Astronomy 102, Midterm Exam #2

Thursday November 13, 2003

2.00 pm – 3.15 pm

Do not turn the pages of the exam until you are instructed to do so.

You are responsible for reading the following rules carefully before beginning.

Exam rules: You may use only a writing instrument and a calculator while taking this test. You may not consult any computers, books, notes – neither on paper nor stored in a calculator – nor each other. All of your work must be written on the attached pages, using the reverse sides if necessary. Important equations, numbers and conversion factors, used in the problems, are found in the last pages of the exam, in the form of the Useful Equations sheet, the How Big Is That sheet, and the graph of circumferences versus mass for white dwarfs, neutrons stars, and black holes. The final answers must be indicated clearly. Exams are due at 3:15, and will be available to be reclaimed in recitations and lectures next week.

The questions are each worth five (5) points. Partial credit is available for those questions involving essays, short answers, drawings or explicit calculations, and for multiple-choice questions indicated possibly to have more than one correct answer (e.g. “check all answers that apply”).

Name: ___________________________________

ID number: _______________________________

Recitation: ________________________________

1. Occasionally Cygnus X-1 emits short bursts of light seen at ultraviolet wavelengths, in the form of a train of pulses that dies off towards the end. One such burst, seen with the Hubble Space Telescope by Joe Dolan (2001, PASP 113, 974), is shown in the Figure below.

Describe what effect produces these bursts and what does the period of these bursts correspond to?

2. Match the pictures to the names listed below.

A	B	C	D	E

___ Tim Wakefield

___ Johnny Damon

___ Pedro Martinez

___ Manny Ramirez

___ Jason Varitek

3. A certain star is in orbit with a much less luminous companion. Its orbital plane is edge-on to the line of sight. Its speed in orbit is 130 km/s. The overall velocity of the two-star system (that is, the velocity of their center of mass) along the line of sight is -90 km/s. What is the maximum wavelength (in centimeters) of a Doppler-shifted absorption line which, seen at rest, has a wavelength of 5.0000E-5 cm?

c 4.99850E-5 cm

c 5.00367E-5 cm

c 4.99783E-5 cm

c 5.00067E-5 cm

c 5.00150E-5 cm

c 4.99933E-5 cm

c 4.99633E-5 cm

c 5.00217E-5 cm

4. A certain star is in orbit with a much less luminous companion. Its orbital plane is edge-on to the line of sight. Its speed in orbit is 90 km/s. The overall velocity of the two-star system (that is, the velocity of their center of mass) along the line of sight is 130 km/s. What is the minimum wavelength (in centimeters) of a Doppler-shifted absorption line which, seen at rest, has a wavelength of 5.0000E-5 cm?

c 4.99850E-5 cm

c 5.00367E-5 cm

c 4.99783E-5 cm

c 5.00067E-5 cm

c 5.00150E-5 cm

c 4.99933E-5 cm

c 4.99633E-5 cm

c 5.00217E-5 cm

5. Astronomers find a star that seems to be in orbit about an invisible, 1.9 M_sun companion. At radio wavelengths, bright pulses of light are detected every 0.01 sec from the companion. The companion is

c A normal star.

c A white dwarf.

c A neutron star.

c A black hole.

c Unknown; the evidence is ambiguous.

6. A certain star is in orbit with a much less luminous companion. Its orbital plane is perpendicular to the line of sight. Its speed in orbit is 90 km/s. The overall velocity of the two-star system (that is, the velocity of their center of mass) along the line of sight is 130 km/s. What is the minimum wavelength (in centimeters) of a Doppler-shifted absorption line which, seen at rest, has a wavelength of 5.0000E-5 cm?

c 4.99850E-5 cm

c 5.00367E-5 cm

c 4.99783E-5 cm

c 5.00067E-5 cm

c 5.00150E-5 cm

c 4.99933E-5 cm

c 4.99633E-5 cm

c 5.00217E-5 cm

7. The black hole at the center of the Milky Way has a mass of 2.6´10⁶ M_sun, but the central object has a luminosity of 10⁵ L_sun at most. Assuming an efficiency of 10% for converting mass into radiated energy, what is the maximum rate at which the black hole can be accreting matter?

c 9.1´10⁷ gm/sec.

c 4.2´10¹⁸ gm/sec.

c 2.0´10³⁶ gm/sec.

c 3.1´10⁵⁴ gm/sec.

c None of above.

8. When was the last time the Red Sox won the World Series?

c 1776

c 2004

c 1915

c 1918

c 2003

9. Supernovae happen when

c The outer parts of a rapidly-collapsing dead star bounce off of the surface of the neutron star suddenly formed at its core.

c The outer parts of a rapidly-collapsing dead star bounce off of the horizon of a black hole suddenly formed at its core.

c The outer parts of a rapidly-collapsing dead star are slung gravitationally around the horizon of a black hole suddenly formed at its core, and are ejected at speeds close to the speed of light..

c Matter and antimatter annihilate each other in the center of the star, converting all of their mass into a vast amount of light energy (according to E = mc²) and exploding the star.

c None of above.

10. A certain star is in orbit with a much less luminous companion. Its orbital plane is edge-on to the line of sight. The Figure shows the time-dependence of a Doppler-shifted absorption line emitted by the star, which, seen at rest, has a wavelength of 5.0000E-5 cm.

What is the orbital velocity of the star (in km/s)?

11. What is the overall velocity of the two-star system discussed in Question # 10 (that is, the velocity of their center of mass) along the line of sight. Express your answer in terms of km/s.

12. Degeneracy pressure is due to

c The particle properties of the elementary constituents of matter.

c The wave properties of the elementary constituents of matter.

c The relativity of mass.

c The relativity of time.

c The absolute nature of the speed of light.

13. A certain star is in orbit with a much less luminous companion. Its orbital plane is perpendicular to the line of sight. Its speed in orbit is 130 km/s. The overall velocity of the two-star system (that is, the velocity of their center of mass) along the line of sight is -90 km/s. What is the maximum wavelength (in centimeters) of a Doppler-shifted absorption line which, seen at rest, has a wavelength of 5.0000E-5 cm?

c 4.99850E-5 cm

c 5.00367E-5 cm

c 4.99783E-5 cm

c 5.00067E-5 cm

c 5.00150E-5 cm

c 4.99933E-5 cm

c 4.99633E-5 cm

c 5.00217E-5 cm

14. What is the circumference of a neutron star with a mass of 0.2 M_sun?

c 4 km

c 110 km

c 200 km

c 1000 km

c 95000 km

15. The mass of a white dwarf with the same circumference as the Earth is

c 0.1 M_sun

c 0.9 M_sun

c 1.3 M_sun

c 1.4 M_sun

c None of above.

16. The mass of a neutron star with the same circumference as the Earth is

c 0.1 M_sun

c 0.9 M_sun

c 1.3 M_sun

c 1.4 M_sun

c None of above.

17. The Chandrasekhar limit tells us that

c Accretion disks can grow hot through friction.

c Neutron stars with a mass of more than 3 M_sun are not stable.

c White dwarfs must have a mass of more than 1.4 M_sun.

c Not all stars will end up as white dwarfs.

c Stars with a mass of less than 0.5 M_sun will become black holes.

18. The BeppoSAX satellite was constructed in

c The Netherlands.

c Holland.

c Nederland.

c All of the above.

19. A white dwarf is composed of

c Hydrogen nuclei and degenerate electrons.

c Helium nuclei and normal electrons.

c Carbon and oxygen nuclei and degenerate electrons.

c Degenerate iron nuclei.

c A helium-burning core and a hydrogen-burning shell.

20. The density of a neutron star is

c About the same as that of a white dwarf.

c About the same as that of the sun.

c About the same as that of an atomic nucleus.

c About that same as that of a water molecule.

c None of the above.

21. You observe a student, who rest mass is 75 kg, traveling with 75% of the speed of light? What is the mass of this student in your reference frame?

c 75 kg

c 113 kg

c 99 kg

c 94 kg

c 150 kg

22. What is the ergosphere of a black hole?

23. Which of the following statements about black holes are true (check all correct statements)?

c More energy would be released by dropping a ton of coal or gasoline into a black hole than by dropping a ton of water into the same black hole.

c A space traveler, descending vertically and hovering very close to the equator of a rotating black hole, would be seen to rotate with the black hole by a distant observer.

c Energy can be obtained from the ergo sphere outside the horizon of a rotating black hole.

c Energy cannot be released by accretion onto a black hole because nothing can escape a black hole, once it is inside the horizon.

c Time stops at the horizon of a black hole, from the viewpoint of a distant observer.

24. A star has a luminosity of 0.216 L_sun, and a total lifetime of 1.16E+11 years. How much energy does the star produce in its lifetime?

25. Consider a stellar core that collapses and forms a black hole. Which of the following physical quantities, which can be used to describe the black hole or the stellar core, will not change as a result of this collapse? Check all quantities that remain unchanged.

c Mass.

c Magnetic field.

c Electric Charge.

c Particle properties.

c Stellar type.

26. Which of the following statements describe the observed characteristics of quasars (check all correct statements)?

c The luminosity is much larger than that of an entire galaxy, and originates in two clouds on either side of a visible galaxy.

c The motion of the surrounding stars, seen in Doppler shifts, indicates the imminent swallowing of an entire galaxy by a super massive black hole.

c Most of the radio waves originate from two lobes on either side of a visible galaxy.

c Extremely regularly pulsed radio emission.

c The luminosity is much larger than that of an entire galaxy, and originates in a central region vastly smaller than a galaxy.

c Two narrow jets are evident in the radio emission pattern.

c Most of the visible light appears to come from a star-like object.

c One narrow jet is evident in radio emission pattern.

c Superluminal (apparently faster-than-light) motions are observed.

c Most of the radio waves appear to come from a star-like object.

27. A black hole with a mass of 0.5 M_sun, and spinning near its maximum rate, has 23 percent of its total mass stored outside its horizon, in the form of rotating space-time. How much energy does this represent?

c 1.0E+20 erg

c 2.0E+19 erg

c 3.9E+52 erg

c 2.1E+53 erg

c 9.0E+53 erg

c 2.1E+55 erg

28. Which of the following statements describe the observed characteristics of radio galaxies (check all correct statements)?

c The luminosity is much larger than that of an entire galaxy, and originates in two clouds on either side of a visible galaxy.

c The motion of the surrounding stars, seen in Doppler shifts, indicates the imminent swallowing of an entire galaxy by a super massive black hole.

c Most of the radio waves originate from two lobes on either side of a visible galaxy.

c Extremely regularly pulsed radio emission.

c The luminosity is much larger than that of an entire galaxy, and originates in a central region vastly smaller than a galaxy.

c Two narrow jets are evident in the radio emission pattern.

c Most of the visible light appears to come from a star-like object.

c One narrow jet is evident in radio emission pattern.

c Superluminal (apparently faster-than-light) motions are observed.

c Most of the radio waves appear to come from a star-like object.

29. The black hole in a certain quasar swallows matter at an average rate of 1.5 M_sun/year. If it turns 13 percent of the mass into energy in the form of light, what is its luminosity in solar luminosities?

c 2.2E+13 L_sun

c 1.5E+13 L_sun

c 2.9E+12 L_sun

c 2.7E+54 L_sun

c 3.5E+53 L_sun

c 1.8E+54 L_sun

30. A black-hole candidate is found to have a luminosity, in the form of X-rays and gamma-rays, of 115 L_sun. Assuming an efficiency of 18 percent for converting mass into radiated energy, how many grams of mass must it consume per second to generate its luminosity?

31. The following figure shows a schematic sketch of an elliptical galaxy that harbors a super massive black hole, with twin jets and an accretion disk. Draw and label appropriately the positions of three observers, and their lines of sight to the central object, who would classify the galaxy as a blazar, a quasar, and a radio galaxy.

32. If a gamma-ray burster were to occur in Rochester, it would probably destroy life within

c Rochester.

c Western New York.

c About 3 light-years of Earth.

c About 3000 light-years of Earth.

c None of above.

33. X-rays are produced efficiently by black holes because of

c Radiation by electrically-charged particles that are about to fall through the black hole’s horizon, and have thus been given extremely large accelerations gravitationally.

c The swirl of space-time just outside the black hole’s horizon, where 10-30% of the hole’s total energy can be stored.

c Electrically-charged particles that have been ejected by the black hole in the form of a pair of jets, traveling at very high speeds.

c Large pulsations of the black hole’s horizon.

c None of above.

34. X-rays are not produced efficiently by normal stars and white dwarfs because

c The gravity of these objects is insufficient to impart large accelerations to charged particles, which thus cannot emit X-rays.

c The thick accretion disks that normally surround these objects absorb all of the X-rays.

c They lack the relativistic jets possessed by massive black holes.

c The gas pressure (in stars) or degeneracy pressure (in white dwarfs) inhibits the production of X-rays.

c None of above.

35. The following signatures would indicate that a black hole is spinning (check all that apply):

c Features on the event horizon that can be seen by a distant observer to rotate.

c Features in the ergo sphere that can be seen by a distant observer to rotate.

c Matter in stable orbits with a circumference of 3.5 C_S.

c Matter in stable orbits with a circumference of less than 3.0 C_S.

c Photons in orbits with a circumference different from 1.5 C_S.

36. Consider the active galaxies shown in the pictures. Match the picture to the type of galaxies listed below.

A	B
C	D

___ Quasar Galaxy

___ Blazar Galaxy

___ Radio Galaxy

___ Seyfert Galaxy

37. Two 1.8 M_sun neutron stars, orbiting each other at close range, suddenly spiral into each other and coalesce. This produces (check only one option):

c A black hole and a gamma-ray burst.

c A 3.6 M_sun neutron star.

c A very massive accretion disk and two jets of relativistic particles.

c A supernova.

c None of the above.

38. Which of the following black-hole symptoms are observed in GRO J1655-40, one of the best-known “stellar” black-hole candidates (check all correct symptoms)?

c Ejection of material at speeds near the speed of light.

c Details of the structure of its massive accretion disk.

c Enormous luminosity emitted from an extraordinarily small space.

c X- and g-ray emission.

c Gravitational deflection of the light of more distant stars.

39. A bright star is seen to be orbiting with a companion that is a strong source of visible light. From the orbital speed and mass of the bright star, it is inferred that the mass of the companion is 1.6 M_sun. The companion object is most likely to be

c A normal star.

c A white dwarf.

c A neutron star.

c A black hole.

c Unknown; the evidence is ambiguous.

40. Consider two white dwarf stars with the same mass, one perfectly normal and the other in which all the electrons have been replaced by particles with half the mass of the electron but which are otherwise the same. Which white dwarf is larger in circumference, and why?

Circumferences of white dwarfs, neutron stars and black-hole event horizons

Useful Equations (so far)

Length contraction, time dilation and velocity addition:

Minkowski absolute interval:

Useful rearrangements of the Absolute Interval formula:

Mass-energy equivalence:

Mass of a moving object:

Doppler shift:

Schwarzschild circumference:

Circumference of a spherical object of diameter d:

C = p d

How big is that?

Diameter of hydrogen atom	1.06 ´ 10^-8 cm
Diameter of the Moon	3.5 ´ 10^3 km
Diameter of the Earth	1.3 ´ 10^4 km
Diameter of the Sun	1.4 ´ 10^6 km
Diameter of the Milky Way galaxy	1.7 ´ 10^5 ly
Distance to the Moon	3.8 ´ 10^5 km
Distance to the Sun	1.5 ´ 10^8 km
Distance to the next nearest star	4 ly
Distance to the center of the Milky Way	2.7 ´ 10^4 ly
Distance to the nearest galaxy	1.7 ´ 10^5 ly
Mass of hydrogen atom	1.67 ´ 10^-24 gm
Mass of the Moon	7.4 ´ 10^25 gm
Mass of the Earth	6.0 ´ 10^27 gm
Mass of the Sun	2.0 ´ 10^33 gm (1 MO)
Mass of the Milky Way galaxy	5 ´ 10^10 MO
Luminosity of the Sun	3.8 ´ 10^33 erg/s (1 LO)
Luminosity of the largest stars	10^5 LO
Luminosity of the Milky Way galaxy	10^10 LO
Luminosity of quasar 3C 273	10^12 LO
Earth’s rotation period	8.64 ´ 10^4 s (1 day)
Moon’s revolution period	28 days
Earth’s revolution period	365.25 days (1 year)
Sun’s revolution period within Milky Way	2.4 ´ 10^8 years
Age of the solar system	4.6 ´ 10^9 years
Expected life span of the Sun	1.5 ´ 10^10 years
Age of the Universe	1.3 ´ 10^10 years
Earth’s equator rotation speed	0.47 km/s
Earth’s revolution speed	30 km/s
Sun’s speed within the Milky Way	220 km/s
Milky Way’s speed within the local Universe	500 km/s

Typical lengths:
Normal star diameter	10^6 km
Distance between stars	a few ly
Normal galaxy diameter	10^5 ly
Distance between galaxies	10^6 ly
Typical masses:
Smallest star	0.1 MO
Normal star	1 MO
Giant star	10 MO
Normal galaxy	10^10 - 10^11 MO
Galaxy cluster	10^14 - 10^15 MO
Typical luminosities:
Normal star	1 LO
Giant star	10^3 - 10^5 LO
Normal galaxy	10^9 - 10^10 LO
Quasar	10^12 - 10^13 LO
Typical time spans:
Planetary revolution	1 year
Galaxy rotation	10^7 - 10^9 years
Life of giant stars	10^6 - 10^9 years
Life of normal star	10^10 years
Typical speeds:
Planetary orbits	10 km/s
Stellar motion in galaxy	100 km/s
Between nearby galaxies	100 km/s
Other important constants:
1 ly = 9.46 ´ 10^12 km = 9.46 ´ 10^17 cm	1 Mly = 10^6 ly
1 km = 10^5 cm	1 erg = 1 gm cm^2/s^2
1 hour = 3600 seconds	1 year = 3.16 ´ 10^7 seconds
π = 3.14159265359	Hubble’s constant: H0 = 20 km/(sec Mly)
Speed of light: c = 2.99792458 ´ 10^5 km/s = 2.99792458 ´ 10^10 cm/s = 1 ly/year	Newton’s gravitational constant: G = 6.67 ´ 10^-8 cm^3/(gm s^2)