This post is the final part of a series on how to write a paper. The first was on abstracts, the second on introductions, the third on related work and fourth on methodology and analysis of results.
I’m combining future work and conclusions into a single post since they are often found combined in a single section in a paper. While a conclusion is always necessary, sometimes people don’t include future work. While I don’t think it’s always necessary to have a future work section, I would argue that it’s always worthwhile to include some mention of future work.
Let’s start with Future Work.
The future work section is a place for you to explain to your readers where you think the results can lead you. What do you think are the next steps to take? What other questions do your results raise? Do you think certain paths seem to be more promising than others?
Another way to look at the future work section, is a way to sort of “claim” an area of research. This is not to say that others can’t research the same things, but if your paper gets published, it’s out there that you had the idea. This lets people know what you’re thinking of doing next and they may ask to collaborate if your future research area crosses over theirs.
If you do include a future work section, it should be pretty short. The goal should not be to go into a bunch of details, but instead just a sentence or two explaining each idea. It should just provide enough information as to a possible research path and why the path may be important. Motivation is always key in research. I stressed earlier that you need to motivate your research. This also applies to future work. If you can’t motivate a good reason to continue research down some path, then why should/would you?
Conclusions are the last section people read in your paper, and therefore it’s what they leave remembering. You need to make sure they walk away thinking about your paper just the way you want them to.
Your conclusions needs to do three main things:
- Recap what you did. In about one paragraph recap what your research question was and how you tackled it.
- Highlight the big accomplishments. Spend another paragraph explaining the highlights of your results. These are the main results you want the reader to remember after they put down the paper, so ignore any small details.
- Conclude. Finally, finish off with a sentence or two that wraps up your paper. I find this can often be the hardest part to write. You want the paper to feel finished after they read these. One way to do this, is to try and tie your research to the “real world.” Can you somehow relate how your research is important outside of academia? Or, if your results leave you with a big question, finish with that. Put it out there for the reader to think about to.
- Optional Before you conclude, if you don’t have a future work section, put in a paragraph detailing the questions you think arise from the work and where you think researchers need to be looking next.
Things to not do in your conclusion:
- Introduce new information. The conclusion is for wrapping up everything you’ve done. It’s not a place to say “oh yeah, and we also got result y.” All results should be first presented and detailed in the result section. Think of the conclusion as a place to reflect on what you’ve already said earlier in the paper.
- Directly re-quote anything you’ve already written. I’ve seen conclusions that are almost identical to the abstract or a collection of sentences from throughout the paper. As a reader, it makes me think the author was lazy and couldn’t be bothered to actually summarize their results for the paper. Take the time to write a proper conclusion so that the reader walks away with good thoughts about your work.
- Write a conclusion longer than your introduction. A conclusion should be short, and to the point. You’ll rarely see them over 3 paragraphs, and three is often long. A lot of the time they are usually only one or two. Think about a conclusion as a chance to see how concisely you can summarize your entire research project. It’s your “30 second” research spiel.
Next week I plan on posting my general pet peeves when a) reading papers and b) reading reviews of papers. Do you have any?
Thesis summary & future work
- This Is Spinal Tap (1984)
The beginning of the end
As was discussed in the introduction, this work is split into two distinct sections, one dealing with carbon-rich evolved stars (chapters 6 & 7) and one dealing with oxygen-rich evolved stars (chapter 8). The aim has been to identify dust forming around these stars. Several interesting new results have been found. In the next section there is a precis of the outcome of studying the optical properties of solids (see Chapter 4). The discovery of an error in previous laboratory-produced spectra (Dorschner et al 1978, Friedemann et al 1981, Pegourie 1988) has had some interesting implications for work in later chapters. The results of the work on carbon stars are summarised in section 9.3, and then in the following section the results of the work on oxygen-rich stars is discussed. Finally, the future work arising from these studies is discussed in section 9.5.
In chapter 2, the basics of stellar evolution and nucleosynthesis were discussed so that the origins of the building blocks of dust grains could be recognized and the evolution of dust type with the evolution of the star could be understood. This chapter also had implications for the meteoritic work discussed in chapter 3. The work on meteoritic data was intended to help the reader to understand how the isotopic study of the meteoritic samples leads to the identification of the sources of the samples by comparison with nucleosynthesis models. The physical nature of circumstellar grains was also discussed, along with the discrepancies between the results from the studies of these samples and the astronomical models (i.e. dust species formed, grain formation and growth models, radiative transfer models) for such grains.
Optical properties of solids
In order to interpret the observed astronomical spectra it is necessary to have a good understanding of the way in which electromagnetic radiation interacts with solids. This was the aim of chapter 4. A simple explanation of how the physical properties of a solid determine its spectrum was discussed in section 4.2, followed by a brief discussion of the special case of very small particles of solids in section 4.3. The difference between the spectral properties of bulk medium and those of a medium consisting of particles whose diameter is small compared with the wavelength of light incident on it was explained. One of the major findings of this work was the discovery of an error in many of the published spectra of silicon carbide and some other dust types. This error was exposed whilst trying to reconcile meteoritic SiC data with the numerous astronomical observations which had, until now, presented a discrepancy between the type of SiC carbide believed to form around carbon-rich AGB stars and that found in meteorites, also believed to form around such stars. Meteoritic SiC grains are all of the beta-SiC type, while astronomical observations seemed to be best explained by the presence of alpha-SiC. The probability of a grain forming as alpha-SiC and then somehow transforming into beta-SiC is very low, and therefore this discrepancy could not be easily explained. This problem actually arose through a misunderstanding of the optical properties of solids, which lead to the imposition of a matrix-correction factor applied to those spectra taken using a dispersion matrix. Having discovered this problem, uncorrected SiC spectra were used and have had a profound effect on the fitting of the 11.3 µm feature seen in the spectra of carbon stars (see next section and chapter 6). The work on optical properties was followed, in chapter 5, by a catalogue of spectra of minerals which may constitute some of the dust around evolved stars. The differences and similarities between the various spectra were discussed, and the possible condensation sequence of such minerals in the circumstellar environment around evolved stars was outlined.
The work on carbon-rich stars was split into two section based on the specific dust/molecular species of interest, i.e. silicon carbide (SiC; chapter 6) and PAHs/HACs/interstellar diamonds (chapter 7). In chapter 6, we discussed the presence of an 11.3 µm feature in the infrared spectra of carbon stars which has been attributed to silicon carbide (Hackwell 1972; Treffers & Cohen 1974). Circumstellar SiC is particularly interesting because it is found in meteorites and the meteoritic grains appear to have suffered very little alteration during their travels through the interstellar medium (see Chapter 3). Since the discovery of the 11.3 µm feature, there has been considerable of curiosity about the exact nature of the silicon carbide dust around these stars, and to this end, many astronomers have used laboratory spectra to try to constrain the properties of the dust (Friedemann et al. 1981; Borghesi et al. 1985, Pegourie 1998; Groenewegen 1995, Speck et al. 1997a,b). As mentioned above, until now there has been a discrepancy between the meteoritic and astronomical work of silicon carbide grains. This discrepancy seems to have arisen through the use of an erroneous correction factor applied to the laboratory data used for fitting spectral features. Having eliminated the problem with the laboratory data, it was found that the 11.3 µm feature was fitted using beta-SiC, rather than alpha-SiC as was previously found (e.g. Speck et al. 1997 a,b; Groenewegen 1995). This removes the discrepancy between meteoritic and astronomical results at least as far as the grain type is concerned. It does however introduce other questions which were successfully avoided by astronomers while the meteoritic dust was not seen as representative of the dust around C-rich AGB stars. For instance, the SiC grains found in meteorites are relatively large (up to 26 µm in diameter), whereas the grains expected to cause the 11.3 µm feature are less than about 0.1 µm in size (see section 3.2.2). Isotopic studies of the grains found in meteorites show that even the noble gases trapped in them have signatures of AGB-star formation, and therefore the large grains were also formed in these regions. While we cannot observe these grains due to their large diameters, that does not mean they do not exist. At present, there are no grain growth mechanisms that can produce such large grains and radiative transfer models have consistently ignored large grain sizes (e.g. Bagnulo et al. 1995). This needs to be addressed. It was also found that many of the observed 11.3 µm features could be best fit using self-absorbed SiC (i.e., the 11.3 µm SiC feature in both emission an absorption simultaneously), rather than SiC in pure emission.
The second interesting result arising from the work of the SiC feature in the spectra of carbon stars was the discovery of three sources with SiC absorption features, a phenomenon previously observed in only one stellar spectrum (AFGL 3068; Jones et al. 1978). Observations of all four sources exhibiting the SiC absorption feature are shown in chapter 6. Furthermore, two of these spectra also showed evidence for interstellar silicate absorption. The best fits to the spectra of these stars was found to use self-absorbed silicon carbide. These observations show that carbon stars can produce enough SiC to eventually develop optically thick dust shells. These may also be the sources where the dust shell is dense enough to be able to produce large SiC grains needed to explain meteoritic data.
UIR bands in carbon star spectra
A discussion of the nature and origin of the so-called unidentified infrared (UIR) bands was presented in chapter 7. The origin of these bands is believed to be some sort of carbonaceous grain(s) or molecule(s) interacting with ultraviolet light. There have been many suggestions for the origin of these grains/molecules, including the formation around carbon stars. Unfortunately, carbon stars do not produce UV radiation to excite to UIR bands and so even if the grains/molecules do form in these regions they would not be detectable in infrared spectra. This suggests that, if the UIR band carriers do form around carbon stars, we just need to find carbon stars with a source of UV radiation in order to detect them. To this end, the spectra of three stars with hot-star companions were studied. The results in chapter 7 showed that UIR bands were indeed detected in the spectra of two of these stars, and thus at least some form of UIR band carrier must form in the circumstellar shells around carbon stars. Unfortunately, many of the UIR bands observed in other objects are outside the range of our 8-13 µm observations. In order to investigate the UIR bands in carbon star spectra, we need to have observations with a wider wavelength range. This avenue can be explored through the ISO-SWS spectra of such sources (see section 9.5).
Dust around oxygen-rich AGB stars was discussed in chapter 8. The problem with oxygen-rich stars, as opposed to the carbon-rich stars already discussed, is that the number of different dust species that are expected to form is much larger, and the spectra of many such species are quite similar (see chapter 5). There has been a suggestion that the dust around oxygen-rich stars evolves, and thus their infrared spectra evolve. With this in mind, the spectra of 80 oxygen-rich AGB/supergiant stars were divided into six groups based of their spectral features. It was assumes that the sequence of groups represented some sort of dust evolution, and hence various correlations of spectral features with physical parameters of the stars were sought (e.g. mass-loss rate, spectral type etc.). As in previous work (Hashimoto et al 1990, Little-Marenin & Little 1990), no correlations were found except with the asymmetry function (see Chapter 8), which implies that the light curve of an O-rich star becomes more asymmetric as the star evolves. In addition, the spectral features for each of the stars in this sample were identified. The results of this were as follows:
1) There is little or no evidence of corundum (Al2O3) in these circumstellar shells. This was unexpected, since this is the first dust-type expected to form and is postulated to become a nucleation site for further dust species to form. Many dust formation and radiative transfer models have been found to improve with the addition of corundum. However, a feature that has previously been attributed to some form of Al2O3, can be better explained as due to silicon dioxide. The non-detection of Al2O3 has certain implications. Either this particular grain type does not form, or it forms in such small quantities that it remains undetectable. If the latter is true, radiative transfer models could be used to determine an upper limit to the amount of Al2O3 that forms around O-rich stars. If the former is true, the proposed condensation sequence of O-rich grains around these stars need to be re-evaluated
2) Silicon dioxide (SiO2) is the best explanation for both the 12.5-13 µm feature, previously attributed to Al2O3, and the peak seen in several spectra in this sample at 9.2-9.35 µm. This feature has not been mentioned before, possibly due to the lower resolution of previous observations (e.g. IRAS). The detection of the ``SiO2''-feature implies that such grains should be included into grain growth/formation mechanisms and radiative transfer models. Such work has already been started by Morioka et al. (1998).
3) The spectral differences between the various silicates, particularly the magnesium silicates, are too subtle for a more exact identification of the major 9.7 µm feature in the observed 10 µm spectra than ``silicates'' or possible ``magnesium silicates''. The only possible way to identify the minerals present in these spectra more accurately, would be using much longer wavelength observations, where slight differences in the mineralogical composition of the dust has a much greater effect on the positions of the spectral features (see next section).
The research presented in this thesis seems to have raised more questions that it has answered. There are several lines of research arising from this work which should be pursued.
Firstly, the work on the optical properties of silicon carbide came about through a collaboration with Anne Hofmeister at Washington University in St. Louis. It is our intention to investigate thoroughly the optical properties of silicon carbide, with a view to explaining how different physical parameters (e.g. grain size, shape, crystal structure) affect the shape of the infrared feature. This will hopefully eliminate any misunderstanding of the published spectra used for astronomical interpretations and allow better identifications of the existing infrared spectra of carbon stars. When this is done, the understanding of the nature of SiC grains forming around carbon stars should be greatly improved and can be incorporated into grain formation/growth models and radiative transfer models for such stars. Furthermore, we plan to investigate the optical properties of more minerals of astronomical interest, with a view to producing a definitive database of such materials. The spectra will cover large wavelength ranges, and explanations of the differences between similar samples will be produced. This should allow better interpretation of spectra of astronomical objects which are associated with dust and remove any ambiguity caused by differences between the various laboratory techniques used in producing mineral spectra.
Having reconciled the differences between astronomical observations and meteoritic laboratory data, at least as far as the type of silicon carbide forming is concerned, we now have several further discrepancies to resolve. The most important of these is the grain size problem. The grains found in meteorites can be as large as about 25 µm, and although as mentioned above observing these grains would be a problem, that does not mean they do not exist. It is therefore desirable to discover the mechanism by which these large grains could be produced. Since these grains obviously do exist, they should also be included into radiative transfer models. It would be interesting to see how the need to grow large grains affects models for mass-loss from these stars. As mentioned above, the carbon stars which exhibit absorption features may be the ideal place to start when incorporating large grain sizes into the models. Most of the radiative transfer models produced previously (e.g. Bagnulo et al. 1995) have used the flawed alpha-SiC optical properties (e.g. Pegourie 1988), and therefore need to be re-evaluated using the optical properties of beta-SiC. Previous radiative transfer models have also neglected to include self-absorption. As shown in chapter 6, self-absorbed SiC produced good fits to many SiC features in carbon star spectra. This also needs to be addressed.
A second line of research, which follows from chapter 7, is to investigate the UIR bands in carbon star spectra further. The ISO-SWS spectrum of one of the stars which has already been shown to exhibit at least one UIR band (TU Tau), will allow a more detailed look at the UIR bands, and a comparison with the UIR bands observed in other objects.
Also following from chapter 7 is the possibility of finding a way to detect diamonds in carbon star spectra, if they do indeed form there. As discussed in chapter 7, the problem with the 8-13 micron spectra is that the features seen in the meteoritic diamond spectra coincide with those of amorphous hydrogenated carbon. However, it may be possible to look for diamond features in the ISO-SWS spectra. It is not clear whether, in order to see diamond infrared spectra, source of UV must be present (c.f. PAHs). However, even if this is the case, observations of carbon stars with hot star companions may provide the right environment for such features to be produced. Furthermore, diamonds have an interesting ultraviolet spectrum of their own (Andersen et al. 1998), and it may be possible to use carbon stars in binaries systems to look for diamonds in the UV.
Thus far, the study of the 10- and 20- µm spectra of oxygen-rich stars has produced disappointingly vague results (chapter 8). The spectra produced by ISO may permit a more accurate identification of the minerals comprising the dust around oxygen-rich stars. It can be expected that combining the high resolution, large wavelength range observations of ISO with a new comprehensive database of laboratory spectra will permit circumstellar dust around these objects (and others) to be better understood. The observations of crystalline silicates in ISO-SWS AGB-star spectra (Water et al 1996) are fascinating. The results here (chapter 8) have provided no evidence for crystalline silicates around such stars. The non-observance of crystalline silicate features in the 10- µm spectra, together with the observation of features for such species at longer wavelength requires further investigation. It may be possible to use these results to constrain the quantity of crystalline dust formed, or to provide insight into the possible different formation sites of the amorphous and crystalline species.
The sample of oxygen-rich stars presented in chapter 8 includes several Red Supergiants (RSGs). The spectra of these stars seem to fit nicely into the same categories as the oxygen-rich AGB stars. Further investigation into the similarities and differences between the dust features of the two groups (RSGs and AGB stars) should be undertaken.
There is a ``new'' dust species discussed in chapter 8 - silicon dioxide (SiO2). Although SiO2 has been mentioned by previous authors (e.g. Pegourie & Papoular 1985), it has never been seriously considered as a major constituent of circumstellar dust. Having shown, in chapter 8, that SiO2 likely to be present in the circumstellar dust around oxygen-rich AGB stars, further investigations need to take place. For instance, as mentioned in section 8.5, the observations of the 9.25 µm and 12.5-13 µm features may constrain the polytype and relative quantity of SiO2 forming in these regions. Again, we have a dust type which has previously been excluded from radiative transfer models and grain formation mechanisms. This needs to be addressed.
Finally, there are two stars, one carbon-rich (TX Psc) and one oxygen-rich (T Cet), which were excluded from the two samples (chapter 6 and chapter 8 respectively) due to their bizarre spectra. These stars need to be further investigated and explanations for their unusual spectra need to be found.