Foundations of Astronomy (MindTap Course List)
14th Edition
ISBN: 9781337399920
Author: Michael A. Seeds, Dana Backman
Publisher: Cengage Learning
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Chapter 14, Problem 8P
To determine
The peak wavelength associated with luminosity of Neutron star given in problem 7 and identifies the band of EM spectrum which it belongs.
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As we have discussed, Sirius B in the Sirius binary system is a white dwarf with MB ∼ 1M , LB ∼ 0.024L ,and rB ∼ 0.0084r . For such a white dwarf, the temperature at the center is estimated to be ∼ 107 K.If Sirius B’s luminosity were due to hydrogen fusion, what is the upper limit of the mass fraction of thehydrogen in such a white dwarf?Step 1: Calculate the observed energy production rate per unit mass (remember luminosity is energy outputper unit time).Step 2: Use the per unit mass energy generation rate of hydrogen fusion (via PP chain) to estimate thepossible hydrogen mass fraction given the condition at the center of the white dwarf.
As a star runs out of hydrogen to fuel nuclear fusion in its core, changes within the star usually cause it to leave the main sequence, expanding and cooling as it does so. Would a star with a radius 12 times that of the Sun, but a surface temperature 0.5 times that of the Sun, be more, or less luminous than the Sun?
Show and explain your reasoning.
You may assume the surface area of a sphere is A = 4πr2.
Using the HR diagram, what is the approximate range of relative luminosities covered for a main sequence star at 10 000 K?
Would this star be most like Rigel or Sirius?
Chapter 14 Solutions
Foundations of Astronomy (MindTap Course List)
Ch. 14 - Prob. 1RQCh. 14 - Prob. 2RQCh. 14 - Prob. 3RQCh. 14 - Prob. 4RQCh. 14 - Prob. 5RQCh. 14 - Prob. 6RQCh. 14 - Prob. 7RQCh. 14 - Prob. 8RQCh. 14 - Prob. 9RQCh. 14 - Prob. 10RQ
Ch. 14 - Prob. 11RQCh. 14 - Prob. 12RQCh. 14 - Prob. 13RQCh. 14 - Prob. 14RQCh. 14 - Prob. 15RQCh. 14 - Prob. 16RQCh. 14 - If the Sun has a Schwarzschild radius, why isnt it...Ch. 14 - Prob. 18RQCh. 14 - Prob. 19RQCh. 14 - Prob. 20RQCh. 14 - Prob. 21RQCh. 14 - In what sense is a black hole actually black?Ch. 14 - If you are falling into a black hole and you point...Ch. 14 - Prob. 24RQCh. 14 - Prob. 25RQCh. 14 - Prob. 26RQCh. 14 - How Do We Know? How does peer review make fraud...Ch. 14 - Prob. 1PCh. 14 - Prob. 2PCh. 14 - Prob. 3PCh. 14 - Prob. 4PCh. 14 - Prob. 5PCh. 14 - Prob. 6PCh. 14 - Prob. 7PCh. 14 - Prob. 8PCh. 14 - Prob. 9PCh. 14 - Prob. 10PCh. 14 - Prob. 11PCh. 14 - Prob. 12PCh. 14 - Prob. 13PCh. 14 - Prob. 14PCh. 14 - Prob. 15PCh. 14 - Prob. 16PCh. 14 - Prob. 1SOPCh. 14 - Prob. 2SOPCh. 14 - Prob. 1LTLCh. 14 - Prob. 2LTLCh. 14 - Prob. 3LTLCh. 14 - Prob. 4LTLCh. 14 - Prob. 5LTL
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- Consider two stars, A and B, of equal size. You take a spectrum of each star and findthat the flux of star A peaks at a wavelength of 9000 ̊ A and the flux of star B peaksat 3000 ̊ A. What is the relative luminosities of the two stars? Which star is the hotterone? If star A is at a distance of 10 pc, what distance would star B have to be inorder for both stars to appear equally bright as viewed from Earth?arrow_forwardThe center star in the head of the asterism Scorpius is Dschubba. Assume that Dschubba is a spherical blackbody with a surface temperature of 28,000 K and a radius of 5.16 × 109m, located at a distance of 123 parsecs from Earth. Determine the following for Dschubba:(a) luminosity relative to the Sun (note that L = 3.83 × 1026W ).(b) absolute bolometric magnitude (note that M = 4.74).(c) apparent bolometric magnitude.(d) radiant flux at the star’s surface (in SI unit).(e) radiant flux at Earth’s surface (in SI unit).(f) peak wavelength λmax when plotting the plank function against wavelength (in nm)arrow_forwardAppendix J lists the stars that appear brightest in our sky. Are most of these hotter or cooler than the Sun? Can you suggest a reason for the difference between this answer and the answer to the previous question? (Hint: Look at the luminosities.) Is there any tendency for a correlation between temperature and luminosity? Are there exceptions to the correlation?arrow_forward
- A star with spectral type A0 has a surface temperature of 9600 K and a radius of 2.2 RSun. How many times more luminous is this star than the Sun? (if it is less luminous enter a number less than one) 36.854 This star has a mass of 3.3 MSun. Using the simple approximation that we made in class, what is the main sequence lifetime of this star? You may assume that the lifetime of the sun is 1010 yr.arrow_forwardA star with a radius 1.7 times that of the Sun has a surface temperature T=10,000 K. Calculate the luminosity of this star and express your answer in units of the Solar luminosity (the Solar luminosity = 3.84 x 1026 W and the Solar radius = 7 x %3D 108 m). Choose the option below that most closely matches your answer. Select one: а. 20 O b. 100. O C. 26. O d. 5. O e. 1000arrow_forwardlambdamax = 600nm (5000K/T) L ∝ R2 T 4 1. What is the peak wavelength of an O star of temperature 50,000 K? What range of the spectrum is this?arrow_forward
- The Plummer sphere is a model for some star clusters, and it has the gravitational potential as given in the provided image. M and rp are both constant. What is the density profile ρ(r)? When the Plummer sphere is observed from a large distance along the z axis, what is its surface density, Σ(R), where R is the distance from the center?arrow_forwardConsider the image above of the Cassiopeia A (Cas A) supernova remnant. The supernova explosion that caused this remnant was observed on earth about 300 years ago. It is about 3000 pc away. Since that time, the shockwave from the supernova has expanded to form the roughly spherical cloud pictured above. From the center point to the edge of the cloud is about 3 pc. Compute the angular diameter of the Cas A supernova remnant as viewed from Earth. Express your answer in arcminutes.arrow_forwardFor the PP chain 0.7% of the mass participating in nuclear fusion is liberated as energy which produces a star's luminosity. Assume that the core of a main sequence star consists of 10% of its total mass. Hence, estimate the lifetime of a star on the main sequence in terms of its luminosity L/L. Give your answer in years. You may use the observed mass-luminosity relation L x M³.5, where M is the star's total mass. Using typical values, calculate estimates for the main sequence lifetime of a KO star and a 05 star. Describe briefly why your estimate might be more accurate for K stars compared to O stars.arrow_forward
- A cloud of mean number density n ~ 3000 cm-3 and radius 3 pc has an ionising source with luminosity at 13.6 eV of L13.6eV = 2.18 x 109 erg s- at the centre. (a) What is the size of the HII region in pe? [og = 2 x 10-13 cms-]. %3D (b) What assumptions are involved in part a) (c) Discuss why the HII region will drive a shock into the rest of the cloud, and calculate the post-shock density. (d) Show why this HII region will destroy the cloud.arrow_forwardUsing the HR diagram what is the approximate range of relative luminosities covered for a main sequence star at 10 000 K?arrow_forwardA star with spectral type A0 has a surface temperature of 9600 K and a radius of 2.2 RSun. How many times more luminous is this star than the Sun? (if it is less luminous enter a number less than one) This star has a mass of 3.3 MSun. Using the simple approximation that we made in class, what is the main sequence lifetime of this star? You may assume that the lifetime of the sun is 1010 yr. Compare this to the lifetime of a A0 star listed in Table 22.1 (computed using a more sophisticated approach). Is the value you calculated in the previous problem longer or shorter than what is reported in the table? (L for longer, S for shorter) (You only get one try at this problem.)arrow_forward
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