HSC Physics Module 9.7 Summary
1. Our understanding of celestial objects depends upon observations made
from Earth or from space near the Earth
Discuss Galileo’s 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 moon’s surface was uneven, rough, and full of cavities and 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 Earth’s surface however, as most wavebands are filtered out by the atmosphere. The only wavebands that predominantly reach Earth’s surfaces are visible light, microwaves and radio waves.
EMR Waveband Wavelength (m) Absorption by atmosphere Gamma rays <10-10 Absorbed X-rays 10-11 to 10-7 Absorbed UV light 10-8 to 4x 10-7 Mostly absorbed Visible light 4x10-7 to 7x10-7 Not absorbed Infra-red 7x10-7 to 1x10-2 Mostly absorbed Radio waves 1x10-3 to 1x106 UHF, VHF, HF, MF
and LF frequencies not absorbed. Rest absorbed.
As a result of the absorption by the atmosphere of electromagnetic wavebands, ground-based telescopes 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 resolution of 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] λ = 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.
The image to the left has a poorer resolution than the one on the right, as the stars are less distinct. The sensitivity of 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 Earth’s 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 aren’t absorbed by the atmosphere. The distortion of EMR wavebands is also known as seeing, and is due to tiny, rapidly changing temperature variations in Earth’s 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.
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
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
REFER TO PRAC 9.7.1 f)
METHOD
Circles of variable diameter were constructed out of paper. M&Ms, which represented photons, 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, and recording the intensity of light. Take a recording of ambient light as a control to increase the investigation’s validity => DO NOT LOOK DIRECTLY AT SUNLIGHT
RESULTS/CONCLUSION
As aforementioned, number of photons was plotted against diameter squared, yielding a linear 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 and reality (photons are massless, does not show wave properties of light etc.)
2. Careful measurement of a celestial object’s position in the sky (astrometry)
may be used to determine its distance
Define the terms parallax, parsec, light-year
Parallax is 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.
A parsec is 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.
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 Earth’s 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 Earth’s 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.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 to
o Limits in resolution (e.g. atmospheric blurring), which increase the error of reading o The refraction of light in Earth’s atmosphere
Ground-based telescope => V.L.T. (Very Large Telescope) o Built by the European Southern Organisation o Minimum angle of parallax: 0.01-arcsec
o Allow for distances up to 100pc to be measured o Only a few hundred stars are this close
o Limited by atmospheric blurring (despite interferometry and adaptive optics), and refraction of light in Earth’s atmosphere
Space-based telescope => Hipparcos (HIgh Precision PARallax COllecting Satellite) o Launched by the European Space Agency in 1989
o This allows for distances up to 1000pc to be measured => Hipparcos has measured the parallax of around 100 000 stars.
o Hipparcos’s parallax measurements are limited by the precision of the reading equipment
Future telescope => GAIA
o Due for launch in 2012 by the European Space Agency as a follow-up to Hipparcos o Minimum angle of parallax: 10 microarcseconds
o Allows for measured distances up to 100 000pc o Parallaxes of >200 million stars can be measured o Limited by the precision of the reading equipment
As can be seen, space-based telescopes are able to achieve a much more precise
measurement of parallax angles than ground-based telescopes, as space telescopes are not limited by atmospheric effects.
Sources of information
o http://outreach.atnf.csiro.au/education/senior/astrophysics/parallaxlimits.html o ESO (European Space Organisation) and NASA website
3. Spectroscopy is a vital tool for astronomers and provides a wealth of
information
Account for the production of emission and absorption spectra and compare these
with a continuous blackbody spectrum
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 discrete frequencies, given by
o If the electron had been excited to an even higher excited state, then it can return to its ground state in one single jump, or by a set of smaller jumps
o Each particular jump down between energy levels represents different quantities of energy, 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 continuous spectra (see below)
o Each element has a unique emission spectra, thus its emission spectra is a ‘fingerprint’ for the element
Absorption spectra
o 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 a
discrete quantity of energy
o The gas absorbs the photons from the continuous source, but only at the wavelengths matching the differences in energy levels
o The atoms then re-emit the light as the electrons jump back down, but in all different directions => only a fraction of the re-emitted radiation is in the direction of the incidence light
o The absorbed wavelengths appear as dark lines on an otherwise continuous spectrum
o The dark lines on the absorption spectrum for an element correspond to the bands 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 absolute temperature, described by a black body curve (or a Planck curve)
o As the temperature of the body increases, the peak wavelength becomes shorter, and the intensity of emitted radiation increases
o Most high-density hot bodies approximate a black body
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)
Whilst not required by the syllabus, Wien’s displacement law provides a quantitative means of calculating a star’s temperature if the peak wavelength emitted is known:
Where:
o λmax = maximum wavelength emitted [m] o T = Temperature of black body [K] o W = Wien’s constant = 2.898x10-3
mK
This equation may be given however, which would simply require reading the peak wavelength 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 beam
2. The beam passes through a glass prism, which disperses the light into its spectrum 3. 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 available for more sophisticated analysis
o Diffraction gratings can be used instead of a prisms to increase the spectral resolution of images obtained
o Collimators are used instead of slits to narrow the light beam
o 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 CCD that 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 astronomical spectra
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 gas clouds (mostly hydrogen and helium) that glow due to intense UV light from nearby stars Emission spectrum => dominated by strong emission 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 absorption or emission depending on the abundance of nebulae in a galaxy => young galaxies tend to show emission spectra, whilst older galaxies tend to show absorption
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 their composition, surface temperature, and other features.
Stellar spectrum consists of absorption spectrum characteristic of the atmospheric elements superimposed 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 very
different spectral lines
Different atoms and molecules produce spectral lines of very different strengths at different temperatures
o For example, at lower temperatures molecules can exist near the surface, whilst at higher 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 A Fine Girl/Guy Kiss Me)
o There are also other spectral classes (see below) that have been discovered in recent times
o Each spectral class is divided into 10 sub-classes, with 1-10, where 1 is the hottest and 10 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, N
emission 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 7500 – 10000 White Strong Ionised metal
lines
0.6 F 6000 – 7500 White-yellow Medium Weak ionised
Ca+ lines
3
G 5300 – 6000 Yellow Weak Ionised Ca+
lines, metal 8
lines
K 3800 – 5300 Orange Very weak Ca+ Fe, strong molecules, CH, CN
12
M 2100 – 3800 Red Very weak Molecular
bads e.g. TiO, neutral metals
76
L 1200 – 2100 Red Negligible Neutral
metals, metal hydrides
Brown dwarf, numbers uncertain
T <1200 Red Negligible Methane
bands
Brown dwarf, numbers uncertain Below is a diagram showing the stellar spectra of different spectral classes, which
demonstrates the link between spectrum and spectral classes.
Recall that stars of the same surface temperature (or spectral class) can have different luminosities
This suggests that one star has more surface area than the other (i.e. one star is larger than the other)
This has led to the development of luminosity classes to also define a star Luminosity class Description
Ia Bright supergiant
Ib Supergiant
II Bright giant
III Giant
IV Subgiant
V Main sequence dwarf
VI Subdwarf
VII Dwarf
For example, the Sun is a G2 V star
Describe 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 surface temperature of the star
By assigning a star a spectral class based on its spectra, the corresponding surface temperature can be inferred
Alternatively, the effective surface temperature can be calculated by determining the peak intensity wavelength of radiation from a star, and substitute it into Wien’s law
ROTATIONAL VELOCITY
Recall that the Doppler effect causes the lengthening or shortening of wavelengths due to rotational motion
As a star rotates, one side is moving away relative to Earth, and one side is moving towards Earth.
The side moving away from Earth is red-shifted due to the Doppler effect, and one side is blue-shifted
This causes the broadening of absorption spectral lines, which can then be analysed to determine the rotational velocity of a star
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 away relative to Earth, its spectrum will be red-shifted If a star is moving towards Earth, its spectrum will be blue-shifted
By measuring the distance the spectrum is shifted, the star’s velocity away from or towards Earth can be calculated
By combining this with the star’s sideways velocity, the star’s translational velocity relative to the Sun can be calculated
DENSITY
The lower the density a star’s surface, the lower the gas pressure At lower pressures, gases produce sharper absorption spectral lines
Thus high density and pressure within a star’s atmosphere can also broaden the absorption spectral lines
Supergiants have lower atmospheric density and pressure, whilst main sequence stars have higher 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 star’s atmosphere produce the absorption lines on a star’s 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 star’s atmosphere The relative intensity of the absorption lines indicates the abundance of that element
Perform a first-hand investigation to examine a variety of spectra produced by
discharge tubes, reflected sunlight, or incandescent filaments
METHOD
Sunlight’s spectrum was observed by going outside, pointing a spectroscope away from the Sun, and recording the spectrum observed. An incandescent light’s 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 incandescent light 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 by staying 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 filament’s and discharge tube’s spectra, thus controlling the variables
Qualitative data was collected => reliability of data not important (though repeated observation and comparison to others helps!!!)
4. Photometric measurements can be used for determining distance and
comparing objects
Define absolute and apparent magnitude
The apparent magnitude (m) of an object is a measure of how bright an object appears when viewed from 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 influenced by 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 body’s 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]
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
Outline spectroscopic parallax
Spectroscopic parallax is a method of determining the distance to a star using the H-R diagram and the distance modulus formula
The steps involved in spectroscopic parallax are:
1. Measure the apparent magnitude (m) of a star using photometry
2. Determine the spectral class and luminosity class of a star using spectroscopy 3. 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 the absolute 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 the estimates in determining the absolute magnitude
Spectroscopic parallax is useful however for calculating approximate distances, as often there 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 are
useful
The observation of a star’s colour depends on the sensitivity of the detection method to different 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 star’s spectrum and the spectral sensitivity of the eye
o For example, the peak intensity of blue giants lie in the UV/violet part of the spectrum, yet appear blue-white to the human eye
The brightness or apparent magnitude of stars appears to change when viewed through different 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 a
photometer, 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 star o This is called the colour index of a star, and is defined by
o B = mB = apparent magnitude as viewed through a blue filter o 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 of the detection method to different colours
o Colour index can be used to determine the spectral class of a star, which can then be used to determine its distance from Earth
NOTE: Absolute magnitudes are also dependent on colour sensitivity, so ensure that when using 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 of silver salts to light
Filter Central wavelength (nm)
Ultraviolet (U) 350
Blue (B) => photographic 440
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 original signal by millions of times
o Photodiode, which consists of a solid state device that acts as a light detector o 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
Advantages of using photoelectric devices over photographic methods include
o 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 can detect 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 digital images, 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 can only record a single image
o Faster processing => CCDs provide images much faster than photographic film o Increased astronomical sensitivity => CCDs can record images from fainter objects o 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 a
significant 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 Wilkinson Microwave Anisotropy Probe.
CHARGED-COUPLED DEVICES (CCDs)
CCDs consist of a light-sensing array developed since the 1970s that records incident photons by means of the photoelectric effect => the same technology (but much simpler) is used in digital cameras
CCDs are an improvement on previous photographic technologies because…
o 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 of magnitude
o The collected image is immediately computerized, allowing for instant digital storage, enhancement, and analysis
CCDs have had a highly significant impact on our understanding of celestial objects, as they have allowed for significantly more accurate analysis of obtained celestial images
SPACE TELESCOPES
Space telescopes are telescopes launched into Earth’s orbit, taking images outside of Earth’s atmosphere
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 because… o 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 a higher 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 greater sensitivity
Thus space telescopes have had a significant impact on our understanding of celestial objects, 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 universe’s expansion
WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP)
WMAP is a NASA Explorer mission launched in 2001 to make fundamental measurements on cosmology (the study of the universe as a whole)
WMAP was launched on a spacecraft to measure differences in temperature of the Big Bang’s remnant radiant heat
WMAP was a significant improvement in measurement technology, as it provided the following data:
o Reported the first detection of pre-stellar helium
o Placed 50% tighter limits on the standard model of cosmology
o 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 cold spots
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 the light 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 SOURCE
RESULTS
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 (remember magnitudes 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 red star has a positive colour index, whilst a blue star has a negative colour 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 photometric measurements, specifically colour index
Other variable which weren’t 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.
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 system’s centre of mass lies at the point where the following relationship holds true: where from the diagram above
o m1 and m2 = the masses of the respective stars [kg]
o r1 and 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 is designated 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 Earth’s line-of-sight
The stars regularly eclipse each other, causing periodic minima in the brightness of the system, as seen on a light curve
o The primary minima correspond to the greatest decreases in brightness, which depends on the tilt of the orbit, the relative size of the stars, their surface temperatures, and their atmospheric structures
Eclipsing binary system are more easily detected if period of each star is short, hence most eclipsing binaries are close systems
The diameter of each star can be determined by the duration of each eclipse, and the period of 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 indicates
a partial 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-lined absorption spectrum
As the stars move in their orbit, they may have no relative motion to Earth’s line-of-sight, thus have no Doppler shift
Spectroscopic binaries are best detected if the component of velocity measured by Doppler shift is large (maximised when plane of orbit is parallel to Earth’s line-of-sight), and the period of each star’s orbit is short (i.e. a close system)
The period of the alternating Doppler shift reveals the period of each star’s orbit, and the degree of Doppler shift reveals the velocity of each star
ASTROMETRIC
Astrometric binaries are detected by an apparent wobble in a star’s proper motion One of the stars is too faint to be observed
The centre of mass follows a straight path
Measurements of the visible star’s wobble reveal the period of orbit and size, allowing for an estimation of the mass of the system
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 star’s mass
o For this reason binary stars are VERY important, as they provide the only direct method of measuring a star’s mass
The analysis of the motion binary stars enable astronomers to calculate the mass of stars due 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 celestial objects, such as through the mass-luminosity relationship
o If the luminosity of main sequence stars are plotted against their mass, the following relationship becomes apparent
o This relationship shows that as the mass of a star increases, it’s luminosity increases at a much faster rate
o Luminosity is a measure of the rate of the consumption of a star’s fuel, thus higher mass 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 up the 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 STARS
Solve problems and analyse information by applying:
DEFINITIONS
m1+m2 = total mass of the binary system (m1 mass of star 1, m2 mass of star 2) [kg] r = separation distance of the stars [m]
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 Physics
REMEMBER
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 stars are ones that appear to vary in brightness with time Most stars vary in brightness over time, e.g. the Sun’s 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 star system eclipsing the other
o Rotating variables => Large cool/hot spots cause the brightness to noticeably change as the star rotates
INTRINSIC VARIABLES
The brightness variation is due to internal changes of the star => the luminosity (power output) 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-periodic and periodic
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<-15 within
hours, then gradual fade over weeks
Accretion of gas leading to runaway nuclear explosion
Novae Sudden increase of ~10 magnitudes over a few days, then fades over years to original brightness
A close binary pair, with one star leaking gas onto a white dwarf, until enough gas accrues to cause surface nuclear explosion
Symbiotic stars Varies semi-regularly over a range of about 3 magnitudes
A close binary pair of a red giant and white dwarf => outbursts from red giant fall onto white dwarf
Flare 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 radiation pressure, the two primary forces that determine a star’s size
Periodic variables include Cepheids, Mira, RV Tauri, and RR Lyrae variables Type 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 <1 <2 Old giants stars with M=~+0.6 Below is an H-R diagram showing the various locations of variables
Explain the importance of the period-luminosity relationship for determining the
distance of cepheids
The study of Cepheids in the Small Magnetic Cloud in the early 20th century revealed a relationship between the period of a Cepheid and its absolute magnitude
1. Cepheids with longer periods of brightness variations have higher luminosities A Cepheid’s 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 stars 2. Type II (W Virginis) Cepheids => small, old, red, first-generation stars 3. 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 be determined from the period of brightness variation
Consequently, the distance to a Cepheid can be calculated using the distance modulus formula
METHOD FOR CALUCLATING DISTANCE TO A CEPHEID
1. Establish the type of Cepheid through spectral analysis 2. Determine the period from its light curve
3. From the period-luminosity relationship, use the period to determine the star’s average absolute magnitude (M)
4. From direct observation, measure the star’s average apparent magnitude (m) 5. Use the distance modulus formula to calculate the distance to the star
Thus the luminosity-period relationship has proved significant in determining distances to Cepheids
o This has allowed for distances to be calculated within our galaxy, and to neighbouring 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 eclipsing binaries:
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 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 each
star is faster.
RELIABILITY/VALIDITY
The computer simulation provided a highly accurate model of our current understanding of eclipsing 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.
6. Stars evolve and eventually die
Describe 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 helium and other ionised gases)
o Interstellar medium forms after the death of larger stars, hence matter is essentially recycled
o The dust in gas clouds obscures or blocks light coming from nebula, thus it is difficult 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 nearby star (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 a denser core
The density of the core gradually increases over time, which increases the gravitational forces 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 solar masses 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 are converted to kinetic energy, so the gas cloud heats up
The heat creates an outwards pressure that opposes the gravitational collapse (called the 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 whilst the 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, which increases the temperature of the core
Once the core’s temperature reaches approximately 10 million Kelvin, the fusion of hydrogen is triggered, which provides a long-lasting energy source that stabilises the star => the star is now a zero-age main sequence star
o Gas clouds of less the 0.08 solar masses cannot heat sufficiently to trigger the fusion of hydrogen
o Gas clouds of greater than 30 solar masses are too unstable during collapse due to overheating, and blow apart to form smaller stars
The above processes have been limited the formation of a single star in a gas cloud, but most 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 eventually form multiple stars
o Multiple stars can also be formed from the fragmentation of a star, as a star spins 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 star’s life in terms of the physical processes involved
The key stages in a star’s 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
The core is called a protostar when the core stabilises (i.e. forces are balanced), and the surrounding cloud becomes luminous.
The star continues to shrink and heat up => when it reaches a temperature of around 1x107K and 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 pressure outwards, thus the star stops contracting
o The star remains on the Main Sequence of the H-R diagram for around 90% of its lifetime
o The position a star enters the Main Sequence depends on its mass => a higher mass star 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 of thermonuclear reactions in Main-Sequence stars
POST-MAIN SEQUENCE
Recall the mass-luminosity relationship, which demonstrates that a star of higher mass consumes 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 heavier
elements, 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 enough temperatures to commence helium fusion to carbon, with hydrogen fusion in the core => this star is called a Red Giant
o 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 starts contracting 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 the core will have the required temperature and pressure to allow hydrogen fusion => this is called shell burning.
o This expands and cools the star, causing it to move off the Main Sequence towards the top-right of the H-R diagram
As the star contracts, gravitational potential energy is converted to kinetic energy, so the core 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) for stars less than 2.6 solar masses, or smoothly for higher mass stars
o After helium fusion starts, the star contracts again, thus the star’s surface temperature 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 of fuel)
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 by thermonuclear reactions
The two main nuclear reactions in Main-Sequence stars are the proton-proton chain and the carbon-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 only eventually dominates in cooler Main-Sequence stars like the Sun
The proton-proton chain consists of the following three reactions:
Where…
o ν = neutrino (small, massless, chargeless particle) o e+
= positron (positive electron) o γ = gamma photon
o 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 more massive than the star, where the core temperature exceeds 1.6x107K=> both reactions can still proceed simultaneously however
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.
Helium fusion occurs in the core of a star through the triple alpha reaction (recall that a helium 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 other elements have been synthesised in stars
All Main Sequence stars fuse hydrogen nuclei to produce helium nuclei through aforementioned thermonuclear reactions in the core
The mass of a star determines the elements that can be further fused in a post-Main Sequence star through exothermic nuclear reactions
Elements up to iron (atomic number 26) can be fused in the shell of a post-Main Sequence star => 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 of different 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 0.1 He C, O 120x106 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 lead o 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
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 star’s material away from the star’s core, which eventually forms an expanding shell-shaped nebula => this is called a planetary nebula
o The name planetary nebula is historical, as early astronomers believed these nebula to 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
