AQA a level astrophysics chapter 2 – Flashcards

The apparent magnitude, m, of a star in the night sky is a measure of its brightness, which depends on the intensity of the light received from the star.

first classified stars in six magnitudes of brightness, a star of magnitude 1 being one of the brightest in the sky, and a star of magnitude 6 being just visible to the human eye without a telescope on a clear night. The scale is called the Hipparcos scale.

It was established on a scientific basis in the 19th century by defining a difference of 5 magnitudes as a hundredfold change in the intensity of light received from the star.

One light year is the distance light travels through space in 1 year.

1 parsec is defined as the distance to a star which subtends an angle of 1 arc second to the line from the centre of the Earth to the centre of the Sun.

The absolute magnitude, M, of a star is defined as the star's apparent magnitude, m, if it was at a distance of 10 parsecs from Earth.

The total energy per second, P, emitted by a black body at absolute temperature T is proportional to its surface area A and to T^4, in accordance with the following equation known as Stefan's law.

The wavelength at peak intensity, lambda max, is inversely proportional to the absolute temperature T of the object, in accordance with the following equation, known as Wien's displacement law.

The curves are called black body radiation curves. A black body is defined as a body that is a perfect absorber of radiation (absorbs 100% of radiation incident on it at all wavelengths) and therefore emits a continuous spectrum of wavelengths.

You can assume a star is a black body because any radiation incident on it would be absorbed and none would be reflected or transmitted by the star.

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In using the inverse square law here, you assume that the radiation from the star spreads out evenly in all directions and no radiation is absorbed in space.

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Atoms, ions, and molecules in these hot gases absorb light photons of certain wavelengths. The light that passes through these hot gases is therefore deficient in these wavelengths and its spectrum therefore contains absorption lines.

hydrogen atoms in the n=1 state (the ground state) do not absorb visible photons, because visible photons do not have sufficient energy to cause excitation from n=1.

The spectrum of light from a star contains absorption lines due to a corona or atmosphere of hot gases surrounding the star above its photosphere. The photosphere emits a continuous spectrum of light.

The wavelengths of the absorption lines are characteristic of the elements in the corona of hot gases surrounding a star. By comparing the wavelengths of these absorption lines with the known absorption spectra for different elements, the elements present in the star can be identified.

Because the absorption lines vary according to temperature, they can therefore be used in addition to temperature to determine the spectral class of the star. Note that the hydrogen absorption lines correspond to excitation of hydrogen atoms from the n=2 state to higher energy levels.

These lines, called the Balmer lines, are only visible in the spectra of O, B, and A class stars as other stars are not hot enough for excitation of hydrogen atoms due to collisions to the n=2 state. In other words, hydrogen atoms in the n=2 state exist in hot stars such atoms can absorb visible photons at certain wavelengths, hence producing absorption lines in the continuous spectrum of light from the photosphere.

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The main sequence, a heavily populated diagonal belt of stars ranging from cool low power stars of absolute magnitude +15 to very hot high-power stars of absolute magnitude about −5. The greater the mass of a star, the higher up the main sequence it lies. Star masses on the main sequence vary from about 0.1 to 30 or more times the mass of the Sun.

Giant stars that have absolute magnitudes in the range of about +2 to −2 emit more power than the Sun and are 10 to 100 times larger. Red giants are cooler than the Sun.

Supergiant stars have absolute magnitudes in the range from about −5 to −10 and are much brighter and larger than giant stars. They have diameters up to 1000 times that of the Sun. They are relatively rare compared with giant stars.

White dwarf stars have absolute magnitudes between +15 and +10 and are hotter than the Sun, but they emit much less power. They are much smaller in diameter than the Sun.

A dwarf star is a star that is much smaller in diameter than the Sun.

A giant star is a star that is much larger in diameter than the Sun.

The Sun is a middle-aged star about 4600 million years old. It produces energy as a result of nuclear fusion in its core converting hydrogen into helium. The core temperature must be of the order of millions of kelvin to maintain fusion. The fusion reactions release energy which maintains the core temperature. Radiation from the core heats the outer layers of the Sun causing light to be emitted from its surface (photosphere).

A star is formed as dust and gas clouds in space contract under their own gravitational attraction becoming denser and denser to form a protostar -In the collapse, gravitational potential energy is transformed into thermal energy as the atoms and molecules in the clouds gain kinetic energy so the interior of the collapsing matter becomes hotter and hotter. -If sufficient matter accretes to form the protostar, the temperature at the core of the protostar becomes high enough for nuclear fusion to occur. If there is insufficient matter, the star does not become hot enough for nuclear fusion to occur and it gradually cools when it has stopped contracting. -Energy released as a result of nuclear fusion of hydrogen to form helium increases the core temperature, so fusion reactions continue to occur as long as there are sufficient light nuclei. As a result of continuing fusion reactions, the outer layers of the protostar become hot and a light-emitting layer (the photosphere) is formed and the protostar becomes a star.

Main sequence stars like the Sun are in a state of internal equilibrium in the sense that gravitational attraction acting inwards is balanced by radiation pressure.

Main sequence: -The newly formed star reaches internal equilibrium as the inward gravitational attraction is balanced by the outward radiation pressure. The star therefore becomes stable with constant luminosity. -Its absolute magnitude depends on its mass - the more mass it has, the greater its luminosity, so it joins the main sequence at a position according to its mass. -The star remains at this position for most of its lifetime, emitting light as a result of 'hydrogen burning' in its core.

Red giants: -When most of the hydrogen in the core of the star has been converted to helium, the core collapses on itself, and the outer layers of the star expand and cool as a result. The star swells out and moves away from its position on the main sequence to become a giant or a supergiant star. -The temperature of the helium core increases as it collapses and causes surrounding hydrogen to form a 'hydrogen-burning' shell which heats the core further. -When the core temperature reaches about 108 K, helium nuclei in the core undergo fusion reactions in which heavier nuclei are formed, mostly beryllium, carbon, and oxygen. The luminosity of the star increases, and the wavelength at peak intensity increases because it becomes cooler. -The red giant stage lasts about a fifth of the duration of the main sequence stage. The evolution of a star after the red giant stage follows one of two paths according to its mass. Below a mass of about 8 solar masses, a red giant star sooner or later becomes a white dwarf. A star of higher mass swells out even further to become a supergiant that explodes catastrophically as a supernova.

White dwarfs: -When nuclear fusion in the core of a giant star ceases, the star cools and its core contracts, causing the outer layers of the star to be thrown off. -The outer layers are thrown off as shells of hot gas and dust, which form so-called planetary nebulae around the star. This happens through several mechanisms including ionisation in the star's outer layers as the layers cool, causing the layers to trap radiation energy that suddenly breaks out. -If the mass of the red giant star is between 4 and 8 solar masses, the core becomes hot enough to cause energy release through further nuclear fusion to form nuclei as heavy as iron in successive shells. The process stops when all the fuel (i.e., the light nuclei) has been used up. -After throwing off its outer layers, the star is now little more than its core, which at this stage is white hot due to release of gravitational energy. If its mass is less than 1.4 solar masses, the contraction of the core stops because the electrons in the core can no longer be forced any closer. The star is now stable and has become a white dwarf, which will gradually cool as it radiates its thermal energy into space and eventually becomes invisible. If its mass at this stage is greater than 1.4 solar masses, it does not form a white dwarf. Instead, it explodes catastrophically as a supernova.

when nuclear fusion ceases in the core of a red giant star, the outer layers of the star are thrown off and if the mass of the core and remaining matter is less than 1.4 solar masses, the star stabilises as a white dwarf. The repulsive force between the electrons in the core pushing outwards counterbalances the gravitational force pulling the core inwards.

Nuclear fusion ceases when there are no longer any nuclei in the core that release energy when fused. This happens when iron nuclei are formed by fusion because they are more stable than any other nuclei so cannot fuse to become even more stable. If the core mass exceeds 1.4 solar masses, the electrons in the iron core can no longer prevent further collapse because they are forced to react with protons to form neutrons.

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The exploding star releases so much energy that it may outshine its host galaxy. The event is called a supernova because it is much brighter than a nova, or 'new' star, in the same galaxy.

A supernova is typically a thousand million times more luminous than the Sun. Its absolute magnitude is therefore between −15 and −20. In comparison, the absolute magnitude of the Sun is +4.8. This increase of luminosity occurs within about 24 hours. Measurements of their subsequent luminosity show a gradual decrease on a time scale of the order of years. Thus the tell-tale sign of a supernova is a sudden and very large increase in luminosity of the star corresponding to a change of about 20 magnitudes in its absolute magnitude.

A supernova explosion throws the matter surrounding the core into space at high speeds. Elements heavier than iron are formed by nuclear fusion in a supernova explosion. Such fusion reactions occur as the shock wave travels through the layers of matter surrounding the neutron-filled core. The supernova explosion scatters the matter surrounding the core into space. Thus the supernova remnants in space contain all the naturally-occurring elements. Note that helium is formed from hydrogen in fusion reactions in main sequence stars. Other elements as heavy as iron are formed progressively in fusion reactions in red giant stars. Elements heavier than iron cannot be formed in main sequence and red giant stars. Their existence in the Earth tells you that the Solar System formed from the remnants of a supernova.

A supernova explosion also causes an intense outflow of neutrinos and gamma photons. Neutrinos from supernova 1987A were detected three hours before light was detected from it. The light seen from the explosion was produced when the shock wave hit the outer layers of the star. In contrast, the neutrinos produced by nuclear fusion as the shock wave made its way through the interior travelled much faster than the shock wave, reaching the surface hours before the shock wave.

A neutron star is the core of a supernova after all the surrounding matter has been thrown off into space. A neutron star is extremely small in size compared with a star such as the Sun. If its mass was the same as that of the Sun: -its diameter would be about 30 km -its surface gravity would be over two thousand million times stronger than at the surface of the Sun.

Extremely high density Only has neutrons small diameter

A black hole is an object so dense that not even light can escape from it. This is because the escape velocity (the velocity that something would need to escape from the black hole) is above the speed of light c.

A supernova core contains neutrons only. But if its mass is greater than about 3 solar masses, the neutrons are unable to withstand the immense forces that are pushing them together. The core collapses on itself and becomes so dense that not even light can escape from it. The object is then a black hole. It can't emit any photons, and it absorbs any photons that are incident on it.

The event horizon of a black hole is a sphere surrounding the black hole from which nothing can ever emerge.

What happens inside a black hole can't be observed. A black hole attracts and traps any surrounding matter, increasing its mass as a result. Matter falling towards a black hole radiates energy until it falls within the event horizon. Inside the black hole, matter is drawn towards a singularity at its centre.

The key characteristic of a black hole is its mass. It may also be charged, and it may or may not be rotating. Matter that falls into a black hole contributes its mass, its charge, if any, and its rotational motion, if any. Any other property carried by in-falling matter is lost. For example, the properties of a black hole are unaffected by the chemical elements in the matter dragged into the black hole. This information about the in-falling matter is lost in the black hole.

A further possibility is that a white dwarf or a neutron star might have pulled matter off a binary companion star and turned into a black hole when its mass exceeded 3 solar masses. Or both stars in a binary system might have become neutron stars and merged to become a black hole.

Their random directions indicated that they are from extra-galactic sources. Individual bursts were found to last from a fraction of a second to several minutes, followed by a much fainter longer-lived optical afterglow.

Short-lived bursts lasting from about 0.01 s to about 1 s are thought to be associated with black holes, due to either the merger of neutron stars to form a black hole or a neutron star falling into a black hole.

Long-lived bursts lasting from about 10 s to 1000 s are associated with the collapse of a massive star in a supernova.

The term 'absolute magnitude' is important because it enables a comparison between stars in terms of how much light they emit.

The sudden collapse of the core makes the core more and more dense until the neutrons can no longer be forced any closer. The core density is then about the same as the density of atomic nuclei, which is about 1017 kg m−3. The core suddenly becomes rigid, and the collapsing matter surrounding the core hits it and rebounds as a shock wave, which propels the surrounding matter outwards into space in a cataclysmic explosion.

Type I supernovae have no strong hydrogen lines present and are further subdivided into three groups: Ia, Ib, and Ic.

Type Ia supernovae show a strong absorption line due to silicon. They rapidly reach peak luminosity of about 109 times the Sun's luminosity then decrease smoothly and gradually. They are thought to occur when a white dwarf star in a binary system attracts matter from a companion giant star, causing fusion reactions to restart in which carbon nuclei form silicon nuclei. The fusion process becomes unstoppable as further matter is drawn from the giant star, and the white dwarf explodes.

Because Type Ia supernovae reach a known peak luminosity, they are characterised by the presence of a strong silicon absorption line, so they are used to find the distance to their host galaxy. A supernova can temporarily outshine its host galaxy, so the detection of a type Ia supernova in a galaxy at an unknown distance enables the distance to the galaxy to be found.

standard candles.

This method of measuring distances to distant galaxies has led to the prediction of a new form of energy called dark energy.

Type Ib supernovae show a strong absorption line due to helium - these are thought to occur when a supergiant star without hydrogen in its outer layers collapses. After reaching peak luminosity, their light output decreases steadily and gradually.

Type Ic supernovae lack the strong lines present in types 1a and 1b - these are thought to occur when a supergiant without hydrogen or helium in its outer layers collapses. After reaching peak luminosity, their light output also decreases steadily and gradually.

Type II supernovae have strong hydrogen lines - these are thought to occur when a supergiant that has retained the hydrogen or helium in outer layers collapses. Their peak luminosity is not as high as type Ia supernovae, and their light output decreases gradually but unsteadily.

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Supermassive black holes of almost unimaginable mass are thought to exist at the centre of many galaxies. At the centre of a galaxy, stars are much closer together than they are at the edges of the galaxy. A supermassive black hole at the centre could pull in millions of millions of stars. Such black holes can therefore gain enormous quantities of matter and are called supermassive black holes.

Distant galaxies have also yielded evidence of a supermassive black holes at each centre. The Sombrero galaxy, M104, has fast−moving stars in orbits close to its centre, indicating a supermassive black hole of mass equal to 1000 million solar masses.

Gamma-ray bursts release vast amounts of energy in the form of jets of gamma radiation shooting out from the poles of supergiant stars when they collapse or fall into a black hole. Astronomers have estimated that the energy output from a typical gamma ray burst is about the same as the total energy output from the Sun over its entire lifetime.