Astro 7N: the Artistic Universe
Review Notes for Unit 3
In addition to these notes, refer to the game's companion "Encyclopedia," for Unit 3:
https://theastroventure.com/encyclopedia/unit3/index.html
Information on the test itself
("Test 2" covers Units 3 & 4)
•
50 multiple-choice questions (5 answer choices each)
•
Half of the questions will relate to material from each of major topics in Unit 3 —
a. the Sun and the "proton-proton chain"
b. brightness, the Inverse-Square Law, and parallax
c. nearest stars, brightest stars, and the H-R diagram
d. the "main sequence" and stellar mass
e. stellar evolution, white dwarfs, neutron stars, and black holes
f.
stellar habitable zones and the "Drake Equation"
g. extrasolar planets
(the other half of the questions will relate to topics in Unit 4; see Unit 4's review notes)
•
Some questions will be identical to those given in the game material — selected
from "Copper’s" quiz questions and those in with the lessons' dialogue
•
Some questions will be drawn directly from the "Sample Test 2 Questions" packet
•
Additional questions similar in nature to questions you have seen before
•
Several of the test's questions will refer directly to the H-R diagram
These notes provide a concise list of things you need to know for the Unit 3 portion of Test 2.
You may also review these concepts by going into your completed Part 3 game, and using
the “Repeat a Lesson” feature of the in-game Pause Menu (press either the 'P' or 'escape'
key to open it, at any time during the game), or talking to "Copper" either in the dorm
lobby or at the end scene of Unit 3 for quizzes.
The "Encyclopedia" (link, above) provides another version of the relevant material.
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1. The Sun
Properties of the Sun
•
Composed mostly of gas — hydrogen (73 %, by mass) and helium (25 %, by mass)
•
Stable due to balance of gravity (inward force) and gas pressure in its hot interior
(outward force)
•
Gas pressure provided by nuclear fusion reactions in the Sun's core, going on at a
temperature of 15 million degrees Kelvin
•
Diameter is 109 x Earth's; mass is 333,000 x Earth's
•
Luminosity is equivalent to 4 × 1024 100 Watt light bulbs
•
99.9 % of all of the mass of the Solar System is in the Sun, alone
•
Sun has been shining for 4.5 billion years, and will continue for about another 5.5
billion years
•
Sunspots are slightly-cooler regions on the Sun’s surface due to magnetic activity
preventing hot material from rising in that region; have 11 year cycles
Nuclear Fusion
•
a long-lasting source of energy in stars: 4 protons combine to make helium-4
(2 protons and 2 neutrons) and release energy in gamma rays
•
this is called the Proton-Proton Chain
Step 1: two protons collide at very high speed, and stick together;
one of them changes into a neutron; ends with a Deuterium nucleus
( 2H : 1 proton and 1 neutron, bound together), plus released energy
Step 2: Deuterium nucleus from Step 1 collides with another proton, and makes
a Helium-3 nucleus ( 3He : 2 protons and 1 neutron, bound together),
plus some more excess energy released
Step 3: two Helium-3 nuclei combine to make a Helium-4 nucleus
( 4He : 2 protons and 2 neutrons, bound together),
releasing back 2 protons in the process and some more extra energy
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•
Although it requires a lot of energy initially to cause the high-speed collisions
between protons and nuclei during each step of the "p-p chain," a little bit of extra
energy is generated and released in every step
•
The energy output from the p-p chain comes from E = m c2
•
The mass of a Helium-4 nucleus is less than the mass of 4 protons;
some of that mass is converted into energy (in the form of gamma-ray photons)
Layers of the Sun — from inside to outside
core : at the center; high density and temperature; where nuclear reactions occur
and gamma rays are produced
radiative zone : photons are repeatedly re-absorbed and re-emitted; the energy of
an individual photon can take on average 170,000 years to pass through
convective zone : hot gas rises and cold gas sinks; light traverses in about 1 week
photosphere : temperature 5,780 K; this is the "surface" of the Sun that we see;
photons have been converted to visible wavelengths; can see "granules" due
to convection bringing material up and down in cells
chromosphere : red or orange color; temperature about 4,500 K; we see through
this, down to the photosphere
flare : an eruption coming out of Sun due to magnetic activity
prominence : a hoop-shaped eruption out of Sun due to magnetic activity
corona : low density; temperature about 1 million K; visible during solar eclipses
solar wind : charged particles coming from Sun’s surface, escaping to deep space;
the solar wind permeates the whole Solar System
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2. Brightness, the Inverse-Square Law, and Parallax
Inverse-Square Law
•
•
•
•
•
luminosity ( "L " ) is the absolute power output, at the source (e.g., a star's surface)
brightness ( "B " ) is apparent output, as observed at some distance ( "d " ) away
the Inverse-Square Law determines how bright a star appears, based upon its
luminosity (intrinsic brightness) and its distance;
B = L/4𝝅d2
or
B ∝ L/d2
If two stars have the same luminosity and one is ten times farther away than the
other, it will appear 1/102 times as bright (that is, 100 times fainter)
example: If star A is 4 times as luminous as star B, then stars A and B would appear
equally bright if star A were 2 times as far away as star B
Parallax Method to Measure Distances
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The basic concept is to view a star from two locations on opposite sides of Sun
(Earth, but 6 months apart), and look for minute changes in its apparent position.
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These locations in Earth's orbit are on opposite ends of the "baseline"
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This is like holding something — say, your finger — up in front of your face, and
closing or covering one eye and then the other; your finger will appear to move
back and forth a lot more than objects in the background in your field of vision.
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Some simple small-angle trigonometry can approximate distances to nearby stars.
•
For stellar parallax measurements, the baseline is 1 AU (average distance between
the Earth and Sun).
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The target star appears to move (relative to more-distant stars) by an angle 2 times
the parallax angle; so, ...
D = 1/p
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D is the distance in parsecs, p is the parallax angle in arcseconds (1 / 3600 degree)
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examples:
• a star with measured parallax angle of 0.1 arcsec is 1 / 0.1 = 10 parsecs away
• a star with a parallax angle of 0.02 arcsec is 1 / 0.02 = 50 parsecs away
•
Sometimes a star that appears fainter is still closer than one that appears brighter,
because the star that appears brighter is actually more luminous.
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3. the Nearest Stars, Brightest Stars, and the H-R Diagram
Hertsprung-Russell Diagram (the "H-R Diagram") — Very Important!
red
giants
ma
in s
equ
enc
e
Sun
white
dwarfs
(example of an H-R diagram)
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horizontal axis: stars' surface temperature, increasing from right to left
• cooler stars are redder (temperatures down to around 2,300 K or so)
• hotter stars are bluer (temperatures up to around 40,000 K or so)
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stars' effective surface temperature is estimated using its spectral class
• the major spectral classes of stars, from hotter to cooler, run ...
O-B-A-F-G-K-M
a popular mnemonic is “Oh, be a fine girl/guy, kiss me”
(or, “Only bored astronomers find gratification knowing mnemonics”)
•
•
spectral class is determined using the absorption spectrum, where absorption
lines from different chemical elements with different levels of ionization arise
at different temperatures
vertical axis: luminosity, expressed in terms of the luminosity of the Sun ( "L⊙" )
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Nearest Stars
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Alpha Centauri is the closest star, 4.3 light years (or 1.35 parsecs) from the Sun;
actually part of a triple star system, with its brightest member similar to Sun
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Most of the nearest stars are cool and dim, and fall on the lower right of the H-R
diagram; this is because most stars in general have these properties.
Brightest Stars
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The brightest star in the nighttime sky is Sirius (the “Dog Star”), which is twice as
massive as Sun; it has a binary companion star, a white dwarf.
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The "brightest stars" (that is, as we see them from Earth) have more varied properties
— red and blue, low and high luminosity, with some on the lower right of the H-R
diagram, but others near where the Sun is, some on the upper left, and some on the
upper right (red giant region)
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The "brightest stars" tend to be biased towards stars that already have high
luminosities, so that they appear bright to us even at large distances; we simply
cannot see low-luminosity stars if they are too far away (even if greater in number)
4. Main Sequence and Stellar Mass
Properties of a Star
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luminosity, mass, size, temperature, and age
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size and temperature directly affect luminosity, as in: L ∝ R 2 x T 4
• a larger size = larger light-emitting surface area = greater luminosity
• higher temperature = much greater luminosity (also peaks in bluer colors)
Main Sequence
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main-sequence stars located on H-R diagram in a band from lower right across to
upper left — around the slightly-wavy red line in the example H-R Diagram (above)
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when on the main sequence (which occupies the majority of a star's lifetime), stars
are burning Hydrogen into Helium in their cores (by the p-p chain)
•
for stars on the main sequence, higher temperature stars have a higher luminosity
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•
red dwarfs (cool, faint, and small) on lower right; blue giants (hot, bright and large)
on upper left
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mass determines where on the main sequence a star lives, and what the main
sequence lifetime is for the star; more-massive main sequence stars are on the
upper left of H-R diagram; masses range from about 0.1 to 100 times the mass of
the Sun; sizes range from 0.1 to 15 times the radius of the Sun
•
luminosities of main sequence stars range from 10 –3 to 10 6 times that of the Sun
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ages range from a few million years for more-massive stars, to much more than 14
billion years — the current age of the Universe — for less-massive stars
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Remember: the more-massive stars use their greater fuel supply more rapidly
Stars Not on the Main Sequence
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red giants and supergiants: burning helium or even heavier elements in their cores
(not hydrogen anymore); starting to die; size is large, so they are very luminous
even though they are relatively cool; top right of H-R diagram
•
white dwarfs: hot, small and dim, so they fall on lower left of H-R diagram; the
cooling and fading cores left over from expired low-mass stars
You should be able to identify, on an H-R diagram, ...
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hot and cold stars; or blue and red stars
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high- and low-luminosity stars
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large- and small-radius stars (look at the diagonal lines with "R⊙" labels, above)
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high-mass and low-mass stars (recall relationship with main-sequence luminosity)
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stars converting hydrogen to helium at their cores
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red giants and white dwarfs
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stars that will have a long or short lifetime (recall its relationship with mass)
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5. Stellar Evolution:
White Dwarfs, Neutron Stars, & Black Holes
Sequence of Events in the Lifetime of Solar- and Lower-Mass Stars
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Sun’s history: stellar nursery, protostar, main sequence, red giant, planetary nebula,
white dwarf
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a planetary nebula is the ejected envelope (the layers outside the core) of a low- to
intermediate-mass star
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the end state of the former-star's core is a white dwarf; held up against gravity not
by gas pressure anymore, but by pressure of electrons; about the size of the Earth
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"brown dwarfs" have a mass less than 8 % of the Sun, and never heat up enough to
have nuclear reactions in their core; also called “failed stars”
Fate of More-Massive Stars
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much shorter lives on the main sequence as stars' mass increases
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hydrogen burning on the main sequence; when core hydrogen is exhausted, then
helium burning in the core (while swelling into a red giant)
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when core helium supply is exhausted, then carbon burning, and then even-heavier
nuclei burning (all while swelling even larger, into a red supergiant)
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leads to the so-called "onion skin" model — concentric shells of fusion zones
involving different chemical elements, with the heaviest going on towards the core
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stops burning around iron ("Fe"), because iron is very stable and reactions involving
iron do not produce energy — instead they cost more energy than they release, so
no further gas pressure support for the star against its own gravitational collapse
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"Type II" supernova, a violent explosion with the star's core left behind; the
explosion itself creates a short-lived highly-energetic environment which briefly
makes possible the fusion of elements heavier than iron — like gold, silver, etc.
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if the remaining core is about 1.4 – 3 solar masses, it becomes a neutron star —
radius of 5 – 6 km, or roughly "city-sized"
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if the core's mass > 3 solar masses, it becomes a black hole —
infinitesimally-small radius, "compressed to a point" of infinite density
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Black Holes
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the end state of the highest-mass stars ( > about 40 solar masses), left behind after
supernova explosion
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the gravity of these collapsed (very dense) objects is so great that even light cannot
escape
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black holes do not "suck things in"; if you are far enough away from them, they act
like normal objects with the same mass
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the event horizon is the spherical boundary around a black hole from within which
nothing can escape — not even light (i.e., the "escape velocity" within this distance
exceeds the speed of light — "nature's speed limit," nothing can go faster)
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the speed of the orbit of a star in a binary system with a black hole can be used to
measure the black hole's mass (think back to Kepler's Laws, in Unit 2)
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the intense gravity around a black hole warps space, so that a clock appears to slow
down as it falls in; that is, light's delivery of the image of the clock to an observer
outside is delayed more and more as the clock nears the event horizon
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strong tidal forces operate near a black hole, and objects are stretched out because
the force on the nearer part can be so much greater than the force on farther parts
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at the center of a black hole is a singularity — a point of infinite density
Review of the Fates of Stars
(see also the Summary Table, on the last page of these notes)
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If a star begins with a mass < about 8 solar masses:
• the core becomes a white dwarf — collapse stops because of degeneracy
pressure of electrons; core radius same as Earth’s.
• the white dwarf is surrounded by released outer layers — a planetary nebula
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If a star begins with about 8 – 40 solar masses:
• final core-collapse is preceded by a Type II supernova
• the core becomes a neutron star — collapse stops because of degeneracy
pressure of neutrons; radius 5 – 6 km (city-size).
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If a star begins with > about 40 solar masses:
• final core-collapse is preceded by a Type II supernova
• the core becomes a black hole — collapse does not stop; all the mass
becomes concentrated at a singularity.
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6. Habitable Zones and the Drake Equation
Habitable Zone
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definition: the region around a star where liquid water could be present on a
planet’s surface — not too hot as to be all boiled off or dried out, and not too cold
as to be permanently frozen over
• a less-massive star would have habitable zone closer to the star
• a more-massive star would have habitable zone farther from the star
•
while it is commonly assumed that life requires liquid water, even life on Earth can
be found in some "extreme" environments: deep underground; in near or total
darkness; high acidity; high radiation; in methane ice; extreme heat and/or pressure
Drake Equation
•
where:
a method to estimate the number, N, of communicating / technological civilizations
in our galaxy at a given time; originally presented by Dr. Frank Drake of the Search
for Extraterrestrial Intelligence (SETI) program:
N = R * × fp × ne × fl × fi × fc × L
N = the current number of "intelligent,"
"communicating" civilizations in the
Milky Way Galaxy
R* = the rate of formation of "habitable"
stars in the galaxy (number per year)
fl = the fraction of these planets (from ne)
on which life actually develops
fi = the fraction of planets with life that
eventually give rise to "intelligent" life
fp = the fraction of these stars (in R*) that
form planetary systems
fc = the fraction of intelligent species that
develop into technological civilizations
capable of interstellar communication
ne = the average number of Earth-like
planets in these systems (from fp)
L = the average lifetime of communicating,
technological civilizations (in years)
Our present knowledge of the galactic neighborhood lends varying degrees of confidence
for estimates of the factors' likely values. Naturally a number of assumptions — some
more obvious than others — go into each. The Drake Equation really serves more as a
basis for hypothetical discussion than as anything like a law of nature; we expect you to at
least be familiar with what the terms are, without needing to remember any numerical
values for each of them.
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7. Extrasolar Planets
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The first extrasolar planets were discovered and confirmed in 1992 by Penn State
Professor Alex Wolszczan; rather than by a "normal" star, they were found in orbit
around a dead neutron star; these planets would be unlikely to support life, now.
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Many of the planets discovered in the late 1990’s and early 2000’s were planets
around the mass of Jupiter (or larger) that are very close to their parent stars.
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Thousands of planets have been discovered since, mostly by the "Kepler" mission
(named after the same Kepler of "Kepler's Laws") using the transit method — the
brightness of the star decreases regularly due to the planet passing right in front of it
(kind of like a miniature partial eclipse — occuring once every planet orbit).
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The transit method uses Kepler’s 3rd law to find the distance of the planet from its
star, again with P 2 = a 3; then the planet’s temperature can be calculated (based on
distance, and the star's luminosity & spectral type) to see if it is in that star’s
habitable zone; the amount of drop in the star’s brightness can also tell the planet’s
size.
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Several extrasolar planets have been discovered in the habitable zones around their
stars; hard to determine whether they are "Earth-like" with regard to other properties.
8. Summary Questions & Stellar Evolution Summary Table
Here are some general questions you should be able to answer:
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How do low mass, intermediate, and high mass stars live their lives?
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What is the end state of a low-, intermediate-, or high-mass star?
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What is the H-R Diagram and how is it used?
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What is the main sequence, and how are different properties of stars related for
stars on the main sequence?
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Where do different types of stars lie on the H-R diagram?
(some examples: the Sun, red giants, "A"-type main-sequence stars, white dwarfs,
massive main-sequence stars, stars with a temperature of 10,000 K, etc.)
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If "star A" is a more massive main-sequence star than "star B," and "star A" appears
fainter, which star is farther away?
(answer: "star A"; it must be farther away,
because its luminosity is also greater than "star B" due to its higher mass)
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How are extrasolar planets detected?
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How does the habitable zone change depending on the mass of a star?
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The table below has some general information on differences in stars of various masses.
https://theastroventure.com/encyclopedia/unit3/stars/mass.html has more info about the
importance of a star's initial mass, but do not worry about memorizing that entire table's
worth of numbers; instead focus on the general differences between stars of different mass
ranges (called "low-," "medium-," and "high-"mass stars), described below ...
typical lifetime
"Low-mass" stars
"Medium-mass" stars
"High-mass" stars
(from less than, up to a
few times the Sun's
mass; our Sun falls into
this category)
(from around a few times
the Sun's mass, up a few
tens of solar masses)
(from a few tens of solar
masses — say, 30 or 40
times, and greater)
billions of years,
or even trillions
maybe a few tens or
hundreds of millions
of years
just a few million years
elements up through iron
(Fe), in the core
fusion can create
elements up to...
just low-mass elements —
examples: He, C, N, O
end stage
the outer layers of the star
are released and become
a "planetary nebula"
"Type II" supernova
"Type II" supernova
leaves behind a...
white dwarf
neutron star
black hole
size of remnant
roughly Earth-sized
roughly city-sized
infinitesimally-small point
← (stuff in between →
the other two)
(recall the "onion skin"
analogy)
Here also are some other "Encyclopedia" companion site links worth noting...
•
an example Hertzsprung-Russell ("H-R") Diagram with main sequence drawn in:
https://theastroventure.com/encyclopedia/ ...
... media/images/H-R_diagrams/HRdiag_MSline_1024x781.png
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an H-R Diagram filled in with the nearest & brightest stars you visited in the game:
https://theastroventure.com/encyclopedia/ ...
... media/images/H-R_diagrams/HRdiag_filled_1024x781.png
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