one of 0.5 solar masses, which star will evolve from the main sequence first, and possibly accrete from the other in the future? Will it be the heavier or lighter star?

As the 5 solar mass star is so much larger, the temperature and pressure within the star are much greater than in the 0.5 solar mass star. This means that the heavier star will burn through fuel much faster, evolving from the main sequence long before the lighter star.

This system is a prime candidate to become a cataclysmic variable as the heavier star is likely to evolve into a white dwarf over time, while the companion star remains on the main sequence.
Source: Author pagea

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