As part of PHY241, you will be expected to complete a simple observing project using the 16-inch telescope on the roof of the Hicks Building. This project is designed to give you basic hands-on experience of astronomical observing and data reduction, and can be completed in a few hours of telescope time. The observing must be done in groups of three students, so please find others interested in doing the same project as you. If you can't find a group to work with, I shall be happy to recommend some options. You must notify me by email of your final choice of partners by the deadline at the start of week 2: Monday, 3 October 2016. If you have not chosen a group by then, you shall be assigned to one by me!

There are 3 aspects to the observing project:

Planning: Well before your scheduled observing run, you must discuss with me or Paul Kerry (E26): which objects to observe, what time of night to observe, what filters you require, what sequence of exposures you require, etc. You will find the specifications of the Hicks Observatory useful in your planning. You will need to include a section on your planning in the final report. This section must contain a calculation of the transit time and the transit altitude of your chosen object. You may find the positional astronomy notes (here, here and here) of use.

Observing: Your observing sessions will be supervised by Paul Kerry and must be completed in a specified period: Wed, 5 October - Friday, 9 December 2016 (weeks 2-11), although please note that observing is not possible over weekends and there may be short periods when Paul Kerry is unavailable.

Sign-up sheets will be posted on the Astronomy Noticeboard outside the Astronomy Lab (E36), along with full instructions on how to contact Paul Kerry on the night. Although you should be able to complete all your observations in a single session, to allow for the vagaries of British weather we expect you to sign up for at least two evenings per week until you have successfully completed your observing. If you cannot do this, you must discuss the problem with me or Paul Kerry before the start of the designated observing period, or as soon as the problem (e.g. illness) becomes apparent. Note that reading week is not a holiday. We expect you to sign up during reading week as usual.

Attendance at the observing is compulsory - you will not receive any marks for the project if you fail to show up or, if the weather is bad for part of the specified observing period, you have not made every effort to sign up for other time slots. Note that, unless previously agreed with me or Paul Kerry, if you are unable to attend a successful observing session with the other members of your group, it will not be possible for you to observe at a later date on your own. Note also that no resit of the observing project is possible, so missing it will make it much more difficult to pass the module.

We strongly advise signing up for observing as soon as possible: students who fail this module tend to be those who leave signing up until the last minute and then suffer from poor weather at the end of the observing period. This is no excuse, as there are usually clear periods at the start of the observing period which no students sign up for. Only if the entire period is unusable, or if you have genuinely serious reasons as to why you could not do the observations (which in most cases must be supported by documentary evidence), will this component not count towards the final mark.

Data reduction and report: After you have obtained your observations, you will need to reduce and analyse your data using the computers and software available in the Astronomy Lab. Note that this element of the project, and the subsequent write-up, must be your own work - do not work in your observing groups. You should be able to reduce your data using the skills you learn in this course. In case of difficulty, see myself or Paul Kerry for assistance.

Your write-up should be similar to a formal laboratory report. There must be sections describing the planning stage, the observations (a description of the equipment used, the observing conditions and the data that was taken), the data reduction and the data analysis. You will be penalised if you omit an analysis of the errors, and if you fail to compare your results with literature values. Some advice on how to write the report is here, and the rubric used to mark the report is here. I strongly recommend peer marking each other's reports with this advice and rubric in mind.

You may well want to prepare your reports using the Jupyter notebook - it is possible to produce PDF documents from the notebook. Please submit hard copies of your reports to the departmental office by the deadline: Friday 3rd February 2017 (16:00). In addition please do email your notebook (if you used it) to Stuart Littlefair. Note that this deadline is the final week of term, and has been set to make the observing window as long as possible. However, you will undoubtedly have other pieces of work to hand in around this time, so it is in your interests to complete your observing and hand in your report as early as possible in the semester.

The Project

Some examples of the data obtained for previous projects are given here. All students will attempt the same project, which is described below.

Hertzsprung-Russell (HR) diagram of an open cluster.
The aim here is to measure the distance and age of an open cluster. A list of open clusters is available here.

Make sure that you pick a cluster that is visible from Sheffield at the start of the night. You can do this using Cartes du Ciel on any University PC, Stellarium on your own PC, or the on-line ING Object Visibility page (where you must enter the longitude and latitude of Sheffield in the following format: 358 30 51 53 22 50 185). Even if you use an online tool to choose your cluster, you must manually calculate the transit time and altitude and present this calculation in your report.

The cluster you select must also be small enough so that the majority of the cluster fits within the 18' x 12' field of view of the CCD, i.e. don't select one much larger than 20' in diameter. However, don't pick one that is too compact either, as the individual stars in the cluster will be difficult to resolve. The cluster should also have a reasonably large number of stars (definitely greater than 50; greater than 100 would be best). Finally, the cluster should not be too distant or reddened and hence faint, and must be of sufficient age to show a relatively clear main-sequence turn off. The latter two items can be checked by inspecting existing HR diagrams of the cluster using WEBDA (simply enter the name of your chosen cluster in the Display the Page of the Cluster box).

When you have reduced your data to create a H-R diagram, you should fit an isochrone to the data to determine the cluster age and distance.

When you construct an observed HR diagram, you must correct for both atmospheric extinction and interstellar extinction. The atmospheric extinction correction can be made by assuming standard values for the extinction coefficient, as given in table 2, and then transforming all of your measured magnitudes to above-atmosphere values. Be careful, however, as it is possible that you will have already corrected for atmospheric extinction if you used a photometric zero point determined from one of the cluster stars.

To correct for interstellar extinction, you must use the formula \((B-V)_0 = (B-V) - E(B-V)\), where \((B-V)_0\) is the intrinsic colour index of the cluster (i.e. corrected for interstellar extinction), \((B-V)\) is your observed (i.e. uncorrected) colour index, and \(E(B-V)\) is the colour excess (or reddening) in magnitudes. Hence you will find that you will have to shift your data in the x-direction on the HR diagram in order to align it with the isochrone, and the value you shift it by is equal to the reddening, \(E(B-V)\). Once you have determined \(E(B-V)\) in this way (and checked it against the value given by WEBDA), you will then have to correct your V-band apparent magnitudes using the equation: \(V_0 = V - A_V\), where \(V_0\) is the intrinsic V-band apparent magnitude of the cluster (i.e. corrected for interstellar extinction), \(V\) is your observed (i.e. uncorrected) V-band apparent magnitude, and \(A_V\) is the visual extinction in magnitudes. The ratio \(A_V / E(B-V)\) is usually denoted by the symbol \(R_V\) and a generic value for our galaxy covering a large wavelength range is \(R_V = 3.2\pm0.2\). Hence the formula to correct your V-band apparent magnitudes becomes:
\[V_0 = V - R_V \times E(B-V) = V - 3.2 E(B-V).\]
Once you have corrected the y-axis of your data in this way, the difference between the isochrone and your data in the y-direction on the HR diagram will give you the distance modulus of the cluster.

To determine the age of your cluster, you will have to plot a series of isochrones of different ages, using the WEBDA value for the age as a guide. The isochrone which best matches the main-sequence turn-off point gives the age of the cluster.

Isochrones can be generated using the isochrones Python library, which is installed on the Astronomy Python Server. The documentation for this library is found here, and instructions for creating an isochrone for a given age is located here.

It is likely you will find that the determination of the interstellar extinction, distance and age of the cluster will be an iterative process.