Astronomy Exam 2
The lowest mass for a true star is 1/12 the mass of the Sun. What is the luminosity of such a star based upon the mass-luminosity relationship?
(1/12)^4= (.083)^4= 4.7X10^-5
It was noted in class that modern day astronomy uses reflecting telescopes rather than refracting telescopes. List three reasons why refracting are not used anymore
1. large lenses are heavy and sag under gravity 2. can't use adaptive optics 3. hard to make lenses without defects
Star A and Star B have different apparent brightnesses but identical luminosities. Star A is 10 light-years away from Earth and appears 36 times brighter than Star B. How far away is Star B?
Because Star A and Star B have identical luminosities, the difference in their apparent brightness is due solely to distance. For Star A to appear 36 times brighter than Star B, it must be 6 times closer, since 62 = 36. Therefore, the distance to Star B is 6 × 10 light-years = 60 light-years from Earth.
Star A and Star B have different apparent brightnesses but identical luminosities. If Star A is 20 light-years away from Earth and Star B is 40 light-years away from Earth, which star appears brighter and by what factor?
Because Star A and Star B have identical luminosities, the difference in their apparent brightness is due solely to distance. Star B is twice as far from Earth as Star A. Star A is therefore 22 = 4 times brighter than Star B.
if a 3 solar mass star and a 20 solar mass star are formed together in a binary system which star would A) evolve off the main sequence first? B) form a carbon and oxygen rich white dwarf?
A) 20 Mo B) 3Mo
What are the approximate spectral classes of stars with the following characteristics? A. Balmer lines of hydrogen are very strong; some lines of ionized metals are present. B. The strongest lines are those of ionized helium. C. Lines of ionized calcium are the strongest in the spectrum; hydrogen lines show only moderate strength; lines of neutral and metals are present. D. The strongest lines are those of neutral metals and bands of titanium oxide.
A. A; B. O; C. G; D. M.
Which method would you use to obtain the distance to each of the following? A. An asteroid crossing Earth's orbit B. A star astronomers believe to be no more than 50 light-years from the Sun C. A tight group of stars in the Milky Way Galaxy that includes a significant number of variable stars D. A star that is not variable but for which you can obtain a clearly defined spectrum
A. Radar would be the best tool for measuring distances to objects in the solar system. B. A parallax measurement would be best for this nearby star. C. Cepheids or RR Lyraes would be useful for determining the distance to this cluster. D. The method using the H-R diagram and getting a spectrum to determine the luminosity class of the star.
Two protostars, one 10 times the mass of the Sun and one half the mass of the Sun are born at the same time in a molecular cloud. Which one will reach the main sequence stage, where it is stable and getting energy from fusion, first?
As you can see in Figure 21.12 Evolutionary Tracks for Contracting Protostars, the more massive a star is, the more quickly it goes through each stage of being a protostar. Thus, the 10 solar mass star will become a real star (one that supplies its energy through fusion) first.
Astronomers find that 90% of the stars observed in the sky are on the main sequence of an H-R diagram; why does this make sense? Why are there far fewer stars in the giant and supergiant region?
Being on the main sequence means that the star is converting hydrogen to helium in the core. Since stars are made mostly of hydrogen, this process takes approximately 90% of a star's life. Thus it makes sense that the 90% of the stars observed at some particular time would be undergoing this process. Being a red giant star is a brief stage in the life of each star, when the star is readjusting to the loss of energy from the fusion of hydrogen. In a relatively short time (in the timescale of stars), the core collapses until it is hot enough for the fusion of helium into carbon, restoring the star's equilibrium. Since this is only a brief stage in the life of the star (taking only a few percent of the star's life), it makes sense that only a few percent of stars will be found in the giant stage at any given time.
Describe the evolution of a star with a mass similar to that of the Sun, from the protostar stage to the time it first becomes a red giant. Give the description in words and then sketch the evolution on an H-R diagram.
During the protostar stage, gravity gathers gas and dust toward a central location, which increases in temperature and pressure. Eventually, the temperature and pressure at the center of the gas and dust will reach critical thresholds and the nuclear fusion of hydrogen into helium will begin in what is now called the core. When this happens, the protostar officially becomes a zero-age main sequence star. For the next 10 billion years or so, the star will stably undergo nuclear fusion as it remains on the main sequence. Once the hydrogen gas runs out in the core, gravity will begin to re-collapse the stellar atmosphere above the core, which in turn increases the temperature and pressure within the core again. While this occurs, a hydrogen shell around the core will begin nuclear fusion, causing the star to swell and become more luminous as it enters the red giant phase. Eventually, the temperature and pressure in the core will reach another set of critical thresholds and the nuclear fusion of helium into carbon will commence in an explosive helium flash, officially beginning a more stable phase.
New stars form in regions where the density of gas and dust is relatively high. Suppose you wanted to search for some recently formed stars. Would you more likely be successful if you observed at visible wavelengths or at infrared wavelengths? Why?
Dust is an efficient absorber of visible radiation, and so star-forming regions often cannot be observed at visible light wavelengths. Infrared radiation does penetrate the dust, and so infrared observations are an essential tool for studying regions of star formation.
There are fewer eclipsing binaries than spectroscopic binaries. Explain why.
Eclipses only happen when stars are lined up in such a way that one star passes in front of or behind. Spectroscopic need only detect change in velocity associated with orbital motion
If Betelgeuse had a mass that was 25 times that of the Sun, how would its average density compare to that of the Sun? Use the definition of where the volume is that of a sphere.
From Exercise 47, the radius of Betelgeuse is found to be 900 times that of the Sun. Since density is defined as mass divided by volume, and keeping values in terms of the Sun's, the values given would result in a density of times that of the Sun. (25/(900^3)=3.4x 10^-8
Star Spectrum 1 G, main sequence 2 K, giant 3 K, main sequence 4 O, main sequence 5 M, main sequence
Hottest: Star 4, spectral type determines relative temp., O is the hottest Coolest: Star 5, "", M is the coolest Most Luminous; Star 4, highest temp, upper main sequence Least Luminous: Star 5, lowest temp, lowest main-sequence location
The best parallaxes obtained with Hipparcos have an accuracy of 0.001 arcsec. If you want to measure the distance to a star with an accuracy of 10%, its parallax must be 10 times larger than the typical error. How far away can you obtain a distance that is accurate to 10% with Hipparcos data? The disk of our Galaxy is 100,000 light-years in diameter. What fraction of the diameter of the Galaxy's disk is the distance for which we can measure accurate parallaxes?
If the uncertainty is 0.001 arcsec, 10 × 0.001 arcsec = 0.01 arcsec. D = 1/p so D = 100 pc for 10% distances. This is approximately 300 light-years, so we can measure 300/100,000 = 0.003 or 0.03% of the disk of the Milky Way.
The evolutionary track for a star of 1 solar mass remains nearly vertical in the H-R diagram for a while (see Figure 21.12 Evolutionary Tracks for Contracting Protostars). How is its luminosity changing during this time? Its temperature? Its radius?
In this vertical region on the diagram, luminosity is dropping while the surface temperature remains constant. This is a stage where the material of the star is falling inward without any hindrance and since the star has less and less surface area with which to give off radiation, its luminosity is decreasing together with its radius.
If two stars are in a binary system with a combined mass of 5.5 solar masses and an orbital period of 12 years, what is the average distance between the two stars?
Kepler's third law is applied: D3 = (M1 + M2)P2, D3 = (5.5)(12)2 = 792,
A protostar will be much much luminous than the Sun, but it's temperature is much smaller, how is this possible?
L is proportional too R^2T^4, if L is bigger and T is smaller R is bigger
Why do astronomers place telescopes in Earth's orbit? What are the advantages for the different regions of the spectrum?
Light from some bands of the electromagnetic spectrum does not penetrate Earth's atmosphere, so direct detection of those bands requires putting telescopes in space. For this reason, X-ray and gamma-ray space-based observatories are essential. Even in bands that do penetrate the atmosphere, like millimeter wavelengths, "pollution" from terrestrial sources can swamp faint astronomical signals, making it advantageous to place telescopes in space at these bands also. Infrared radiation is absorbed by water in Earth's atmosphere, so the higher up the telescope can be located, the less absorption by water it will have to deal with.
The Orion Nebula is about two million years old. Do you expect to find any white draws in the Orion Nebula.
No, white dwarfs come from stars which last longer than hundreds of millions of years so Orion is too young
The spectrum of the Sun has hundreds of strong lines of nonionized iron but only a few, very weak lines of helium. A star of spectral type B has very strong lines of helium but very weak iron lines. Do these differences mean that the Sun contains more iron and less helium than the B star? Explain.
No. The primary reason that stellar spectra look different is the stars have different temperatures. Most stars have compositions very similar to that of the Sun.
Which of the following can you determine about a star without knowing its distance, and which can you not determine: radial velocity, temperature, apparent brightness, or luminosity? Explain.
Not knowing distance: velocity, temperature, apparent magnitude The radial velocity and temperature can be estimated by a spectrum The apparent brightness can be directly observed. Luminosity must know distance
The star Sirius A has an apparent magnitude of −1.5. Sirius A has a dim companion, Sirius B, that is, 10,000 times less bright than Sirius A. What is the apparent magnitude of Sirius B? Can Sirius B be seen with the naked eye?
Remember that a difference in brightness of a factor of 100 corresponds to a difference of five magnitudes. We note that 10,000 = 1002, so the difference would be 10 magnitudes. Therefore, the magnitude of Sirius B is -1.5 + 10 = 8.5. This is too faint to be seen by the naked eye.
Name and describe the three types of binary systems
Spectroscopic: components not easily seen separately but indicated by periodic variations in radial velocity Visual Binary: two components are telescopically resolved Eclipsing Binary: one star blocking the light of the other by passing in front of it
Star A has apparent magnitude of +3, star B has an apparent magnitude of +6. Which is Brighter, does this mean your answer to a has a greater luminosity?
Star A is brighter, No apparent magnitude depends on luminosity and distance, star A might be less luminous but closer
What is the main reason that the spectra of all stars are not identical? Explain.
Stars have different temperature, each element has a characteristic temperature at which the spectral lines are the strongest.
Describe how the 21-cm line of hydrogen is formed. Why is this line such an important tool for understanding the interstellar medium?
The 21-cm line is formed when hydrogen atoms in which the proton and electron are aligned "flip" so that the proton and electron are anti-aligned. Hydrogen atoms that are in the anti-aligned state will be excited into the aligned state by collisions, and will subsequently emit a photon with a wavelength of 21 cm, giving rise to the line. The line is important because it is produced by neutral hydrogen everywhere. Since cold hydrogen atoms make up the largest part of the interstellar medium, the 21-cm line allows us to study the most common component of interstellar gas.
Suppose you were handed two H-R diagrams for two different clusters: diagram A has a majority of its stars plotted on the upper left part of the main sequence with the rest of the stars off the main sequence; and diagram B has a majority of its stars plotted on the lower right part of the main sequence with the rest of the stars off the main sequence. Which diagram would be for the older cluster? Why?
The crucial idea here is that the more massive the star, the more quickly it goes through each stage of its life. The older cluster would be represented by diagram B, which indicates that higher-mass stars have already evolved past the main-sequence stage of their lives, while the lower-mass stars continue to be on the main sequence. Diagram A indicates a young cluster, as only the higher-mass stars have reached the main-sequence stage and the lower mass stars are still protostars and have yet to reach zero-age main sequence.
In the H-R diagrams for some young clusters, stars of both very low and very high luminosity are off to the right of the main sequence, whereas those of intermediate luminosity are on the main sequence. Can you offer an explanation for that? Sketch an H-R diagram for such a cluster.
The most massive stars go through each stage of their lives most quickly, while the lowest-mass stars do everything more slowly. In a cluster in which both the most and least luminous stars lie to the right of the main sequence, the most massive stars have already converted the hydrogen in the core to helium and are beginning to evolve to the supergiant stage. The lowest-mass stars have yet to arrive on the main sequence and begin hydrogen fusion; they are still contracting (and moving toward the main sequence as a consequence).
Suppose you wanted to observe a planet around another star with direct imaging. Would you try to observe in visible light or in the infrared? Why? Would the planet be easier to see if it were at 1 AU or 5 AU from its star?
The planet will be easier to see if it is farther away from its parent star; closer planets would be even more likely to be lost in the glare of the parent star. The ratio of the brightness of the planet to the brightness of the star is very small at all wavelengths, but will be larger in the infrared than in visible light so observations should be made in the infrared.
An astronomer is investigating a faint star that has recently been discovered in very sensitive surveys of the sky. The star has a magnitude of 16. How much less bright is it than Antares, a star with magnitude roughly equal to 1?
The star would be 10-6 times the brightness of Antares (i.e., 1,000,000 times fainter): 1o^-6
The star Betelgeuse has a temperature of 3400 K and a luminosity of 13,200 LSun. Calculate the radius of Betelgeuse relative to the Sun.
The total luminosity of a star is given by the total energy emitted per square meter times the total surface area of the star. According to the information given in the problem, we thus have Lstar = 4Rstar2T4. The radius of the star squared is then given by Rstar2 = Lstar/(4Tstar4). A similar equation applies to the Sun. If we then take the ratio of the two equations, and use the temperature of the Sun of 5800 K, (Rstar/RSun)2 = (Lstar/LSun)(TSun4/Tstar4) = (105)(5800/3000)4 = 1.4 106, Rstar/RSun = 1200. The radius of Betelgeuse is 1200 times larger than the radius of the Sun and would stretch beyond the orbit of Jupiter.
On which edge of the main sequence band on an H-R diagram would the zero-age main sequence be?
The zero-age main sequence would be on the left edge of the main sequence band.
Suppose you want to search for brown dwarfs using a space telescope. Will you design your telescope to detect light in the ultraviolet or the infrared part of the spectrum? Why?
Very low-mass stars or brown dwarfs are relatively cool, with temperatures of only about 2000 K. Such stars emit most of their light in the infrared and practically none in the ultraviolet.
What revisions to the theory of planet formation have astronomers had to make as a result of the discovery of exoplanets?
We now understand that planets can migrate in the protoplanetary disk through gravitational friction or drag. For example, Jupiters can migrate inward and be quite close to their stars (hot Jupiters). We now understand that planet formation is more chaotic and less orderly than we imagined. Instead of all the planets orbiting in one plane and in the same direction, we now see some planets orbiting at right angles to the plane of the other planets or even moving backward. We also learned that it is possible to have stable planets orbiting a system of two stars.
How do stars typically "move" through the main sequence band on an H-R diagram? Why?
When nuclear fusion begins, a star is plotted on the left edge of the main sequence band (the zero-age main sequence) and then makes a slow progression up and to the right edge of the main sequence band. As a star converts hydrogen to helium in its core, it gradually increases in luminosity and size. Note that this is a very short distance for the star to travel, and it takes 90% of its lifetime to do so. Because the main sequence is a fairly narrow band of properties, for most practical purposes, astronomers state that a star is nearly fixed in place on the H-R diagram and undergoes only minimal changes during its hydrogen core fusion stage.
a) star with no nuclear reactions going on in the core, which is primarily of carbon and oxygen b) star of uniform composition from center to surface, it contains hydrogen but has no nuclear reactions going on in the core c) stare that is fusing hydrogen to form helium in its core d) star that is fusing helium to carbon in the core and hydrogen to helium in a shell around the core e) star that has no nuclear reactions going on in the core but is fusing hydrogen to helium in a shell around the core
a white dwarf b protostar c sun, main sequence d red giant 2nd stage e red giant 1st stage
Arrange them in order of their evolution a white dwarf b protostar c sun, main sequence d red giant 2nd stage e red giant 1st stage
b c e d a
If two stars in a binary pair spiral closer together but do not exchange any material, how would their masses and orbital period change?
no exchange, mass doesn't change if they are closer, Kepler's law says that the period is shorter
If most stars become white dwarfs at the ends of their lives and the formation of white draws is accompanied by the production of a planetary nebula, why are their more white draws than planetary nebular in the galaxy?
planetary nebula are given off by most white dwarfs, however they spread out and dissipate fairy quickly, the white dwarf lives much longer
What principle characteristic of a stars spectrum most dominates which spectral class letter of the alphabet?
temperature color helium line strength
What observation can you make that tells you that a binary star system is an eclipsing binary?
the light from the binary varies periodically
Why can't the distances to most stars in our Galaxy be measured using parallax?
they are too far away, the paradox angle is too small