Problem Set 7 Due April 18,2002
This problem set has two parts. For the second part you will visit the 21-inch telescope in the dome near the Lecture Hall. You need to sign-up for a primary and for a back-up time slot on the sheets outside Prof Rieke's office (Room 262). You should sign up before the end of the day on Friday, April 5. The back-up time would be used only if your primary time is clouded out.
Part One :
Problem 1 (5 pts): Assume that the mass of the Milky Way galaxy is 1.5x1011 MSun and that all of the mass is concentrated into a small volume at the center of the galaxy.
a. Plot the rotation speed in km/sec as a function of distance from the center of the galaxy out to a radius of 25 kpc.
b. Compute the escape velocity from the galaxy at the Sun's distance of 8.5 kpc from the center.
Problem 2 (worth 4 points): An interstellar cloud has a total mass of 4.5x1035 kgs. This cloud fragments and forms stars. Assume that 25% of the cloud’s mass goes into stars, a high but not unreasonable star formation efficiency. You may further assume this cloud only forms relatively high mass stars – M ≥ 3.0MSun up to a maximum mass of 30MSun . If the newly formed stars are distributed in mass according to the Initial Mass Function presented in lecture, how many 4.0MSun stars are formed? How many 5.0MSun stars are formed? How many 15.0MSun stars are formed?
Problem 3 (worth 3 point) A star is observed to have V=10.5 and have B-V=0.67. Its spectrum shows that is an A0 star whose B-V intrinsically is 0.0. If there were no interstellar dust, how much brighter would this star appear?
Problem 4 (worth 3 points): Compute the Jeans mass for a cloud whose temperature is 35°K and whose density is 1.5x108 particles/m3.
Part Two: ( Worth 10 points)
You may find it convenient to review Lecture 1 which discussed astronomical coordinates and Problem 1 from Problem Set 1 which considered what RA is overhead at what tiem of year at night. You will observe at least one object that is either a galaxy, a planetary nebulae or a star cluster. You will need to be careful to pick targets that are both above the horizon now and which are bright enough to be seen through the 21-inch telescope. How can you figure out what is visible from Tucson now? Any object which has a declination>-15° can be observed with the 21-inch (if we were outside of the city and away from buildings, we could observe to closer to the horizon limit which is set by our latitude (32°) and which can be compute from -90°+latitude = most southerly declination that rises above the horizon). In practice, the 21-inch can point to about 30° above the horizon. We can figure out what range of right ascensions are visible at night in early April from the definition of right ascension. Recall that 0 hr right ascension = position of sunrise on the first day of spring = March 21. These mean that at sunrise a position with a right ascension 90° different will be overhead on the meridian at sunrise. Right ascension increase towards the east so the location with have a right ascension which is 90°/15°/hr = 6 hr less or 18 hrs. To shift from March 21 to April 14 involves 3/4 of a month or 1.5 hrs of RA later. We would also like to observe before midnight rather than at sunrise so we want to observe objects whose right ascension are even smaller - 6 to 10 hrs less so we can observe from ~8:30pm to 10pm. This means that you want to find sources with right ascensions in the range of 8 hrs to 13hrs and declinations greater than -15°. Choose a total of 4 targets: one galaxy, one planetary nebula, and 2 star clusters (either open or globular is OK but note which types you have selected).
Two good catalogs to use in selecting objects are the Messier Catalog (see http://www.seds.org/messier/) and the NGC or New General Catalog. Another possible source of information is the "Observer's Handbook" printed each year by the Royal Astronomical Society of Canada. Try to pick the brightest and biggest objects in the categories you are looking for. Objects with magnitudes listed as fainter than ~12 will be very difficult to see. When you select your sources, note down the names and coordinates for your objects. You also need to look at what epoch the coordinates refer to -- precession changes right ascension and declination for a source continuously. If no epoch is stated (you should seem something like RA(1950) meaning the right ascension refers to epoch 1950), it is likely that the catalog is assuming epoch 2000 but you might want to find the same object listed in another catalog that does give the epoch. Because you will not be observing at exactly the epoch for which the coordinates are given, you will need to compute the precession between the catalog epoch and the night of your observation. Here's a short recipe of how to do this:
For example: Compute the precession for the galaxy M31 which lies at 00h 42m 44.32s and +41° 16' 08.5" from 2000.0 to Sept 1, 2009.
To finish the calculation, you would add these differences to the original coordinates to get the position for Sept 1, 2009. Note that M31 cannot be observed now!
Precess your objects' coordinates to your observing date before going to the telescope so you can compare your values with where the telescope actually points.
To turn in:
Names and catalog positions for the four objects you selected.
Coordinates for all four objects precessed to the day on which you observed.
The coordinates reported by the 21-inch when one of objects was actually centered in the eyepiece.
A brief written description or sketch of the appearance of the object you observed.