Topic Four Astrophysics

Contextual Outline

The wonders of the Universe are revealed through technological advances based on tested principles of physics. Our understanding of the cosmos draws upon models, theories and laws in our endeavour to seek explanations for the myriad of observations made by various instruments at many different wavelengths. Techniques, such as imaging, photometry, astrometry and spectroscopy, allow us to determine many of the properties and characteristics of celestial objects. Continual technical advancement has resulted in a range of devices extending from optical and radio-telescopes on Earth to orbiting telescopes, such as Hipparcos, Chandra and HST.

Explanations for events in our spectacular Universe, based on our understandings of the electromagnetic spectrum, allow for insights into the relationships between star formation and evolution (supernovae), and extreme events, such as high gravity environments of a neutron star or black hole.

This module increases students understanding of the nature and practice of physics and the implications of physics for society and the environment.

Note stars are all in a state of equilibrium with gravity pushing inwards and radiation and gas pressure pushing out

Galileo was the first person to point a telescope into the night sky after refining the design. He built the refracting telescope that produced an upright image and masked out the edge of the front lens of his telescope to overcome spherical aberration. As a result, he was able to make systematic astronomical observations and deductions of the features of the moon.

Galileo made the following qualitative observations of the moon:

The moon was rough like the earth

Had vast plains (mare), high mountains and deep valleys

Quantitative:

Calculating the height of a mountain from a measurement of its shadow when they were near the edge of the shadow and directly facing the earth, estimated they were at least several kilometres high

Other important observations

Moons of Jupiter

Phases of Venus

Sunspots on the sun

Thousands of new stars that were not visible by the naked eye

Implications:

These observations provided evidence that challenged the prevailing Aristotelian view that was endorsed by Church of Rome where the heavens were perfect and unchanging, where earth was the centre of the universe (heliocentric model)

These observations were evidence for the Copernicus geocentric model as the moons of Jupiter were as predicted in the Copernican system

The phases of Venus showed that Venus must orbit the sun as Copernicus had suggested

Galileos contributions would fundamentally challenge the way in which science regarded space and astronomical bodies

This was a result of an advance in technology where the telescope allowed distant objects to be seen closer

Information on the cosmos comes entirely from the analysis of the electromagnetic radiation. However, the Earths atmosphere and ionosphere prevent certain EM waves from either completely or partially reaching the earths surface. As a result, ground based astronomy is restricted to wavebands (part of electromagnetic spectrum covering a specific range of wavelengths) primarily to visible light and radio waves.

Problems associated with the detection of EM waves from the atmosphere:

Selective absorption

The highly energetic gamma rays and x-rays ionise molecules making up the atmosphere and are therefore strongly absorbed in the upper atmosphere

Some bands of UV radiation are strongly absorbed by the ozone layer of the atmosphere while others penetrate to the ground

Infrared wavelengths are partially absorbed

*Long wavelength radio waves are reflected by the ionosphere

Implications:

The atmosphere does not scatter or absorb the visible and radio band very much, consequently, optical telescopes can be effectively used at ground level e.g. Anglo-Australian Telescope or radio telescopes e.g. Parkes

In order to be able to study and analyse these absorbed wavebands/study the cosmos;

Telescopes must be placed in space above the Earths atmosphere

E.g. Hubble space telescopes are used to make observations of every region

Instead of the expensive procedure of placing them into space, infrared sensitive telescopes may be placed on mountains tops

This means less light pollution and temperature fluctuations experienced by the instruments are less. This minimises the time to stabilise expansion or contraction initiated shake in the telescope lens and mounting

For:

To be able to study the electromagnetic spectrum

Improve our knowledge of the universe e.g. the discovery of a quasar

Sensitivity this is the measure of its light gathering power

A telescope with high sensitivity means that I can collect large amounts of light, hence allowing very faint objects to be observed

Sensitivity is directly proportional to the diameter of the lens/mirror

Resolution - this is the ability of a telescope to clearly distinguish between two very close objects

Resolution is usually described in terms of the smallest angle of separation between two points of light such a two stars close together. Resolution depends on the diameter of the objective lens and the wavelength of the light. A telescope with low resolution will see closely positioned stars as fuzzy and blurred.

Theoretical resolution = 2.1 x10^5 x

D

Atmospheric distortion and resolution:

Ground-based astronomy is beneath a constantly changing sea of air, water vapour, other gases and dusts. This means that there will be variations in temperature and pressure and thus will alter the density of the atmosphere. This causes corresponding changes in the refractive index which causes stars to twinkle (exhibiting rapid variations in colour and intensity). As a result, this atmospheric distortion causes images to shimmer and go in and out of focus, thus lowering the overall theoretical resolution of the telescope

Aberrations caused by impurities in the medium (air) as the radiation passes through it. This has the effect of reducing the ability to clearly resolve detail in distant objects by scattering the EM wave.

The true colour of images is altered because at ground level the variations in absorption with wavelength mean that we are not seeing an accurate reproduction of the intensity of the spectrum. All these affects are accentuated if the object being observed is lower in the sky because the path length the light has to travel through the atmosphere is greater. E.g. the reason why a blue sky is seen is because the atmosphere scatters light

Absorption of radiation:

Gamma rays, x-rays, ultraviolet, infrared and parts of the radio region of the electromagnetic spectrum are absorbed and scattered to different extents by the atmosphere. Ground-based astronomy in these wavebands is very difficult because of the low intensity of radiation reaching the ground. So much light from the violet end of the visible waveband is scattered, making the daytime sky bright blue, that optical astronomy is virtually impossible other than at night.

Other:

The atmosphere also scatters extraneous light into the telescope from unwanted sources such as nearby houses, cars and towns. This light pollution is increasingly becoming a major problem for astronomers.

Adaptive Optics:

This uses a system of electronically controlled thrusters (actuators) of supports which adjust the shape or angle of the telescope mirror to correct the effects of atmospheric turbulence. It uses a fast feed back system as sensors quickly detect atmospheric distortion (such as absorption and scattering) which is analysed by a computer. Thrusters are then used to bend the flexible mirror into the shape that produces the best possible image in order to improve resolution. These corrections are made up to 1000 times per second and can be as small as 0.02 microns to minimise loss of scattered photons.

The success of adaptive optics relies on the detection and correction taking place every quickly compared to the length of time over which the distortion lasts. The image correction relies on the presence of a bright point source or star in the field to be imaged. Where such a star does not exist, a laser beam is fired into the atmosphere to provide an artificial star.

Active Optics:

Active optics systems are designed to correct changes in the surface shape of large primary mirrors that occur as the telescope tilts or the mirror temperature changes or due to gravity. It uses a slow feedback system to correct the sagging or deformities in order to retain the sensitivity of the telescope. By slowing monitoring the reflection of the wavefront off it, its possible to apply pressure to various parts of the primary and correct the deforming effects by using actuators to ensure a sustains its original resolution

When light leaves the primary mirror, it is slowly sampled by a wavefront sensor. This can detect how incoming light has been altered, and by sampling slowly, changes observed n the wavefront is due to deformities in the primary mirror, rather than uncontrollable atmospheric effects. Therefore it must be done slowly in order to eliminate the effect of atmospheric turbulence.

Interferometry:

Interferometry is a technique used to study optical or radio-wave interferences (it is more effective with radio waves). Interferometry works by the superposition of signals/wavefronts in order to create a sharper image and thus improve the resolution and sensitivity.

It is based on the principle of a large diameter mirror that gives a sharper image because the reflections of the wavefront at various points across the diameter add via the law of superposition. The resolution of such an instrument is similar to that of a telescope with a diameter equal to the separation of the two antennae.

It is used to unblur images from large optical telescopes and process information about the source of the radio wave e.g. size and separation of stars. Very Large Array (VLA) is an example of interferometry

The telescope is a device used for helps to overcome the limitations of the human eyes for astronomical studies. There are 2 types of telescopes: refracting and reflecting

Reflecting telescope

This applies the principle of refraction to obtain images. It consists of 2 lens:

Object lens used to gather/collect light

Eyepiece lens used to magnify the image

Disadvantages

Light must pass through the objective lens for an image to be obtained

The lens can only be supported at the edge

Large, heavy lens will deform under its own gravity and heat. The deformity of the objective lens cause a distortion to the image obtained

Reflecting telescope

This applies the principle of reflection of light to obtain images

Advantage this is that it reflects rather than reflects, hence can be fully supported

Disadvantage a large objective mirror also deforms to an extent

Possible Solutions

Many small mirrors appropriately connected to form a large objective mirror. This reduces the deformities

Using active optics as explained previously

Larger telescopes with lens/mirrors of larger diameter will have a higher sensitivity and resolution. This can be investigated by placing a black iris in front of the objective lens of a small telescope. Use the telescope to bring a page of writing on a wall some distance away into focus. Then slowly close the iris to reduce the effective diameter of the objective lens. It is noticed that the letters begin to become blurred, indicating the resolution is decreasing. Further more, as the amount of light gathered decreases, the letters rapidly reduce.

Parallax this is the apparent change in position of a nearby object as seen against a distant background due to the change in position of the observer

Parsec One parsec is the distance that corresponds to an annual parallax of 1 arc sec

Light year this is the distance light travels in a year

1pc = 3.26 light years = 206265 AU

1AU = 1.5 x 1011 m (distance between earth and sun

Trigonometric parallax is the technique used to calculate the distance to an object from the observer using trigonometry and parallax

Annual parallax is half the angle through which the star appears to shift as the earth moves from one side of its orbit to the other

Parallax data is collected by photographing the same star field twice, from opposite points of earths orbit in order to use the baseline of and then measuring the annual shift of stars against a background of distant stars. This allows the parallax to be calculated. The annual parallax can be calculated from half this angle, giving a right angled triangle with a baseline of 1 AU. Basic trigonometry can then be used to determine the lengths of the sides and hence the distance to stars.

For example, a star that has a parallax of say 1 arc second will be at a distance of:

Tan P = D/d

d = D/tanp

= 1.5 x10^11/tan (1/3600)

= 1pc

A large number of relatively near stars, whose distances can be calculated accurately from parallax measurements, are used as reference stars for a range of techniques to estimate distances to much more distant stars, including some in neighbouring galaxies.

If the parallax angle is smaller, then the star is further away, and if the angle is larger, the star is closer.

d = 1/p

Where d = distance from star

P = parallax angle in arcsecs

The usefulness of trigonometric parallax measurements is limited because the parallax angle of nearby stars is extremely small. Current telescopes have a limited resolution and accuracy and hence limited in measuring small angular shifts

Further more, this is combined with the seeing effect of the atmosphere, making measurements of small angles very difficult.

The maximum distance of measurements to reasonable accuracy is approximately 33pc, which is approximately 0.03 arcsec

Solutions

Using a larger baseline, however this is impossible as for this to happen; earths orbital radius has to be increased.

Putting telescopes above the atmosphere and in the space reduces the limit to which trigonometric parallax measurements are restricted by avoiding the effects of the earths atmosphere.

E.g. Hipparcos has precision to 0.01 arcsecs which is 10 times more accurate than ground based measurements.

Gaia is planned to be launched and intended to have a precision to 10 microarsecs, 100 times more precise than hipparcos

Spectroscopy is the analysis of spectra produced by an object to obtain information on its features.

The spectrum is a range of wavelengths of electromagnetic waves. Under the visible range, these wavelengths are observed as colour. There are 2 types:

Continuous spectrum e.g. white light, rainbow

Line spectrum e.g. emission and absorption spectrum

Continuous blackbody spectrum

This is produced when an object emits all wavelengths of the electromagnetic spectrum. Under the visible range, a continuous band of colours is observed. Black bodies emit a complete spectrum of electromagnetic waves where the radiation emitted is related to the temperature of the body. This radiation is produced by the oscillation of electrons.

Continuous spectra are given off by hot solids, liquids and high pressure gases. The intensity of the spectrum varies smoothly with frequency, with a maximum that depends on the temperature of the body.

R O Y G B I V

Emission Spectrum

An emission spectrum has the appearance of coloured lines as seen against a dark background.

This is produced when gases or atoms are excited in a flame or an external energy source that causes the transition of electrons into higher energy states. When they return to the ground state, they emit the energy as photons, which form an emission spectrum.

For this reason, the emission wavelengths are often called the emission lines. Each element has its own characteristic emission spectrum

Absorption Spectrum

An absorption spectrum consists of dark lines as seen against a colourful background

This occurs when white light from a continuous spectrum source passes through a cool non luminous gas. Some of the components wavelengths are absorbed by the electrons of the gaseous atoms. These electrons then make a transition into the higher energy state and eventually return to their ground state, releasing the energy as photons. The wavelengths emitted are identical to the ones emitted.

However, the radiation is emitted in all directions in space, and hence the energy obtained in the viewing direction is less than the original directional energy. Thus the spectral lines appear darker in these wavelengths than others.

A prism spectrometer was used in order to view the spectra produced by reflected sunlight. It produced an absorption spectrum due to the earths atmosphere

The device used in spectroscopy is called a spectrometer. There are 2 types

Prism spectrometer

Diffraction grating spectrometer

Astronomical spectra are examined by using a spectroscope, or recorded and measured with a spectrograph, mounted at the focus of a telescope. A spectrograph consists of 3 parts:

1. Collimator This uses a narrow slit and one or more mirrors or lens to form a parallel beam from a single light source such as a star

2. Dispersive element Either a prism or diffraction grating consisting of a thin piece of glass with thousands of lines etched down it. They both disperse the light beam.

3. Device to view/record the different wavelengths this may be a viewing telescope, a focussing mirror with photographic plate or film, or an electronic imaging device such as a charge coupled device (CCD) detector.

Note: Diffraction grating works by the diffraction of light, creating an interference pattern. Since the maximum interference for each wavelength occurs at a different angle, a diffraction grating effectively disperses the different wavelengths in a light beam.

Stars These emit a continuous spectrum similar to a black body. However since light is absorbed by gases in its cooler outer atmosphere, dark absorption lines appear against the continuous background of light emitted from each star. The wavelengths of the absorption lines can be used to determine the elements and molecules present in the atmosphere of the star

Emission Nebulae These emit an emission spectrum. They are regions of gas and dust which glow because they are illuminated with UV light from stars within the nebulae. As excited electrons in the atoms and ions within the nebula drop to lower energy levels, line spectra are produced with emission lines in the ultraviolet, visible, and infrared and radio bands, characteristic of the elements that make up the nebula along with strong hydrogen emission lines (red/pink)

Galaxies This emits a continuous spectrum. They are made up of gas, dust and millions of stars. The spectrum of a galaxy is generally the composite of various spectra. These are normally red shifted

Quasar This emits a continuous spectrum with a few emissions lines that fluctuate in intensity rapidly. They are very distant objects that produce vast quantities of continuous radiation at all wavelengths

A stellar spectrum consists of an approximate black body radiation spectrum for the temperature of the stellar surface, superimposed with absorption lines characteristic of the elements present in the stellar atmosphere.

Stars can be classified into 7 spectral classes based on their surface temperatures

O B A F G K M

Oh Boy Angry Fearnside Gonna Kill Me

Higher surface temp ( Lower surface temp

In each spectral class, it is then subdivided from 0 ( 9

Bo B 1 B2 B9

Higher surface temp ( Lower surface temp

By analysing the stellar spectra, we can classify them according to their surface temperatures and colour

Spectral Class

Spectral Features

Surface Temp

Colour

Mass (sun = 1)

O

Ionised helium

Weak hydrogen

> 25000

Blue

30

B

stronger hydrogen

neutral helium

25000 -11000

Blue white

8

A

Strong hydrogen

Ionised metals

11000-8000

White

2.5

F

Weaker hydrogen

Ionised heavier metals

Neutral metals

8000-6000

Yellow white

1.4

G

Ionised calcium strongest

Many neutral metals

6000-4800

Yellow

12

K

Neutral metals dominate

Hydrogen lines very weak

4800-3500

Orange

0.7

M

Strong neutral metals

Molecules particularly titanium oxide

< 3500

Red

0.3

Surface Temperature

This can be deduced based by using Weins law. A spectroscope is used to determine the wavelength of maximum output in analysing the prominence of spectra or by plotting the intensity of the radiation as a function of its wavelength and using the wavelength when it peaks.

Weins law : T x peak = 2.89 x10-3

Rotation velocity

This can be determined by analysing the optical Doppler shift effect caused by the rotation of the star. As a star rotates about its own axis, the spectral lines will be both blue and red shifted. This is because one side moves towards the observer (blue shift) ad the other side moves away from the observer (red shift)

Thus the individual spectral lines will be broadened by an amount depending on the rotational velocity of the star. The faster a star rotates, the more broadening of spectral lines is observed.

Translational velocity

This is also determined by analysing the Doppler effect on the absorption lines. If a star is approaching the observer, every absorption line in the spectrum of the star is shifted toward the blue end of the spectrum by the same amount. If the star is moving away, all the lines are shifted towards the red end. The amount by which all the lines are shifted depends on the component of the velocity of the star along the line of sight.

Density

The broader the spectral lines, the higher the density of the atmosphere surrounding the stars. This is different to the rotational velocity analysis as the intensity varies across the line in different way from the effect of rotation.

Chemical composition

This can be determined by comparing the absorption spetrum of the star to the absorption spectra on the earth.

First identify the wavelength at which the black body curve is at its highest intensity. Then use Weins law in order to predict its surface temperature

Photometry is the measurement of the brightness of stars and other celestial objects

The brightness of a star depends on its

Luminosity

Radius2

Temperature

Distance-2

Apparent magnitude This is the number given to a star to indicate its brightness as measured from earth

Absolute magnitude This is the number given to a star to indicate its brightness as measured at 10 parsecs away

Since the brightness of a star depends on its luminosity and its distance to the earth, the apparent magnitude will vary with the distance to the observer. The further the observer is, the fainter the star and the higher the apparent magnitude. The closer the observer is the brighter the star and the lower the apparent magnitude.

Since absolute magnitude is measured from 10pc away, it is a fixed number and hence the brightness of stars can be properly compared. Absolute magnitude is estimated for distant stars by comparison with reference stars of the same spectral class and of known distance.

Thus if both the apparent and absolute magnitudes were known, then the distance can be worked out with the formula of

If a star is further away than 10 pc, its apparent magnitude m is larger than its absolute magnitude M, because the star appears fainter at the greater distance. If closer than 10 pc, it would appear brighter and m would be smaller than M.

Where M is the absolute magnitude

M is the apparent magnitude

d is the distance in parsecs

Spectroscopic parallax is the process of using the Hertzsprung-Russel diagram and the distance modulus formula to determine the approximate distance of a star.

This method involves

Using photometry to measure the apparent magnitude of the star

Using spectroscopy to determine the spectral class as well as the luminosity class in order to determine which group the star belongs to

Use the H-R diagram to find the absolute magnitude. By drawing a vertical line up from the position on the horizontal spectral class axis until it intercepts with the luminosity class, we can read off the stars luminosity on the vertical axis.

Using the distance modulus formula

The apparent magnitude of a star can vary depending on the detector used. A human eye is more sensitive to the yellow-green region of the visible spectrum and hence red and blue stars are not judged to be as bright as they really are. (Red stars are seen to be brighter and bluer stars seen to be dimmer)

Similarly, a photographic film or detector is most sensitive to the blue region of the spectrum.

The visual magnitude (V) refers to the magnitude as judged by the eye or a photometer fitted with a yellow green filter

The photographic magnitude (B) refers to the magnitude as detected by photographic film or a photometer fitted with a blue filter.

Colour index is determined by the photographic magnitude minus the visual magnitude

CI = B - V

They are useful as they provide a more accurate reading of magnitude when both values are used. It is a fast and simple method and can be used to determine the colour and spectral class of a star.

Photographic photometry

This is the technique used to identify the brightness of a star based on photographic images. It involves making a photograph of a portion of the sky and when the image is developed, the size and density of each spot is measured. Brighter stars expose a larger area of film and appear as larger denser sports. Each sport is compared to standard spots and densities to determine the star magnitude.

Advantages

It is a fast method and the brightness of a large group of stars can be identified at one time

Fine detail of a star can be recorded photographically, often to high resolutions achieved electronically

Disadvantages

Restricted to the visible range of the EM spectrum

Sensitive to blue colour which leads to inaccurate measurements of brightness

Photoelectric photometry

This is the technique used to identify the brightness of a star by converting the amount of light input into electric signals. They use a combination of a filter and an electronic sensor such as a CCD. In general the brighter the star, the greater the electric signal. (more generally used)

Advantages

Responds uniformly to all wavelengths of the EM spectrum and hence allows the study of a much broader region of the EMR than done by photographic film

They are more efficient in catching photons, hence a greater sensitivity to intensities of light

Fast response for computer analysis, can be done quickly and remotely

Disadvantages

Slower than photographic for comparison and studying a large group of stars

Cannot achieve the same resolution

Produce simulated starlight from the incandescent lamp in a ray box kit, commonly available in school science laboratories. This has the advantage that coloured filters mounted in 35 mm slide frames can easily be inserted in the light path. If this is not available, filters can be held by hand in front of any incandescent lamp.

Use a light intensity probe attached to a datalogger to measure the intensity of light at a set distance from the lamp. Set the datalogger to operate in manual or snapshot mode. A photographers hand-held light meter is a suitable alternative to measure light intensity.

Place different coloured filters, one at a time, between the lamp and the light probe. For each filter, measure the intensity of light with the datalogger. You should note that the filters used in photometry, unlike those in a ray box kit, transmit a carefully calibrated range of frequencies.

For each filter, also observe the light through a hand-held spectroscope to see qualitatively what effect the filter has on the spectrum of white light produced by the lamp. Use the in-built scale to measure the range of wavelengths transmitted.

Record all your observations systematically in a suitable table. Compare your qualitative and quantitative observations for different filters.

Use your observations to predict the effect of different filters on the measurement of apparent magnitude of stars of different spectral type.

Key discoveries in imaging and measurement of celestial bodies follow the introduction of improved technology.

Tyhco Brahes large metal and wooden quadrants and scales allowed an enormous improvement in the measurements of the position of celestial bodies. Kepler then used Brahes measurements to calculate that the orbit of Mars was elliptical, undermining the accepted geocentric belief of circular orbits.

The invention of photography in the 19th century allowed length and integrated exposures which produced a permanent image that could be measured and analysed. This allowed starts to be accurately compared over time, allowing the time-varying phenomenon such as variable stars to be studied. Measurements of plates allowed magnitudes of objects to be studied. Measurements of plates allowed magnitudes of objects to be determined and faint objects such as galaxies to be discovered. The development of the spectrograph led to the discovery of helium in the sun before it was found on earth. Furthermore this has developed into using photomultipliers and CCDs in photometry that electronically enable a greater understanding by improving on the measurement technologies

The Hubble telescope combined long exposure photographic plates with spectral observations to discover the galaxies were separate from the milky way and that the universe is expanding. These discoveries had profound social and philosophical implications.

More recently, developments in electronics have allowed astronomers to observe wavelengths other than visible light. The advent of computers and space telescoped has allowed them to detect and image objects such as nebulae and galaxies across the EM spectrum.

Binary stars consist of two stars orbiting around their common centre of mass. Approximately half of all stars are actually binary star systems. They are classified accordingly to the method used to detect them

Visual

These are those that can be resolved by a telescope where binary stars can be actually seen orbiting one another

Astrometric

This consists of 2 stars but one star is too faint to be detected in anyway. Only one star can be seen

The only means of detection is the wobble effect from the orbital motion of the visible star. This is deduced from the periodic perturbation (variation in the designated orbit of one body due to the influence of another body)

Spectroscopic

These are unresolved pairs of stars that can only be detected from the shifting of their spectral lines. During its orbit, one star will be moving towards the observer and the other moving away. The receding star experiences a red shift while the approaching star experiences a blue shift in their absorption spectra.

Periodic doubling of the spectral lines indicates it is a spectroscopic binary

Eclipsing

These are unresolved stars that can only be detected by the characteristic of the light intensity of the 2 stars. In the eclipsing binary, one star of the pair eclipses the other at regular intervals, leading to variations in the brightness of the light.

When the brighter star (usually the small one) eclipses the duller star (usually the bigger one), the combined intensity dips slightly. When the duller star eclipses the brighter star, the combined intensity drops more steeply. As shown below

The difference between the flat and curved bottom is that a total eclipse occurs with the flat bottom and a partially eclipses creates the curved bottom

Binary star systems are important as they enable astronomers to calculate the mass of stars. By observing the system, we can determine the period of the motion, the separation and hence the total mass can be calculated using Keplers law.

Astronomers need to know the mass of stars in order to understand the processes that that give a star its energy at different stages of its evolution.

Variable stars are those that vary their brightness

This can be classified into two types

Intrinsic These change their brightness due to processes within the star e.g. rate of nuclear fusion, surface temperature

Extrinsic These change their brightness due to external process

Eclipsing binary

Rotating variables (have large and cool spots that change the stars brightness as they rotate

Intrinsic variable stars are classified into

Periodic These vary brightness in a regular cycle with a fixed period

Mira

RV tauri

Cepheids

RR lyrae

Non periodic Change their intensity in an irregular way

Super novae

Novae

Flare stars

R coronae Borealis

T Tauri

Cepheids are supergiant stars that are intrinsic periodic variable stars with a characteristic light curve. They change their radius and surface temperature periodically which results in a change in their brightness. The temperature change is due to an increased rate of fusion during contraction and a decreased rate during expansion.

There are two types

Type I massive, young second generation stars

Type II small, old and red first generation stars

It was found that when the absolute magnitude of the cepheids is graphed against their corresponding periods, a linear relationship is obtained. This means their period of their brightness is directly related to their average luminosity. The period varies from 3-50 days where the longer Cepheids being more luminous than those with shorter periods.

Thus we can measure the period of variation of a Cepheid variable, we can easily determine its luminosity immediately. We can then calculate the distance to the star by using the inverse square law or by applying the distance modulus equation.

Due to the correlation between their periods and the average absolute magnitude, they are very useful in determining the distance to different galaxies

The Hertzsprung Russell diagram is a plot of the surface temperature/spectral class/colour against their absolute magnitude/luminosity of stars. The H-R diagram is important since it enables astronomers to classify stars and understand its evolution.

Important features

Star temperature decreases towards the right, hence stars on the left are blue (spectral class O) while those on the right are red (spectral class M)

The radius of a star increased vertically for each spectral class. Therefore a red star near the bottom of the diagram will have a smaller radius than a red star near the top of the diagram

When a star is plotted, it will fall into one of the main distinct groups, each characteristic of a specific stage in star lifetime.

Main sequence This is where the majority of stars ( greater than 90%) lie and most of these are found on the cooler part of the band

They fuse hydrogen to helium in their cores and exist in a state of equilibrium between the force of gravity pushing inwards and the radiation and gas pressure pushing outwards

The point at which the stars joins the main sequence at the lower edge of the band is called the zero age main sequence

It becomes more luminous and massive in moving from the bottom right to the top left

Red giants this is when the nuclear fusion of helium occurs at the core

They are extraordinarily large in size

White dwarfs This is when no more nuclear fusion occurs, basically a collapsed star corpse.

The vertical axis of the H-R diagram may show the stars mass relative to the sun, its absolute luminosity or its luminosity relative to the sun. The horizontal axis may show the stars surface temperature, its spectral class or its colour index.

Stars fall into distinct groups in the H-R diagram, with common characteristics of luminosity (hence, mass) and temperature (hence, colour), and at a similar evolutionary stage. The regions include:

the main sequence (diagonally from bottom right to top left),

the red giants (middle to upper right side cool, but very luminous, therefore very large),

the white dwarfs (bottom middle and left hot, but low luminosity, therefore small)

the supergiants (across the top of the H-R diagram both very hot and very luminous).

A higher mass start evolves more quickly than a lower mass star

Sample analysis

Star A is low and to the right of the main sequence, therefore it is a protostar, at a very early stage of its life, and heading for the main sequence. It is very cool, but is nearly as luminous as the sun, therefore it is very large.

Star B is on the main sequence, so it has begun to produce energy by fusion of hydrogen into helium. Its low surface temperature shows it to be a red star, while its low luminosity, and position at the bottom of the main sequence, show it to be a dwarf. As a low-mass star, it will consume its fuel very slowly and spend a very long time on the main sequence.

Star C is on the main sequence and is steadily converting hydrogen to helium by fusion. Its surface temperature is approximately 6000 K (remember that the scales are logarithmic), so it is a yellow star like the sun. It is also approximately as luminous as the sun, therefore it must be of similar mass to the sun.

Star D is in the region of red giant stars. It is relatively cool, but about 1000 times as luminous as the sun, therefore it must be very large. It has consumed most of its fuel and is near the end of its life.

Star E is very hot and very luminous, about 10 000 times as luminous as the sun, but it is on the main sequence. It must therefore be a very young star, as such a star consumes its fuel quickly and would not stay on the main sequence very long. It is very massive and will have a short, violent life, ending in a supernova.

Star F is a hot white star, but from its low luminosity, and its position on the H-R diagram, we can see that it is very small. It is a white dwarf and is at the end of its life.

Blue stars initially have a bigger gas cloud and more fuel and enter the main sequence at the top left such as the 10 solar mass star. They burn fuel the quickest and survive as stars only for a fraction compared to the smaller mass stars.

Stellar formation begins with the gravitational contraction of a vast nebula of interstellar dust and molecular gas clouds, mainly hydrogen. This process begins slowly, but quickly speeds up as the density increases more quickly at its centre and experiences greater gravity. Also, a shock wave moving through a gas cloud could trigger the cloud to contract sufficiently to form a star.*

The cloud now has two parts

A rapidly contracting core

Slower contracting surroundings of gas and dust.

As the core contracts, the gravitational potential energy converts into thermal energy. This increasing temperature produces an outward pressure that opposes the gravitational force. This pressure increases and builds up as the core becomes hotter, eventually stopping the collapse and stabilising the size of the core.

This state before a new star begins to produce any nuclear energy in its core is called a protostar. It eventually develops strong stellar wind that blows away the remnants of the surrounding cloud. Hence without an energy source, the contraction of the core is very slow, ranging from a hundred thousand years for a big star to several million years for a small star. This decrease in size causes it become less luminous, but also heats the core.

If the core mass is above between 0.01 to 100 solar mass, it will eventually reach a temperature high enough to trigger the nuclear fusion of the hydrogen within it (approx 8 million kelvins). If the mass were lower, the protostar would not have heated sufficiently to begin nuclear fusion, and if it were greater, it wouldve overheated and blown itself up forming smaller clouds and protostars.

The evolutionary stages through which a star passes during its life depends on the initial mass of the star.

Stellar Formation

Material accumulated at the centre of a nebula collapses under its own gravity and forms an expanding core of hot dense matter. The heat radiated from the core causes the surrounding cloud to become luminous. The luminous cloud with its hot dense core is known as the protostar as it has not reached the stage in which nuclear fusion has begun. The increasing density of the core begins to slow further in falling of matter.

Eventually the protostar ( if it has a mass greater than 0.08 solar mass) will reach a temperature where the fusion of hydrogen begins, entering the main sequence

Small mass stars

A small star of 0.3 solar masses would take about a billion years to join the lower right hand side of the main sequence. Since the star is comparatively small, the rate of hydrogen fusion in the core is low and the surface temperature also being low. Such stars are therefore red and very long lived

These small mass stars remain in the main sequence for over 30 billion years. Since they are too small to reach the higher temperatures required to fuse helium, when a large core of helium is formed in such stars, fusion ceases. Then the star contracts to become a white dwarf. Without the fusion to oppose it, gravity collapses the star and the potential energy is converted into heat, resulting in a small, very hot white dwarf, which will eventually radiate its heat away and fade.

Sun-like mass stars

These are stars of about 0.5 to 5 solar masses that have enough mass to fuse hydrogen to helium and then helium to form carbon and heavier elements. When a sufficiently large helium core forms, fusion ceases and gravity collapses the star until a shell of hydrogen begins to fuse. This expands and cools the star, turning it into a red giant. When the hydrogen in the shell is used up, the star collapses again until the temperature is high enough to fuse helium to carbon. When this occurs, the star expands and cools again.

Eventually the carbon formed in the core prevents further fusion and the star once more collapses inwards. The heart produced by this collapse may blow off the outer layers of the star in a nova explosion. The outer layers spread away from the star, forming a planetary nebula while the small core that remains forms a white dwarf star.

Large mass stars

These are stars with masses greater than 5 solar masses, and elements heavier than helium can be fused in the core. The star moves to the left and right of the H-R diagram. This is due to the fusion of each successive element ceasing, and causing the collapsing and fusion of the next element. Eventually a core of iron is formed and fusion ceases (fusion of iron and heavier elements does not release energy). When the iron core is large enough, the star collapses and causes a supernova explosion, blowing away most of the stars mass. The fate of the core depends on the mass that remains (could become a neutron star, white dwarf or a black hole)

Smaller and cooler main sequence star (about 20 million Kelvin)

The predominant type of nuclear reaction is the proton-proton chain reaction. It is a slow process

1. Fusion of two hydrogen nuclei to form a heavy hydrogen nucleus. One proton decays into a neutron with the release of a position and neutrino

2. Fusion of a proton and deuterium nucleus to form helium 3 nucleus, with the release of gamma radiation

3. Fusion of two helium 3 nuclei to form a helium 4 nucleus and two free protons which may participate in further PP chain reactions

Bigger and hotter main sequence stars

The predominant reaction is the carbon-nitrogen-oxygen (CNO) cycle. This requires a higher temperature and also converts 4 protons into 1 helium nucleus. This is fast and releases a lot of energy. Carbon is used as a catalyst

1. Four successive protons combine with a carbon nucleus to produce nitrogen, then oxygen and finally carbon again plus a helium nucleus

2. The first and third collision triggers the decay of a proton into a neutron and a position, thus increasing the number of neutrons in the nucleus

3. The second and fourth collision simply increases the number of protons in the nucleus

4. This process if cyclic as the a carbon nucleus is present at both the start and the end, allowing the process to be repeated.

Post main sequence stars

Since helium is plentiful in the core, three helium nuclei can fuse to form a carbon nucleus through the triple alpha reaction. This process occurs when a star is at the stage of a red giant

3 42 He ( 126 C + gamma radiation

The carbon atom can then easily fuse with another helium nuclei to form oxygen

126 C + 42 He ( 168 O + gamma radiation

If a star is massive enough, further exothermic shell-burning reactions can take place in successively deeper shells within the star. This converts carbon to neon and magnesium, oxygen to silicon and sulfur and then to iron. Here ends the energy source as further fusion will not release anymore energy.

Initially only hydrogen and helium were present in the universe after the big bang. All other elements were synthesised by fusion during the life and death of stars. The mass of the star and the stage of life of the star determine which elements are synthesised.

Further helium is produced by fusion of hydrogen in main sequence stars either by PP or CNO chain reactions. The rate at which fusion proceeds depends on the temperature and pressure at the core and hence mass of the star. These fusion reactions are exothermic and the energy is eventually released as radiation

Elements heavier than helium are produced by fusion in post main sequence stars,

Beyond iron, the reactions are endothermic, but inside red giant stars, heavier nuclei can still be formed by nucleosynthesis

The first process is a slow capture of neutrons inside red giants that have achieved a helium burning shell. The neutrons are captured by nuclei to form heavier ones. This slow process is capable of generating elements up to lead on the periodic table, including gold

The second process is a fast capture in a supernova explosion. In such an environment, there is sufficient energy available to allow the rapid formation of the elements heavier than lead such as uranium

A star cluster consists of a few hundred to thousands of stars that are about the same age. The stars in a cluster are believed to have condensed from interstellar gas clouds at the same time. The age of a cluster can be determined by its turn off point the point it leaves the main sequence.

An old cluster will have a low cut off point. This is because it contains a high mass stars and hence consumers more energy to counteract the gravitation collapse. It will evolve off the main sequence faster than younger stars.

A young cluster will have a higher cut off point

i. is a young star cluster

ii. is a much older cluster

Open clusters these are very young clusters with higher cut off points than globular clusters in a region of about 25pc

Globular clusters these are older clusters of stars closely packed together in a spherical or globular shape. It contains thousands to millions of stars 10-30pc across

The fate of a star when it does depends on its mass.

1. Planetary nebula These are huge clouds of gas and dust produced when the outer layers of a star are blown away when fusion ceases in the star and it collapses inwards. Approximately a quarter of the star can be blown outwards to form a planetary nebula which expands outwards from the white dwarf that remains

2. Supernovae This is a violent explosion of uncontrolled nuclear reactions that completely blows away the various layers of a massive star (occurs when original mass is greater than 5 solar masses). It occurs when an iron core builds up and fusion ceases in very large stars. It is in such explosions that nuclear reactions occur in which elements heavier than iron are created

3. White dwarfs these are small and very hot remnants of stars in which fusion has ceased. Without fusion to oppose it, gravity collapses the star and potential energy is converted to heat. It will eventually radiate its stored heat away and fade away to become a brown, then black dwarf. The collapse is eventually hated by quantum effects of matter where closely spaced electrons cannot be in the same energy level

4. Neutron stars/pulsars This is the extremely dense remnant of the core where the inward force of gravity exceeds the maximum force of the outward pressure. Matter is condensed to the density of nuclear material and a neutron star with a diameter of about 10km is formed. This huge decrease in radius results in a very hot and rapidly spinning star with an intense magnetic field. They emit X-rays and as they rotate, sweep across the sky. (also known as pulsars)

5. Black holes This is the crushed remnant of the core of a very massive star. The force of gravity is so great that when fusion ceases, nothing can stop the star from collapsing. The matter is crushed down to a point of infinite density, known as singularity, which is infinitely small. Around the singularity is a region called the event horizon, where the escape velocity required is greater than the speed of light, thus even light cannot escape from a black hole. Thus they would appear as small black spheres in space.

Discuss why some wavebands can be more easily detected from space

Discuss Galileos use of the telescope to identify features of the moon

The electromagnetic spectrum is loosely divided into bands because the range of the wavelength is vast. It is divided based on wavelengths and on how the radiation can be produced and detected

Discuss the problems associated with ground-base astronomy in terms of resolution and absorption of radiation and atmospheric distortion

Section One

Our understanding of celestial objects depend upon observations made from earth or from space near the earth

Seeing is the distortion of the image of a distant light source by the earths atmosphere

Identify data sources, plan, choose equipment or resources for and perform an investigation to demonstrate why it is desirable for telescopes to have a large diameter objective lens or mirror in terms of both sensitivity and resolution

Outline methods by which the resolution and/or sensitivity of ground-based systems can be improved including:

Adaptive optics

Interferometry

Active optics

The speed is the major difference between adaptive optics and active optics

Define the terms resolution and sensitivity of telescopes

Section Two

Careful measurement of a celestial objects position in the sky(astrometry) may be used to determine its distance

Define the terms parallax, parsec, light-year

Explain how trigonometric parallax can be used to determine the distance to stars

Discuss the limitations of trigonometric parallax measurements

Gather and process information to determine the relative limits to trigonometric parallax distance determinations using recent ground based and space based telescopes

Section Three

Spectroscopy is a vital tool for astronomers and provides a wealth of information

Account for the production of emission and absorption spectra and compare these with a continuous blackbody spectrum

Perform a first hand investigation to examine a variety of spectra produced by discharge tubes, reflected sunlight or incandescent filament

Describe the technology needed to measure astronomical spectra.

Identify the general types of spectra produced by stars, emission nebulae, galaxies and quasars

Describe the key features of stellar spectra and describe how these are used to classify stars

Describe how spectra can provide information on surface temperature, rotational and transition velocity, density and chemical composition of stars

Analyse information to predict the surface temperature of a star from its intensity/wavelength graph

Section Four

Photometric measurements can be used for determining distance and comparing objects

Define absolute and apparent magnitude

Explain how the concept of magnitude can be used to determine the distance to a celestial object

Outline spectroscopic parallax

Explain how two-colour values(ie colour index B-V) are obtained and why they are useful

Describe the advantages of photoelectric technologies over photographic methods for photometry

Perform an investigation to demonstrate the use of filters for photometric measurements

Identify data sources, gather, process and present information to assess the impact of improvements in measurement technologies on our understanding of celestial objects

Section Five

The study of binary and variable stars reveals vital information about stars

Describe binary stars in terms of the means of their detection

Visual

Astrometric

Spectroscopic

Eclipsing

Explain the importance of binary stars in determining stellar masses

Classify variable stars as either intrinsic or extrinsic and periodic or non periodic

Explain the importance of the period luminosity relationship for determining the distance of Cepheids

Section Six

Stars evolve and eventually die

Describe the process involved in stellar formation

Present information by plotting Hertzsprung-Russell diagram for: nearby or brightest stars, stars in a young open cluster, starts in a globular cluster

Outline the key stages in a stars life in terms of the physical process involved

Analyse information from a H-R diagram and use available evidence to determine the characteristics of a star and its evolutionary stage

Present information by plotting on a H-R diagram the pathways of stars of 1, 5 and 10 solar masses during their life cycle

Describe the types of nuclear reactions involved in main-sequence and post main sequence stars

Discuss the synthesis of elements in stars by fusion

Explain how the age of a globular cluster can be determined from its zero age

Explain the concept of star death in relation to:

Planetary nebula

Supernovae

White dwarfs

Neutron stars/pulsars

Black holes