hsc physics module 9.7 summary

8/12/2019 HSC Physics Module 9.7 Summary

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HSC Physics Module 9.7 Summary

1. Our understanding of celestial objects depends upon observations madefrom Earth or from space near the Earth

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

Galileo did not invent the telescope, but was able to build a telescope that produced a clear enough

image to observe the features of the moon. He used higher quality glass than used before, and

produced his own lenses in order to build an improved telescope that had a magnification greater

than 3x.

His interest in celestial bodies caused him to point the telescope at the moon, and be the first

person to record observations made of the moon from the telescope. He observed and recorded

that the moons surface was uneven, rough, and full of cavitiesand prominences. Galileo was able to

calculate the height of mountains on the moon from the measurement of their shadows. This

challenged the view held by the Catholic Church, who believed that all celestial bodies were

perfect.

Discuss why some wavebands can be more easily detected from space

Nearly all wavebands of the electromagnetic spectrum are present in space, and most are directed

towards Earth. Not all wavebands reach Earths surface however, as most wavebands are filtered out

by the atmosphere. The only wavebands that predominantly reach Earths surfaces are visible light,

microwaves and radio waves.

EMR Waveband Wavelength (m) Absorption by

atmosphere

Gamma rays


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As a result of the absorption by the atmosphere of electromagnetic wavebands, ground-basedtelescopes can only detect visible light, microwaves and radio waves coming from space.

Observations of other wavebands need to be conducted from space, such as from the Hubble Space

Telescope.

*Additional to atmospheric absorption of infra-red radiation, ground-based infrared telescopes are

limited by the radiation given off as heat by Earth-based sources.

Define the terms resolution and sensitivity of telescopes

The theoretical resolutionof a telescope is its ability to detect distinct objects in space. A telescope

with poor resolution would not be able to distinguish two close celestial bodies such as binary stars

as distinct bodies. The equation for calculating resolution is the following.

where

R = resolution [arcsec] = wavelength of EMR [m] D = diameter of telescope [m]

Whilst this equation is not required in the syllabus, it is useful for demonstrating the effect of

wavelength and diameter on the resolution of a telescope. A smaller value of R corresponds to an

increased resolution, as arcsecs is a measure of angles. Therefore an increased wavelength

decreases the resolution of a telescope, whilst an increased diameter telescope, or larger collecting

area, would increase the resolution of a telescope. Therefore, a radio telescope such as the Parkes

telescope would have a poor resolution, as it measures radio waves, which have a large wavelength.


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The image to the left has a poorer resolution than the one on the right, as the stars are less distinct.

The sensitivityof a telescope is a measure of its ability to detect E.M.R. radiation from space. A

telescope with a high sensitivity is able to detect faint objects, whilst a telescope with poor

sensitivity detects radiation from a smaller range. The sensitivity of a telescope can be improved by

having a larger radius. The Parkes telescope, due to its large radius, has a high sensitivity, despite

having a poor resolution.

The image of the right has been taken from a telescope with a higher sensitivity, and thus has been

able to detect more light coming from space.

Discuss the problems associated with ground-based astronomy in terms of

resolution and absorption of radiation and atmospheric distortion

Ground-based astronomy has several problems due to the presence of Earths atmosphere. The

absorption of most E.M.R. wavebands limits the use of ground-based telescope systems to visible

light, microwave and radio wave detection. This limits the ability of ground-based systems to detect

features of the universe, as much of the radiation emitted from celestial bodies is of the other

wavebands.

Ground-based systems are also limited by the distortion of wavebands that arent absorbed by the

atmosphere. The distortion of EMR wavebands is also known as seeing, and is due to tiny, rapidly

changing temperature variations in Earths atmosphere, which change the path of EMR radiation,

particularly visible light. This causes the resolution of wavebands to decrease, as the radiation is

blurred by the atmosphere. For example, the theoretical resolution of the Anglo-Australian

telescope is 0.027 arcsec, but is restricted to a resolution of 1 arcsec due to the distortion of light in

the atmosphere. This is about the same resolution as a small 100mm telescope, which demonstrates

the problem of atmospheric distortion of radiation. Longer wavebands such as radio waves are less

affected by atmospheric distortion, though radio waves can be absorbed by water droplets in the

atmosphere.


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Outline methods by which the resolution and/or sensitivity of ground-based

systems can be improved, including:

adaptive optics interferometry active optics

There are a number of methods and technologies that have been developed in order to combat the

problem of atmospheric distortion for ground-based systems. These include interferometry, active

optics, and adaptive optics.

Interferometry

Interferometry is a method of improving the resolution of ground-based radio telescopes.

Interferometry involves laying out many radio dishes in a large pattern, and then combining their

signals together through computerised systems. A sample layout is shown below.

The combined signal behaves as a single signal, but as it has been collected over a large radius, the

resolution of the signal is improved through effectively increasing the diameter of the telescope.

Radio waves are not affected by atmospheric distortion as much as visible light, so ground-based

systems using interferometry are able to achieve a significantly high resolution.

Another example of interferometry in telescopes is the Space Interferometry Mission (SIM),

launched by NASA. A satellite was launched into space, and is connected by satellite communication

to a ground-based radio telescope. The large distance between the ground and space telescope give

a long baseline for the interferometry system, thereby significantly enhancing the resolution of

images obtained.

Interferometry techniques have also been used in optical telescopes. A technique called speckle

interferometry uses many images from a telescope. Each image is captured using a short enough

exposure to effectively freeze atmospheric blur. The multiple images are then processed by a

computer to produce images of celestial bodies with an increased resolution.

Active optics

Active optics is a recent development to improve the resolution of ground-based optical telescopes.Active optics systems detect errors in the image due to the deformities in the mirror, and then


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automatically correct the image. Deformities in the mirror can be caused by the mirror sagging

under its own weight due to movement, and by temperature changes. The light is sampled by a

wavefront sensor after the light has been reflected off the primary mirror, and before it passes

through the final lens. The wavefront detector slowly samples the light, and is able to detect any

distortions in the light due to deformities in the mirror. This information is then fed into a computer,

which is able to rectify deformities in the mirror. It does so through an array of actuators behind the

mirror that are able to change the shape of the primary mirror. The shape of the primary mirror is

changed every few minutes, and this keeps it in optimum shape.

Before the use of active optics, mirrors were made to be several metres thick in order to reduce

deformities. This meant that optical telescopes were limited to a diameter of around 6m, and the

mirrors were still subject to deformities. With active optics, lightweight primary mirrors of up to 10m

in diameter and 20cm thick have been used, such as in the Keck telescopes in Hawaii.

Adaptive optics

Adaptive optics relies on a similar feedback system to active optics in order to improve the

resolution of images. The difference with adaptive optics is that they rectify errors due to

atmospheric distortion, and rely on a much faster feedback system. A wavefront sensor samples the

incident light up to 1000 times per second by analysing the light coming from a nearby target star, or

from a laser beam, which a tilting mirror keeps in the image. These corrections are processed by a

computer, which alters a rapidly adaptive mirror to rectify the blurring of light due to atmospheric

distortion. The diagram below shows a simplified schematic diagram of an adaptive optics system.

The rapid calculations require considerable computing power, and the technology to make the

rapidly adaptable mirror is expensive. Nevertheless, it is able to overcome the decrease in resolution

by atmospheric distortion of electromagnetic radiation, as can be seen in the diagrams below.

Identify data sources, plan, choose equipment or resources for, and perform an

investigation to demonstrate why it is desirable for telescopes to have a large

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


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REFER TO PRAC 9.7.1 f)

METHOD

Circles of variable diameter were constructed out of paper. M&Ms, which representedphotons, were laid flat inside each circle, and the maximum number of M&Ms without

overlapping was recorded. Number of photons was plotted against diameter squared,

which yielded a linear relationship.

Another method is to reflect light off mirrors of varying diameters into light meters, andrecording the intensity of light. Take a recording of ambient light as a control to increase the

investigations validity => DO NOT LOOK DIRECTLY AT SUNLIGHT

RESULTS/CONCLUSION

As aforementioned, number of photons was plotted against diameter squared, yielding alinear relationship => sensitivity of light is proportional to diameter SQUARED

RELIABILITY

The method was repeated several times, and an average taken Results were compared to other groups, who measured similar results The data points were close to the line of best fit => PRECISION

VALIDITY/ACCURACY

The experiment and results reflected the aim Only one variable was changed (diameter of circle), all the others were controlled The final result was checked against reliable textbooks, online websites, and scientific

journals, which gave the same result.

The method was a model, and so was LIMITED due to discrepancies between model andreality (photons are massless, does not show wave properties of light etc.)


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

Define the terms parallax, parsec, light-year

Parallaxis the apparent change in position of an object relative to a distant background due to a

change in the position of the observer. In relation to celestial bodies, parallax occurs as the Earth

orbits the Sun. The changing position of Earth causes celestial bodies to appear to be changing

position, as our perspective of celestial bodies relative to their background is changing. Parallax can

be demonstrated by holding your finger out in front of your eyes, and covering one eye, then the

other. Your finger appears to move relative to the background as your perspective changes, yet your

finger has remained still.

Aparsecis a measure of distance, commonly used when calculating celestial distances. More

specifically, one parsec is equal to the distance from the Earth to a point that has an annual parallax

of one arcsecond.

One parsec is equal to 3.26 light-years. Annual parallax will be discussed below. The parsec is used

commonly in astrometry, which is the branch of astronomy concerned with the position of celestial

bodies.

A light-yearis the distance that light travels in one Earth year. It is approximately equal to 9.5x1015

m.


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Solve problems and analyse information to calculate the distance to a star given its

trigonometric parallax using:

Angles of deviation used in trigonometric parallax calculations are normally calculated at 6 month

intervals, where the diameter of the Earths elliptical orbit around the Sun is a maximum.

As can be seen in the above triangle the distance of the star from Earth can be calculated using

trigonometry.

The large distances from Earth to celestial bodies means the angle of deviation is very small. Proxima

Centauri has the smallest angle of deviation, which is 0.772arcsecs. At angles this small, the

following approximation can be used.

Also, the radius of Earths orbit is 1 AU (astronomical unit). Therefore, the above formula becomes

where

d=distance from Earth [parsecs, pc]

p=parallax *arcsecs, +

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

Trigonometric parallax is a method of determining distances to celestial objects by using parallax. If

the change in position of the observer and the angle of deviation due to parallax is known, the

distance to the celestial body can be calculated using trigonometry.


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Through the tan ratio

Rearranging

Discuss the limitations of trigonometric parallax measurements

Trigonometric parallax measurements rely on accurate measurements of the angle of deviation of

celestial bodies. Angles of less than 0.01arcsec are impossible to use, as they have an error of 10%

due to limits in resolution, such as due to atmospheric blurring. The refraction of light in the

atmosphere changes the angle measured, and thus reduces the accuracy of small angles measured.

In addition, parallax readings are limited by the precision of the measuring equipment, as the angles

measured in trigonometric parallax are very small. This means that trigonometric parallax is only

useful for calculating distances up to around 100 parsecs, which is a small distance in astronomical

terms.

Gather and process information to determine the relative limits to trigonometric

parallax distance determinations using recent ground-based and space-based

telescopes

Recall that trigonometric parallax determinations are limited due too Limits in resolution (e.g. atmospheric blurring), which increase the error of readingo The refraction of light in Earths atmosphere

Ground-based telescope=> V.L.T. (Very Large Telescope)o Built by the European Southern Organisationo Minimum angle of parallax: 0.01-arcseco Allow for distances up to 100pc to be measuredo Only a few hundred stars are this closeo Limited by atmospheric blurring (despite interferometry and adaptive optics), and

refraction of light in Earths atmosphere

Space-based telescope=> Hipparcos (HIgh Precision PARallax COllecting Satellite)o Launched by the European Space Agency in 1989o Minimum angle of parallax: 0.001-arcsec


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o This allows for distances up to 1000pc to be measured => Hipparcos has measuredthe parallax of around 100 000 stars.

o Hipparcoss parallax measurements are limited by the precision of the readingequipment

Future telescope=>GAIAo Due for launch in 2012 by the European Space Agency as a follow-up to Hipparcoso Minimum angle of parallax: 10 microarcsecondso Allows for measured distances up to 100 000pco Parallaxes of >200 million stars can be measuredo Limited by the precision of the reading equipment

As can be seen, space-based telescopes are able to achieve a much more precisemeasurement of parallax angles than ground-based telescopes, as space telescopes are not

limited by atmospheric effects.

Sources of informationo http://outreach.atnf.csiro.au/education/senior/astrophysics/parallaxlimits.htmlo ESO (European Space Organisation) and NASA website
http://outreach.atnf.csiro.au/education/senior/astrophysics/parallaxlimits.htmlhttp://outreach.atnf.csiro.au/education/senior/astrophysics/parallaxlimits.htmlhttp://outreach.atnf.csiro.au/education/senior/astrophysics/parallaxlimits.html


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3.Spectroscopy is a vital tool for astronomers and provides a wealth ofinformation

Account for the production of emission and absorption spectra and compare these

with a continuous blackbody spectrum

Recall that electromagnetic radiation consists of a wide spectrum of wavelengths Three types of spectra are emission spectra, absorption spectra, and continuous spectra

Emission spectra

o Produced by energy supplied to a low-density gas, (e.g. a low-pressure sodium lamp)o An atom absorbs the exact required energy, the an electron will become excited and

jump from its ground state to a higher energy state (excited state)

o When the electron returns to its ground state, it emits photons of discretefrequencies, given by

o If the electron had been excited to an even higher excited state, then it can return toits ground state in one single jump, or by a set of smaller jumps

o Each particular jump down between energy levels represents different quantities ofenergy, and so a spectra of discrete frequencies of photons are given off => this is

the emission spectra

o The emission spectra consists of only discrete wavelengths, rather than a continuousspectra (see below)

o

Each element has a unique emission spectra, thus its emission spectra is afingerprint for the element

Absorption spectrao Produced by a relatively cool, non-luminous gas in front of continuous spectra

source (e.g. the relatively cool gas overlying the hotter, denser gas of a star)

o As mentioned above, for an electron to jump to an excited state, it absorbs adiscrete quantity of energy

o The gas absorbs the photons from the continuous source, but only at thewavelengths matching the differences in energy levels

o The atoms then re-emit the light as the electrons jump back down, but in alldifferent directions => only a fraction of the re-emitted radiation is in the

direction of the incidence light

o The net effect is that the incident light is deficient in the absorbed wavelengths


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o The absorbed wavelengths appear as dark lines on an otherwise continuousspectrum

o The dark lines on the absorption spectrum for an element correspond to thebands on its emission spectrum

Continuous blackbody radiation

o Produced by a hot solid, liquid, or high-density gas (e.g. a tungsten filament)o Recall that a blackbody is a hypothetical object capable of absorbing all the

electromagnetic radiation falling on it

o A black body re-emits EMR in a continuous spectrum related to its absolutetemperature, described by a black body curve (or a Planck curve)

o As the temperature of the body increases, the peak wavelength becomesshorter, and the intensity of emitted radiation increases

o Most high-density hot bodies approximate a black bodyo A continuous black body spectrum appears simply as a continuous spectrum


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Below is a diagram showing the three different types of spectra as applied to a star

Analyse information to predict the surface temperature of a star from its

intensity/wavelength graph

Consider the intensity/wavelength graph for a black body below:

The peak wavelength emitted depends on the temperature of the black body Stars approximate black bodies, so if the peak wavelength emitted from a star is known,

then its temperature can be estimated off an intensity/wavelength graph (provided that the

shapes at differing temperatures are known)


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Whilst not required by the syllabus, Wiens displacement law provides a quantitative meansof calculating a stars temperature if the peak wavelength emitted is known:

Where:o max= maximum wavelength emitted [m]o T = Temperature of black body [K]o W = Wiens constant = 2.898x10-3mK

This equation may be given however, which would simply require reading the peakwavelength of the graph, and rearranging the formula

Describe the technology needed to measure astronomical spectra

Astronomical spectra is measured with a spectroscope A simple spectroscope consists of light source, slits, a prism, and a photographic plate, and a

spectrum can be observed by the following steps

1. Light from a telescope is passed through a slit to form a flat, vertical beam2. The beam passes through a glass prism, which disperses the light into its spectrum3. The dispersed light falls onto a photographic plate, which records the spectrum

A simple spectroscope is useful for observing spectra, but there are new technologies availablefor more sophisticated analysis

o Diffraction gratings can be used instead of a prisms to increase the spectral resolution ofimages obtained

o Collimators are used instead of slits to narrow the light beamo Improved lenses and mirrors have been developed (including collimating mirrors)o Photo electric detectors, such as CCDs (Charged coupled devices) are used to detect

light, as they convert 80%-90% of incident photons into the recorded image. This is an

improvement of photographic plates which only convert 1% of photons.

The S-Cam is a technology currently in development. The S-Cam is a new CCDthat can record the position and colour of individual photons of light, and

quickly compile the information into a database by a computer.

o Sophisticated computer analysis have significantly aided in the analysis of astronomicalspectra


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

and quasars

Object Description Spectrum Example

Star A large, self-

luminous,

celestial body of

plasma

Continuous spectrum

created by the inner

layers of a star, which

acts as a black body.

Absorption spectrum

created by the

atmosphere of a star.

Emission

nebula

Regions of low-

pressure gasclouds (mostly

hydrogen and

helium) that

glow due to

intense UV light

from nearby

stars

Emission spectrum=>

dominated by strongemission lines

characteristic of the

gas composition

Galaxy Collection of

billions of stars,

gas, and dust.Spectrum

dominated by

mix of stars

Continuous spectrum

from the stars in a

galaxy***May be

absorptionor

emissiondepending

on the abundance of

nebulae in a galaxy =>

young galaxies tend

to show emission

spectra, whilst older

galaxies tend to show

absorption


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Quasar Very energetic

and distant

galactic nuclei,

which dominate

the total energy

output

Emission spectrum

superimposed on

continuous spectrum

due to fast moving

gas clouds

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

classify stars

Stellar spectroscopy is the analysis of the spectra of stars in order to learn more about theircomposition, surface temperature, and other features.

Stellar spectrum consists of absorption spectrum characteristic of the atmospheric elementssuperimposed on an approximate black body continuous spectrum for a given temperature

Most stars consist of a very similar set of elements and compounds, yet stars can exhibit verydifferent spectral lines

Different atoms and molecules produce spectral lines of very different strengths at differenttemperatures

o For example, at lower temperatures molecules can exist near the surface, whilst athigher temperatures atoms become ionised => these two situations produce very

different spectral lines

Stars have been classified into spectral classes based on their observed spectrum.o The main spectral classes are O B A F G K M in order of decreasing surface temperature

(Oh Be AFine Girl/Guy Kiss Me)

o There are also other spectral classes (see below) that have been discovered in recenttimes

o Each spectral class is divided into 10 sub-classes, with 1-10, where 1 is the hottest and10 is the coolest (e.g. the Sun is a G2 star)

Spectral class Temperature

(k)

Colour Strength of

hydrogen lines

Other spectral

features

% of main

sequence stars

W >50,000 Blue Weak He, C, Nemission lines

Extremely rare

O 31,000-50,000 Blue Weak Ionised He+

lines, strong

UV continuum

0.00003

B 10,000-31,000 Blue-white Medium Neutral

helium lines

0.1

A 750010000 White Strong Ionised metal

lines

0.6

F 60007500 White-yellow Medium Weak ionised

Ca+lines

3

G 53006000 Yellow Weak Ionised Ca+

lines, metal

8


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lines

K 38005300 Orange Very weak Ca+Fe, strong

molecules, CH,

CN

12

M 21003800 Red Very weak Molecular

bads e.g. TiO,neutral metals

76

L 12002100 Red Negligible Neutral

metals, metal

hydrides

Brown dwarf,

numbers

uncertain

T


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This has led to the development of luminosity classes to also define a starLuminosity class Description

Ia Bright supergiant

Ib Supergiant

II Bright giant

III GiantIV Subgiant

V Main sequence dwarf

VI Subdwarf

VII Dwarf

For example, the Sun is a G2 V starDescribe how spectra can provide information on surface temperature, rotational

and translational velocity, density and chemical composition of stars

TEMPERATURE

As mentioned above, the absorption spectrum produced by a star depends on the surfacetemperature of the star

By assigning a star a spectral class based on its spectra, the corresponding surfacetemperature can be inferred

Alternatively, the effective surface temperature can be calculated by determining the peakintensity wavelength of radiation from a star, and substitute it into Wiens law

ROTATIONAL VELOCITY

Recall that the Doppler effect causes the lengthening or shortening of wavelengths due torotational motion

As a star rotates, one side is moving away relative to Earth, and one side is moving towardsEarth.

The side moving away from Earth is red-shifted due to the Doppler effect, and one side isblue-shifted

This causes the broadening of absorption spectral lines, which can then be analysed todetermine the rotational velocity of a star


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TRANSLATIONAL VELOCITY

The Doppler effect can also be used to determine translational velocity The detected absorption spectrum of a star can be compared to a standard spectrum, such

as a the hydrogen spectrum

If a star is moving awayrelative to Earth, its spectrum will be red-shifted If a star is moving towardsEarth, its spectrum will be blue-shifted By measuring the distance the spectrum is shifted, the stars velocity away from or towards

Earth can be calculated

By combining this with the stars sideways velocity, the stars translational velocity relativeto the Sun can be calculated

DENSITY

The lower the density a stars surface, the lower the gas pressure At lower pressures, gases produce sharper absorption spectral lines Thus high density and pressure within a stars atmosphere can also broaden the absorption

spectral lines

Supergiants have lower atmospheric density and pressure, whilst main sequence stars havehigher density, so knowing the density of a star gives information on the luminosity class of a

star

CHEMICAL COMPOSTITION

As discussed above, the molecules, atoms, and ions in a stars atmosphere produce theabsorption lines on a stars spectrum

Each molecule, atom, and ion has a unique absorption spectrum Comparing the measured absorption lines of a star to those produced by an element under

laboratory conditions indicates the presence of particular elements in a stars atmosphere

The relative intensity of the absorption lines indicates the abundance of that element


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Perform a first-hand investigation to examine a variety of spectra produced by

discharge tubes, reflected sunlight, or incandescent filaments

METHOD

Sunlights spectrum was observed by going outside, pointing a spectroscope away from theSun, and recording the spectrum observed. An incandescent lights filament was observed

by pointing the spectroscope at an incandescent light in a darkened room, and recording the

observed spectrum. The spectrum of hydrogen, neon, and sodium lamps were observed by

pointing the spectroscope at each lamp one at a time in a darkened room, and recording the

observed spectrum.

o To observe emission spectra, place various low pressure gases in front incandescentlight sources

RISKS

Do not point spectroscope directly at the Sun

Do not touch or knock discharge tubes, and place them in a sturdy position with cushioning,as they are depressurised and can IMPLODE

Limit exposure to high frequency radiation (e.g. X-rays) produced by discharge tubes bystaying one metre back (inverse square law => intensity greatly reduced)

RESULTS/CONCLUSION

RADIATION SOURCE OBSERVED SPECTRUM

Reflected sunlight Continuous spectrum

Incandescent filament Continuous spectrum

Hydrogen lamp Distinctive violet, blue, green, and red bands

Neon lamp Many distinctive blue, green, yellow, orange, and red bands

Sodium lamp Yellow doublet

Reflected sunlight and the incandescent filament both produced continuous spectrum The discharge tubes produced emission spectra

VALIDITY/ACCURACY

The results obtained corresponded to the expected results The observations were compared to reliable sources, such as textbooks, websites, and

scientific journals, which corroborated the collected data

Natural sunlight was limited when observing the incandescent filaments anddischargetubes spectra, thus controlling the variables

Qualitative data was collected => reliability of data not important (though repeatedobservation and comparison to others helps!!!)


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4. Photometric measurements can be used for determining distance andcomparing objects

Define absolute and apparent magnitude

The apparent magnitude(m) of an object is a measure of how bright an object appears when viewedfrom Earth. As it is a measure of brightness, it is influenced by distance, and celestial matter that

may alter the brightness of the star. It is measured on a logarithmic scale, where a body of apparent

magnitude 1 is 100 times brighter than that of an apparent magnitude of 6. Apparent magnitude

ranges from -27, that of the Sun, to around +30, the faintest object detected by the Hubble

telescope.

The absolute magnitude(M) of an object is the brightness a star would have if it was observed from

10 parsecs away. Absolute magnitude is a measure of luminosity. It is also a logarithmic scale: for

each five magnitudes lower, a star is 100 times more luminous. This measurement allows

astronomers to compare features of stars more accurately, as absolute magnitude is not influencedby distance.

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

celestial object

The two primary factors that influence the apparent magnitude of a celestial body are luminosity

and distance. As absolute magnitude is a measure of a bodys luminosity, a relationship exists

between apparent magnitude, absolute magnitude, and distance.

Take for example the magnitudes of the stars Sirius and Betelgeuse. Sirius has an apparent

magnitude of -1.4, and Betelgeuse has one of +0.45. The absolute magnitude of Sirius, however, is

+1.4, whilst the absolute magnitude of Betelgeuse is -5.1. As can be seen in this comparison, the

apparent magnitude of Sirius is lower than that of Betelgeuse due to the distances to each star

(Sirius is much closer to Earth than Betelgeuse), and thus a relationship exists.

This relationship is:

The expression m-M is also known as the distance modulus.

Rearranging

where

M = absolute magnitude [no units]

m = apparent magnitude [no units]

d = distance to Earth [parsecs, pc]


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Solve problems and analyse information using:

and

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

star

As described above, the relationship between the absolute magnitude and the apparent magnitude

of a body can be calculated if the distance to Earth from the star is known. The formula is the

following:

where

M = absolute magnitude [no units]

m = apparent magnitude [no units]

d = distance to Earth [parsecs, pc]

NOTE: log = log10

The ratio of the brightness of two stars can also be calculated by considering that magnitude is

measured on a logarithmic scale. For every five magnitudes lower, a body is 100 times brighter. This

can be expressed mathematically as the following:

Rearranging

where

IA/IB= the ratio of brightness of two body A and B

mA= the magnitude of body A

mB= the magnitude of body B


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Outline spectroscopic parallax

Spectroscopic parallax is a method of determining the distance to a star using the H-Rdiagram and the distance modulus formula

The steps involved in spectroscopic parallax are:1. Measure the apparent magnitude (m) of a star using photometry2. Determine the spectral class and luminosity class of a star using spectroscopy3. On the H-R diagram, draw a vertical line from the relevant spectral class to the

middle of the star group corresponding to the luminosity class.

4. Draw a horizontal line from the obtained point to the vertical axis, and read theabsolute magnitude off the axis

5. Using the distance modulus formula, calculate the approximate distance to the star

The distance measured by spectroscopic parallax has a large percentage error, due to theestimates in determining the absolute magnitude

Spectroscopic parallax is useful however for calculating approximate distances, as oftenthere is no other method available to calculate a more precise distance

Explain how two-colour values (eg colour index, B-V) are obtained and why they areuseful

The observation of a stars colour depends on the sensitivity of the detection method todifferent wavelengths of light

The human eye is most sensitive to the yellow-green(550nm) part of the visual band Photographic film is most sensitive to the blue(~440nm) part of the visual band The overall colour of a star as viewed by the naked eye is both a combination of the stars

spectrum and the spectral sensitivity of the eye

o For example, the peak intensity of blue giants lie in the UV/violet part of thespectrum, yet appear blue-white to the human eye


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The brightness or apparent magnitude of stars appears to change when viewed throughdifferent colour filters, as shown below.

o A star field viewed through a red (left) and blue (right) filter The apparent magnitude of a star as viewed by the naked eye is called the visual magnitude

Star colours can be determined by using a standard set of coloured filters in front of aphotometer, and measuring the brightness of each

o The three standard coloured filters are ultraviolet, blue, and visual (yellow-green)filters, or the UVB set

The difference in brightness seen through different filters is a measure of the colour of a staro This is called the colour indexof a star, and is defined byo B = mB= apparent magnitude as viewed through a blue filtero V = mV= visual magnitude

The higher the colour index the more red the star is The lower the colour index, the more blue the star is Colour index typically ranges from -0.6 (O spectral class) to +2.0 (M spectral class) AO stars have a colour index of zero Two-colour values such as colour index are useful because:

o Colour index can determine the true colour of a star, independent of the sensitive ofthe detection method to different colours

o Colour index can be used to determine the spectral class of a star, which can then beused to determine its distance from Earth

NOTE:Absolute magnitudes are also dependent on colour sensitivity, so ensure that whenusing the distance modulus formula, both apparent and absolute magnitude are of the same

coloured filter

Describe the advantages of photoelectric technologies over photographic methods

for photometry

Photographic film records images using light-sensitive film emulsion through the reaction ofsilver salts to light

Filter Central wavelength (nm)

Ultraviolet (U) 350

Blue (B) => photographic 440

Visual (V) 550


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Photoelectric technologies use the photoelectric effect to produce a voltage Photoelectric technologies include:

o Photomultiplier tube, which consists of a vacuum tube that multiplies the originalsignal by millions of times

o Photodiode, which consists of a solid state device that acts as a light detectoro Charged-coupled device(CCD), which consists of millions of photovoltaic cells that

record incident light, and convert it to a digital signal to produce a digital image =>

also found in digital cameras

Advantagesof using photoelectric devices over photographic methods includeo Sensitivity=> a typical CCD records ~70% of incident photons, whilst photographic

film records 2%-3%

o Response to range of wavelengths=> CCDs and other photoelectric technologies candetect infrared radiation (e.g. in night-vision cameras) and UV, whilst photographic

film is restricted to the visible light band.

o Image manipulation and enhancement=> photoelectric devices can record digitalimages, so computer technologies can enhance, enlarge, add false colour, or

subtract selected wavelengths to aid in analysis

o Wider detection=> CCDs can record many objects at once, whilst photographs canonly record a single image

o Faster processing=> CCDs provide images much faster than photographic filmo Increased astronomical sensitivity=> CCDs can record images from fainter objectso Greater detection manipulation=> CCDs can either record a broad spectrum, or a

narrow band of EMR for specific analysis

Identify data sources, gather, process and present information to assess the impact

of improvements in measurement technologies on our understanding of celestial

bodies

Many recent developments in astronomical measurement technologies have had asignificant impact on our understanding of celestial objects, and allowed for new directions

in astronomical thinking

Such technologies include charged-coupled devices (CCDs),space telescopes, and WilkinsonMicrowave Anisotropy Probe.

CHARGED-COUPLED DEVICES (CCDs)

CCDs consist of a light-sensing array developed since the 1970s that records incidentphotons by means of the photoelectric effect => the same technology (but much simpler) is

used in digital cameras

CCDs convert photons into electrical signals, which are then used to form a pixilated image


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CCDs are an improvement on previous photographic technologies becauseo They can measure a wider range of EMR wavelengths, allowing for a more thorough

analysis of stars

o They have increased the light-gathering power of telescopes by almost two orders ofmagnitude

o The collected image is immediately computerized, allowing for instant digitalstorage, enhancement, and analysis

CCDs have had a highly significant impact on our understanding of celestial objects, as theyhave allowed for significantly more accurate analysis of obtained celestial images

SPACE TELESCOPES

Space telescopes are telescopes launched into Earths orbit, taking images outside of Earthsatmosphere

Some space telescopes include HIPPARCOS (launched 1989 by ESA), the Hubble telescope(launched 1990 by NASA), and GAIA (due to be launched 2013 by ESA)

Space telescopes are an improvement on previous measurement technologies becauseo Radiation detected by space telescopes is not subject to atmospheric distortion,

allowing for the most of the EMR spectrum to be detected and analysed => this

provides greater understanding of stellar radiation

o Radiation detected is not subject to atmospheric distortion, meaning images have ahigher resolution without the need for adaptive optics, astrometric measurements

are more accurate => this is particularly useful with parallax measurements

(astronomers predict that GAIA could measure parallax of >200 million stars) and

resolving globular star clusters, which has enhanced our understanding of stellar

evolution

o Images obtained are much less subject to background radiation, allowing for greatersensitivity

Thus space telescopes have had a significant impact on our understanding of celestialobjects, as they have allowed for a greater range of the EMR spectrum to be measured, and

provided significantly more accurate data of celestial bodies.

o e.g. The Hubble telescope allowed the Hubble constant to be calculated within 10%,allowing for a greater understanding of the universes expansion

WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP)

WMAP is a NASA Explorer mission launched in 2001 to make fundamental measurements oncosmology (the study of the universe as a whole)


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WMAP was launched on a spacecraft to measure differences in temperature of the BigBangs remnant radiant heat

WMAP was a significant improvement in measurement technology, as it provided thefollowing data:

o Reported the first detection of pre-stellar heliumo Placed 50% tighter limits on the standard model of cosmologyo Measured, with very high significance, temperature shifts induced by hot gas in

galaxy clusters

o Improved visual measurements of the polarization patterns around hot and coldspots

WMAP led to the production of the new Standard Model of Cosmology Thus WMAP has had a highly significant impact on our understanding of celestial objects

through the collection of new and more accurate measurements, and the development of

new cosmological models.

More information can be found at:http://map.gsfc.nasa.gov/Perform an investigation to demonstrate the use of filters for photometric

measurements

METHOD

A light box was set up in a darkened room with a red cellophane filter placed in front of thelight source. A light meter was directed towards the light source, and readings were taken

with no additional filtering, a yellow filter, then a blue filter placed in front of the light

meter, and results were recorded. The process was repeated for blue-filtered light. DO NOT

LOOK DIRECTLY AT THE LIGHT SOURCERESULTS

Light Filter Intensity (x2000 lux)

Red No filter 580

Yellow (Visual) 530

Blue (B) 33

Blue No filter 100

Yellow (V) 45

Blue (B) 60

By considering magnitudes, B-V for the red star produces a positive result (remembermagnitudes decrease as brightness increases), which reflects expected results

B-V for the blue star produces a slightly negative result, which was expected. As can be seen, a redstar has apositivecolour index, whilst a bluestar has a negativecolour

index

RELIABILITY

Multiple results were taken, and an average was obtained The range of results for each data point was minimal, thus indicating precise results Our results were compared to other groups, all of which produced similar results

VALIDITY

The method tested the aim by demonstrating the use of colour filters in photometricmeasurements, specifically colour index
http://map.gsfc.nasa.gov/http://map.gsfc.nasa.gov/http://map.gsfc.nasa.gov/http://map.gsfc.nasa.gov/


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Other variable which werent tested were minimised, such as external light The use of technology (i.e. the light meter) produced accurate results The results matched the expected results, and corroborated with reliable information

sources such as textbooks, reputable websites, and scientific journals.


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

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

spectroscopic and astrometric

A binary star system consists of two stars orbiting around their common centre of mass

The systems centre of mass lies at the point where the following relationship holds true:where from the diagram above

o m1and m2= the masses of the respective stars [kg]o r1and r2= the radii of each star from the centre of mass [m]

The brighter star in a binary pair is designated with the letter A, and the dimmer isdesignated with B

Binary stars are classified by their means of detection The classes of binary stars dealt with in this course are visual, eclipsing,spectroscopic, and

astrometric

VISUAL

Can be resolved into two stars by a telescope => they can be detected visually Visual binaries orbit very slowly, and can take many years to be confirmed as a binary pair The period and radius of each orbit can be measured by visual observation and analysis,

allowing the mass of the overall system to be calculated (see below)

ECLIPSING

Eclipsing binaries whose orbital plane is oriented so that it is almost parallel to Earths line-of-sight

The stars regularly eclipse each other, causing periodic minima in the brightness of thesystem, as seen on a light curve

o The primary minima correspond to the greatest decreases in brightness, whichdepends on the tilt of the orbit, the relative size of the stars, their surface

temperatures, and their atmospheric structures


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Eclipsing binary system are more easily detected if period of each star is short, hence mosteclipsing binaries are close systems

The diameter of each star can be determined by the duration of each eclipse, and the periodof the stars can be determined by the period of either the primary or secondary eclipses

A flat-bottomed eclipse indicates a total eclipse, whilst a curved-bottomed eclipse indicatesapartial eclipse

SPECTROSCOPIC

Spectroscopic binaries are detected by the alternating Doppler shifting of their spectral lines As the stars orbit, one star will typically have a component of velocity away from Earth, and

the other towards

This causes small red and blue Doppler shifts of the system, causing a double-linedabsorption spectrum

As the stars move in their orbit, they may have no relative motion to Earths line-of-sight,thus have no Doppler shift

The doubling of spectral lines occurs periodically, indicating the presence of a binary system


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Spectroscopic binaries are best detected if the component of velocity measured by Dopplershift is large (maximised when plane of orbit is parallel to Earths line-of-sight), and the

period of each stars orbit is short (i.e. a close system)

The period of the alternating Doppler shift reveals the period of each stars orbit, and thedegree of Doppler shift reveals the velocity of each starASTROMETRIC

Astrometric binaries are detected by an apparent wobble in a stars proper motion One of the stars is too faint to be observed The centre of mass follows a straight path Measurements of the visible stars wobble reveal the period of orbit and size, allowing for an

estimation of the mass of the system


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Explain the importance of binary stars in determining stellar masses

There is no method of measuring the mass of an isolated star Measuring the gravitational effect of a star on another object provides a method of

determining a stars mass

o For this reason binary stars are VERY important, as they provide the only directmethod of measuring a stars mass

The analysis of the motion binary stars enable astronomers to calculate the mass of starsdue to the presence of gravity between the two stars

The above relationship is used to determine stellar masses

Determining the mass of stars allows astronomers to further our understanding of celestialobjects, such as through the mass-luminosity relationship

o If the luminosity of main sequence stars are plotted against their mass, the followingrelationship becomes apparent

o This relationship shows that as the mass of a star increases, its luminosity increasesat a much faster rate

o Luminosity is a measure of the rate of the consumption of a stars fuel, thus highermass stars consume fuel at a much faster rate => high mass stars thus a have a much

shorter lifetime

o Additionally, the luminosity-mass relationship shows that as luminosity increases upthe main sequence on an H-R diagram, so does the mass => this provides a new

interpretation of the H-R diagram

o SUCH ANALYSIS DEMONSTRATES THE HIGH IMPORTANCE OF BINARY STARSSolve problems and analyse information by applying:

DEFINITIONS

m1+m2= total mass of the binary system (m1mass of star 1, m2mass of star 2) [kg] r = separation distance of the stars [m]


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T = orbital period of the binary system (s) G = 6.67x10-11m3kg-1s-2= Universal gravitation constant The above formula can be derived from equating gravitational force to centripetal force

around the centre of mass, and substituting in the orbital speed

The full derivation can be seen on p.307 of Jacaranda PhysicsREMEMBER

Check the units and dimensions at every line of working Convert all units to S.I. units when using a formula with a constant such as G r is the distance between the centres of mass of each star => you must add the radius of the

star if the distance from the surface is given.

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

Variable starsare ones that appear to vary in brightness with time Most stars vary in brightness over time, e.g. the Suns solar flares cause brightness variations

of ~0.1%

Other stars significantly vary with brightness, and are tracked on a light-curve Below is a diagram showing the classification of variable stars

EXTRINSIC VARIABLES

The variation in brightness is due to a process external to the body of the star itself Extrinsic variables include

o Eclipsing binaries=> the variation in brightness is due to one star of the binary starsystem eclipsing the other

o Rotating variables=> Large cool/hot spots cause the brightness to noticeably changeas the star rotates

INTRINSIC VARIABLES

The brightness variation is due to internal changes of the star => the luminosity (poweroutput) of the star varies

Many intrinsic variables occupy specific locations on an H-R diagram (see below0 Intrinsic variables can be further classified as non-periodicandperiodic


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NON-PERIODIC

Variation in brightness does not follow a regular intervals => the variation is non-periodic Also called cataclysmic or eruptive stars Such stars include supernovae, novae, symbiotic stars, flares stars, R Coronae Borealis, and T

Tauri

Type Brightness variation Physical description

Supernovae Increase to M outbursts from red

giant fall onto white dwarfFlare stars Sudden increase >2

magnitudes, then fade

within hours

Red dwarfs experiencing intense

outbursts of energy from a small area

on surface

R Coronae Borealis Sudden decrease of about 4

magnitudes, slowly

fluctuating back to normal

Yellow supergiant accumulates carbon-

rich dust clouds that obscure surface

T Tauri Vary irregularly Young protostar still contracting from

gas cloud in which they lie

PERIODIC

Show periodic brightness variations Period can range from hours to hundreds of days, and is mostly sinusoidal Brightness variation occurs generally as the stars pulsate in size, surface temperature,

and colour

1. Pulsation occurs due to disequilibrium between gravitational force and radiationpressure, the two primary forces that determine a stars size


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Periodic variables include Cepheids, Mira, RV Tauri, and RR Lyrae variablesType Period (days) Brightness change

(magnitudes)

Description

Cepheid 1-50 0.1-2.0 Very luminous yellow supergiant. Type I

(young) and Type II (older)

Mira 80-1000 2.5-10 Red giants and supergiants

RV Tauri 20-150 No typical value Yellow supergiants

RR Lyrae


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The study of Cepheids in the Small Magnetic Cloud in the early 20thcentury revealed arelationship between the period of a Cepheid and its absolute magnitude

1. Cepheids with longer periods of brightness variations have higher luminosities A Cepheids period can be determined from its measure light curve

Further analysis revealed that there are two types of Cepheids:1. Type I (classical) Cepheids => massive, young, second-generation stars2. Type II (W Virginis) Cepheids => small, old, red, first-generation stars3. Astronomers can determine the Cepheid type from spectral analysis

The following graph demonstrates the period-luminosity relationship

As the graph shows, the luminosity (or absolute magnitude) of a Cepheid can bedetermined from the period of brightness variation

Consequently, the distance to a Cepheid can be calculated using the distance modulusformula

METHOD FOR CALUCLATING DISTANCE TO A CEPHEID1. Establish the type of Cepheid through spectral analysis2. Determine the period from its light curve3. From the period-luminosity relationship, use the period to determine the stars

average absolute magnitude (M)

4. From direct observation, measure the stars average apparent magnitude (m)5. Use the distance modulus formula to calculate the distance to the star


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Thus the luminosity-period relationship has proved significant in determining distancesto Cepheids

o This has allowed for distances to be calculated within our galaxy, and toneighbouring galaxies as well

Perform an investigation to model the light curves of eclipsing binaries using

computer simulation

METHOD

A java application on the following website was used to simulate light curves of eclipsingbinaries:

http://www.astro.cornell.edu/academics/courses/astro101/herter/java/eclipse/eclipse.htm.

The spectral classes of each main sequence star were altered (F and F, F and B, F and M)

whilst the separation (12 solar radii) and angle of view (5) was kept constant. The resulting

light curve was recorded and compared. The spectral class (B and F) and angle (5) was then

kept constant, and the separation was altered.

RESULTS

Spectral classes B and F, 5 angle to plane, 12 solar masses separation

Spectral classes B and F, 5 angle to plane, 25 solar masses separation

Spectral classes F and F, 5 angle to plane, 12 solar masses separation
http://www.astro.cornell.edu/academics/courses/astro101/herter/java/eclipse/eclipse.htmhttp://www.astro.cornell.edu/academics/courses/astro101/herter/java/eclipse/eclipse.htmhttp://www.astro.cornell.edu/academics/courses/astro101/herter/java/eclipse/eclipse.htm


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Spectral classes M and F, 5 angle to plane, 12 solar masses separation

The first simulation demonstrates total eclipses, indicated by the flat-bottomed troughs As the more luminous star is eclipsed by the less luminous star, a primary trough occurs. As

the less luminous star is eclipsed by the more luminous star, a secondary trough occurs. In

this simulation, luminosity is related to spectral class as main sequence stars are modelled.

The troughs have a shorter duration as separation increases, as the orbital velocity of eachstar is faster.

RELIABILITY/VALIDITY

The computer simulation provided a highly accurate model of our current understanding ofeclipsing binaries.

The results are based on precise mathematical analysis, hence are very reliable. Variables were controlled in the simulation, thus a valid method was followed.


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6.Stars evolve and eventually dieDescribe the processes involved in stellar formation

A star forms from a region of large quantities of interstellar medium called a nebula,which consists of interstellar dust and gas (mostly hydrogen molecules, but also heliumand other ionised gases)

o Interstellar medium forms after the death of larger stars, hence matter isessentially recycled

o The dust in gas clouds obscures or blocks light coming from nebula, thus it isdifficult to observe the process in stellar formation => X-ray, infra-red and radio

wave radiation penetrate dust, so these telescopes provide the information on

stellar formation

The gas cloud is triggered into gravitational collapse, such as the explosion of a nearbystar (e.g. supernova), the first burst of radiation from a nearby star, or collisions

between gas clouds.

The gas cloud starts contracting due to the gravitational between particles to form adenser core

The density of the core gradually increases over time, which increases the gravitationalforces between the core and gas molecules, thus the star contracts even faster

o The rate at which a star contracts depends on its size => a star of 0.2 solarmasses would take billions of years to contract to a protostar, whilst a star of 30

solar masses would take only 30 000 years.

As the core contracts, the gravitational potential energy of the gas particles areconverted to kinetic energy, so the gas cloud heats up


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The heat creates an outwards pressure that opposes the gravitational collapse (calledthe hydrostatic equilibrium), only slightly at first, but it gradually builds

When the star is hot enough, the outwards pressure stabilises the size of the core whilstthe surrounding gas continues to fall inwards => at this stage the star is called a

protostar

With no source of energy, the gas cloud in a protostar continues to collapse, whichincreases the temperature of the core

Once the cores temperature reaches approximately 10 million Kelvin, the fusion ofhydrogen is triggered, which provides a long-lasting energy source that stabilises the star

=> the star is now a zero-age main sequence star

Not all gas clouds form stars however


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o Gas clouds of less the 0.08 solar masses cannot heat sufficiently to trigger thefusion of hydrogen

o Gas clouds of greater than 30 solar masses are too unstable during collapse dueto overheating, and blow apart to form smaller stars

The above processes have been limited the formation of a single star in a gas cloud, butmost often more than one star forms from a gas cloud, creating a binary star system or a

cluster of stars

o The contracting gas clouds could form multiple cores, which would eventuallyform multiple stars

o Multiple stars can also be formed from the fragmentation of a star, as a starspins faster as it contracts (conservation of angular momentum) => this can also

lead to a system of planets around a star

Summary

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

The key stages in a stars life are summarised in the flow-chart below:

NEBULA TO MAIN SEQUENCE A star initially forms from a cloud of dust and gas (interstellar medium) called a nebula. The nebula gradually collapses under its own gravity to form several cores of matter The gravitational potential energy is converted to kinetic energy, thus the core heats up, and

provides radiant pressure to oppose the gravitational forces inwards


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The core is called aprotostar when the core stabilises (i.e. forces are balanced), and thesurrounding cloud becomes luminous.

The star continues to shrink and heat up => when it reaches a temperature of around 1x107Kand sufficient pressure, hydrogen fusion commences in the core, and the star becomes a

Main Sequence star

o There is a balance between the gravitational force inwards and radiant pressureoutwards, thus the star stops contracting

o The star remains on the Main Sequence of the H-R diagram for around 90% of itslifetime

o The position a star enters the Main Sequence depends on its mass => a higher massstar will start on the Main Sequence at a higher point

See above for a more detailed description of star birth, see below for a description ofthermonuclear reactions in Main-Sequence stars

POST-MAIN SEQUENCE

Recall the mass-luminosity relationship, which demonstrates that a star of higher massconsumes its fuel at a higher rate (thus giving higher surface temperatures)

o A star of 0.3 solar masses stays on the Main Sequence for around 30 billion years,whilst an O class stays on the Main Sequence for only 30 000 years

When the helium content in the core reaches around 12%, the fusion of hydrogen stops The future of the star depends on its mass:

o A small mass star (less than 0.5 solar masses) will not be able to fuse heavierelements, so the star collapses to form a white dwarf, which are the hot remnants of

a star

o A core of a star of greater than 0.5 solar masses is able to reach high enoughtemperatures to commence helium fusion to carbon, with hydrogen fusion in the

core => this star is called a Red Gianto When a star runs out of fuel in the core (i.e. it cannot fuse heavier elements), the

star collapses under its own gravity, and can form a white dwarf, neutron star, or

black hole depending on its mass

RED GIANT

As mentioned above, when a Main Sequence star runs out of hydrogen fuel it startscontracting due to the lack of energy to oppose the gravitational force

If a star has a high enough mass, the temperature and pressure in the shell surrounding thecore will have the required temperature and pressure to allow hydrogen fusion => this is

called shell burning.


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o This expands and cools the star, causing it to move off the Main Sequence towardsthe top-right of the H-R diagram

As the star contracts, gravitational potential energy is converted to kinetic energy, so thecore heats up, and allows the fusion of helium if a star has a high enough mass, and fuse

hydrogen in the shell

o This may happen in a helium flash(helium fusion starts suddenly in the core) forstars less than 2.6 solar masses, or smoothly for higher mass stars

o After helium fusion starts, the star contracts again, thus the stars surfacetemperature increases, and it moves towards the left of the H-R diagram

A star remains a red giant until the fusion of heavier elements stops (i.e. the star runs out offuel)

See below for a more detailed description of star death


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

Sequence stars

As mentioned above, main-sequence stars remain stable due to the energy radiated bythermonuclear reactions

The two main nuclear reactions in Main-Sequence stars are the proton-proton chain and thecarbon-nitrogen-oxygen (CNO) cycle => MEMORISE THESE REACTIONS

PROTON-PROTON CHAIN

The proton-proton chain occurs in all stars once they reach the main sequence, but onlyeventually dominates in cooler Main-Sequence stars like the Sun

The proton-proton chain consists of the following three reactions:

Whereo = neutrino (small, massless, chargeless particle)o e+= positron (positive electron)o = gamma photono Hydrogen-2 = deuterium

The first two reactions must proceed twice before the last reaction takes place As six hydrogen nuclei go into the reaction but two come out, the overall reaction is The mass of four hydrogen nuclei more than the mass of a helium nucleus => the lost mass is

converted to energy according to E=mc2, which provides the energy for the star

CARBON-NITROGEN-OXYGEN (CNO) CYCLE

The CNO cycle is another thermonuclear reaction in stars, but only dominates in stars moremassive than the star, where the core temperature exceeds 1.6x10

7K=> both reactions can

still proceed simultaneously however


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The CNO cycle consists of the following reactions:

Note that the carbon-12 acts as a catalyst The net reaction is still that four hydrogen nuclei combine to produce a helium nucleus, and

release the energy similarly to the proton-proton chain due to the overall mass deficit.

POST-MAIN SEQUENCE


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Helium fusion occurs in the core of a star through the triple alpha reaction (recall that ahelium nucleus is called an alpha particle)

Carbon then can fuse with a helium nucleus to produce oxygen Elements up to iron can be fused in the core to provide energy for the star => beyond

Discuss the synthesis of elements in stars by fusion

Hydrogen and helium were the only elements present in the primordial universe => all otherelements have been synthesised in stars

All Main Sequence stars fuse hydrogen nuclei to produce helium nuclei throughaforementioned thermonuclear reactions in the core

The mass of a star determines the elements that can be further fused in a post-MainSequence star through exothermic nuclear reactions

Elements up to iron (atomic number 26) can be fused in the shell of a post-Main Sequencestar => elements beyond iron are fused in endothermic reactions, thus are not fused in the

core of a star

o A supergiant can develop an onion-like structure of many layers of shell burning ofdifferent elements, though only for a short period of time (heavier elements fuse

more quickly) => the fusion of silicon to iron typically lasts only for one day

Fusion fuel Core

products

Core

temperature (K)

Mass (solar

masses

H He 4x106 0.1He C, O 120x10

6 0.4

C Ne, Na, Mg,

O

600x106 4

Ne O, Mg 1.2x109

Approx. 8

O Si, S, P 1.5x109 Approx. 8

Si Ni to Fe 2.7x109 Approx. 8

Elements beyond iron are produced in two ways:o The slow capture of neutrons in a helium-burning

shell of a red giant can produce elements up to leado The fast capture of neutrons in a supernova explosion,

which provides enough energy to produce elements

up to uranium

Explain the concept of star death in relation to:

planetary nebula supernovae white dwarfs neutron stars/pulsars black holes


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A star dies after it stop fusing element to produce the energy required for stable existence The processes involved in star death depend on the mass of the star

PLANETARY NEBULA

Occurs for stars of less than 5 solar masses A star of this size can fuse helium in the shell, but does not fuse oxygen in the core The unsupported hells become unstable, and produce bursts of energy known as thermal

pulses and high superwinds These pulsations blow eventually around a quarter of the stars material away from the

stars core, which eventually forms an expanding shell-shaped nebula => this is called a

planetarynebula

o The name planetary nebula is historical, as early astronomers believed these nebulato be planets

WHITE DWARFS

Occurs for stars of less than 5 solar masses White dwarfs are the remnant core of a star after material has been blown off to form a

planetary nebula


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No fusion reactions proceed, so the core collapses due to gravitational forces to a sizearound the size of Earth, forming a very dense, glowing core called a whitedwarf

The balancing force comes from electron degeneracy pressure, which results from aquantum effect where closely-spaced electrons are prevented from being on the same

energy level

A white dwarf has a surface temperature of around 10 000K but a relatively low luminositydue to its small size, so it exists at the bottom-left of an H-R diagram

A white dwarf eventually radiates its remnant energy, and becomes a brown dwarf White dwarfs have a maximum mass of 1.4 solar masses (can be higher for rotating white

dwarfs) => beyond this mass the gravitational forces are too strong for electron degeneracy

pressure to balance the force

SUPERNOVAE

This occurs for stars of greater than 5 solar masses Larger stars are also subject to the pulsations that blow material away, and form a rapidly

contracting core

The high mass of the star however means that electron degeneracy pressure is not enoughto balance the gravitational forces, so the star continues to contract until degenerate

neutronpressure halts the contraction.

The surrounding layers are bounced back, causing a supernova explosion

A significant quantity (~1046J) of gravitational energy is emitted in a few seconds, leavingbehind a very dense core

Iron and other heavy nuclei are ripped apart, releasing a large number of neutrons => theseneutrons can be captured to produce heavier nuclei

NEUTRON STARS/PULSARS

Occurs for stars between 8 solar masses and 25 solar masses If the residual matter from a supernova forms a core of between 1.4 and 3 solar masses, a

neutron star will be formed

The mass of the star means that gravitational forces overcome the electron degeneracypressure, crushing the protons and electrons together to form a sea of neutrons

Below 3 solar masses, the neutron degeneracy pressurebalances the gravitational forces, sothe collapse halts to form a neutron star of around 10km in diameter


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A neutron star formed is a very dense, hot star that is rapidly rotating (dozens of times persecond) due to conservation of angular momentum as the star shrinks to a significantly small

fraction of its initial diameter

Neutron stars also have a very strong magnetic field (108T) that emits an beam ofelectromagnetic radiation

As the magnetic axis rarely aligns with the rotation axis, the electromagnetic beam sweepsacross space as the neutron star rapidly rotates

If the Earth is aligned with the beam, the neutron star can be detected (most commonly withradio telescopes) from the very regular pulsations of radiation detected => this is why

neutron stars are also called pulsars

BLACK HOLES

Occurs for stars greater than 25 solar masses When the remnant core of a supernova is greater than 3 solar masses, the gravitational

forces are strong enough to overcome the neutron degeneracy pressure

No known force is able to counter the significant gravitational forces, so the matter iscrushed to a single point of infinite density called a the singularity

The gravitational forces are so strong that not even light can escape the singularity from acertain radius called the event horizon, hence the celestial object is called a black hole

Black holes cannot be directly detected due to the lack of EMR emitted, but can be detectedfrom its effect on surrounding objects

o For example, material accelerated into a black hole emit X-rays that can be detected


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Explain how the age of a globular cluster can be determined from its zero-age mainsequence plot for a H-R diagram

A globular cluster contains hundreds of thousands of old stars in a sphere of around 100light-years in diameter that have evolved from a giant molecular cloud

o This is in contrast to an open cluster, which contains a few hundred young stars in agroup of around 10 light-years in diameter

The relative ages of open clusters and globular clusters is known because open clusterscontain O and B spectral class stars, whilst globular clusters do not => higher mass stars have

a shorter lifetime, so a cluster containing high mass stars is a relatively young cluster

The diagram below shows an H-R diagram of an open cluster and a globular cluster against aZero-Age Main Sequence (ZAMS) line

o Luminosities can easily be determined, as the stars in a cluster are about the samedistance to Earth


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The globular cluster has a lower turn-off point from the ZAMS line and a more developedgiant branch than the open cluster

o In other words, the highest remaining point of the Main Sequence group is lower forthe globular cluster

Lower mass stars have a longer lifetime than higher mass stars due to the mass-luminosityrelationship, so if more low mass stars have become red giants, then the cluster must be

older

Thus as the star ages, it appears to peel off the main sequence, as higher mass starsprogressively become red giants

In other words, the lower the turn-off point from the ZMAS line in an H-R plot of a globularcluster, the older the cluster

The age of a globular cluster can be estimated by considering the lifetimes of the stars thathave left the ZAMS line, and the lifetimes of those still on the line

o In the above diagrams, the open cluster on the left is estimated to be about 600million years old, whilst the cluster on the left is about 13 billion years old

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

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


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Consider the H-R diagrams below of (left to right) nearby and brightest stars, stars in a youngopen cluster (such as the Pleiades), and stars in a globular cluster

The plot of the nearby or brightest stars shows a random sampling, so all the prominent stargroups are present

Star clusters were formed at the same time however, so they are not a random samplingsince they are all of the same age

The plot of the young open cluster lies almost entirely within the ZAMS line The plot of the globular cluster however consists of the bottom half of the ZAMS line, and a

number of stars occupying the red giant region, indicating that the missing Main Sequence

stars have become red giants and shifted to the right

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

10 solar masses during their life cycle

Stars of 1, 5, and 10 solar masses enter the H-R diagram on a track shown below:

The H-R diagram below shows the life cycles of stars of 1 and 5 solar masses:


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For a star of 1 solar masso The star enters the Main Sequence at the position indicatedo Once it has fused all the hydrogen in the core, it proceeds to burn hydrogen in the

shell, causing expansion and cooling of the stars surface

o The core contracts due to gravity, causing the temperature and pressure to increase=> once it reaches the right conditions, helium begins to fuse to carbon in a helium

flash

o The star contracts until helium fusion stops in the core and shell burning again,causing it to contract

o No further fusion occurs so luminosity decreases, and the star contracts due togravity, causing the surface temperature to rise => the star becomes a white dwarf

o NOTE: The evolutionary track from the red giant to white dwarf should be lower (i.e.the star does not sweep upwards as shown)

For a star of 5 solar masseso The star follows a similar track to the 1 solar mass star, but enters the Main

Sequence at a higher point due to its higher masso The star experiences a supernova however and becomes a neutron star, so does not

exist on the H-R diagram after the supernova

Below is an H-R diagram of a star of 10 solar masses


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For a star of 10 solar masseso The star follows a similar evolutionary pathway to the 1- and 5- solar mass stars,

but at a higher luminosity into the supergiants region

o The star is able to fuse elements heavier than helium in the core, so moves leftand right in the giant region more often

o The star then goes to a supernova and a black hole, and thus exits the H-Rdiagram in the supergiants region

Analyse information from an H-R diagram and use available evidence to determine

the characteristics of a star and its evolutionary age

Many characteristics of a star can be determined directly from an H-R diagram, such ascolour, surface temperature, chemical composition, and luminosity.

The position of a star on the H-R diagram can also help determine what type of star it is:


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Thus from an H-R diagram, we can determine the characteristics and evolutionary age of astar according to its position

For aprotostar(lower than Giants, to the right of Main Sequence)o It is at the beginning of its lifeo No fusion proceeds in the coreo Very cool but luminous, therefore large in size

For a Main Sequence staro It is in the middle of its life, and remains in the Main Sequence for the majority of its

lifetime

o Hydrogen fusion in the core to produce helium either by the proton-proton chain orthe CNO cycle

o A main sequence star towards the top left of the H-R diagram is young,o Stars higher on the Main Sequence burn their fuel at a much higher rate, and are

larger in size than those lower on the Main Sequence => stars towards the bottom of

the Main Sequence are considered dwarfs For a Giant

o It is towards the end of its life, as it has consumed most of its fuelo It is relatively cool but luminous, thus is largeo It is fusing hydrogen to helium in its shell, and may be fusing helium to carbon

through the triple alpha reaction in its core

For a Supergianto It is towards the end of its life, as it has consumed most of its fuelo It is relatively cool but very luminous, thus it is very largeo It is fusing heavier elements in its core, and fusing various other elements in its shell

in an onion-like structure

For a white dwarfo It is at the end of its life, as it is no longer fusing elements to produce energyo It is a relatively hot star but not very luminous, thus it is very small (i.e. is a dwarf)o It is the remains of a former star, and is probably surrounded by a planetary nebula

hsc physics module 9.7 summary

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