D.2 Stellar characteristics and stellar evolution

D.2 Life cycle of stars

A Nebula is a stellar nursery - a region of dust and gas where new stars are born. The Orion Nebula (M42) is the nearest nebula and can be seen with the naked eye.

Collapsing gas cloud Dense regions in the clouds collapse due to gravity Gravitational potential energy changes to kinetic energy As it gets smaller the protostar(s) at its centre gets hotter Once the star contracts enough that its central core can fuse hydrogen to helium, it becomes a "main sequence" star. that its central core can fuse hydrogen to helium, it becomes a "main sequence" star.

The Sun formed 4.5 billion years ago, as the Solar System coalesced from a cloud of gas and dust. The sun is a main sequence star. This is the longest, most stable period of a star’s life. It converts hydrogen to helium in its core, generating heat and light.

D.2 How the sun works PlE8&feature=relmfu

Equilibrium between radiation pressure and gravity

When the hydrogen runs out After the star has used up about 12% of its hydrogen, its core will contract increasing its temperature. This heats the outer layers where fusion continues. The star leaves the main sequence and moves over to the Red Giant branch

A planetary nebula occurs at the end of a red giant’s life. The outer layers of the red giant start to drift off into space. This is The Eskimo Nebula

The Cat’s Eye Nebula

What remains is white dwarf (a very hot, dense star). This white dwarf is Shapley 1 about 1000 light years away from Earth.

White dwarfs The white dwarf can’t contract more because electrons in the core cannot occupy the same orbits at the same time (this is called electron degeneracy and is due to the Pauli exclusion principle) CHANDRASEKHAR LIMIT – The mass of the white dwarf cannot exceed 1.4 solar masses

Small and white in colour. Small and white in colour. Since they are white they are comparatively hot. Since they are white they are comparatively hot. Fusion is no longer taking place, and a white dwarf is just a hot remnant that is cooling down. Fusion is no longer taking place, and a white dwarf is just a hot remnant that is cooling down. White dwarfs

Eventually a white dwarf will cool to become a black dwarf. Since the time required for a white dwarf to become a black dwarf is longer than the age of the universe (13.7 billion years), no black dwarfs exist yet.

A giant star is much larger and brighter than a normal main-sequence star. Giant stars can be up to 100 times larger up to 1,000 times brighter than our the Sun.

After the hydrogen in a giant star's core has been used up, they become red supergiants - the largest stars in the universe in terms of volume. These stars have very cool surface temperatures (3500–4500 K).

Anatomy of a RED SUPERGIANT and neon

Death of a large star In the core of a red super giant, lighter elements fuse until they form iron. Iron nuclei absorb energy when they fuse and so the process slows down. Decreased pressure in the core, means the outer layers are not held up and so they collapse inwards. As the core is so dense, the outer material collides and bounces off, resulting in a huge explosion.

Supernovae The dying star explodes violently, producing an extremely bright object for weeks or months.explodes Temperatures rise to 10 billion K. Enough energy to cause medium weight elements to fuse, forming heavy elements (up to Uranium in the Periodic Table).

The remnants of a supernova in the constellation Cassiopeia, all that can be seen by astronomers. Supernovae are rare – once every century in a typical galaxy. But the core remains…

It is made almost entirely from neutrons, compressed like a giant atomic nucleus. If the mass of the remnant of a supernova is less than 3 solar masses (the Oppenheimer-Volkoff limit), it becomes a neutron star. Calvera, the closest neutron star found in the constellation Ursa Minor

Evolution of stars > 8M sun After the supernova the remnant has a mass above the Chandrasekhar limit (1.4M sun ). Degeneracy pressure is not enough to support the star so electrons combine with protons to form neutrons. A neutron star is formed

Evolution of stars > 8M sun The neutron star left over after the supernova remains stable provided its has a mass of no more than 3 solar masses (the Oppenheimer- Volkoff limit)

A star with a mass greater than 20 times the mass of our Sun may produce a black hole at the end of its life. Black holes are objects so dense that not even light can escape their gravity and since nothing can travel faster than light, nothing can escape.

Evolution of stars > 20M sun Neutron stars with masses substantially more than the Oppenheimer-Volkoff limit (3 solar masses) continue to collapse as the neutron pressure is insufficient. They become Black holes At the centre of the black hole is a singularity The boundary around the singularity where even light does not have sufficient escape velocity to escape is called the event horizon or gravitational radius.

D.2 Life cycle of a star worksheet

D.2 Measuring the sun’s diameter

Measuring the diameter of the sun

Luminosity (symbol L) Luminosity is defined as the amount of energy radiated by the star per second (The power radiated by the star) Measured in Watts (J.s -1 )

Black-body radiation Black Body - any object that is a perfect emitter and a perfect absorber of radiation object does not have to appear "black" Stars behave approximately as black bodies

Black-body radiation The amount of energy per second (power) radiated from a star (its luminosity) depends on its surface area and absolute temperature according to L = σAT 4 where σ is the Stefan-Boltzmann constant (5.67 x W.m -2.K -4 )

Wien’s law – Finding the temp of a star λ max T = constant (2.9 x mK)

Example The sun has an approximate black-body spectrum and most of its energy is radiated at a wavelength of 5.0 x m. Find the surface temperature of the sun. From Wien’s law 5.0 x x T = 2.9 x T = 5800 K

Spectral ClassColourTemperature/K OBlue – BBlue - white – AWhite7 500 – FYellow - white6 000 – GYellow4 500 – KYellow - red3 000 – MRed2 000 – You need to remember the classes and their order and approximate temperatures. How will you do this?

Spectral classes Oh be a fine girl….kiss me!

Apparent brightness (symbol b) Apparent brightness is defined as the amount of energy per second per unit area of detector b = L/4πd 2 where d is the distance from the star (in m) L is the luminosity (in W)

Apparent brightness and Luminosity b = L/4πd 2 d = (L/4 π b) ½

More information from spectra The spectrum of a star can have dark absorption lines across it. Each dark line represents the absorption of light at a specific frequency by a chemical element in the outer layers of the star

More information from spectra The absorption spectrum thus gives us information about a star’s chemical composition

Very hot stars Very hot stars do not show an absorption spectrum as all the gas is ionised so there are no bound electrons orbiting around the nuclei in the star. Thus absorption spectrums can also tell us something about the temperature of a star.

Hertzsprung – Russell diagram

The point of classifying the various types of stars is to see is any patterns exists. A useful way of making the comparison is the H-R diagram. Each dot on the diagram represents a different star. The point of classifying the various types of stars is to see is any patterns exists. A useful way of making the comparison is the H-R diagram. Each dot on the diagram represents a different star. The vertical axis is the luminosity of the star. It should be noted that the scale is not a linear one. The vertical axis is the luminosity of the star. It should be noted that the scale is not a linear one. The horizontal axis is the spectral class of the star in the order OBAFGKM. This is the same as a scale of decreasing temperature. Once again the scale is not a linear one. The horizontal axis is the spectral class of the star in the order OBAFGKM. This is the same as a scale of decreasing temperature. Once again the scale is not a linear one. The result of such a plot is shown on the next slide The result of such a plot is shown on the next slide Hertzsprung – Russell diagram

A large number of stars fall on the line that goes from the top left to bottom right. This line is known as the MAIN SEQUENCE and stars that are on it are known as the main sequence stars. Our sun is a main sequence star. These stars are ‘normal’ stable stars- the only difference between them is their mass. They are fusing hydrogen to helium. The stars that are not on the main sequence can also be put into categories. A large number of stars fall on the line that goes from the top left to bottom right. This line is known as the MAIN SEQUENCE and stars that are on it are known as the main sequence stars. Our sun is a main sequence star. These stars are ‘normal’ stable stars- the only difference between them is their mass. They are fusing hydrogen to helium. The stars that are not on the main sequence can also be put into categories. Hertzsprung – Russell diagram

Cepheids!

Mass v luminosity relation (Main sequence) L α M 3.5

Mass v luminosity relation Since the luminosity could be the total energy given out by the star (E) divided by the lifetime of the star T we get E/T α M 3.5 Since E = Mc 2 from Einstein’s formula Mc 2 /T α M 3.5 T α M T α M -2.5

Lifetime of a star T α M -2.5 The bigger the mass of a star, the shorter its life (it “burns” out quicker) A star with a mass 10x greater than the sun will have a life time a factor (1/1000) less than the sun

Example question

D.2 Using cepheids to measure distance rPw

At distances greater than Mpc, neither parallax nor spectroscopic parallax can be relied upon to measure the distance to a star. At distances greater than Mpc, neither parallax nor spectroscopic parallax can be relied upon to measure the distance to a star. When we observe another galaxy, all of the stars in that galaxy are approximately the same distance away from the earth. What we really need is a light source of known luminosity in the galaxy. If we had this then we could make comparisons with the other stars and judge their luminosities. In other words we need a ‘standard candle’ –that is a star of known luminosity. When we observe another galaxy, all of the stars in that galaxy are approximately the same distance away from the earth. What we really need is a light source of known luminosity in the galaxy. If we had this then we could make comparisons with the other stars and judge their luminosities. In other words we need a ‘standard candle’ –that is a star of known luminosity. The outer layers of Cepheid variable stars undergo periodic expansion and contraction, producing a periodic variation in its luminosity. The outer layers of Cepheid variable stars undergo periodic expansion and contraction, producing a periodic variation in its luminosity. Cepheid variables

Cepheid variable stars are useful to astronomers because of the period of their change in brightness turns out to be related to the average luminosity of the Cepheid. Thus the luminosity of the Cepheid can be calculated by observing the variation in brightness.

The process of estimating the distance to a galaxy (in which the individual stars can be imagined) might be as follows: The process of estimating the distance to a galaxy (in which the individual stars can be imagined) might be as follows: Locate a Cepheid variable in the galaxy Locate a Cepheid variable in the galaxy Measure the variation in brightness over a given period of time. Measure the variation in brightness over a given period of time. Use the luminosity-period relationship for Cepheids to estimate the average luminosity. Use the luminosity-period relationship for Cepheids to estimate the average luminosity. Use the average luminosity, the average brightness and the inverse square law to estimate the distance to the star. Use the average luminosity, the average brightness and the inverse square law to estimate the distance to the star.

Cepheid calculation - Example

From the left-hand graph we can see that the period of the cepheid is 5.4 days. From the second graph we can see that this corresponds to a luminosity of about 10 3 suns (3.9 x W).

With a telescope the brightness of the star is measured to be b = 9.15 x W.m -2

Now using the relationship between apparent brightness, luminosity and distance d = (L/(4πb)) ½ d = (3.9 x /(4 x π x 9.15 x )) ½ d = 5.8 x m = 615 ly = 189 pc

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