# Observing Techniques: exercises and assignments

Exercises will be assigned in class, to be handed in one week later.
Where you can, use sensible values to complete the answer.

THE ELECTROMAGNETIC SPECTRUM and associated objects.
Problem set 1:

TELESCOPES
Problem set 2:
• Kitchin 1.1.1, 1.1.4

TELESCOPES and PHOTOMETRY
Problem set 3:
• Work out the field of view, plate scale, and the sampling limit (smallest features which can be properly imaged) for the WHT1 Cassegrain focus (Primary mirror D=4200mm, f/11 focus), with a 2000x2000 CCD chip having square 15 micron pixels). Also work out the size of the diffraction-limited spot and the image size corresponding to typical atmospheric turbulence. Do the same for the Prime Focus and finally for the Nasmyth focus of the telescope.
• A camera is attached to the WHT cassegrain. The telescope beam is "collimated" (each point-like source forms a set of parallel rays) and then focussed on the detector. The final focal ratio is f/3. The chip is the same as before. What is now the field of view, plate scale, and the sampling limit?
• What is the distance of 61 Cygni? Could we detect it's proper motion in the duration of this lecture course, with the equipment available? (see below for details)
• The night sky at La Palma on a particular day has a V-band brightness of 21.8 mag arcsec-2. What is the flux from a square area of sky of size 10 arcmin x 10 arcmin?

THE ATMOSPHERE
• In the section "adaptive optics" on the web page, mention is made of real-time "tip-tilt" image correction. How might you do this post-hoc rather than in real-time, and without the mechanical device to correct the x-y error?
• Which measurables enable us to determine the absolute magnitudes of stars? Describe possible strategies.

• What is the Julian date at the start of the first lecture (to the nearest minute).
Photometry 1:
• To what stellar magnitude can you just detect a star with a 1m telescope of 70% overall efficiency in 1 hour of exposure time? Assume S/N of 5 is adequate or justify a different choice. "Efficiency" includes the camera etc. How long would you need to expose to obtain a flux measurement with 99% accuracy? The sky background is 21.4 mag arcsec-2. Assume a V-band filter is in use.
• After working this out, run this iraf script to experiment with the integration time.
Photometry 2:
• Look at the table of Photometric bands (Bradt 8.2). This gives the central wavelength and effective width of each band. The table also gives the flux that a star with magnitude 0 would have (in that band). In fact this defines m=0 for this photometric system.
Is this consistent with the rule-of-thumb for the V-band zero point given on the photometry page, i.e.
1003 photons cm-2 s-1 Angstrom-1 and if so does it hold for all the other photometric bands listed?
2pt bonus Is the flux density given in the Bradt table consistent with the other expression given on the photometry page, i.e.
10-26erg cm-2 s-1 Hz-1 for m=16.4, and does this hold for all bands? If not, what is the magnitude scale based on? Look up the term "AB magnitude" (e.g. on the web) and connect it with the foregoing.
PHOTOMETRY and intro to SPECTROSCOPY
Problem set 4:
• What does the term "airmass" (AM) refer to, and how is it defined? What is "extinction" and explain the units in which it is expressed (Kitchin from p 306). Look up the typical values of extinction at an observatory such as La Palma and calculate it's effect at AM=2 for various wavelengths (such as those of Bradt's photometric bands), expressing the answer in magnitudes and linear units. What is the largest meaningful value of airmass? Note: you may find useful information at http://www.ast.cam.ac.uk/ING/Astronomy/astronomy.html
• A grating with 600 grooves/mm is illuminated by collimated light at an angle of 10o from the normal. What is the angular dispersion at a wavelength 500nm in the m=+2 order? At 800nm? For 800nm wavelength, which orders propagate?

SPECTROSCOPY
Problem set 5:

1. Consider a grating with 600 grooves/mm which is illuminated at 10 degrees from the normal - the blaze gives the grating high efficiency over a large wavelength range in this configuration. You decide to make a spectrograph using this arrangement, i.e. fixing the input angle at 10 degrees. Which orders propagate at 500nm? In the m=+2 order, work out the focal length of the camera you would need to have a linear dispersion such that a wavelength increment of 0.1nm corresponds to two pixels (pixel size 20 micron) at the detector.
2pt bonus How would you set up the collimator? Let us say you want the spectrograph to be "fed" by light from a D=4m telescope at the f/8 focus of the telescope. In principle you want the spectrograph to accept all the light in the seeing spot (also called the seeing disk) without degrading the spectrum quality.

2. It is said that most spectrographs require a collimated beam. But the beam from a star is perfectly collimated... Give as many reasons as you can for the formation of a focus followed by recollimation. The main exception to the rule is the "objective prism spectrograph", in which the starlight indeed is allowed to fall on the dispersing element. What is it about this application that makes this viable?

3. Calculate the line-of-sight velocity with respect to the Earth of a star when the Balmer H-alpha line in its spectrum is observed to be at a wavelength of 655.2 nm. Present the answer with the appropriate level of precision. In this calculation should you use the rest wavelength of the line in air or in vacuum? The observation was made at La Palma Observatory on a certain date. Using the iraf task rvcorrect, or any other tool or formula, convert the line-of-sight velocity you have calculated to one of the standard systems, such as Heliocentric.
You will need the following data:
date of observation:   1/1/2003
time of observation:  UT=0
coordinates of object:  RA 7h, Dec +3o
observatory: lapalma (this will be recognised by rvcorrect, for other programs you may need the observatory latitude and longitude, 28:46 N, 17:53 W). Describe why this correction is necessary.

COORDINATE SYSTEMS
What is today's date? What was the Julian date at 2:00 am this morning? What is the Julian date and why is it used in astronomy? What is the time at this instant and what is the UT at this instant? What is the sidereal time now?

ASSIGNMENTS (We will work on these together)

1. Observing Write and defend an observing proposal for the 2m INT telescope at La Palma. The winning proposal will be carried out. Be prepared to criticise your peers, and to defend your own proposal.

2. Optical Practicum: directly measure the rotation speed of the sun in km/s.