Astronomy 250 Problem Set No. 5

Part 1. (12 points) Constructing an HR Diagram

1. List of stars measured including their names, positions, magnitudes, and signal/noise ratios in their spectra.
2. List of assigned spectral types for the stars.
3. `See list at end for stars and their spectral types.`
4. A color-magnitude diagram with both spectral types and temperatures indicated (use Table 1). Plot apparent magnitudes on the vertical axis with dim at the bottom and bright at the top. Plot temperature along the horizontal axis with hot to the left and cool to the right. Note that this is similar to the form of an HR diagram but until we know the distance to the Pleiades, we cannot convert apparent magnitude to absolute magnitude (or luminosity).

On the plot above, the theoretical main sequence has been plotted by shifting by 6 magnitudes.

1. You should have seen that m-M~=6 :
2. From examining your plot, you should have found that the spectral type at the tip of the main sequence is about B6V with Mv~-0.9. Knowing that MV=+4.7 for the Sun, compute the luminosity at the tip of the main sequence in solar units. Compute the mass and approximate lifetime of a star at the tip of the main sequence using the relations presented at the end of the lecture on binary stars and stellar masses.
3. This is the age we would give the Pleiades star cluster.

4. (worth 2 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?
5. Note that in lecture I forgot the factor of 1/0.35 – I didn’t take off if your values were 1/0.35 larger (eg. 5737,3397, and 2569 stars)

6. (worth 1 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?

Its V would be 10.5 - 2.01 = 8.48 without dust.

List of Stars and Spectral Types

NAME RA DEC V SpType (RA and DEC are in decimal form)

HD 23630 3.74083 23.9667 2.87 B7III

HD 23850 3.76917 23.9167 3.64 B8III

HD 23302 3.69917 23.9667 3.71 B6III

HD 23408 3.71417 24.2333 3.88 B7III

HD 23480 3.72250 23.8167 4.18 B6IV

HD 23338 3.70417 24.3333 4.31 B6V

HD 23862 3.77083 24.0000 5.09 B7P

HD 23753 3.75750 23.3000 5.45 B8V

HD 23288 3.69750 24.1333 5.46 B7IV

HD 23324 3.70250 24.7000 5.65 B8V

HD 23432 3.71583 24.4167 5.76 B8V

HD 23923 3.77917 23.5667 6.17 B9V

HD 23441 3.71750 24.3833 6.43 B9.5V

HD 23712 3.75250 24.8500 6.46 K5

HD 23873 3.77250 24.2500 6.60 A0V

HD 23568 3.73417 24.4333 6.80 B9V

HD 23642 3.74250 24.1500 6.81 B9V

HD 23410 3.71417 23.0000 6.85 A0V

HD 24076 3.79917 23.8333 6.93 A2V

HD 23763 3.75917 24.2167 6.95 A1V

HD 23632 3.74083 23.6667 6.99 A1V

HD 23387 3.71083 24.1833 7.18 A1.5V

HD 23631 3.74083 23.7667 7.26 A2V

HD 23489 3.72417 24.1167 7.35 A2V

HD 23155 3.67750 24.9333 7.51 A2V

HD 23851 3.76917 23.1333 7.52 K

HD 23948 3.78250 24.2167 7.54 A0V

HD 23628 3.74083 24.4500 7.66 A4V

HD 23643 3.74250 23.5333 7.77 A3V

HD 23409 3.71417 23.9000 7.85 A2V

HD 23157 3.67917 23.5000 7.90 A9V

HD 23158 3.67917 23.4500 7.90 F5V

HD 23463 3.72083 24.0500 7.96 K2

HD 23886 3.77417 24.1167 7.97 A3V

HD 23361 3.70750 23.8833 8.04 A3V

HD 23194 3.68417 24.4167 8.06 A5V

HD 23924 3.77917 23.2000 8.10 A7V

HD 23512 3.72750 23.4833 8.11 A0V

HD 23863 3.77083 23.7500 8.12 A7V

HD 23611 3.73917 22.8000 8.13 A3

HD 23246 3.69083 24.2500 8.17 A8V

HD 23156 3.67917 24.2167 8.23 A7V

HD 23607 3.73917 24.0000 8.25 A7V

HD 23733 3.75417 24.1833 8.27 A9V

HD 23567 3.73417 24.6833 8.28 A9V

HD 23585 3.73583 23.8500 8.37 A9V

HD 23791 3.76250 23.1167 8.37 A8V

HD 23325 3.70250 24.1167 8.58 A0

HD 23375 3.70917 24.3167 8.60 A9V

HD 23464 3.72083 22.9833 8.66 G0V

HD 23608 3.73917 23.9833 8.69 F3V

HD 23665 3.74583 23.4167 8.80 K0

HD 24132 3.80750 24.3833 8.83 F2V

HD 23326 3.70250 23.5500 8.95 F2V

HD 23289 3.69750 23.1167 8.95 F3V

HD 23351 3.70583 24.7833 8.99 F3V

HD 23778 3.75917 24.0333 9.05 F4V

HD 23247 3.69083 23.9833 9.07 A2

HD 23912 3.77583 23.2500 9.10 F3V

HD 23732 3.75417 25.0667 9.13 F4V

HD 23949 3.78250 24.0833 9.17 A0

HD 23713 3.75250 24.0000 9.25 F6V

HD 23511 3.72750 23.9667 9.29 F4V

HD 23513 3.72750 22.9667 9.38 F5V

HII 1132 3.72750 23.7667 9.42 F6

HD 23061 3.66583 24.3333 9.47 F5V

g 3.79133 24.34503 7.42 A2

H 3.74408 23.45642 7.72 K0

n 3.73642 24.1239 9.46 F8

o 3.71139 24.47278 9.70 F8

p 3.75764 23.89667 10.02 F9

q 3.73214 23.43056 10.52 F9

r 3.77375 23.68861 11.35 G2

s 3.72842 23.34444 12.02 G8

t 3.71897 24.71306 12.05 G5

u 3.68472 24.08806 12.51 G1

v 3.73861 24.23833 12.61 G9V

x 3.71881 25.01417 14.36 K2V