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PHYS 175, FALL 2014
HW #7 S OLUTION
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17.1 Explain the difference between a star’s apparent brightness and its luminosity.
Luminosity is an intrinsic property of a star, independent of an observer, measured
in units of power (energy per unit time). Apparent brightness is a function of the
distance of an observer from a star and its luminosity. Therefore, two similar stars
with identical luminosities can have very different apparent brightnesses if they are
at different distances from an observer. Similarly, the converse can occur where two
stars of dissimilar luminosities are staggered from the observer such that they have
the same apparent brightness (the dim star is closer than the bright one).
17.9 The star Zubenelgenubi (from the Arabic for ”scorpion’s southern claw”) has an
apparent magnitude of 12.75, while the star Sulafat (Arabic for ”tortoise”) has an
apparent magnitude of 13.25. Which star appears brighter? From this information
alone, what can you conclude about the luminosities of these stars? Explain your
answer.
Zubenelgenubi appears to be brighter, since it has a lower apparent magnitude (remember that a negative apparent magnitude is very bright). Since we only know the
apparent magnitudes, we cannot say which is brighter (see §17.1).
17.11 Would it be possible for a star to appear bright when viewed through a U filter or
a V filter, but dim when viewed through a B filter?
The filter letter designations are known as the photometric system and are a a standardized set of bandpass coefficients used throughout the astronomical community.
What that translates to (for the purposes of this introductory class) is that each filter
is transparent to a limited band of wavelengths, but is opaque at lower and higher
wavelengths than that band. U stands for ultraviolet and passes wavelengths between 365 nm ± 66 nm, B is for blue and admits between 445 nm ± 94 nm, and V is
for visual (the visible range includes visual and spans B V G R) which lets light in
the range 551 nm ± 88 nm through. So for a star to be bright at U and V, but dim at
B, means that the spectrum has a big dip in it in-between the two bands. This is very
unlikely, since stars are blackbody radiators, and their emission spectrum is concave up (generally peaked, and not dipped). There are small dips in this spectrum
because a star is not a perfect blackbody - there are narrow elemental absorption
dips due to the star’s own composition, and also broader absorption bands due to
the star’s atmosphere. But neither of those effects would cause a dip as broad as the
entire B band, so that it was dimmer than both U and V.
PHYS 175, FALL 2014
HW #7 S OLUTION
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17.15 A fellow student expresses the opinion that since the Sun’s spectrum has only
weak absorption lines of hydrogen, this element cannot be a major constituent of
the Sun. How would you enlighten this person?
The Sun is a type G2 star, so we expect to see strong absorption lines of some neutral
metals and particularly ionized calcium (see Table 17-2 in the text and Figure 17-11).
The Sun, like most all stars, is about 74% H by mass, so it is mostly comprised of
hydrogen. What we observe in stellar spectra are absorption lines in the stars’ outer
atmosphere. In order for there to be prominent H emissions (particularly the Balmer
series), the star needs to have a surface temperature of about 9,000 K. Hotter than
that and the H is almost completely ionized; cooler (like the Sun, at 5,800 K) and
very little of the H in the atmosphere can be excited to produce an emission.
17.35 The star GJ 1156 has a parallax angle of 0.153 arcsec. How far away is the star?
For this we use the very simple formula d = p1 , where d is the distance we seek (in
1
pc) and p is the parallax angle (in arcsec). Using this, we find d = 0.153
≈ 6.54 pc.
This is roughly 21.3 ly away.
18.1 If no one has ever seen a star go through the complete formation process, how are
we able to understand how stars form?
Since stars take longer to go through their life cycles than planets are able to support
civilizations capable of observing and studying them, we have to make due with a
bit of scientific reasoning and observations of many similar stars in various stages of
their life cycles. Physics has matured in the last 100 years to provide a very good understanding (but not complete, as our knowledge continues to grow) of gravitation,
gases and plasmas, quantum mechanics, nuclear reactions, thermodynamics, and
statistical mechanics. Combined with this is the rapid pace of development in computational physics and the computing power that can fit in the palm of your hand –
we can now simulate much of stellar evolution to make predictions about what we
observe. This allows us to more than speculate about the evolution of stars.
18.3 If an interstellar medium fills the space between the stars, how is it that we are
able to see the stars at all?
This gas and dust is exceedingly sparse by the standards of what we are used to experiencing on Earth. For example, the air you’re breathing as you read this contains
roughly 1019 atoms per cm3 , whereas even in a dense nebula, there are only a few
thousand H atoms per cm3 . The interstellar medium is even less dense (nearly a
vacuum by laboratory standards on Earth).
PHYS 175, FALL 2014
HW #7 S OLUTION
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18.15 What happens inside a protostar to slow and eventually halt its gravitational contraction?
The gravitational energy causes Kelvin-Helmholtz contraction, which increases the
pressure, density and temperature of the central region of a protostar. Once the temperature exceeds a few million K, H begins to fuse into He (via the p-p chain in a
Sun-sized protostar, or the CNO cycle in a larger one). The energy released in the
thermonuclear fusion reactions causes an outward pressure that eventually stops
the contraction.
18.28 Briefly describe four mechanisms that compress the interstellar medium and trigger star formation.
1) Simple gravitational collapse: a cold, dense collection of gas and dust will begin
to collapse under it’s own mutual gravitational attraction. 2) T Tauri stars: these
stars eject gas in a bipolar outflow, and when this ejected mass collides with the
interstellar medium, it can cause a shockwave that compresses it enough to trigger
star formation. 3) Galactic spiral arms: matter piles up in the arms of spiral galaxies,
much like a traffic jam of gas and dust, the matter may be dense enough for stellar
formation to occur. 4) Supernovae: the matter violently ejected in a supernova event
may also trigger star formation in a manner similar to 2). 5) Young O and B stars: the
UV radiation and strong stellar winds from the types of stars can work in a similar
fashion to 2) and 4).
18.31 The visible-light photograph below shows the Trifid Nebula in the constellation Sagittarius. Label the following features on this photograph (you may use
a sketch and arrows to indicate your selections): (a) reflection nebulae (and the
star or stars whose light is being reflected); (b) dark nebulae; (c) H II regions; (d)
regions where star formation may be occurring. Explain how you identified each
feature.
See the annotated figure on the next page. A) Reflection nebulae are typically blue,
owing to the reflected starlight. B,D) Dark nebulae are scattered throughout this image, so what I indicated with the arrows are only a few examples. These regions are
also regions that can have active stellar formation, because they are dense and cold
enough to allow for sufficient gravitational collapse. C) HII regions are emission
nebulae, with ionized H emissions giving the red coloration to the light.
PHYS 175, FALL 2014
HW #7 S OLUTION
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