Astrophysics Repaired)

8/8/2019 Astrophysics Repaired)

1/55

HSC Physics Option Module: Astrophysics

Summary

Robert Lee Chin Page | 1

1. Earth-based observations Discuss Galileos use of the telescope to identify features of the Moon

Galilei Galileo did not invent the telescope, but he improved its design. He built refracting

(lens) telescopes, which formed upright images and also covered the edges of his telescope toreduce spherical aberration and form clearer images.

Galileo identified and gather evidence on:

-the moons of Jupiter

-the phases of Venus

-sunspots on the sun,

-many new stars

-the rings of Saturn

-features of the moon

In particular, he was able to make qualitative and quantitative observations of geographicalfeatures of the moon. This included mountains, craters and lava flows which he called seas.

This provided evidence against the (then) popular view that all heavenly objects were perfect

and unchanging.

Discuss why some wavebands can be more easily detected from space

Almost all information from space comes in the form of EMR. The EMR spectrum is divided

into wavebands. Each particular waveband covers a specific range of wavelengths in the

EM spectrum. The Earths atmosphere absorbs, diffracts and scatters some wavebands more

than others.

The high energy gamma and x-rays ionise molecules and are therefore strongly absorbed by

the upper atmosphere. Most UV radiation is absorbed by the ozone layer while some

penetrates to the ground. Water vapour and gases in the atmosphere reflect most of the

infrared radiation. Visible light and most radio waves are able to fully penetrate to the ground

This limits ground-based astronomy to the visible and radio wavebands. In order to study the

other EMR effectively, one must go above the atmosphere. Infrared radiation can be studied

by placing infrared telescopes on mountaintops above the densest regions of the atmosphere.


2/55


Summary


Absorption of EMR wavebands by the Atmosphere:

Define the terms resolution and sensitivity of telescopes

Resolution

Resolution aka resolving power is a measure of a telescopes ability to clearly distinguishbetween two very close objects in space. When this occurs, the objects are said to be resolved.

0

10

20

40

70

80

90

30

MicrowaveUVGamma

Ozone layer

X-rays

100

Visibl

e RadioInfrared

50

60

Altitude (km)

Wavelength

Ionosphere

Mesosphere


3/55


Summary


Telescope resolution is limited by:

-imperfections in the lens/mirror

-diffraction i.e. bending of light around objects or through gaps

Resolution is quantitatively defined by the angle of separation between two light wavefrontse.g. a binary star. It is measured in radians or arcs seconds. The resolving power of a

telescope is given by. The smaller the angle of resolution, the greater the resolving power.

Hence, a smaller wavelength and larger diameter size improve resolution.

Sensitivity

Sensitivity is a measure of the light gathering power of a telescope i.e. its ability to clearly

detect photons from sources in space- the more light that can be detected, the fainter the

object that can be seen. The sensitivity of a telescope is the minimum intensity of light that

needs to be detected to form a suitable image. Quantitatively, sensitivity is proportional to the

surface area of the aperture. Telescopes with large apertures are nicknamed light buckets

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

Atmospheric Distortion

Ground-based telescopes view space from beneath the dynamic mixture of gases, dust and

water vapour of the atmosphere. Variations in temperature and pressure with altitude cause

corresponding changes in the refractive index, causing stars to twinkle. Or more correctly,

the object shimmers in and out of focus, lowering the resolution of the telescope. The true

colour of images is altered due to variations in absorption with wavelength. Objects lower in

the sky are even more susceptible because the light has to travel through more atmosphere to

reach the ground. The atmosphere also scatters unwanted light from nearby cities and vehiclesinto the telescope.

Absorption of radiation

Gamma rays, x-rays, UV, some infrared and the longer wavelength radio waves are absorbed

and scattered by the atmosphere. This means the intensity of these EMR reaching the ground

is very low, so ground-based astronomy is very difficult. Furthermore, much light from the

violet end of the visible waveband is scattered (making the sky blue) so optical astronomy is

impossible during daytime.

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

Two light sources that have been

resolved have separate diffraction

Two light sources with overlapping

diffraction fringes cannot be resolved


4/55


Summary


-adaptive optics

-interferometry

-Active optics

The easiest approach to reduce atmospheric distortion is to place the telescope as high in the

atmosphere as possible. This means placing telescopes on very high mountaintops, above thedensest regions of the atmosphere. Another advantage is the remoteness means there are no

unwanted light sources from human activity.

Active Optics

Active optics aims to increase sensitivity by compensating for imperfections in the telescope

mirror. Sensitivity is proportional to the surface area of the mirror; however, larger mirrors

are more susceptible to distortion and the thicker it needs to be. Active optics uses many

small composite mirrors, each controlled by its own actuator which pushes or pulls on the

back of the mirror to actively adjusting its shape accordingly. The mirrors are adjusted about

once a minute.

One of the best examples is the Keck observatory, at the top of an extinct Hawaiian Volcano,

Mauna Kea. It comprises of 36 hexagonal mirrors to give the same sensitivity as a 10m

diameter mirror.

Adaptive O

Adaptive optics aims to increase resolution

by measuring and compensating for atmospheric

distortion. Similar to active optics, adaptive optics

uses actuator-controlled composite mirrors but has much faster

response speed. It involves sampling part of the incident light using a wavefront

sensor to measure the amount of atmospheric distortion. The system relies on a bright

reference star or artificial laser pulse to detect this distortion. The mirrors are adjusted using

actuators, up to 1000 times per second, effectively neutralising atmospheric changes.

The Keck

Observatory

telescope mirror


5/55


Summary


Interferometry

Resolution depends on the diameter of the

aperture. Interferometry uses the principle of

several small telescopes linked in an array to

give a higherresolution

. The device

used is called

an

interfero

meter and is most

commonl

y used in radio telescopes because they can be linked over

great distances.

Radio interferometry works by combining the same radio sources (which are slightly out of

phase due to time differences) electronically, so that they interfere by superposition.

Radio telescopes in different continents (and even satellites) can be linked to from a very long

baseline (up to 3 times the Earths diameter). This technique is called very large baseline

interferometry (VLBI) and it used to produce extremely high resolutions.

Optical interferometry aims to produce a brighter image by using constructive interference of

the incoming wavefronts. It is mainly used for determining stellar distances and diameters.

Gather, process and present information on the next generation optical telescopes

The next generation telescopes are designed to have lighter, larger mirrors than before. This

allows astronomers to view fainter objects with higher resolution and ensures stability in the

mirrors.

Spin casting and rotating mercury

The shape of the mirror constantly changes to

keep the rays of light at one focal point Diameter x

Resolution of two mirrors in interferometer

mode separated by x is equal to a single

mirror with diameter x


6/55


Summary


Lighter mirrors can be made by spinning the glass into a hyperbolic shape as it cools.

A new generation of parabolic mirrors uses rotating liquid mercury and gallium alloys. The

layer is only 2mm thick and they are low cost compared to conventional mirrors. They are

restricted to facing only directly upwards and objects cannot be tracked.

Thin and replica mirrors

A recent development in mirrors is the production of 1mm thick mirrors made from curved

sheet-glass attached to a honeycomb backing structure. A prototype has already been

fabricated for the HSTs successor, the James Webb Space telescope, expected to be launched

in 2014.

Another technique involves replicating pre-existing mirrors by applying a graphite reinforced

honeycomb composite (GRHC). When the GRHC cures, it is used as a template for new

mirrors.

Extremely large telescopes: The Giant Magellan telescope (GMT), Thirty Meter

Telescope (TMT) and European-Extremely large telescope (E-ELT)

The largest, the E-ELT has a diameter of 42 metres and is predicted to be 15 times more

sensitive than the current largest 10 metre Keck telescopes. The TMT has a 30 metre diameter

and the GMT has a 24.5 metre mirror. They are expected to be completed by 2020.

All rely on adaptive optics to make their resolution as powerful as any space based

observatories.

Identify data sources, plan, choose equipment or resources for, and perform aninvestigation to demonstrate why it is desirable for telescopes to have a larger

diameter objective lens or mirror in terms of both sensitivity and resolution

Investigation: Aperture size and its effect on sensitivity and resolution

Aim: To demonstrate why it is desirable for telescopes to have large diameter aperture in

terms of sensitivity and resolution

Resolution

The following table summarises data on a range of telescopesTelescope Primary mirror

diameter (m)

SA primary

mirror (m2)

Theoretical

resolution

(arcseconds)

Theoretical

gain in

magnitudes

Human eye 0.007 0.001 17 0

6 inch refractor 0.15 0.02 0.8 7

Faulkes

Telescope

2.0 3 0.06 12

Anglo-Australi

an telescope

3.9 12 0.03 14

Keck telescope 10 79 0.01 16


7/55


Summary


Note: The gain in magnitudes is related to the sensitivity. A more sensitive telescope can

detect objects many magnitudes fainter than the human eye.

Describe the relationship between sensitivity and mirror diameter.

As mirror diameter increases, the sensitivity increases.

Plot the theoretical gain in magnitude against SA primary mirror and describe the

relationship

As the SA increases, the gain in magnitude (i.e. the sensitivity) increases.

Plot the theoretical resolution vs. Aperture diameter and describe the relationship


8/55


Summary


It is observed that as the mirror diameter increases, the angle of theoretical resolution

decreases i.e. as diameter increases, resolution increases.

2. Parallax

Define the terms parallax, parsec, light-year

Parallax is the change in apparent position of a nearby object viewed along two different lines

of sight. Quantitatively, it is measured as the angle between the two lines. Trigonometric

parallax is half the annual parallax.

A parsec is an astronomical unit of distance. It is defined as the distance away a star would

need to be in order for its annual parallax to be 1 degree. In terms of annual parallax, a parsec

is the distance at which the radius of Earths orbit subtends and angle of 1 degree.

Definition of a parsec:

Viewpoint A

Viewpoint B

Viewpoint BViewpoint A


9/55


Summary


A light year is an astronomical unit of distance. It is defined as the straight line distance light

travels in a vacuum in 1 year. .

Converting AU to parsecs

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

Trigonometric parallax is half the angular shift of a star (in arc seconds) as observed from

Earth over a period of 6 months i.e. half the annual parallax. Because even our closest stars

are so distant, a considerable change in the observers position is required to notice any

change in the stars relative position. By observing parallax in 6 month intervals (from

opposite points of the Earth), the change in the observers position becomes twice

Earth-to-Sun distance or 2 Astronomical Units (AU). Observing 6 months apart maximises

the parallax angle by maximising the baseline and neutralises the slight eccentricity of Earthsorbit

1 AU

1 arc second

1 parsec


10/55


Summary


Using trigonometry,, dis the unknown distance from the Sun to the Star andp is the

trigonometric parallax angle. Therefore dcan be calculated by .

Solve problems and analyse information to calculate the distance to a star given itstrigonometric parallax using:

Using the above example, when the parallax of the star (p) is 1 arc second, then the distance d

in parsecs is given by . Remember:

Examples:

1) The star 40-Eridini is 5 pc away. Calculate its parallax in:

a) Arc seconds.

b) Degrees

c) A star has a parallax of 0.3 arc seconds. Calculate its distance from the Earth

in:

a) parsecs

d

2 AUp

= Sun

= Earth

= nearby star

= distant star


11/55


Summary


b) light years

Discuss the limitations of trigonometric parallax measurements

The seeing or shimmering effect of Earths atmosphere limits the precision of parallax

measurements. The smallest parallax that can be observed from Earth is 0.01 arc seconds.

This means only about 700 of the closest stars (within 100 pc) can be measured by

Earth-based telescopes. The limitations can be lessened by using space-based telescopes

above the atmosphere or by using a larger baseline for the annual parallax e.g. placing a

satellite in orbit around the sun at a distance from Earths orbit.

Gather and process information todetermine the relative limits to trigonometric parallax distance determinations using

recent ground-based and space-based technologies

Resolution of ground-based telescopes is currently limited to 0.01 arcseconds (100 pcs), due

to atmospheric distortion. Only about 1000 stars within 20 parsecs can be accurately

measured.

Space based telescopes do not suffer atmospheric distortion, so parallax measurements are

determined by the quality and size of the aperture. In 1989, the European Space Agency

(ESA) launched the Hipparcos satellite, which has catalogued accurate parallax

measurements down to 1 milli-arcsecond (mas) for distance measurements of 120 000 stars

out to about 1000 pcs.

Future space telescopes include Gaia and the Space Interferometry Mission (SIM). GAIA has

an accuracy of 10 micro arcseconds (10-5 arcsec) and will catalogue over 1 billion stars

within distances of 100 000 pcs while SIM will use optical interferometry to give parallax of

4 micro arcseconds within 10% accuracy of distances up to 25 000 pcs. The data collected

will allow for a dynamic 3D map of the Milky Way.

Using a satellite to give a

larger baseline


12/55


Summary


3. Spectroscopy

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

Emission Spectra

Emission spectra of a chemical element/compound consist only of radiation of a discrete

number of wavelengths. It appears as bright lines against a dark background. This radiation is

produced by hot diffuse gases, such as in a gas discharge tube.

Electrical/heat energy supplied to the atoms/molecules raises the energy level of the electrons.

As the electrons fall back down to their ground state, they emit a quantum of energy which

corresponds to one of the observed wavelengths. The bright lines of emission spectra

correspond to all of the possible energy transitions. The relative intensity of each line depends

on the composition of the gas.

Emission Spectra for Hydrogen:

Absorption Spectra

Absorption Spectra

consist of a

continuous range of

wavelengths, with

discrete gaps at particular wavelengths. It appears as dark lines on a continuous background

of colours. It is produced when a continuous spectrum of light passes through cool gas e.g. in

the Sun, the dark lines result from specific wavelengths being absorbed by cooler gases in the

outer layers.

Atoms/molecules in the gas absorb quantum of energy which corresponds to specific

wavelengths of light. This causes the energy level of the electrons to jump before falling

back to ground state, remitting absorbed wavelengths in all directions. Thus, the intensity of

light transmitted at these wavelengths is reduced. The relative intensity of the lines depends

on the size and density of the gas cloud.

Hot gasSpectrograph

Wavelength (nm)

Each element has its own unique emission spectra


13/55


Summary


Absorption spectra for hydrogen:

Continuous Blackbody Spectrum

Blackbody spectrum consists of a continuous range of wavelengths with no lines. It appears

as a continuous rainbow of colours. It is produced by thermal emission of hot substances

e.g. the surface of the Sun acts as a blackbody at high temperatures.

The higher the temperature, the shorter wavelength of peak intensity emission i.e. the

maximum intensity is inversely proportional to the temperature of the hot surface. This is

shown by: where, is the wavelength (nm) and T is the temperature (K). This

is also why hotter stars appear blue and cooler stars red.

Spectrograph

Cool

gas

Wavelength (nm)

Wavelength (nm)


14/55


Summary


Emission Spectra Absorption Spectra

Continuous Blackbody

Spectrum

Consists of radiation of only

a discrete wavelengths

Consists of a continuous

range of wavelengths, with

gaps corresponding to

discrete wavelengths

Consists of a continuous

range of wavelengths, with

no gaps

Appears as white linesagainst a dark background

Appears as dark lines againsta continuous background of

colours

Appears as a continuousrange of colours

Produced by hot diffuse

gases

Produced when light from a

hot source passes through

cool gas

Produced by thermal

emission from. solids, liquids

& high-pressure gases

Wavelengths emitted depend

on electron energy

transitions of gas atoms

Wavelengths absorbed

depend on electron energy

transitions of gas atoms

All wavelengths produced at

varying intensities

Intensity varies with

wavelength, depending ongas composition

Intensity varies with

wavelength, depending ongas composition and density

Intensity varies smoothly

with wavelength. The peakemission is inversely

proportional to the

temperature

Describe the technology needed to measure astronomical spectra

A spectroscope is a device used to visually observe spectra. A spectrograph is a device

mounted onto a telescope used to record and measure spectra and the recorded photograph is

called a spectrogram.

A spectrograph or spectroscope consists of three parts:

Intensity of

radiation

emitted

Wavelength (nm)

30001000 2000IRUV

Visible

4000 K

5000 K

3000 K


15/55


Summary


The collimator uses a narrow slit and mirrors or lenses to form a parallel beam of light from a

light source.

The second part disperses the light into its component wavelengths to produce the spectra. It

consists of wither a triangular prism or a diffraction grating which can be further subdividedinto transmission or reflection gratings. Diffraction gratings consist of thousands of parallel

slits per cm which cause the light to spread out into a spectrum. Most modern spectroscopes

use diffraction gratings because they scatter less light and give better resolving power than

prisms.

The third part allows the spectra to be viewed or recorded. It consists of either a telescope, a

focusing mirror with a photographic plate or an electronic image device such as a charged

couple device (CCD). Fibre optics may be used to simultaneously obtain multiple spectra.

Prism spectroscope:

Transmissi

on grating:

Reflection grating:

Identify the general types of spectra produced by stars, emission nebulas, galaxiesand quasars

Stars

Stars act as blackbodies and therefore produce spectra that depend on their surfacetemperature according to Planks Blackbody radiation. Absorption spectra are produced as the

result of the radiation passing through the stars cooler atmosphere.

Emission nebulas

Emission nebulae are regions of hot gas (mainly hydrogen) and dust that become heated by

radiation from nearby hot stars. As the electrons in the nebulae drop back to their lower

energy level, they produce emission spectra in the UV, visible, infrared and radio bands

(depending on the nebula composition).

Galaxies

Galaxies consist of up to billions of stars, nebula and planets all circling a common centre.Therefore, the spectra for galaxies combine the spectra of all these celestial objects. They

Collimator

Viewing

slit

Focussing


16/55


Summary


emit light from the entire EM spectrum, particularly infrared and radio. Absorption lines of B

and K type stars are common, along with emission lines for hydrogen, nitrogen, carbon and

silicon. Almost all galaxies are moving radially away from the Milky Way, so the spectra are

red-shifted.

QuasarsQuasars are distant point sources producing vast amount of radiation across the entire EM

spectrum, but mostly in the radio band. The spectra consist of broad, high-intensity emission

lines that are extremely red-shifted. There are only 1-2 LY across and are believed to be

formed by gas being swallowed up by black holes,

Describe the key features of stellar spectra and describe how this is used to classifystars

A stellar spectrum is the spectrum of radiation emitted by a star. Stellar spectra consist of a

black body spectra superimposed with absorption lines characteristic of the elements in thestars atmosphere.

The shape of the curve, particularly the position of the peak emission wavelength and the

absorption lines for specific elements indicates the surface temperature.

To produce lines for hydrogen, the temperature must be in the range of 4000-12000K while

helium must be in the 15000-30000K range. Too low temperatures and the electrons will

produce faint absorption lines, too high and the atoms will be completely ionised, again

resulting in no absorption lines.

When different stars are compared, there is a change in colour as luminosity increases. Thecoolest stars are red, then orange, yellow, white and blue for the hottest stars.

Stars can thus be classified into spectral class: O, B, A, F, G, K, M (mnemonic: Oh Be A Fine

Girl Kiss Me) from hottest to coolest. There are 10 further subdivisions from hottest to

coolest: A0-A9.

Spectral Class Colour Surface

Temperature

Absorption line Spectral Features

O Blue


17/55


Summary


F White-yellow 10 000-7000 K Weakly neutral H

Stronger neutral Mg, Si, Fe, Ca, Ti

G Yellow 7000-5000 K Strong metals esp. Ca

Weak H

Many single lines ionised and neutralmetals

K Orange 5000-4000 K Strong metals

Molecules e.g. CH, CN

Almost nonexistent H

M Red 4000-3000 K Strong molecules esp. TiO

Spectral Class Example Star

O5 Naos

B3 Achermar

A7 Altair

F0 Canopus

G5 Capella

K2 Arcturas

M1 Autares

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

Surface Temperature

The surface temperature can be determined by observing the position of the peak wavelength

emission. According to Wiens Displacement law, where

peak wavelength is inversely proportional to the surface temperature. Therefore stars that are

blue are hotter than stars that are red.

Translational Velocity (relative motion)

The proper velocity of a star relative to the sun is made of two components: the radialvelocity and the translational velocity. The radial velocity is a measure of whether the star is

moving towards us or away and how fast it is moving. Translational velocity is a measure of

the motion of a star across our line of sight.

The radial velocity obtained by observing the Doppler shift of a star, compared to

laboratory-measured spectra. If a star is moving towards us, the wavelengths will contract and

there will be a blue-shift. Conversely, if a star is moving away the wavelengths will stretch

out and there will be red-shift. A red-shift indicates the star is moving away while a

blue-shift indicates a star is moving towards us. The faster the radial velocity, the greater the

Doppler shift.


18/55


Summary


The translational velocity is measured by determining the change in position of the star over

long time periods. The distance of a star obtained from parallax measurements is used to

determine the translational velocity.

Velocity components of a star:

Rotational velocity

If a star is rotating,

then one edge is moving

towards us while the other

is receding. One edge will

therefore be red-shifted and

the other side will be

blue-shifted by the same amount. The centre will not exhibit Doppler shift. Individual

spectral lines are broadened by an amount dependant on the rotational velocity of the star- the

faster it rotates, the more the lines broaden.

In the case of binarystars, the rotational

velocity around their

centre of mass can be determined using the Doppler Effect. The two stars periodically

approach and recede; hence the spectral lines will be alternately blue-sifted and red-shifted.

From this, the speed of approach and recession can be calculated, which is then used to

determine orbital periods and rotational velocities.

Density

The surface density and therefore surface pressure of a star broadens the spectra lines.

Increased gas pressure produces more rapid collisions between atoms during emission orabsorption of radiation. These collisions result in electrons shifting energy levels, hence

Proper Velocity

Translational

Velocity

Distant

Star

Radial Velocity

Proper

motion

Sun

Increasing wavelength (nm)

Laboratory measured

Red shift spectra

Blue shift spectra

Non-rotating spectra

Increasing wavelength (nm)

No Doppler

Blue-shift

Red-shift

Star Earth

Combined blue and red shift broaden the spectral lines


19/55


Summary


producing broader spectral lines. Dwarf stars with high density produce the broadest spectral

lines whilst super giants produce narrow spectral lines.

Chemical Composition

Each element, ion or molecule has its own characteristic emission lines which represent the

various electron energy levels. These lines are in the same position in a stars absorptionspectrum. Comparing a stars absorption lines with the emission lines for known elements

allows the stars composition to be determined.

Perform a first-hand investigation to examine a variety of spectra produced bydischarge tubes, reflected sunlight or incandescent filaments

Investigation: Using a CD as a Spectroscope

Aim: To observe and examine a variety of spectra produced by discharge tubes, reflectedsunlight or incandescent filaments.

Equipment:

For the spectroscope:

-a silvered CD

-cardboard box

-cardboard tube

-craft knife

-aluminium foil

-sticky tape

-digital camera

-computer, for analysing spectra images

Method:

1/ At night stand 20m from the light source and holding the CD 40cm in front of your

chest look at the reflection of the light on the silvered side of the CD. The bright and

dark lines or regions are emission and absorption lines respectively.

2/ Take a picture of the reflection for later analysis and comparison

Results:

Light source Spectra Features

Tungsten filament light

bulb (argon gas)

argon

Light sources:

-tungsten filament light bulb

-Neon light sign

-Yellow-orange street light (sodium vapour lamp)

-Mercury vapour lamp

-Halogen car light


20/55


Summary


Neon light sign

Sodium vapour lamp Strong peaks in yellow,

Mercury vapour lamp Strong peaks in yellow,

orange, yellow-green

Halogen car light (xenon

gas)

xenon

Conclusion:

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

Examples:

1) The graph shows blackbody radiation curves for three temperatures:

Energy radiated (K) vs. (nm)


21/55


Summary


a) Define a black body

A black body is an object that is emits or absorbs radiation perfectly i.e. it emits or absorbs

radiation across the entire EM spectrum, at varying intensities.

b) Explain the relevance to astrophysics of black body radiation

The black body radiation curve can be used to determine the surface temperature of stars.

c) Explain how Wiens law is used to determine the temperature and composition

of a star

Wiens law states that the peak wavelength emission of a blackbody is inversely proportional

to its surface temperature i.e. Rearranging, It can be used to predict the surface temperature

of a star:. From the surface temperature and the colour of the star, the stars

chemical composition and spectral class can be predicted.

4. Determining distance using photometric measurements

Luminosity is the measure of the power emitted by a star and depends upon the size (radius)

and surface temperature of the star. Given the same temperature, large stars are more

luminous than small stars and given the same radius, hotter stars are more luminous than

cooler stars.


22/55


Summary


Brightness (I) of a star is a measure of the intensity of radiation reaching Earth from a star.. It

depends on the intrinsic luminosity (L) of the star and its distance (d) away.

Mathematically:

Define absolute and apparent magnitude

Apparent magnitude (m) is the brightness of a star as observed from Earth. Brighter stars have

lower magnitude and an increase in 1 represents a decrease in apparent brightness of 2.512.

Absolute magnitude (M) is the brightness a star would have when observed from a distance

of 10 parsecs. Absolute and apparent magnitude use the same scale, therefore, more negative

number correspond to higher luminosity. It is estimated by comparison with reference stars of

the same spectral class and known distance (from parallax).

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

If a star is closer than 10 pc, m is larger than M and if it is further than 10 pc., the reverse is

true. The amount by which the absolute magnitude (M) and apparent magnitude (m) differ

depends on the star. If both m and M are known, the difference modulus can be used to

calculate the distance to a star:

For stars closer than 10 pc, the distance modulus is negative, while for stars further than 10

pc, it is positive.

Solve problems and analyse information using and

to calculate the absolute or apparent magnitude of stars using data and a reference

star

Examples:

1) Our Sun has an apparent visual magnitude of -26.5 and an absolute visualmagnitude of +4.83. Explain why these magnitudes are different

Apparent magnitude is a measure of the intensity as viewed from Earth whereas absolute

magnitude is a measure of the intensity when viewed at a distance of 10 parsecs. The more

negative the value for absolute or apparent magnitude the more negative the value. Therefore,

because we are closer to the Sun than 10 pc, the apparent visual magnitude of the Sun is

negative while its absolute magnitude is positive i.e.

2) A star of the sixth magnitude is located 40pc from the Sun. Calculate its absolute

magnitude


23/55


Summary


A star has an apparent magnitude of +8 and an absolute magnitude of 0. Calculate the

parallax of them star.

3) Use the table to answer the following questions

Star Apparent magnitude (m) Absolute magnitude (M)

Arcturus 0.00 -0.3

Betelgeuse +0.41 -5.6

Hadar +0.63 -5.2

Sirius -1.51 +1.4

Vega +0.04 +0.5

a) Identify which star is the brightest to an observer on the Earth. Explain your

answer.

For an observer on Earth, we use the apparent magnitude. The more negative the value, the

brighter the star appears. Therefore, the brightest star to an Earth observer is Sirius, with

m=-1.51


24/55


Summary


b) Calculate the distance to Vega

c) Calculate how much brighter Betelgeuse appears than Hadar

d) Calculate how much brighter Betelgeuse actually is compared to Hadar.

Outline spectroscopic parallax

Stereoscopic parallax is a technique used to determine the distance to a star by comparing the

absolute and apparent magnitude. The term parallax is simply an analogy for distance.

A stars spectrum indicates its spectral class or temperature, which are located on the

horizontal axis of a Hertzprung-Russel diagram and its luminosity, located on the vertical

axis. By finding the position where the lines intercept, the absolute magnitude (on verticalaxis) can be determined. The apparent magnitude can be directly-measured using photometry.


25/55


Summary


The distance modulus equation can then be used to determine the distance in pc. This method

is not precise, but is useful as an estimation of distances to stars.

Explain how two-colour values (i.e. colour index, B-V) are obtained and why theyare useful

Colour index values are useful because they allow the surface temperature of starts to be

determined without spectra.

Stars may have 3 different magnitudes depending on the instruments used to view them: the

human eye, a photographic emulsion (light-sensitive colloid) or a photocell. The eye is most

sensitive to yellow-green light; photographic emulsions are most sensitive to blue-violet light;

photocells perform well at all wavelengths. Hence, a blue star would appear brighter on a

photograph than to the eye.

Blue or photographic magnitude (B) is the magnitude of a star measured through a blue filter

so it only allows wavelengths of ~440 nm to pass through. The visual magnitude (V) is

measured through a yellow-green filter which allows wavelengths of 550 nm to pass

through.

The colour index is the difference between the photographic and visual magnitude i.e. . It

follows that if is positive (, then the star will be redder and therefore, cooler. If is negative (,

then the star will be bluer and therefore, hotter.

Colour Index: Relative size of

magnitudes

Relative Colour Relative

temperature

Relative

Spectral Class

More positive redder Cooler Towards O

More negative bluer Hotter Towards M


26/55


Summary


In the above graph, the star emits more energy in the B waveband than the V waveband.

The colour index is calibrated so that a (white) main sequence star (spectral class A,

luminosity class V) has a CI of 0.00. The CI for hotter stars will be negative CI while forcooler stars it will be positive.

Describe the advantages of photoelectric technologies over photographic methodsfor photometry

Photographic photometry

Photographic photometry uses visual comparison of star images on photographic plates.

Brighter stars appear larger and denser on the plate and it is possible to obtain photometry for

thousands of stars using a single image, using a laser to scan and produce a digitised image. It

B intensity

(440 nm)V intensity

(550 nm)


27/55


Summary


does not calibrate stars accurately; however, it provides higher resolution than photoelectric

devices.

Photoelectric photometry

Photoelectric devices include: photomultiplier and charged-coupled device (CCD).

A photomultiplier (vacuum tube technology) converts weak light into stronger electrical

current. It consists of an evacuated tube, with a thin glass window that allows photons to enter

and hit a photo-cathode. Electrons are emitted in proportion to the light intensity (termed

secondary emission) and a series of 9-14 electrodes (dynodes), of increasing voltage are

used to accelerate the electrons. Secondary emission creates an increasing the number of

photoelectrons and hence, a larger measurable current.

Photomultiplier:

A CCD (solid-state technology) uses an array of millions of light-sensitive pixels on a

silicon chip to measure current. The pixels act as capacitors, storing charge proportional to

the light intensity. The accumulated charge in each capacitor can be rapidly scanned and

analysed via computer.

Advantages of photoelectric over photographic technologies

-Objects can be scanned extremely quickly with quick response time (due to electronic

detectors

-More uniform response across the entire visible spectrum

-Sensitive to a wider range of wavelengths esp. infrared and can be altered to increase

sensitivity for different wavelengths

-Give more accurate measurements of magnitude

-Data can be collected remotely and transmitted digitally

-Data is processed more easily

+100+200 V

+300 V

+400 V+500 V

+600 V

+700 V

Thinwindow Photo-cathode

Anode to

measuring

device

Incoming

photon


28/55


29/55


Summary


e) Predict the likely spectral class for Betelgeuse. Explain.

The colour index for Betelgeuse is positive, meaning that it emits more energy towards the

red end of the visible spectrum than the blue end. Red stars are cooler than blue stars; hence

it is a cool red star. Betelgeuse is most likely to be M-type, A1 spectral class.

2) A star is observed to have an apparent magnitude of 6.0 and is 20 parsecs from

Earth. Calculate its absolute magnitude.

3) Use the table below to answer the following questions

Star Apparent visual

magnitude

Absolute visual

magnitude

Spectral Class

Acturus 0.00 -0.3 K2

Betelgeuse +0.41 -5.6 M2

Hadar +0.63 -5.2 B1

Sirius -1.51 +1.4 A1

Vega +0.04 +0.5 A0

a) Predict which star is hottest. Explain.

Stars with a spectral towards O are hotter. The spectral classes, in order of temperature are O,

B, A, G, K, M. Therefore, Hadar is the hottest star.

b) Predict the colour of Arturus. Explain.

Artucus is spectral class K2, which corresponds to a relatively cool star which emits the

orange waveband of the visible spectrum most intensely.

c) Predict which star is the faintest when viewed from Earth. Explain.


30/55


Summary


Viewed from Earth refers to the apparent visual magnitude. More positive values for

magnitude correspond to fainter stars. Thus, Hadar is the faintest star when viewed from

Earth.

d) Calculate the distance to Hadar.

Perform an investigation to demonstrate the use of filters for photometricmeasurements.

Aim: To observe the effect of various coloured filters on the brightness of a light source

Equipment:

-Red, Blue and yellow-coloured filters-data logger with light intensity probe attachment

Method:

1/ Place light meter on flat table in a well-lit room (fluorescent lighting)

2/ To simulate a red star,

Results:

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

objects.

Space technology has allowed telescopes to overcome atmospheric distortion. However, these

telescopes are expensive to launch and usually only last several years before falling back to

earth due to orbital decay.

Hubble Space Telescope (HST)

The HST purpose was to photograph nearby stars and distant galaxies to improve ourunderstanding of the universe. It carried 5 scientific instruments:


31/55


Summary


Instrument Name Purpose/description Observed

wavebands

Wide Field and Planetary

Camera (WF/PC)

2 optical cameras, each with 4 CCDs

WF: wider viewing angle

PC: greater magnification

Visible

Goddard High resolution

spectrograph (GHRS)

Record spectra in high resolution UV

High speed photometer (HSP) Measure brightness of fast-moving

objects

UV, visible

Faint object camera (FOC)

faint object spectrograph

(FOS)

High-resolution imaging devices. Used

photon-counting digicon rather than

CCDs

Visible

The impact of these technologies has been:

-to constrain the value of the Hubble constant the rate of expansion of the universe.

--However, by observing distant supernovae, it found that the rate of expansion of the

universe may be accelerating

-It demonstrated the connection between galaxies and their central black holes

-High-resolution images of the collision of comet shoemaker-Levy 9 in 1994 were

crucial in developing an understanding of the dynamics of comet collisions with

Jupiter-Discovery of proplyds (dense gas discs surrounding newborn stars) and the optical

sources of gamma-ray bursts

- the Hubble-deep and ultra-deep space field images, which utilised the sensitivity of

the HST to obtain optical images of galaxies billion of years away, which has

generated a wealth of scientific papers.

Cosmic Background Explorer (COBE)

COBEs purpose was to measure the cosmic microwave background radiation (CMB) and

provide measurements to shape our understanding of the cosmos. It carried 3 instruments:

Instrument Name Purpose/description Observed

wavebands

Differential Microwave

Radiometer (DMR)

Microwave instrument designed to map

variations in the CMB.

microwave

Far-Infrared Absolute

Spectrophotometer

(FIRAS)

Spectrophotometer designed to measure the

spectrum of the CMB

Infrared

Diffuse InfraredBackground Experiment

Multi-wavelength infrared detector designed tomap dust emission

Infrared


32/55


Summary


(DIRBE)

The DMR provided data on the structure formation of the Universe, indicating cluster so

galaxies and vast empty regions. DIRBE detected 10 new IR-emitting galaxies, which were

able to provide data on very cold dust (VCD). It was also able to collect data on interplanetarydust (IPD) and concluded it originates from asteroids. DIRBE was also able to model the

Galactic disc of the Milky Way, indicating it is not a thick disc. COBE provided important

constraints on the star formation rate, although it was unable to resolve the exact star

formation history, so future observations are necessary.

Wilkinson Microwave Anisotropy Probe (WMAP)

WMAP purpose was to measure temperature variations in the CBM to study the geometry,

content and evolution of the Universe; to test the Big Bang model and cosmic inflation

theory. To achieve this, it had to create an accurate map of the CMB.

Instrument Purpose/description Observed

wavebands

Primary mirror:

Pair of Gregorian

1.4 x 1.6 m

reflecting mirrors

Opposite facing; focus signal into secondary

mirrors.

Secondary

Mirror:

Pair of 0.9 x 1.0

m reflecting

mirrors

Transmit signal to receivers

Radio, microwave

Polarisation-sensi

tive differential

Radiometers

A set of 20, divided into groups, using 5 discrete

frequencies; Measure differences between two

telescope beams

Microwave,

radio

Low-noise

amplifiers

Amplify weak incoming signal n/A

WMAPs measurements have been key to establishing our current model of the cosmos.Among its achievements include:

-mapping the CMB and producing the first microwave high-resolution map of the sky

-determining the age of the universe to be 13.73 0.12 Billion years

-determining that normal atoms called baryons only compose 4.6% of the universe,

23.31.3% is dark matter and 721.5% is dark energy

-narrowing down the possibilities of what occurred during the first trillionth of a

trillionth (10-24) s, ruling out well-known textbook models

Chandra x-ray telescope


33/55


Summary


Chandras purpose was to observe x-rays from high-energy regions of the universe, such as

supernova remnants

Instrument Purpose/description Observed

wavebands

Wolter telescope Consists of nested hyperbolic andparabolic surfaces coated with

iridium/gold, to absorb x-ray photons.

Advanced CCD Imaging

Spectrometer (CIS

10 CCDs

High resolution camera

(HRC)

Has two micro channel plates used to

detect particles and radiation

High- and low-energy

Transmission grating

Spectrometer

Provides high-resolution spectroscopy

over a wide range in the x-ray

x-ray

Data gathered the Chandra has greatly advances the field of x-ray astronomy:

-Images of supernova remnants revealed neuron stars and black holes

-showed for them first time a smaller galaxy being cannibalised by a larger galaxy

-x-ray emissions from main sequence stars

-strong evidence for existence of dark matter

-Observations of neutron stars, pulsars, gamma ray bursts, black holes and possible quark

stars

5. Binary and variable stars

Describe binary stars in terms of the means of their detection: visual, eclipsing,spectroscopic and astrometric

Perform an investigation to model the light curves of eclipsing binaries usingcomputer simulation

Binary stars consist of a pair of stars revolving around a common centre of gravity. They are

grouped according to their method of detection.

Visual Binaries

Visual binaries can be resolved directly via telescope as ellipses traced out relative to

background stars. The mutual separation of the stars is from 100-10 000 AU with an angle of

separation arc seconds. Observations must be made with telescopes of at least 15cm diameter

and a micrometer is used to measure the angle of separation.


34/55


Summary


Eclipsing Binaries

Eclipsing binaries cannot be

resolved via telescope and aredetected by fluctuations in brightness when one star moves in front of the other, and vice

versa.

When the brighter star (blue) moves completely in front of the duller star (red), there is a

slight dip in brightness called a secondary eclipse. When the duller star moves completely in

front of the brighter star, there is a larger dip in brightness, called a primary eclipse.

Light curve for total and partial eclipses:

A similar situation occurs for a partial eclipse, with the dips being a V-shape, rather than

flat-bottomed.

Spectroscopic binaries

More massive star

follows a smaller

elliptical orbit

Barycentre

Secondary eclipse

Primary

eclipse

Time

Intensity

Secondary eclipse Primary

eclipse

Time

Intensity


35/55


Summary


Spectroscopic binaries cannot be resolved via telescope and are detected by the Doppler shift

of their spectra. When one star is approaching, it will produce blue-shift while the other is

receding from the observer and will produce red-shift. The combination of both broadens the

spectral lines. This technique only works when the motion of the stars is transverse to the

observers line of sight (will not work if motion is perpendicular). This method is preferred

to visual binaries as there are more distant stars than near stars and because their speeds areeasily measured using Doppler shift.

Astrometric binaries

Astrometric binaries cannot be resolved properly because only one star is bright enough to

see. The presence of a companion star is inferred by the oscillation or wobbling of the

visible star from the mean path of motion due to the gravity of its companion.

Red-shift

Blue-shift


36/55


Summary


Explain the importance of binary stars indetermining stellar masses

Binary stars provide virtually the only means of directly

measuring the masses of stars other than the Sun. The

mass of a star is key to determining the processes it

undergoes during its lifecycle and endpoint and is

therefore vital in refining our model of stars.

Applying Keplers Laws for a binary system where the

masses of the two stars are similar:

-the stars orbit each other in ellipses with a common centre of motion called the barycentre-the line joining the two stars (radius vector) covers equal area in equal periods.

-The square of the period is directly proportional to the cube of its radius:

Radius of individual star (if M and R are known)By definition, at the barycentre:

Path of mean

proper motion

m1m2

Barycentre

r2r1

R


37/55


Summary


Deriving the formula for total mass of system:

Total mass of systemIf T and R are known, use

If T is given in years and R is in AU, use

Individual masses (given M, R and radius of mass)


38/55


Summary


Other useful identities

Solve problems and analyse information by applying:

Examples:

1) Two stars in a visual binary system have an orbital period of and are

determined to be apart. Calculate the combined mass of the system.

2) [from Question 30, 2004]

An astronomer made regular measurements of the intensity of a star over the course of several

days and obtained the light curve shown below.

(i) Describe the features of this light curve that suggest the astronomer is

observing an eclipsing binary system.

The light intensity of the system varies periodically with time. The dip in luminosity

represents when one star moves completely in front of the other, resulting in a decrease in the

intensity or amount of light coming from the system.


39/55


Summary


(ii) If both starts have equal masses of determine the separation of the two stars.

3) From 2006, Question 30

(a)

(i) Describe the spectroscopic observations that would determine whether a

particular star is really a binary system

The spectra of the system would be observed to show both red-shift and blue-shift as one star

recedes while the other approaches, leading to a broadening of the spectral lines. This would

only occur, however, if the system was viewed transverse to the observers LOS.

(ii) The graph represents the variation in brightness of a binary star systemGiven that the mass of the system is determined to be kg, calculate the average distance

between the stars within the system.


40/55


Summary


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

Variable stars are stars whose brightness, colour or other property varies with time. They are

classified according to the cause of the variation and the periodic nature of the variation.

The brightness of non-periodic variables varies irregularly with time. These include novae

and supernovae

Intrinsic variables are stars whose variation in luminosity is due to physical changes within

the properties of the star itself. Intrinsic stars may be divided into two main subclasses:

*periodic variables

*non-periodic variables (novae and supernovae)

Periodic variables are variables that expand and contract fairly regularly with a defined

period. They can be further subdivided into two main groups:

*cepheids: those that have short, regular periods of days to months (generally blue

stars towards spectral class O)

*long period (Mira Ceti) variables: those with longer, more irregular periods

(generally red giants of spectral class M) and large variations in luminosity

Other examples include RR Lyrae and RV Tauri variables

Irregular period or non-periodic variables can be subdivided into three main groups:

*semi-regular variables: mainly red stars, giants or supergiants which display small

variations in luminosity and constant brightness

*Irregular variables: include most red giants. They have short periods and display

rapid, although small variations in luminosity (include red giants, white dwarfs)

*Eruptive variables: include the novae and supernovae, which display sudden bursts

in luminosity (typically include giants and supergiants, which emit vast quantities of

energy due to their large mass)

Other examples include flare stars, T-Tauri stars and R Coronawe Borealis variables

Extrinsic variables are stars whose variation is due to external properties. They can be dividedinto two main subgroups:


41/55


Summary


*Eclipsing variables: periodic changes in luminosity are due to an eclipsing

phenomena

*Rotating variables: whose variability may be caused by a misalignment of the

rotational axis with the magnetic axis, leading to thermal hotspots on the surface. It

may also be caused by irregularities in the stars chromosphere or an ellipsoidal shape.

Explain the importance of the period-luminosity relationship for determining thedistance of cepheids.

Cepheids are periodic intrinsic variables whose periods of pulsation are proportional to theirluminosity. As they expand, surface temperature increases while luminosity decreases and as

they contract, their surface temperature increases while luminosity decreases.

Typical light curve for a Cepheid:

It has been

found that the maximum intensity occurs just after the minimum radius. Thus, the steep rise

in luminosity is due to the increase in temperature after the star contracts. In 1912, Henrietta

Leavitt discovered the period- luminosity relation, by plotting the luminosity values of

cepheids on a log-log graph.

The period-luminosity relation is given by the equation: , where

Light

Time


42/55


Summary


L is the luminosity, in magnitudes

A is the gradient of the graph

T is the period, in days

B is the y-intercept

Period-Luminosity graph of cepheids:

For cepheids, a definite

relationship exists

between its period of

pulsation and luminosity.

There are two types ofcepheids: Type I

(classical cepheids) and

Type II (younger stars

with lower metal content)

Hence, if we know the

period of pulsation we

can graphically determine

the absolute magnitude. Combining with the apparent magnitude, we can use the distance

modulus to determine the distance.

Cepheid variables are also observed in other galaxies well beyond the scope of parallax

measurements. Thus, if other galaxies contain cepheids, the distances to those galaxies can be

accurately measured. Cepheid variables have been vital in determining the cosmic expansion

of the Universe.

6. Stellar Evolution

Describe the processes involved in stellar formation

Protostar

Type I (classical

cepheids)

Type II

Period, T (days)

Absolute

magnitude

100

-6

10

0

-2


43/55


Summary


Gravity causes interstellar nebula of gas and molecules to collapse. These nebulas have

diameters of LY and masses of solar masses. If the mass exceeds the Jeans mass gravity

overcomes any outward thermal pressure and the clouds begin to collapse.

During contraction gravitational potential energy converts into heat- a protostar. The star

begins to faintly emit visible red and infrared radiation. The temperature is too low for

nuclear fusion to begin yet but its vast size means it is luminous, placing at the top RH corner

of the H-R diagram.

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

Pre-main sequence

Increased temperature increases thermal pressure, opposing gravity and slowing down

contraction. Eventually the protostar reaches a temperature where hydrogen molecules

decompose into atomic hydrogen, allowing further compression and heating to occur. As the

protostar collapses, it rotates and several stars may form by fragmentation to form a cluster.

Surrounding gas and dust are blown away. When maximum luminosity is reached, it is called

a pre-main sequence star.

The mass and composition of interstellar medium determines when and where the star entersthe main sequence (called the Zero-age main sequence). The lower the mass, the longer it

takes the star to enter the zero-age main sequence- stars of less than 0.08 solar masses never

reach the temperatures to begin nuclear fusion.

Protostar:

GPE heat

Pre-Main Sequence: dust

and gas are removed by

the stellar wind

Main Sequence:

Gravity and

outward thermal

pressure are


44/55


Summary


Main Sequence

Once temperature and pressure are high enough for nuclear fusion, the star enters the main

sequence. Outward pressure and gravity are balanced, so the star is stable. Dust and gas not

accreted to the core are removed by the stellar wind. The star begins the process of hydrogen

fusion in its core for energy. It becomes slightly hotter and more luminous as radiation andparticles radiate into space in a stable manner.

Describe the types of nuclear reactions involved in Main-Sequence and

post-Main Sequence stars

Main-Sequence

Main sequence stars produce energy from the conversion of hydrogen to helium in its core.

There are two nuclear fusion reactions involving hydrogen:

-the proton-proton chain

-the carbon-nitrogen cycle

In both cases, the net effect is the same: 6 protons are involved, two of which are regenerated

while the other four are converted into two helium nuclei, two neutrinos, two positrons and

gamma radiation. The net reaction is:

Proton-Proton (PP) Chain

The PP chain occurs in lower mass, cooler MS stars (less than 20 million Kelvin) and takes~7 billion years. There are three steps involved:


45/55


Summary


1. Fusion of two protons (hydrogen nuclei) into a deuterium (rare isotope of hydrogen)

nucleus. One proton decays into a neutron, releasing a positron and a neutrino.

Positrons (positive charge) readily ionise, emitting gamma radiation. Neutrinos have

no mass or charge and pass out of the core.

2. Fusion of a deuterium nucleus and a proton to form a helium-3 nucleus, with energy

in the form of gamma rays also emitted.

3. Fusion of two helium-3 nuclei to form a stable helium-4 nucleus and two protons.

These protons may strike other protons and begin the chain reaction again.

The Carbon-Nitrogen (CNO) cycle

The CNO cycle occurs in higher mass, hotter MS stars (more than 30 million K) and takes 7million years to complete. There are six steps involved:

1. Fusion of a proton and a carbon nucleus to form a nitrogen-13 nucleus and 2 MeV of

energy I the form of gamma radiation.

2. Nitrogen-13 is unstable and decays into Carbon-13, releasing a neutrino and a

position. The positron annihilates itself when it meets an electron, releasing 1 MeV of

energy

3. Fusion of a proton and Carbon-13 to form nitrogen-14, releasing 8 MeV of gamma

radiation.


46/55


Summary


4.Fusion of a proton and Nitrogen-14 to form Oxygen-15 and & MeV of gamma

radiation.

5.Oxygen-15 is unstable and decays into Nitrogen-15, releasing a neutrino, a positron

and 1.7 MeV of energy

6. Fusion of a proton and Nitrogen-15 to regenerate the carbon nucleus, a helium nucleus

and 0.5 MeV of gamma radiation.

Post-Main sequence

Over time, hydrogen-fusion in main sequence stars produces a helium core and an outer

hydrogen-burning shell. When the hydrogen in the core is depleted, hydrogen fusion cannot

occur and gravity causes the core to collapse. GPE is converted into heat, causing the outer

layers to expand. The brightness of the star gradually decreases as the surface area expandsfaster than energy is produced so the star becomes a red giant.

As the core continues to collapse and temperature increases, helium fusion begins explosively

in the helium flash. This causes the star to contract.

Triple Alpha process

End of MS: inner helium

core and outer

energy-producing hydrogen

shell

Core collapses due to

gravity: GPE heat

Heat causes outer layers

to expand- the star

begins the Red Giant

stage


47/55


Summary


In Red Giants, three helium nuclei fuse to form a carbon nucleus in the triple alpha process:

When the core is mainly carbon, helium fuses with carbon to produce an oxygen core. Further

exothermic reactions in the outer hydrogen shell form heavier elements up to iron.

Discuss the synthesis of elements in stars by fusion

The heat of the Big Bang synthesised only hydrogen and helium. All other elements have

been created by stellar nucleosynthesis.

Further helium is produced in MS stars via hydrogen fusion (PP chain in cooler stars, CNO

cycle in hotter stars).Helium fusion produces carbon, oxygen, neon and magnesium in post-MS stars via the Triple

Alpha Process i.e. fusion of the product nuclei with alpha particles.

Beyond iron, the reactions are endothermic and occur in the stages beyond Red Giants,

although elements up to lead may be formed by the slow capture neutron process (S-process)

in red giants. All the elements heavier than gold are produced by the rapid capture neutron

process (R-process) in supernova explosions.

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

main sequence plot for a H-R diagram


48/55


Summary


Stars in a globular cluster are approximately the same age as they were formed by the same

nebula. This means the stars in the cluster have similar chemical compositions and cover the

entire range of stellar masses. The zero-age main sequence plot shows the stars when they

have just begun the main sequence stage.

Globular clusters are observed to be missing high-mass stars (spectral class O and B). This isbecause high-mass stars use their hydrogen more quickly than smaller stars and move off the

main sequence. As a cluster ages, it appears to form a knee, bending upwards from the right

of the MS. The absolute magnitude at this turn-off position is a function of the age of the

cluster.

Thus, the age of a globular cluster can be determined by the position of the massive stars. If

the cluster is:

-old, there will be less of the high-mass stars on the MS

-young, there will be more high-mass stars on the MS

Explain the concept of star death in relation to:

-planetary nebula

-supernovae

-white dwarfs

-neutron stars/pulsars

-black holes

Star death occurs when nuclear fusion in the core of stars ceases and the outward thermal

pressure due to radiation is overcome by the inward force of gravity. The processes that occurnext depend on the mass of the star.

Low mass stars (2-5 solar masses)

After low-mass stars have begun the helium-burning stage, oxygen and carbon accumulate in

the core. In order to remain stable, the outer hydrogen burning shell moves outwards, ejecting

shells or rings of ionised gas around the core, forming what is known as planetary nebulae.

The core temperature is too low for fusion of oxygen and carbon into other elements, so the

core simply contracts, supported only by the quantum effect called electron degeneracypressure which prevents further core collapse. It is now called a white dwarf. Its high mass

and low surface area means it is hot (~105 K), but low luminosity (therefore very faint). It is

now called a white dwarf.

White dwarfs have no energy source as such, simply relying on residual heat from the core.

Eventually, all this heat is radiated into space and the white dwarf is thought to become a cold

brown or black dwarf. However, no black dwarfs are believed to exist as they would take

longer than the age of the Universe to reach this stage.


49/55


Summary


High mass stars (5-8 solar masses)

In more massive stars, nuclear fusion in the core forms elements up to iron. The electron

degeneracy pressure, which prevents electrons from being forced into the nucleus, is

overcome by the inward gravitational force. This causes electrons to be forced into protons,forming neutrons. The core resists further collapse due to the quantum neutron degeneracy

pressure.

Any further collapsing matter simply bounces off the core with an ejection of subatomic

particles called neutrinos, resulting in a supernova explosion. Supernova explosions are

only relatively brief and cannot be seen on an H-R diagram as they are too hot and luminous.

Elements heavier than iron are synthesised during supernova. What occurs next depends on

the core mass of the original star

Neutron stars

If the supernova core mass is 1.4 3.0 solar masses, the neutron degeneracy pressure preventsfurther core collapse, forming a neutron star. Neutron stars are extremely dense, small (10-20

km in diameter), with powerful gravitational and magnetic fields. They emit radiation in the

gamma and x-ray wavebands. Most known neutron stars are called pulsars, which emit beams

of radio waves from their magnetic poles as they rotate (light a lighthouse). When the beams

sweep past the Earth, we detect them as regular radio pulses, hence the term pulsar.

Neutron stars obtain their energy from either from angular momentum from the supernova

explosion which created them, from their intense magnetic fields or from the accretion of

matter from companion stars

Black Holes (>8 solar masses)

For stars that begin greater than 8 solar

masses, the supernova remnant core will be greater than 3 solar masses. At this stage, gravity

completely overcomes even the neutron degeneracy pressure and the core continues to

collapse into a singularity. The gravity is so powerful that not even light can escape its

surface- a black hole is formed!

Gravity

Core mass of 1.4 - 3.0 solar masses:

Electrons stop further collapse

Core mass 1.4 - 3.0 solar masses:

Electrons forced into protons,

forming neutrons i.e. electron

capture. Neutrons prevent

Gravity


50/55


Summary


Present information by plotting Hertzprung-Russell diagrams for: nearby or

brightest stars, stars in a young open cluster, stars in a globular cluster

Core mass > 3 solar masses:

Gravity overcomes neutron


51/55


Summary



52/55


Summary



53/55


Summary


Open Cluster Globular cluster

H-R diagrams vary greatly for different

clusters i.e. some are sparse, others are

densely populated

H-R diagrams are all similar

Giants and supergiants present No supergiants

Giant branch at zero absolute magnitude Giant branch at -3.5 absolute magnitude

Giant branch separate from MS Narrow band connects giant branch with MS

Stars have varying ages Low turn-off point, indicating they are old

clusters


54/55


Summary


Globular Clusters

Globular clusters are generally composed of hundreds of thousands of old, low-metal stars.

As a result, there are no supergiants and few dust and gas clouds, as all the stars have

surpassed this stage. All the stars are about the same distance away from us, so the apparent

magnitude and the absolute magnitude for all stars differs about the same amount. Bymatching up H-R diagrams for absolute and apparent magnitude and using the distance

modulus gives an estimate of the age of the cluster.

All the stars in a globular cluster fall upon a well-defined curve. As each star on an H-R

diagram varies with age, this can be used to estimate the age of the star. The highest mass

stars are the most luminous and the first to become red giants. As the cluster ages, lower mass

stars also begin entering the red giant stage- this forms a turn-off point on the diagram. The

absolute magnitude at this turn-off point is a function of the age of the cluster, so an age

scale can be plotted parallel to the magnitude.

If the main sequence contains O-type stars, the cluster is less than 10 million years old

because this is the amount of time it takes for an O-type star to deplete its core hydrogen. If it

contains A- or B-type stars, the cluster is older than 10 million years old.

Open Clusters

Stars in an open cluster are approximately the same age, mass, chemical composition and the

masses of the stars vary greatly.

Present information by plotting on a H-R diagram the pathways of stars of 1, 5

and 10 solar masses during their life cycle

A star of 1 solar mass e.g. the Sun, enters low on the MS (spectral class M). It remains here

for most of its life, slowing moving up the MS to spectral class F. Once it has depleted

hydrogen in the core, it becomes brighter and moves horizontally right to the Red giants

(spectral class K). Once all its nuclear fuel is depleted, its outer layers are radiated off, leaving

a small, hot core. This makes it spectral class F, towards the bottom LH corner of the

diagram.

A 5 solar mass star enters higher on the MS (spectral class F). It spends less time here beforebecoming a red supergiant (spectral class G). Eventually, it moves off the H-R diagram as it

forms a supernova explosion, which is too hot and luminous to graph. The neutron star that

forms next is also too hot and luminous to be graphed.

A 10 solar mass star enters even higher on the MS, for an even shorter time period. There are

two possible stages which occur next:

-the star can become a blue supergiant (spectral class B-A) which forms a supernova

directly before forming a black hole

-the star many become a red supergiant (spectral class G), before becoming a

supernova, and the a black hole

In both cases, the star simply moves upwards off the H-R diagram


55/55


Summary

Massive stars (e.g. 10 solar masses) will enter high on the MS and will spend a relatively

short period of time there. Next, it will move to the supergiants (spectral class G) before

moving up off the H-R diagram

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

Documents

Astrophysics Repaired)