Year 13 Astronomy master class at the Royal Observatory Greenwich

http://www.rmg.co.uk/royal-observatory/

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The picture on the left is the clock at the Greenwich Meridian and the picture on the right is a view of the Queen’s house and Canary Wharf from the observatory.

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Aaron, Abdi and Sulax waiting to start the day.

The first activity of the day consisted of the students learning about the stellar evolution.

http://www.rmg.co.uk/explore/astronomy-and-time/astronomy-facts/stars/stellar-evolution/

Studying sunlight

In this hands-on workshop, students learnt how astronomers determine the properties of distant stars by examining spectra and applying their knowledge of the electromagnetic spectrum, the reflection, absorption and emission of light, and the Doppler Effect.

The workshop began with a demonstration of the dispersion of visible light through a prism and an investigation of the students’ understanding of the properties of waves and the electromagnetic spectrum. The presenter reviewed the concept of wavelength, different kinds of light, and the wavelengths of visible colours.

Students then progressed through a number of hands-on activities to explore how astronomers study starlight, including:

Matching pictures of common objects to their absorption spectra (graphs of absorption versus wavelength) to consider how an object’s colour depends on to what extent it absorbs and reflects the visible wavelengths of light

Matching images of stars in the Sloan Digital Sky Survey to their emission spectra (graphs of light intensity versus wavelength) to become familiar with the temperature-dependent continuum emission of stars

Observing the distinct spectral lines emitted by different gases in commercial ‘neon’ signs with hand-held spectrographs and applying their knowledge of the wavelengths of visible light to identify the gas used in each sign by its chemical signature

Below left is a picture of the students using a thermal camera you can make out Sulax is on the left as the dark area on his face is his glasses.

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Above right shows Sulax with some interesting footwear and having his thermal picture taken by Radmila Topalovic. The aim of this activity was to show that the radiation given off by stars can give information about their temperature. The image shows that Sulax’s legs are at a different temperature to the rest of him because of the black bag.

http://www.rmg.co.uk/about/the-organization/staff-profiles/astronomers/radmila-topalovic/

A spectrum is a ‘fingerprint’ of an object made of light. The spectrum of visible light is composed of the colours of the rainbow.

The different parts of the electromagnetic spectrum are: gamma ray, X‐ray, ultraviolet, visible, infrared, microwave, radio.

These different types of light differ because they have different wavelengths or frequencies which give them different energies e.g. gamma rays have a short wavelength, a high frequency and a high energy, radio waves have a much longer wavelength, a low frequency and consequently a low energy.

X‐rays and gamma rays have high energy radiation which can damage our DNA and our cells; we would become very ill and eventually die from exposure to this radiation. Even though the Sun emits (high energy) X‐rays and gamma rays life evolved on Earth Life and survived because we have an atmosphere that protects us from this radiation.

We have telescopes for the whole of the electromagnetic spectrum and not just for optical light because we can’t see everything with just optical light, often this light is blocked by dust or there are regions in space that do not emit optical light but appear bright in other wavelengths.

Satellites such as Yohkoh, SOHO (Solar and Heliospheric Observatory) and terrestrial telescopes such as the McMath‐Pierce telescope on Kitt Peak in Arizona have imaged the Sun in X‐ray, ultraviolet and infrared light. X‐ray light has the shortest wavelength, infrared is the longest.

The dark patches in the X‐ray and UV images are bright in the IR (these are called coronal holes, regions in the Sun’s outer atmosphere ‐ the corona where magnetic field lines burst through). The dark features in the IR image are bright in shorter wavelengths. There is absorption of IR light by the gas in these regions.

Examples of solar filters are the hydrogen alpha (Hα) which transmits a wavelength of 656.3 nm, the sodium D, wavelength = 589 nm and calcium K filters, wavelength = 393 nm. Through the Hα filter the Sun is red, Na D is yellow and Ca K is blue.

In the X‐ray and visible wavelengths the Milky Way appears dark with brighter regions above and below, particularly in the X‐ray. In contrast the galaxy is very bright in gamma ray and in the opposite region of the electromagnetic spectrum at the longer wavelengths of infrared to radio – here vast diffuse bright regions can be seen around the galaxy.

There is a lot of dust in the Milky Way which blocks visible light from reaching us, however high energy (short wavelength) and low energy (long wavelength) light can penetrate this dust thus our galaxy appears brighter in these wavelengths. Also there is a lot of gas in the Milky Way at a large range of temperatures (and different energies) thus emerging different wavelengths of light.

It important for astronomers to look at objects in space in all wavelengths so we don’t miss anything! Features we can’t see in visible light we can see in other wavelengths, this way we get a complete picture of the object we are studying.

The Sun appears yellow in colour in visible light. We cannot see the Sun in wavelengths outside of the visible region of the electromagnetic spectrum with our eyes however we can build detectors and telescopes that respond to light of other wavelengths. The Sun looks very different in other wavelengths (below). These have been artificially coloured so that we can see them. Satellites such as Yohkoh, SOHO (Solar and Heliospheric Observatory) and terrestrial telescopes such as the McMath‐Pierce telescope on Kitt Peak in Arizona have imaged the Sun in X‐ray, ultraviolet and infrared light.

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The Milky Way looks very different in different wavelengths. Go to http://www.chromoscope.net/ (above) and see the differences between the images taken in different regions of the electromagnetic spectrum.

Spectroscopy

In the mid-1660s Newton conducted experiments on light at Cambridge. He allowed a beam of sunlight to pass through a glass prism and saw the spectrum of visible light. Different colours have different wavelengths and they are the visible part of the electromagnetic spectrum. He published his results in a paper called The Opticks.

In 1814 in Germany, Josef Von Fraunhofer discovered dark lines in the Sun’s spectrum. These gaps are caused by the absorption of specific wavelengths of light by atoms in the Sun. Measuring the wavelengths of the spectral lines reveals the chemical composition of the Sun, which is 74% hydrogen, 24% helium and 1% heavier elements.

Spectroscopy is an important tool to study physical and chemical properties of stars. Composition is one, motion is another and this becomes apparent through the Doppler Effect. This effect is best described by taking the example of a police car with its siren on, moving at high speed towards an observer. The crests of the sound wave will be closer together as the source moves towards the observer and therefore the frequency of the sound wave will be higher. As the police car moves away from the observer, the crests of the sound wave are spaced further apart and the frequency is lower. The same thing happens with light. If a star is moving slightly closer to us, the light is shifted to a slightly higher frequency. When the star moves slightly further away, the light is shifted to a slightly lower frequency.

The whole electromagnetic spectrum is used to study objects in space. Some parts of the spectrum such as X-rays and gamma rays are blocked by the atmosphere; to see this emission space telescopes are used. Black holes in binary systems (orbiting other stars) and the explosions of distant hypermassive stars have been detected using X-ray and gamma ray telescopes. Observations of radio emission from cold hydrogen gas in the Milky Way in the 1950s revealed the structure of our galaxy and the presence of dark matter and infrared observations taken by terrestrial and space telescopes probe the dusty disks of protostars in star forming regions such as the Orion Nebula.

Stars and star light

Stars are objects that produce enough energy (via nuclear fusion in their core) to maintain their size against gravitational collapse.

As the Universe cooled after the Big Bang stars were formed from the hydrogen gas and fusion reactions in stellar cores produced helium and lots of other heavier elements. Large stars explode into a supernova and eject these elements into space to be recycled.

A star much bigger than our Sun produced heavy elements in its core and went supernova. The ejected gas clumped together over time to form our Solar System – all of the elements we have on Earth come from a star.

The atmosphere distorts light reaching us from space, light pollution reduces our ability to observe faint objects, weather (clouds) affects our view of the night sky.

The peak wavelength of a star’s overall spectrum determines the colour of the star. Shorter wavelengths mean higher energy and bluer stars, longer wavelengths represent lower energy spectra and the star will be redder.

Hydrogen (74%), helium (25%), lithium, calcium, magnesium, sodium, iron (these make up 1% of the Sun).

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Aaron is on one side of the world and Abdi is on the other. Sulax is on both.

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Sulax in the Octagon Room, Flamsteed’s House.

http://www.rmg.co.uk/royal-observatory/flamsteed-house-and-meridian/flamsteed-house/

In the afternoon the students did an activity on the expanding universe. They were introduced to the Citizen Science online project Galaxy Zoo whereby members of the public can classify galaxies and contribute to scientific research. They were given real data on galaxies from the Sloan Digital Sky Survey and used basic equations to determine large-scale properties of the Universe.

During the course of the workshop they were introduced to the concepts of luminosity and intensity and how they relate to distance. They also looked at real spectra of galaxies and used the Doppler equation to calculate their velocities.

They then combined these two sets of measurements to produce a velocity-distance graph and discussed what this result tells us about the nature of the Universe.

They practised applying mathematical techniques including: Using the relationship between luminosity and intensity and understanding their units; Measuring the wavelength (in Angstroms) of a hydrogen emission line from a spectrum and using the Doppler equation to obtain a velocity; Converting between different units including astronomical ones such as parsecs. Plotting a graph to determine the Hubble constant and the age of the Universe in billions of years; Thinking about the statistical significance of such a result.

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The above picture shows Brendan Owens introducing the task to the students.

http://www.rmg.co.uk/about/the-organization/staff-profiles/astronomers/brendan-owens/

The age of the Universe

This activity looks at Hubble’s law (v = H0d) whereby the students used real data from the Sloan Digital Sky Survey to plot a graph from which they obtained the Hubble constant, H0. Students then looked at the possible sources of error in their data and used this to calculate the uncertainty in their value for H0.

We know the Universe is expanding because we look at the light from galaxies and we know they are moving away from us and each other, accelerating with distance. Edwin Hubble first discovered this in 1923 using his 100” reflector on Mount Wilson in the US.

The problems or constraints that might be there in trying to measure the motion of galaxies are that very distant galaxies are faint and difficult to measure; the telescope must have a high sensitivity but also be capable of resolving emission spectra from galaxies. The atmosphere affects observations and so a space telescope is useful for these kinds of studies but they can’t be as big as terrestrial telescopes.

We measure the distance to a galaxy and its velocity by measuring its intensity and finding its luminosity to get the distance and use its spectrum to find the velocity from Doppler shifted lines.

The observational constraint related to galaxies would put an absolute lower limit on the age of the Universe because the most distant galaxy observed must be younger than the age of the Universe i.e. the oldest galaxy seen so far (by the Hubble Space Telescope) is 13 billion light years away, this is 0.7 billion years less than the current value for the age of the Universe.

A larger value of the Hubble constant than 70.1 would give a younger age for the Universe. A steeper gradient of the velocity‐distance graph would mean galaxies have greater velocities at a certain distance, this could suggest a larger acceleration in the expansion of the Universe which may mean a lower density of matter or a greater repulsive force from something like dark energy.

Calculating the Error in H0

The velocity of the galaxy if the measured wavelength, λ of the Hα line = 7094 ± 1 Å shows a redshift (observed wavelength is longer than rest wavelength).

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The error, Δv in the calculated velocity, v can be found by using the equations below:

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The value of H0 for each row in the table (velocity ÷ distance) and taking the average of these values gives a value of 85.218.

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Comparing this number to the gradient of the graph shows a different value of H0. The two values are different because one was calculated using values of H0 from each of the galaxies and the other was taken from a best fit line through the points. This method is more accurate as it uses the whole sample to get a truer estimate of H0 and not individual galaxies where the uncertainty is much larger.

The error in the measured value for H0 is 0.0082. The value of H0 is 50.507 ± 0.008 km s^1 Mpc^1. This is a very small error ‐ looking at the graph and the scatter of points around the line a much larger error in H0 is expected. We did not take into account the error in the distance along with the assumptions about luminosity.

Sources of Error in H0

Hubble’s law states that the recessional velocity of galaxies increases with their distance from us, this is shown in the graph below. The gradient is defined as the Hubble constant, H0 which is usually given the units km s^1 Mpc^1, where Mpc is megaparsec, an astronomical unit equivalent to 3.09 x E19 km.

The distance of a galaxy can be determined from its measured intensity and intrinsic luminosity. Its velocity can be calculated by using its spectrum. A galaxy spectrum often shows strong hydrogen emission lines such as Hα (below). By measuring the wavelength of this observed line and comparing it to the rest wavelength we can tell whether it is redshifted or blueshifted and then we can calculate the velocity of the galaxy using the Doppler equation.

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Every measurement or observation has an uncertainty or error associated with it. The value for the Hubble constant calculated from the motion of one of the galaxies in the SDSS sample is 108.28 km s^1 Mpc^1.

There are a number of assumptions made in the derivation of this value and sources of error. The measured wavelength of Hα from the galaxy spectrum will have an uncertainty that is dependent on the resolution of the instrument used. For example if the measured wavelength is 7094 Å, the error, Δλ = 1 Å. There will also be an error in the laboratory wavelength which would be very small but here we will make it a bit bigger: rest wavelength of Hα = 6562.790 Å, error, Δλ0 = 0.001 Å. We use a value for the speed of light when calculating the velocity from the wavelength, c = 299 792 458 m s^1.

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A typical measured value for the intensity of the galaxy might be 16.26 x E15 W m^2. The associated error, ΔI, for a value of 2 dp accuracy would be                       0.01 x E15 W m^‐2. To calculate the distance to the galaxy we must use its luminosity, in this exercise we assume each spiral galaxy has the same intrinsic luminosity. The value for H0 above was calculated using only one galaxy. A more accurate value of H0 can be measured by using a large sample of galaxies and plotting their velocity vs distance from which H0 can be deduced (graph above).

Calculating the Error in H0

The quantity we wish to determine is derived from several measured quantities. Errors in measured values can be incorporated into functions to determine the error in the final calculated value. Consider two in dependent measured quantities X and Y and their errors ΔX and ΔY. The error in the derived quantity, ΔF can be determined as follows:

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You can find the error, Δv in the calculated velocity, v using the equations below:

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The graph should look like the one below. The equation of a straight line follows the form:

y = mx + c. The gradient of the graph is equal to Hubble’s constant, H0.

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Latest value for H0

The most accurate value for the Hubble constant has been determined using a different technique to Hubble. A satellite called the Wilkinson Microwave Anisotropy Probe (WMAP) has been measuring temperature fluctuations as small as 0.0002 K in the left‐over radiation from the Big Bang (called the cosmic microwave background, CMB) since 2001. Ripples in the CMB indicate the initial conditions for the formation of galaxies and reveal the shape and fate of the Universe.

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The European successor to WMAP, a satellite called Planck is currently mapping the sky using radio receivers operating at very low temperatures. They will reveal anisotropies (temperature differences) in the CMB to a resolution of 1 microkelvin and will determine a more precise value for H0.

image  image                           The above picture on the left shows Brendan checking calculations and the above picture on the right shows Abdi, Aaron and Sulax busy doing the calculations to find the Hubble’s constant.

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