Binary Stars and their Mechanisms Quiz

Answer: Lagrangian points

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.

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.

Answer: No

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!

Answer: Companion

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 than the main sequence Sirius A.

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.

Answer: Contact binaries

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.

Answer: Cataclysmic variable

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.

Answer: The stars are eclipsing

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).

Answer: Angular momentum

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.

Answer: Heavier

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.