Abstract:
The following article concerns the James Webb Telescope Cosmic Mining Project (offered by the Institute for Research in Schools), undertaken by a group of students in Abingdon School. The project focuses on the classification of the spectra (showing the intensity over a range of electromagnetic wavelengths) of stars and galaxies identified by the Spitzer Space telescope as targets for the James Webb telescope, when launched. After this, a variety of more complex ideas related to astronomy were considered and in some cases attempted to be applied to the spectra which had been classified. This research is important and interesting because the detailed information recorded on stars gives insight into their life cycles and the origin and fate of the universe, about which we currently know very little.
Introduction:
For the past seven months, Abingdon School students have been assigned data sets from the Institute for Research in Schools Cosmic Mining project. The task was to classify celestial objects into their specific types based on the shape of their spectra which contributes to identifying potential targets for the James Webb telescope for further research.
Each data set provided by IRIS consisted of 50 AOR (An individual Spitzer observation sequence or Astronomical Observation Request) keys which correspond to a particular spectrum taken from the Spitzer Space Telescope. The spectrum showed the variation in intensity (radiation flux density) of electromagnetic radiation emitted by the star against wavelength.
Each spectrum provided the information required to complete the table in order to determine the type of celestial body.
We also classified galaxies according to their redshift. This indicates the apparent increase in wavelength of a galaxy’s light due to the Doppler effect: as the source of a wave moves away from the observer the wave it emits appears to stretch due to relative motion. This can be used to work out the recessional velocity of the galaxy and hence its distance, since Edwin Hubble and Georges Lemaître showed that the two factors appeared to be directly proportional. This fact also led him to theorise that the universe had in fact always been expanding at the same rate going right back to a single point. This is therefore evidence for the universe having a beginning: the Big Bang.
Background information on telescopes:
There are two telescopes in question, the Spitzer Telescope (the source of all the spectra) and the James Webb Telescope (which is yet to be launched). Using both these telescopes, one can view the full range of infrared wavelengths emitted by the celestial object.
Spitzer Space Telescope[1]
This is “the first telescope to see light from a planet outside our solar system”. It was launched in 2003 and retired on 30 Jan 2020. The main function of the telescope was to observe infrared light (ranging from 3.6 to 160 microns). It provides spectral observations taken by the Infrared Spectrograph. In order to minimise the adverse effects of heating by the Sun, Earth or Moon, it orbits an Earth trail. The telescope was also cooled by a system that used liquid helium.
Figure 1: The Spitzer Space Telescope
James Webb Telescope[2]
The James Webb Telescope is the largest and most sophisticated telescope designed in human history. Being more advanced than the Spitzer Space telescope, it is able to observe infrared wavelengths (ranging 0.6 – 30 microns) which therefore provides more detailed and intricate spectra for analysis. It is composed of a six metre mirror, sunshield and instruments which provide a plethora of pictures and spectrographs to analyse the unknown object.
Figure 2: The James Webb Telescope
Method:
First, we completed the training set and submitted it to one of the mentors from IRIS. The mentors provided a new set of unseen data after successfully classifying everything in the training set.
In order to complete the work efficiently, we classified through division of the workload, with each team member filling out specific columns in the table. For example, one person would identify which spectra corresponded to galaxies so that they could mark potential redshifts into our table of results. The others were in charge of making informed decisions about initial classification which involved studying features of the spectrum. Ultimately, the final classification was discussed as a group.
The visual image provided by the CASSIS (Combined Atlas of Sources with Spitzer IRS Spectra)[3] database was examined; this helped to identify whether the celestial body was unknown, noise or an actual star. 
To the right is an example of noise provided by the CASSIS database.
Then, the continuum of the graph was observed: an increasing gradient implies either a planetary nebula or a forming star. Conversely it would be an ordinary or evolved star.
Finally, the data corresponding to features of the graph was entered in a table such as the one below.
This is an example of the classification table provided by IRIS 
Key terms
Redshift: The apparent change in the frequency of a wave between the source of the wave and the observer caused by relative motion. This causes a shift in the position of the continuum of the spectrum. The extent of this shift can be found using the relativistic doppler equation, in which 
is observed frequency, 
is actual frequency, 
is speed of light and 
are speeds of the observer and source respectively. Redshifts are only observed in galaxies, as these are receding from us due to the expansion of the universe. Taking into account the effects of special relativity this equation becomes: 
Continuum: Gradient of the line in the spectra.
Stellar component: Peak in the optical part of the spectrum (shorter wavelengths)
Red Excess: Presence of continuum at longer wavelengths
Absorption: Dip in the spectrum due to electrons of certain elements being excited and absorbing photons of specific wavelengths of light.
Emission: Bump in the spectrum due to de-excitation of electrons of certain elements emitting photons of specific wavelengths of light.
Atomic Emission Lines: Prominent narrow lines in the spectrum (most common in planetary nebulae). 
Typical features for each classification of stars:[4]
Forming Star: The process of the formation of a star starts when a dense cloud of gas particles and dust called nebula is pulled together under gravity and begins to heat up due to its gravitational potential energy being converted into kinetic and heat energy. Forming stars have low flux density at shorter wavelengths (below 15 microns), but gradually increase in longer wavelengths (above 20 microns). Therefore, it can only be seen by an infrared telescope.
The key features of their spectra are a rising continuum and absorption (dips in the continuum) at 10 microns.
The picture on the left shows the types of forming stars.
The picture on the right is an example of a forming star spectrum.
Ordinary star: An ordinary star is in its main sequence (Occupying the diagonal line lying in the middle of the H-R diagram): during this time it is fusing hydrogen into helium (this is the stage in which the sun is currently in). The force of the star\’s own weight is exactly counterbalanced by the force exerted by the fusion of hydrogen in its core. Thus the star remains the same size during this period. Stars spend most of their lives in their main sequence phase.
The key features of the spectra are a falling continuum and a very smooth spectrum: as the star is in its main sequence no heavy elements (causing disturbances in the continuum) are present in its atmosphere.
The following picture is an example of an ordinary star spectrum
Evolved star: An evolved star has reached the end of its main sequence. Now there is no longer any hydrogen to fuse into helium so the star initially contracts as there is no force caused by nuclear fusion to counteract its own weight pulling it inwards. However this heats up the core of the star sufficiently for it to begin to fuse heavier elements and swell into a supergiant which has a larger peak intensity of light in the visible (red) part of the spectrum. This is a red giant.
Evolved stars also show a falling continuum but minor disturbances in the continuum indicate the presence of certain elements: for example absorptions or emissions at 10/18 microns indicate oxygen (O rich) and at 15 microns indicate carbon (C rich). This due to the unique energy level transitions of electrons in each of these atoms.
The picture on the left shows the types of evolved stars.
The picture on the right is an example of an evolved star.
Planetary Nebula:
Planetary nebulae are formed by an enlarging shell of hydrogen gas surrounding an ageing star, at the end of the life of a red giant. The star (which is too small to explode in a supernova) ejects its outer layers as planetary nebulae leaving its core as a white dwarf. Planetary nebulae exhibit an initially rising continuum which turns over above 25 microns.
The picture is an example of a Planetary nebula.
Results:
Here are some examples of classifications.
Below is an example of a spectrum that is easy to classify. The first step would be to look at the continuum of the spectrum – perhaps the most important feature – and clearly in this case it is rising. As such, it had to be either a planetary nebula or a forming star.
Then, the emissions and absorptions in the spectrum were identified. Here there is an emission at 10 microns and an absorption at around 13 microns. Though the absorptions might indicate a forming star, the shape of the continuum was the overriding factor so the correct classification is a planetary nebula. 
However, in the example below the method of prioritising continuum was not valid, as the spectrum cuts off after 15 microns.
Though the general shape may suggest a planetary nebula, this is in fact a forming star (as the turnover would occur at a longer wavelength for a planetary nebula) with a very short spectrum available.
Results like this (from the training data) required constant rigorous analysis of all the available information, as consideration of the general shape alone would not be enough to classify conclusively (for example one could examine the High Resolution spectrum within the range of wavelengths which one would usually expect to see the trademark shape). 
This is our table of results for the classifications of unknown objects detected by the Spitzer Space Telescope.
Each row in the table describes the specific features of the spectrum of each star which helps determine the type of star.
Discussion:
The results of this project are significant because they provide more detailed information about which stage of their life cycle the stars are in. There is also special emphasis given to the abundance of certain elements within the core of some stars which gives insight into the distribution of certain elements in the universe. This could also indicate the kind of dying star from which the planetary nebula which formed the new star came. More broadly, the information gathered on redshifts can be used to examine the expansion of the universe. This provides evidence for the existence of dark energy.
An alternative approach to the project in order to gain a better understanding of the universe would be to focus on measuring the recessional speed and the Doppler effect of the galaxy by comparing the spectra of distant stars to the spectra obtained by light emitted from chemical elements in a lab, which would have allowed a more practical approach to the research.
The data analysed will be useful for future applications as it pinpoints the most interesting stars and galaxies for the James Webb Telescope to examine when it launches next year: this will be able to give more detailed data on these celestial bodies than ever before (including, for example, the chemical composition of exoplanets orbiting some of these distant stars) and hence accelerate the progress in the quest to better understand the nature and origin of the universe.
During the research, the process of analysing the spectrum is quite repetitive. Therefore, programming a computer algorithm to identify the features of the spectra might have been more efficient and accurate.
Analysis:
Further research on the science behind the project was conducted to relate to the results of the classification of stars.
The H-R diagram:
The H-R diagram provides a different approach to identify the stars through their surface temperature and luminosity. The vertical axis is labelled as the absolute magnitude/magnitude while the horizontal axis is labelled as spectral class/temperature/color. Both axes are logarithmically scaled. The vertical axis (luminosity of the star) is measured in solar units where the Sun’s luminosity = 3.90 x 1026 W. The higher up the axis, the greater power output the star has.[5] The Stefan-Boltzmann law helps us obtain the luminosity of the stars:
The law states that: 
, where 
is the surface area of the sphere; 
is the Stefan-Boltzmann constant, 
and 
is the temperature of the star.
Hence, luminosity is directly proportional to the radius squared.
This shows that the greater the radius of the star, the higher its luminosity. So, for a given temperature, the higher the star is located in the diagram (due to a higher luminosity) the larger radius it has.
This is reflected in the H-R diagram in which the giant stars are situated above the main sequence. The main sequence stars have radii in the range 0.1 R⊙ and 10 R⊙ and the giant stars have radii in the range between 10R⊙ and 100 R⊙.
The horizontal axis is labelled as spectral class in the original diagram. Though, it is sometimes referred to as the temperature or colour. Temperature is directly related to a star’s colour and its spectral classes. The temperature of the star determines the spectral lines emitted by the star. The spectral classes can be represented by letters in the order of decreasing temperature, O, B, A, F, G, K, M. The O stars have surface temperatures around 40000 K, the coldest M stars have surface temperatures around 2500 K. Each class is subdivided into 10 subclasses using numbers from 0 – 9, 0 as warmest and 9 as coldest.[6]
Main features of the Hertzsprung-Russell Diagram:
The main sequence stars occupy most of the diagram. It is the diagonal band that lies in the middle. The sun is an example of a main sequence star.
Luminosity: 10-2 to 106 Lsun
Temperature: 3000 to 50000 K
Radius: 0.1 to 10 Rsun
The giants and supergiants are located at the upper right of the diagram. They are greater in size with higher luminosity compared to the main sequence (around the same temperature as the main sequence). Betelgeuse is an example of a red giant star.
|
Giants: |
Supergiants: |
|
Luminosity: 103 to 105 Lsun |
Luminosity: 105-106 Lsun |
|
Radius: 10 to 100 Rsun |
Radius: greater than 103 Rsun |
White Dwarfs
White Dwarfs are situated on the bottom left of the diagram. They have lower luminosity comparatively and smaller radius (about the size of Earth).
Wien’s Law
This further enhances the relationship between the peak wavelength in the radiation spectrum emitted by a star and its surface temperature. (This relates to both the H-R diagram and the spectrum datas.)
Wien’s Law states that the peak wavelength given by a star:
Where 
is the absolute temperature in Kelvin.
is the Wien’s displacement constant which equals to 
.
∴ The peak wavelength emitted is inversely proportional to temperature .
∴Conversely, the peak frequency is proportional to temperature. 
Figure 3: Intensity vs wavelength graph from the Lummer Pringsheim experiment.
The graph above shows the proportional relationship in both Wien’s law and Stefan-Boltzmann law:
[Wien’s law.]
[Stefan-Boltzmann law.]
How this relates to the spectra
With this law, the peak emission of a star can be determined at a specific wavelength which shows the various proportions of radiation emitted in the EM spectrum.
The spectrum on the left is an ordinary star whilst the right is a planetary nebula. As the nebula has a lower temperature than the ordinary star, Wien’s law suggests that the nebula would then have a longer peak wavelength which, looking at the spectrum, seems to be true. The ordinary star’s spectrum also supports the law as it rises towards the shorter wavelengths (with a peak presumably out of the range of the given wavelengths).
Furthermore, the Stefan-Boltzmann law states that luminosity is proportional to temperature to the power of four. Thus, the ordinary star has a higher luminosity. This is shown in the Hertzsprung Russell diagram in which the ordinary star is situated in the top left of the main sequence section. Overall this suggests that our classifications are consistent with the mathematical equations describing them.
Conclusion
This project was initiated in order to gain a deeper understanding of the nature of the light emitted from stars during their life cycle. Topics beyond the scope of the James Webb project, the initial area being researched, were further investigated in an effort to explain not only the shape of the spectra but the reasons why they were this shape. The results analyzed will go on to aid the identification of unknown objects by the James Webb telescope.
References:
- Calla, C., 2020. Spitzer Space Telescope. Jpl.nasa.gov. https://www.jpl.nasa.gov/news/press_kits/spitzer/
- Jwst.nasa.gov. 2020. Comparison: Webb Vs Hubble Telescope – Webb/NASA. https://jwst.nasa.gov/content/about/comparisonWebbVsHubble.html
- \”Combined Atlas Of Sources With Spitzer IRS Spectra\”. 2020. Cassis.Sirtf.Com. http://cassis.sirtf.com/.
- \”IRIS Data Server\”. 2020. Dataserver.Researchinschools.Org. http://dataserver.researchinschools.org/.
- Richmond, Michael. 2020. \”The Hertzsprung-Russell Diagram\”. Spiff.Rit.Edu. http://spiff.rit.edu/classes/phys301/lectures/hr/hr.html.
- \”The Hertzsprung-Russell Diagram\”. 2020. Ohio State, Lecture 10:Astronomy.Ohio-State.Edu. http://www.astronomy.ohio-state.edu/~jaj/Ast162/lectures/notesWL10.pdf.
Figure References:
- NASA’s Spitzer Space Telescope has concluded after more than 16 years of exploring the universe in infrared light. Image. NASA’s Spitzer Space Telescope Ends Mission of Astronomical Discovery. Feb. 12, 2020 https://www.nasa.gov/press-release/nasa-s-spitzer-space-telescope-ends-mission-of-astronomical-discovery.
- NASA\’s James Webb Space Telescope Completes Primary Mirror Test. 2020. Image. May. 14, 2020 https://www.nasaspaceflight.com/2020/04/nasas-james-webb-completes-primary-mirror-test/.
- Distribution of blackbody radiation which shows Wien’s displacement law. Quantum: Einstein, Bohr and the Great Debate About the Nature of Reality – Manjit Kumar (2009). Aug. 22, 2020 https://publicism.info/science/quantum/2.html
- Spectra and visual images from the Spitzer Space Telescope. Combined Atlas of Sources with Spitzer IRS Spectra. October, 2019 http://cassis.sirtf.com/
- Graphs and tables of classification. IRIS James Webb Telescope research training guidelines and booklets. October, 2019
About the Authors
Ashwin Tennant, Ivan Gabestro, and Scott Yap are Lower sixth pupils of Abingdon School. They are currently studying for their A levels and are keen physicists and mathematicians. They began to work on this project in a physics club in school. The project was chosen as it is closely related to the astronomy module in A level Physics. The project members also have an interest in spectroscopy which links to the spectra being examined. The prospect of a deeper understanding of the physics behind the data was additionally appealing.