Properties of Planetary Nebulae Typewriter (1)
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Astronomy
Date
Apr 3, 2024
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Properties of Planetary Nebulae Goal Stars with approximately the mass of the Sun eject their outer layers before becoming white dwarfs. The result is the formation of a "planetary nebula", such as the Ring Nebula or Helix Nebula. You will use an images of planetary nebulae to estimate how much mass is ejected, and how long the process takes. You will estimate the actual size of the nebula and, given the velocity of the gas, its approximate age. After calculating the mass of the nebula, you will explore whether planetary nebulae replenish the interstellar dust and gas enough to support star formation. Learning Objectives
Upon completion of this exercise, you will be able to
qualitatively describe how a planetary nebula looks at different wavelengths and why it looks that way;
plot the brightness of the nebula as a function of distance from the white dwarf along both the long and short axis;
interpret the plots as the amount of mass loss versus time –
the mass loss history for the nebula;
estimate the angular size of the nebula in arc seconds and the radius in kilometers, and compare the size with the size of the Solar System;
estimate the age of the nebula;
work with the volume and density of the nebula to calculate the approximate mass of the nebula;
based on these calculations, theorize as to whether or not planetary nebulae can be responsible for providing material for new star formation. Background and Theory A planetary nebula is formed when a red giant star approaches the end of its life span and begins to lose a lot of mass very quickly. This mass condenses and forms an expanding shell around the star. This cloud of dust and gas obscures the central star for a time. The temperature radically increases, while the luminosity remains approximately constant, and the star moves to the left across the upper part of the H-R diagram. The hotter, ultraviolet emitting layers of the central white dwarf star become exposed, ionizing the gas in the surrounding nebula. This ionized gas begins to glow, making the nebula luminous. Eventually, the luminosity of the white dwarf falls by as much as 90%. The star is no longer capable of ionizing the nebula, so the nebula gradually fades as it disperses into the interstellar medium. Even th
ough about 30% of the star’s original mass is ejected, because there are so many stars having masses similar to that of the Sun, planetary nebulae are responsible for a large fraction of the mass returned to the interstellar medium each year. Planetary nebulae emit emission line spectra of many different colors, depending upon which atoms and ions are present. Red nebulae are dominated by hydrogen and ionized nitrogen (N+). Green nebulae contain oxygen ions (O++), while blue nebulae shine in the light of ionized helium (He+). Sometimes different regions of the nebula are different colors. We can use these images to determine the mass loss history of the planetary nebulae, its size, and its age.
Part A: Chemical Composition 1.
Each of the images shown below is of a different planetary nebula. Examine each image. Make a table of your own that lists the nebulae and a short description of what you see in the image. Comment on the shape of the nebula, and whether it looks the same in all colors. 2.
These nebulae shine in the visible wavelengths because of line emission. Do the Hydrogen and Oxygen emission come from the same place in the nebula? In general, which comes from closer in, and which further out? Are there any exceptions? 3.
Think back to the explanation of how lines are formed. Electrons in hydrogen are loosely bound, compared to the electrons in this particular oxygen transition. Does the overall trend in the location of the colors make sense? Explain 9UOWGQ SKG[QG
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Dumbbell Nebula Part B: Changing Mass Loss Rate
1.
Examine the images of the Ring Nebula. The brighter regions of the image are places where the density of the nebula is high, since there is more material to create emission, or places where the material is easily ionized. Material close to the central star was probably lost recently, while material far from the star was probably lost some time ago. Briefly give a qualitative description of how these images differ from each other, and then theorize as to why
they differ. 2.
Using the N+ negative image provided, make a plot of the mass loss versus distance from the central white dwarf along the long axis of the nebula. Plot the brightness of the nebula on the y-axis using the scale given with the image, and distance from the white dwarf on the x-axis. Label your axes with arrows indicating increasing brightness, and increasing distance. OSSKW SUYY UGWY MGY MKQO[S³ YMK WOSM GSI OSSKW
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brightest regions appear black, darkest appear white.] Shading Scale 10 9 8 7 6 5 4 3 2 1 Shading Scale 10 9 8 7 6 5 4 3 2 1
3.
On the same graph using a different color
, make the same sort of plot for the short axis of the nebula. Are the two plots similar? Comment on the plots. Graphs for 2 & 3 4.
One way to interpret these data are to guess that the nebula is actually a hollow sphere. The middle is dim because there is less material along the line of sight, while all around the outside the nebula is much brighter because you are looking through more material at the edge of the bubble. How do your observations differ from this model? How are they consistent? )OKKKWKSY´ OYY SUY UKWKKIYQ_ WU[SI OYY YW[OYMKI
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5.
Now let’s interpret your pl
ots as representing the mass loss history of the star, using the fact that material which is more distant from the central star was shed in the more distant past. Has the mass loss been constant over time? Describe the history of the mass loss from the central star. Part C: Size and Age of the Ring Nebula
1.
Estimate the length in arc seconds of the long axis of the nebula in the N+ image. The total image height is about 2 arc minutes (you will need to calculate a scale for the image: 1 mm = _??_ arc minutes). Convert the length of the long axis to arc seconds. 2.
Divide this by 2 to get the radius of the nebula along the long axis in arc seconds. This is the angular radius of the nebula. 3.
Now, use the small angle formula to find the actual radius, R
of the nebula in kilometers. The distance, D
, to the Ring Nebula is about 2.15x10
16
km (~2,300 light years), and the small angle formula is: 206,265
DA
R
[The mystical number 206,265 is simply the number of arc seconds in a radian] 4.
To understand more clearly the size of the nebula, divide the length of the long axis (in km) by the distance from the Earth to the Sun (1AU = 1.5x10
8
km) to put the size of the nebula into AU’s. For a sense of scale, the entire Solar System is about 80 AU across. Compare the size of the nebula to the size of the Solar System. 5.
We will assume that the nebula has been expanding at about 20 km/s since it first began losing mass. Given this speed, and the size of the nebula which you just found, find the age of the Ring Nebula. Don't forget to convert the age from seconds to years so that you have a sensible answer. SU OY MGY SUY GKKS IUSYYGSY U[KW YOSK GKIG[YK YMKWK
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Part D: Mass Return Rate
1.
Use the formula for the volume of a sphere 3
4
3
V
R
to find the volume of the Ring Nebula. Use the same formula to find the volume of the hollow inner part. (You will need to find the radius of this inner part, as in steps B1-B3). 2.
Subtract the inner volume from the outer volume to find the volume that emits light. (Why do we do the subtraction?) 3.
The density of the nebula is very low, n = 1.7x10
-10 kg/km
3
. Multiply this density by the volume to get the mass in the Ring Nebula in kilograms. 4.
Convert this mass to solar mass by dividing by the mass of the Sun (2x10
30
kg). If the original star had a mass of one solar mass, what fraction of its mass did it eject into the nebula? 5.
The entire mass of this nebula will become a part of the interstellar medium. There are about 700 planetary nebulae in our galaxy. Estimate the mass returned to the interstellar medium each year by multiplying the mass of the Ring Nebula by the number of nebulae, and dividing by the lifetime of the Ring (in years), as found in Part B. Is this a large amount of material? What can you compare your answer to? 6.
New stars form at the rate of about one solar mass per year. Can planetary nebulae be solely responsible for producing the gas which is made into these new stars? Explain your answer. [ U[YKW » ¶²·µ+¼½¾
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