Download ASTR 1120H – Spring Semester 2010 Exam 2 – Answers The

ASTR 1120H – Spring Semester 2010
Exam 2 – Answers
PART I (70 points total) – 14 short answer questions (5 points each):
1. What is the proton-proton chain? Why does it occur only in the Sun’s core, not in its
outer regions?
The proton-proton chain is the sequence of thermonuclear reactions
converting H to He + energy that takes place at the center of the Sun. It
occurs in the core and not the outer regions because that's the only
place where the requisite high temperature and density exist.
2. What was the solar neutrino problem? What is thought to be the solution to the
problem?
The solar neutrino problem was trying to understand why
experimentalists were detecting only 1/3rd as many solar neutrinos as
theorists predicted should exist. The solution to the problem is thought
to be neutrino oscillations, where the three types of neutrinos can
change their "flavor" in flight from the Sun to the Earth.
3. Name three observations that demonstrate that the Sun’s photosphere is heated from
below.
Solar limb darkening, the Sun's absorption line spectrum, and
granulation all show that the Sun's photosphere must be heated from
below.
4. What is the evidence that sunspots are caused by strong magnetic fields? How do
these magnetic fields cause the spots?
The splitting of spectral lines via the Zeeman effect is the evidence. The
magnetic fields cause the sunspots by inhibiting convective energy
transport.
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5. List the fundamental parameters of stars that we discussed in class.
Luminosity, surface temperature, radius, chemical composition, and
mass.
6. Sketch a Hertzsprung-Russell (HR) diagram (on the back of this sheet, if necessary).
Be sure to label the axes and to indicate important features and regions on the diagram.
See, e.g., Figure 17-15 on page 453.
7. Briefly describe how you would determine the distance to a star whose trigonometric
parallax is too small to measure.
Use the method of spectroscopic parallax, i.e., use the star's spectrum to
obtain its spectral type and, more importantly in this case, its luminosity
class, then combine that info with the star's apparent brightness to
obtain its distance.
8. What information about stars do astronomers learn from binary systems that cannot be
learned in any other way? What measurements do they make of binary systems to garner
this information?
Astronomers learn about mass from binary stars (a fundamental
parameter that cannot be obtained from single stars). The mass can be
calculated, using Newton's version of Kepler's 3rd law, from the binary
system's period and orbital separation.
9. What are H II regions? Near what kinds of stars are they found? Why do only these
stars give rise to H II regions?
H II regions (also known as emission nebulae) are regions of gas that
have been ionized by UV radiation from nearby hot stars. The
hydrogen nuclei (i.e., protons) and electrons recombine in excited
energy states and when the electron cascades back down toward the
ground state, the transition from n = 3 to n = 2 releases Hα photons (i.e.,
red light). Hot stars are required because cool stars do not have enough
UV radiation to cause this to occur.
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10. Briefly describe, from its origin in the interstellar medium to its arrival on the main
sequence, how a star like the Sun (i.e., a star of 1 solar mass) forms. Plot its pre-main
sequence evolutionary track on the HR diagram (on the back of this sheet, if necessary).
Star formation begins in dense, cold nebulae, where gravitational
attraction causes a clump of material to condense into a protostar.
Subsequent contraction causes the protostar to heat up and begin
glowing. When its core temperature becomes high enough, it begins
thermonuclear fusion, at which point it's a full-fledged star and is
situated on the main sequence of the HR diagram. See Figure 18-10 on
page 478.
11. Explain how a star like the Sun becomes a red giant star.
Once the Sun's core hydrogen has been exhausted (via conversion to
helium and energy), the helium core contracts (since it's not hot enough
to cause helium fusion). The core temperature rises, causing hydrogen
in the surrounding shell to undergo fusion. The resulting luminosity is
greater than during the main sequence phase, causing the outer part of
the star to expand (becoming a giant) and its surface to cool off
(becoming red).
12. On an HR diagram, sketch the post-main sequence evolutionary track of a 1 solar
mass star like the Sun. Be sure to label the ZAMS, the location where the Helium flash
occurs, and the direction in which the star is moving. (Use the back of this sheet, if
necessary.)
See Figure 19-9 on page 507.
13. Explain how and why the turnoff point on the HR diagram of a cluster is related to
the cluster’s age.
The turnoff point of a cluster's main sequence indicates the most
massive stars in the cluster that are still burning hydrogen. Any star
that was more massive than that has already exhausted its core
hydrogen supply and begun its post-main sequence phase. Knowing
that mass allows us to calculate age, via t ∝ 1/(M2.5).
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14. What are Cepheid variables? What two properties do they have that allow
astronomers to use them to determine distances to very remote objects (like galaxies)?
A Cepheid variable is a pulsating, post-main sequence star whose
variability is recognized by the characteristic way in which its
brightness varies: rapid brightening followed by gradual dimming. The
two properties that make Cepheids useful for determining distances to
very remote objects is that they are very bright and that they exhibit a
Period-Luminosity relation.
PART II (30 points) – 6 mathematical problems (5 points each):
1. The mass of a hydrogen nucleus = 1.673 × 10-27 kg. The mass of a helium nucleus =
6.645 × 10-27 kg. How much energy is released by the formation of a single helium
nucleus through thermonuclear fusion?
Energy can be calculated from E = mc2, where m in this case is what's
left over after 4 hydrogen nuclei have been fused into 1 helium nucleus:
E = mc2
= (4 x 1.673 × 10-27 kg – 6.645 × 10-27 kg) (3.00 × 108 m/s)2 = 4.23 × 10-12 J
2. An astronomer observing a binary star finds that one of the stars orbits the other once
every 5 years at a distance of 10 AU. (a) What is the sum of the masses of the two stars?
(b) Suppose the mass ratio of the system is M1/M2 = 0.25. What are the individual
masses of the stars? Give your answers in solar masses.
(a) P = 5 and a = 10, so M1 + M2 = a3/P2 = 1000/25 = 40 Mo.
(b) M1 = 8 Mo, M2 = 32 Mo.
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Consider a star with an apparent magnitude of +12.1 and a parallax angle of 0.010″.
3. What is the distance to this star?
d = 1/p = 1/.01 = 100 pc
4. What is the absolute magnitude of this star? Is this star intrinsically brighter or fainter
than the Sun (the Sun’s absolute magnitude = +4.8)?
m – M = 5 log d – 5, so M = m – 5 log d +5 = 12.1 – 5 log 100 + 5 = 7.1
Because this number is higher than the Sun's value, the star is fainter.
5. At one stage during its pre-main sequence phase, the protosun had a luminosity equal to
100 Lo and a surface temperature of about 2900 K (= 1⁄2 To). At that time what was the
protosun’s radius (in terms of the Sun’s present-day radius, Ro)?
R/Ro = (To /T)2 √(L/Lo) = (To /½ To)2 √(100 Lo /Lo) = (2)2 √(100) = 40
6. Calculate the main-sequence lifetimes of (a) a 10-Mo star and (b) a 0.5-Mo star.
Compare these lifetimes with that of the Sun.
(a) t ∝ 1/(M2.5) = 1/(102.5) = 0.003 times the lifetime of the Sun
(b) t ∝ 1/(M2.5) = 1/(0.52.5) = 5.7 times the lifetime of the Sun
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