Physics Unit 5A: Astrophysics

Physics Unit 5A: Astrophysics
Siobhan Parish

Telescopes Chapter One

Lenses A converging lens makes parallel rays converge to a focus.
The point that they focus to is the principal focus/focal point of the lens A diverging lens makes parallel rays diverge The point where the rays come from is the principle focus/focal point of the lens The distance from the lens to the principal focus is the focal length of the lens The plane on each side of the lens perpendicular to the principle axis containing the principle focus is the focal plane

Lenses Investigating the converging lens
Object at different distances beyond the principal focus. Position of the screen is adjusted until a clear image is seen. Image is real because it is formed on the screen where the light rays meet. If the object is moved nearer the lens, towards the principal focus, the screen must be moved further away. The nearer the object is the to the lens the larger the image is Lamp box

Lenses Object nearer to the lens than the principal focus. Magnified image is formed as lens acts as a magnifying glass. Image can only be seen when you look into the screen from the other side to the object. Image is called virtual because it’s formed where the light rays appear to come from Lamp box

Lenses Ray Diagrams Focal length represented by f, object distance u. Can find the nature of the image formed by a ray diagram by drawing a to scale ray diagram Lens is a single line where refraction takes place Straight line through the centre of the principal lens perpendicular to the lens is the principal axis The principal focus F, is at the distance from the lens on both sides Object represented by an upright arrow

Lenses To form a real image the object must be beyond the principal focus- image is formed on the other side of the lens to the object F 2F Real image (diminished)

Lenses To form a virtual image the object must be between the lens and the principal focus- image is formed on the same side of the lens to the object F 2F Virtual image (magnified)

Lenses How images will appear Linear magnification = Height of image Height of the object This is equal to  Image distance Object distance Object position Image position Nature of image Magnified/diminished Upright/ inverted Application Beyond 2F Between F and 2F Real Diminished Inverted Camera 2F Same size Inverter Magnified Projector < F Same side Virtual Upright Magnifying glass

Lenses 1 u + 1 v = 1 f 1 u + 1 v = 1 f The lens formula
For an object at on the principal axis of focal length f, at distance u from the lens, the distance v from the image to the lens is given by: 1 u v = 1 f When the sign is positive then the object/image is real and when the sign is negative then the object/image is virtual The focal length for a converging lens is always positive Focal length for a diverging lens is always negative

The refracting telescope
Made up of two converging lenses of different focal lengths The lens with the longer focal length is the ‘objective’ because it faces the object The viewer looks through the other lens, the eyepiece Light from the object enter the viewers eye after passing through the objective and then the eyepiece By adjusting the inner and the outer tube the distance between the two objects is adjusted until the image is in focus If being used to view a distant object, the viewer sees an enlarged, virtual and inverted image

Objective lens focuses the light rays to form a real image of the object The light rays cross each other after passing though the objective lens Eyepiece gives the viewer looking through the telescope a magnified view of the real image Magnified view if virtual because it is formed where the rays emerging from the eyepiece appear to have come from

Normal adjustment is when the telescope is adjusted so the image seen by the viewer is at infinity The distance between the two lenses is the sum of their focal lengths The real image of the distant object is formed in the focal plane of the object The eyepiece is adjusted so its focal plane coincides with the focal plane of the objective The light rays that form the real image leave the eyepiece parallel to one another- appear to come from a virtual image at infinity

Ray diagram for a refracting telescope in normal adjustment Real image Virtual image at infinity

angular magnification = β α The refracting telescope If a telescope is in normal adjustment and it makes a distant object appear 3 times larger its angular magnification would be 3 If the angle subtended by the distant object to the unaided eye is 1˚ then then angle subtended by the telescope to the eye would be 3˚ The angle subtended by the final image at infinity to the viewer = β The angle subtended by the distant object to the unaided eye = α

angular magnification = fo fe The refracting telescope h1 is the height of the real image fo is the focal length of the objective lens fe is the focal length of the eyepiece lens tanα = h1 fo tanβ = h1 fe To eliminate h1 from these equations combine them through tanα/tanβ and get the result above CALCULATOR MUST BE IN RADIANS! α β Virtual image Real image

Image brightness Stars are seen as a point object and will be seen brighter through a telescope This is because the telescope objective is wider than the pupil of the eye so can let more light in The light entering the eye pupil or the objective is proportional to the area in each case; the area is proportional to the square of the diameter Diameter of the pupil is about 10mm a diameter of 60mm would collect 36 time more light per second from a star (60/10)2

The greater the diameter of the objective of a telescope, the greater the number of stars that can be seen Planets are magnified using a telescope, where as stars are always seen as point objects Planets are NOT seen as brighter when viewed through a telescope because the virtual image is magnified- spread over a larger part of the field view Therefore, the amount of light per second per unit area of the virtual image is unchanged

Reflecting telescopes
A concave mirror us used instead of a converging lens as the objective in a reflecting telescope The concave reflecting mirror is the primary mirror because a secondary smaller mirror reflects light from the concave reflector into the eyepiece Parallel rays are reflected and focused to a point by the mirror If rays are parallel to the principal axis then the point where the rays are focused is the principal focus, F

The focal length, f, is the distance from the principal focus to the centre of the mirror f F

The Cassegrain reflecting telescope Secondary mirror is a convex mirror near the focal point of the primary mirror Purpose of the convex mirror is to focus the light onto, or just behind, a small hole at the centre of the concave reflector The light passing through the small mirror then passes through the eyepiece Distance from the concave mirror to the point where is focuses parallel rays is increased by using a convex mirror instead of a plane mirror

The viewer will see a virtual image at infinity The effective focal length of the objective is increased by using a secondary convex mirror The image of a distant object is usually brought into focus by adjusting the position of the secondary convex mirror The primary mirror should be parabolic and not spherical to avoid spherical aberration. This would result in the outer beams being brought to focus near the principal focus, but not at it

Comparing refractors and reflectors Reflecting telescopes can be much wider because high-quality concave mirrors can be manufactured much wider than a convex lens can  the wider the objective is, the greater the amount of light they can collect from a star The high quality of a wide concave mirror compared with a wide convex lens is because: - Image distortion due to spherical aberration is reduced with a parabolic mirror - Unwanted colours in the image are reduced. Unwanted colours come from the splitting of white light. This is chromatic abberation

Refracting telescopes Reflecting telescopes Use lenses only and no supporting frames which would block light from the object Have a wider field of view than reflectors because angular magnification is less Shorter and easier to handle than refractors with same angular magnification Greater angular magnification than refractors of same length- greater magnification of distant objects

Resolving power The angular separation of two stars is the angle between the straight lines from the Earth to each star If the telescope just resolves the two stars then the stars can just be seen as two separate images If the telescope is replaced with one of a narrower objective then the images would overlap too much, this is because: - The objective mirror or lens in an aperture which light from the object must pass through- diffraction of light always happens here - Instead of focusing the light to a point the diffraction would cause the image to spread out slightly - Narrower the objective; greater amount of diffraction that occurs so the the greater the spread of the image θ

Diffraction angle of diffraction = λ D
D is the diameter of the circular aperture Diffraction at a circular aperture (gap) can be observed on a screen when a narrow beam of light passes through the circular aperture before reaching the screen The diffraction pattern on the screen shows a central bright spot surrounded by alternate bright and dark rings The intensity of the bright rings decreases with distance from the centre Objective of a telescope is a circular aperture containing a convex lens of concave mirror As the light is focused by the objective, the star would be seen as a magnified virtual image of the diffraction pattern

Diffraction REMEMBER RADIANS!! θ ≈ λ D
Two stars near each other can be resolved if their central diffraction spots do not overlap significantly When writing this numerically it is known as the Rayleigh criterion this states that: the resolution of the images of two point objects is not possible if any part of the central spot lies inside the first dark ring of the other image This means that the angular separation of the two stars must be at lest equal to the angle of diffraction of the first dark ring Angular separation = θ

Diffraction Resolution or resolving power are both to describe the quality of a telescope in terms of the minimum angular separation The Rayleigh criterion applies to the detail visible in extended images as well as to stars Refraction due to movement of air in the atmosphere causes the image of any star seen through a telescope to be ‘smudged’. Due to this, ground based telescopes with objectives of diameter greater than about 100mm do not achieve their theoretical resolution

Diffraction The Hubble Space Telescope has clear images because the telescope has an objective of 2.4m and is above the atmosphere It is above the atmosphere and does not suffer from atmospheric refraction It achieves its theoretical resolution which is about 240 times greater than a 100mm wide telescope It detects images at wavelengths from 115nm to about 1000nm- gives infrared, visible and ultraviolet images

Telescopes and technology
Charge-couple devices The CCD is an array of light-sensitive pixels which become charged when exposed to light When they have been exposed to the light for a certain length of time a capacitor collects the charge in sequence through a connection to an output electrode The voltage of the output electrode is electronically read and the capacitor is discharged before the next pulse is received The output electrode produces a stream of voltage pulses, each ones amplitude is proportional to the light energy

Each pixel has three small rectangular metal electrodes which are separated by a thin insulating layer of silicon dioxide which is the light sensitive material underneath The electrodes are connected to three voltage supply rails Rectangular electrodes and the insulating layer are thin enough to allow light photons to pass through and free an individual electron When collecting charge, the central electrode in each pixel is at 10V and the two outer ones are at 2V  this ensures the free electrons collect under the central electrode

After the pixels have collected charge for a certain time the charge of each pixel is shifted towards the output electrode via the neighbouring pixels. This is achieved by altering the voltage level of each electrode in a sequence of three-step cycles The quantum efficiency of a pixel is the % of incident photons that free an electron About 70% of the photons liberate an electron the quantum efficiency is about 70% Will detect much fainter images than photographic film which only has a quantum efficiency of ~4%

Advantages of a CCD Can record a sequence of fast-changing astronomical images which can be seen by the eye but not recorded on photographic film Its wavelength sensitivity is from less than 100nm to 1100nm is wider than that of the human eye ( nm). It can be used to obtain infrared images However They need to have a larger number of pixels in a smaller area so are expensive Cooled to low temps using liquid nitrogen

Radio telescopes Single-dish telescopes have a large parabolic dish with an aerial at the focal point The atmosphere transmits radio waves in the wavelength 0.001m to 10m Waves reflect from the dish onto the aerial to produce a signal- dish is turned by motors to scan sources and compensate for the Earth’s rotation Amplitude of the signal is a measure of the intensity of the radio waves

The dish is usually made of a wire mesh which is lighter than metal sheets It is just as effective in terms of reflection provided the mesh spacing is less than ~ λ 20 The dish diameter determines the collecting area and the resolving power of the telescope

Uses of radio telescopes Locating/studying strong radio sources in the sky Some galaxies are emitters of radio waves, these galaxies are usually elliptical or spherical without spiral arms. Radio galaxies are found near the centre of clusters of galaxies and their optical images often show violent events, such as the merging or collision of galaxies Mapping the Milky Way Hydrogen atoms in dust clouds emit radio waves of wavelength 21cm- emitted when the electron in a hydrogen atom flips over so its spin changed from being in the same direction as the proton’s spin to a lower energy level. Dust clouds in the spiral arm prevent us from seeing stars etc. radio waves aren’t absorbed by dust so used to map the milky way

Infrared telescopes Large concave reflector which focuses infrared radiation onto an infrared detector at the focal point Used to provide images of objects in space that can’t be seen using optical telescopes A ground-based infrared telescope has to be cooled to stop infrared radiation from its own surface swamping infrared radiation from space Water vapour in the atmosphere absorbs infrared radiation so they must be situated in a place with dry air

Infrared telescopes on a satellite in orbit are not affected by water vapour The telescope still needs to be cooled to a few degrees above absolute zero to be able to detect infrared radiation from weak sources

Ultraviolet telescopes Must be carried on satellites because UV radiation is absorbed by the atmosphere Uses mirrors to focus UV radiation to a UV detector (would be absorbed by glass) UV radiation is emitted by atoms at high temperatures- UV telescopes are used to map hot gas clouds near stars and study glowing comets, supernova and quasars Comparing a UV image of an object with an optical or infrared image gives useful information about hot spots in the object

X-ray and gamma-ray telescopes Need to be carried by satellites X-ray telescopes work by reflecting x-rays off highly-polished metal plates Gamma ray telescopes work by detecting gamma photons as they pass through a detector containing layers of pixels triggering a signal in each pixel it passes through Direction of the incident gamma photons can be determined from the signals In both, diffraction is insignificant and image resolution is determined by the pixel separation

Type Location Wavelength Resolution Advantages Disadvantages Optical Ground or satellite 350nm – 650nm 10-5 HST Detailed images, detect galaxies Suffer from atmospheric refraction (ground) Radio Ground 1mm – 10m 0.2 Lovell Pass through dust in space Large supporting structure needed Infrared 700nm – 1000nm Detects warm objects and dust clouds Mirror needs to be cooled UV Satellite 115nm – 1000nm Has to be above earth’s atmosphere X and gamma ray “Very short” 0.2 INTEGRAL

Surveying the Stars Chapter Two

Star magnitudes One light year is the distance light travels through space in 1 year it equals x 1015m One light year = speed of light x time in seconds for 1 year Light takes about years to travel across the Milky Way galaxy Galaxies are assemblies of stars prevented from moving away from each other by their gravitational attraction They are millions of light years away from each other The most distant galaxies are about ten thousand million light years from each other

Star magnitudes Can tell if a star is close because nearby stars shift against the background of more distant stars as the Earth moves This effect is called parallax – it occurs because the line of sight to a nearby star changes every 6 months due to the diametrically opposite positions of the Earth’s orbit in this time The Earth’s orbit around the Sun is used as a baseline in the calculation to find the distance to the nearby star The mean distance from the centre of the Sun to the Earth is referred to as one astronomical unit, AU x 1011m

Star magnitudes The parallax angle is defined as the angle subtended by the star to the line between the Sun and the Earth The angle is half the angular shit of the star’s line of sight over six months θ is always less than 10˚ Parallax angles are measured in arc seconds, 1 arc second = 1 degree 3600 Star distances are usually expressed for convenience in terms of the parsec (pc) 1 parsec is the distance to a star that subtends an angle of 1 arc second to the line from the centre of the Earth to the centre of the Sun

1 parsec = 3.09 x 1016m = 3.26 light years = 206265 AU
Star magnitudes For telescopes on the ground, the parallax method for measuring distances works up to about 100pc Beyond this distance the parallax angles are too small because of atmospheric refraction Telescopes on the satellites can measure parallax angles more accurately and so can measure distances to stars beyond 100pc 1 parsec = 3.09 x 1016m = 3.26 light years = AU

Star magnitudes Brightness of a star in the night sky depends on the intensity of the star’s light: light energy per second per unit area received from a star at normal incidence on the surface The intensity of sunlight at the Earth’s surface is 1400Wm-2 Intensity of light from the nearest star is a million million times less

Star magnitudes Scale of star brightness is defining five magnitudes as a hundredfold change in the intensity of light received from the star Apparent magnitude and absolute magnitude is used to distinguish between light received from a star and light emitted by the star Absolute magnitude allows a comparison between stars in terms of how much light they emit Stars such as Sirius are ‘first magnitude’ stars and have zero, or negative, apparent magnitudes

Star magnitudes m − M = 5log ( 5 10 )
Apparent magnitude, m, is a measure of the brightness which depends on the intensity of the light received from the star Absolute magnitude, M, is the star’s apparent magnitude if it was at a distance of 10 parsecs from Earth In using the inverse square law (I is proportional to 1/d2) it is assumed that radiation from the star spreads out evenly in all directions and no radiation is absorbed in space USE BASE 10 LOGS NOT BASE e!

Classifying stars When viewing stars through a telescope you’ll see their true colours rather than just white light Star emits thermal radiation which includes visible light and infrared radiation Spectrum of light emitted shows there is a continuous spread of colours which change their relative intensities as their temperature increases Thermal radiation from a hot object at constant temperature consists of a continuous range of wavelengths The distribution of intensity with wavelength changes as the temperature of the object is increased

Classifying stars Graph showing black body radiation curves
A black body is a perfect absorber of radiation and therefore emit a continuous spectrum A star is seen as a black body because any radiation incident on it would be absorbed and none would be reflected or transmitted The spectrum of thermal radiation from a star is a continuous spectrum with an intensity distribution that matches the shape of a black body radiation curve

Classifying stars Black body radiation curves are obtained by measuring the intensity of the thermal radiation from a black body at different constant temperatures Each curve has a peak which is higher and a shorter wavelength than the curves at lower temperatures They follow Wien’s law and Stefan’s law both of which were obtained by analysing the black body radiation curves

Classifying stars λmaxT = 0.0029mK Wien’s law
Wavelength at peak intensity is inversely proportional to the absolute temperature, T, of the object in accordance with the above equation If λmax is measured from its spectrum it can be used to calculate the temperature of the light-emitting outer layer: the photosphere. mK stands for metre kelvin NOT milli kelvin

Classifying stars P = σAT4 Stefan’s law
The total energy per second, P, emitted by a black body at constant temperature T is proportional to its surface area, A, and to T4 σ is the Stefan constant: it’s value is 5.67 x 10-8Wm-2K-4 P is the power output of the star: also referred to as the luminosity Two stars with the same absolute magnitude have the same power output If their surfaces temperatures are equal their radius would be the same, or the cooler star has bigger radius

Classifying stars Stellar spectral classes Spectral class
Intrinsic colour Temperature K Absorption lines O Blue He+, He, H B He, H A Blue-white H (strongest) ionised metals F White Ionised metals G Yellow-white Ionised & neutral metals K Orange Neutral metals M Red ~ Neutral atoms, TiO

Classifying stars Spectrum of light from a star contains absorption lines due to an atmosphere/corona of hot gases surrounding the star above its photosphere Atoms, ions and molecules in the hot gases absorb light photons of certain wavelengths The light that passes through the hot gases is deficient in these wavelengths Spectrum therefore contains absorption lines Wavelengths of the absorption lines are characteristic of the elements in the corona of hot gases Use this to identify elements in the star

Classifying stars The hydrogen absorption lines corresponding to excitation of hydrogen atoms from n=2 to higher energy levels Lines are referred to as the Balmer lines- they’re only in the visible spectra of O, B and A Other stars aren’t hot enough for excitation of hydrogen atoms due to collisions to the n=2 state O, B and A can absorb visible photons at certain wavelengths hence producing absorption lines in the continuous spectrum The ground state doesn’t absorb visible photons as they don’t have sufficient energy to cause excitation from n=1

Hertzsprung-Russell diagram
Dwarf star  smaller diameter than the sun Giant star  larger diameter than the sun

Main sequence diagonal belt of stars ranging from cool, low power stars of absolute magnitude +15 to hot, high power stars of absolute magnitude -5. Greater mass = higher up main sequence Giant stars emit more power than the sun, red giants are cooler than the sun supergiants brighter and larger than giant stars White dwarf hotter than the sun but emit less power. Smaller diameter than the sun

Star is formed as dust and gas clouds in space contract under their own gravitation attraction becoming denser to form a protostar GPE is transformed into thermal energy as the atoms and molecules in the clouds gain KE. Interior of collapsing matter becomes hotter and hotter Matter comes together to form the protostar, core will become hot enough for nuclear fusion to occur. Not enough matter will mean the star stars cooling once it’s stopped contracting

Energy is released as a result of the nuclear fusion of hydrogen to form helium- increases the core temperature so fusion reactions continue as long as there are sufficient light nuclei Continuing fusion reactions mean the outer layers of the protostar becomes hot and light-emitting layer (photosphere) is formed and the protostar becomes a star

A newly-formed star reaches internal equilibrium as the inward gravitation attraction is balanced by the outward radiation pressure Becomes stable with constant luminosity Absolute magnitude depends on its mass: more mass the greater its luminosity Star remains at its position on the main sequence for most of its lifetime emitting light as a result of ‘hydrogen burning’ in its core

When most of the hydrogen in the core is turned to helium the core collapses on itself and the outer layers of the star cool and expand Star swells out and moves away from its position on the main sequence to become a giant or supergiant Temperature of core increases as it collapses and causes surrounding hydrogen to form a hydrogen-burning shell which heats the core further The core temperature reaches about 108K- helium nuclei in the core undergo fusion reactions in which heavier nuclei are formed. Luminosity of the star increases and the wavelength at peak intensity increases because it becomes cooler

Red giant stage lasts a fifth of the duration of the main sequence stage 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 becomes a white dwarf A star of higher mass swells out even further to become a supergiant which explodes catastrophically as a supernova

When nuclear fusion in the core of a giant star stops, the star cools and its core contracts causing the other layers to be thrown off Thrown off as shells of hot gas and dust which form planetary nebulae around the star Happens through ionisation in the stars outer layer as the layers cool causing the layers to trap radiation energy which suddenly breaks out If mass of the red giant is between 4 and 8 solar masses the core becomes hot enough to cause energy release through further fusion Process stops when the light nuclei have been used up

After throwing off outer layers the star is not much more than its core (which is white hot due to release of gravitational energy) If mass is less than 1.4 solar masses the contraction stops as the electrons in the core can’t be forced any closer Star is not stable and has become a white dwarf which will gradually cool as it radiates its thermal energy into space

Supernovae, neutron stars and black holes
Nuclear fusion ceases when there are no longer any nuclei in the core that release energy every second when fused Happens when iron nuclei are formed- can’t be more stable If core mass exceeds 1.4 solar masses the core is forced to react with protons to form neutrons Sudden collapse makes the core increasingly dense Core becomes rigid; collapsing matter surrounding it hits and rebounds releasing a lot of energy This is a supernova; absolute magnitude of a supernova is Absolute magnitude of the sun is 4.8

Elements heavier than iron are formed by nuclear fusion in supernova explosion- occur as the shock waves travel through the layers of matter surrounding the neutron filled core Existence of elements heavier than lead tell us that the solar system formed from the remnants of a supernova: can’t be formed in the main sequence Neutrinos and gamma photons are also caused in a supernova

Characteristics of the different types of supernova Type Spectrum Light output Origin Ia No hydrogen lines; strong silicon line Decreases steadily White dwarf attracts matter and explodes Ib No hydrogen lines; strong helium line Supergiant collapses then explodes Ic No hydrogen; no helium lines II Strong hydrogen and helium lines Decreases unsteadily

A neutron star is the core of a supernova; it’s extremely small in size compared with the Sun Evidence of neutron stars comes from pulsating radio stars Pulsars have extremely strong magnetic fields: they’re rapidly rotating neutron stars that produce beams of radio waves Black hole is so dense that light can’t escape from it Supernovae core contains neutrons if its mass is >3 solar masses: neutrons can’t withstand the forces and the core collapses It is then a black hole- can’t emit photons and absorbs any photons incident on it

An event horizon is a sphere surrounding the black hole from which nothing can emerge The radius of the sphere is Schwarzschild radius, Rs Rs = 2GM c2 Black hole attracts and traps surrounding matter

Evidence for black holes Found in 1971 using a satellite mounted X-ray telescope Found an X-ray source in the same location as a supergiant 2500 parsecs away- labelled it Cyngus x-1 Intensity of the X-rays varied irregularly, indicating a source diameter of 3000km (speed of light x 0.01s) Found that supergiant and X-ray source were orbiting each other in a binary system Mass of X-ray source estimated at ~7 solar masses- this is above the upper limit of 3 solar masses for a neutron star

Supermassive black holes are thought to exist at the centre of many galaxies- can pull millions and millions of stars in Can therefore gain enormous quantities of matter and are referred to as supermassive black holes Images using infrared radiation and radio waves from the centre of the Milky Way indicate stars are orbiting the galactic centre at 1500km/s about 2 parsecs from the centre- indicates a supermassive black hole of mass equal to about 2.6 million solar masses

Cosmology Chapter Three

The Doppler effect The Doppler effect is the change in frequency of wavelength due to the relative movement of an object (distance from the observer) Waves emitted in the opposite direction to the motion of the source are spaced out The observer would detect waves of longer wavelengths and lower frequency. For light this is a RED SHIFT Waves emitted in the same direction to the motion of the source are bunched together The observer would detect waves of shorter wavelengths and higher frequency. For light this is a BLUE SHIFT

The Doppler effect Red shifts and blue shifts are fractional changes in frequency or wavelength v is the radial speed relative to the observer c is the speed of light in a vacuum Doppler shift, z Moves towards the observer Moves away from the observer In frequency ∆f f + v c - v c In wavelength ∆λ λ

The Doppler effect By measuring the shift in wavelength of a star’s line spectrum, the speed of the star relative to the earth can be found The line spectrum of the star is compared with the pattern of the prominent lines in the spectrum according to the star’s spectral class The change in one or more of the lines of known wavelength in the spectral class is then measured and the Doppler shift can be calculated The speed of the star relative to a line can then be calculated from v=zc

The Doppler effect The star is moving toward the earth if the wavelength is shortened due to the star’s relative motion The star is moving away from the earth is the wavelength is lengthened due to the star’s relative motion For binary stars in orbit about each other in the plane as the line from the Earth to the stars, the wavelength of each spectral line of each star changes periodically between: A minimum value of λ – Δλ when the star is moving towards the earth A maximum value of λ+ Δλ when the star is moving away from the earth

The Doppler effect If two stars can’t be resolved they’re called a spectroscopic binary Each spectral line splits into two after the stars cross the line of sight then merge into a single line as they move towards the line of sight If the stars are of different masses they’ll move with the same period but different speeds and orbital radii The change of wavelength will be greater for the faster star (less massive star)

Hubble’s law and beyond
H = v d Hubble’s law and beyond Andromeda is the nearest large galaxy to the Milky Way Hubble studies galaxies which were close enough to resolved into individual stars For each galaxy he measured: - It’s red shift and the speed of recession - It’s distance from Earth by observing the period of Cepheid variables in the galaxy Results showed that galaxies are receding from us- all moving at speed, v, which is directly proportional to distance, d Accepted value of ‘H’ is: 1Mpc  65kms-1Mpc-1

The galaxies close to the Milky Way, like Andromeda, don’t fit Hubble’s law because their gravitational interactions have affected their direction of motion

The Big Bang theory believes that the Universe was created in a massive primordial explosion and has been expanding since Other astronomers support the Steady State theory; this believes that the Universe is unchanging and is the same size now as it was before The Steady State theory explains the expansion of the Universe by saying matter entering the Universe at ‘white holes’ pushes the galaxies apart as it enters Steady State theory couldn’t explain the existence of microwave radiation but the Big Bang theory could

T = 1 H Hubble’s law and beyond No material object can travel as fast as light- even a galaxy whose speed increases with distance d The Hubble constant shows that the speed of a galaxy increases by 65kms-1 for every extra million parsecs of distance To reach the speed of light a galaxy would be almost at a distance of (30000/65) x 3.26 million light years To reach this, light would need to travel for million years Therefore the Universe can’t be older than million years old, age of Universe, T

Evidence for the Big Bang The spectrum of microwave radiation from space matched the theoretical spectrum of thermal radiation from an object at 2.7K This radiation was detected from all direction in space with little variation in intensity: must be universal in origin Background cosmic radiation was created in the Big Bang and has been travelling through the Universe since As the Universe expanded after the Big Bang its mean temperature decreased and is now ~2.7K

Stars and galaxies contain about three times as much hydrogen by mass as helium Other elements are present in negligible proportion When the Universe cooled sufficiently to allow quarks in threes to form baryons, protons formed from the quarks more readily than neutrons This is because the ratio 3:1 of hydrogen to helium gives a ratio of 14:2 proton to neutron ratio

Astronomers discovered that supernovae must be accelerating by studying those of type Ia Concluded that the expansion of the Universe is accelerating Believe this is down to an unknown type of force releasing hidden energy called dark energy Evidence for accelerated expansion is based on differing distance measurements to type Ia supernova by different methods (next slide)

The red shift method: using Hubble’s law to get the distance to each one The luminosity method: Type Ia supernova at peak intensity are 109 times more luminous than the sun- absolute magnitude of about -18. Distance to each supernova can be calculated from its absolute magnitude M, and its apparent magnitude m, using the formula m – M = 5log(d/10) Two methods give results that are different and indicate that the distant type Ia supernova are dimmer and further away than their red shift indicates

Dark energy is thought to be a form background energy present throughout space and time It’s more prominent than gravity at very large distances because it stays constant with distance unlike gravity that becomes weaker Thought to make up around 70% of the total energy of the Universe

Quasars A quasar is characterised by:
Very powerful light output, much greater than that of a star Relatively small size, not much larger than a star Large red shift indicating its distance is between 5000 and light years away Some produce strong radio emissions, but this is not always the case They’re shown through pictures to be fast moving clouds of gases and jets matter being ejected Found in or near galaxies that are often distorted

Physics Unit 5A: Astrophysics

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