By Carroll B.W., Ostlie D.A.
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Additional resources for An introduction to modern astrophysics: Solution manual
10. NII =N t is shown for helium. 11. NIII =N t is shown for helium. NII =NI /] of NII =N t can be neglected for T between 5000 K and 25; 000 K. Use Eq. 9) with ZI D 1, ZII D 2, 2 to evaluate NII =NI for a range of values of T . As shown in Fig. 2, I D 24:6 eV, and Pe D 20 N m one-half of the He I atoms have been ionized when T ' 1:5 104 K. 10 (with Pe D 1000 N m 2 ) with Eq. 9) to evaluate NIII =NII and NII =NI . This results in the graph shown in Fig. 3. One-half of the helium atoms have been twice-ionized when T ' 4 104 K.
1:5 105 kg m 3 / D3 10 5 m: (b) From Eq. 29), the number of random-walk steps of this size from the center to the surface of the Sun is Â Ã2 Â Ã d Rˇ 2 N D D D 5 1026: ` ` The time for a photon to cover this many steps of size ` is tD N` D5 c 1013 s; almost two million years! 12 Because you always look back to an optical depth of about D 2=3, Eq. 17) implies that you see down to a depth s into the star given by Z s 2 Ä ds D : 3 0 At wavelengths where the opacity is greatest, the value of s is smallest.
16. 17(a). (b) See Fig. 5. 18 Using the data in the text and the problem, the mass of the star can be determined from Kepler’s third law to be approximately 1:1 Mˇ . Take the radius of the star to be roughly 1:1 Rˇ for a main-sequence star. The mass of the planet is estimated to by 0:00086 Mˇ . From the data, TwoStars generates a bolometric light curve shown in Fig. 6. 01 mag, in agreement with the value specified in the text. 17(b). 6: The synthetic light curve of OGLE-TR-56b for Prob. 18. 1 In the following, it is easiest to express Boltzmann’s constant as k D 8:6174 temperature of 300 K, 1 kT D 0:0259 eV eV: 40 If kT D 1 eV, then T D 1:16 104 K.
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