lecture14_0702updated 07/01, 21:35
1
- Warm-Hot Intergalactic Medium
Ly Forest • History
- A uniformly dark Gunn-Peterson trough is only seen at redshifts z
> 6. - However, at lower redshifts, there exists a “Lyman alpha
forest” of absorption lines. - The Ly forest was first discovered
by Roger Lynds in 1971. Lynds found many absorption lines in the
spectrum of 4C 05.34 (with z = 2.877, the largest
redshift then known for any quasar), most of which were at
wavelengths shorter than the Ly emission line of the quasar.
Lynds concluded that most of the absorption lines that he saw were
Ly lines from hydrogen along the line of sight to the quasar; the
other absorption lines were from relatively common heavier elements
(such as O, C, N, and Si) at the same redshifts as the absorbing
hydrogen.
As similar distributions of short-wavelength absorption lines began
to be seen in the spectra of additional quasars, astronomers began
using the metaphor of a Lyman alpha “forrest” of absorption
lines.
3
Ly Forest • Figure (a) shows a cartoon of how a quasar spectrum
might
look like if there were no intervening neutral hydrogen between the
quasar and us. - The quasar continuum is relatively flat. Broad
emission features
are produced by the quasar itself (near the black hole and its
accretion disk).
• In some cases, gas near the quasar central engine also produces
“intrinsic” absorption lines, most notably Ly, and relatively high
ionization metal transitions such as C IV, N V, and O VI.
• However, the vast majority of absorption lines in a typical
quasar spectrum are “intervening”, produced by gas unrelated to the
quasar that is located along the line of sight between the quasar
and the Earth.
• Its wavelength is stretched by the expansion of the Universe from
what it was initially at the quasar, and, if it had continued to
travel to us, it would have been stretched some more from the 1216
wavelength it had at the absorber.
4
(a)
(b)
(c)
• The cartoon below shows a quasar with it Ly emission line
redshifted from the UV into the red, and the Ly absorption lines
from four intervening clouds appearing as orange, yellow and
green-blue.
• Each structure will produce an absorption line in the quasar
spectrum at a wavelength of , where is the redshift of the
absorbing gas and is the rest
wavelength of the Ly transition. Since , the redshift of the
quasar, these Ly absorption lines form a “forest” at wavelengths
blueward of the Ly emission of the quasar.
• The region redward of the Ly emission will be populated only by
absorption through other chemical transitions with longer .
λobs = λrest(1 + zgas) zgas λrest = 1216Å zgas < zquasar
λLyα
5
A very nice visualization that shows how different systems absorb
Lyman-alpha, made by Andrew Pontzen. To see this movie, please
download from
http://www.cosmocrunch.co.uk/media/dla_credited.mov
Ly Absorption System • A structure along the line of sight to the
quasar can be described by its neutral
Hydrogen column density N(H I), the product of the density of the
material and the path length along the line of sight through the
gas.
• Classification
- A typical temperature of the diffuse IGM is T ~ 105 K
(corresponding to a thermal broadening b ~ 40 km s-1 in Ly line).
The optical depth at line center is then
- The name “Lyman limit system” is given because at these column
densities, clouds become optically thick to photons with λ <
912, at the Lyman limit. As a consequence, Lyman limit systems are
self-shielded from outside ionizing photons.
- Damped Lyman alpha systems (DLAs) have column densities of
neutral hydrogen comparable to a large galaxy like our own.
7
1017 < N (H I) < 2x1020 cm-2 Lyman limit systems
2x1020 < N (H I) Dampled Ly systems
N(HI) = nHL
As N (HI) increases, the absorption line depth and width
increase.
0 1.9
What are the Ly absorption systems? • Metallicity
- The metallicity of DLAs is typically in the rage . - The Lyman
alpha forests has a lower metallicity of .
• What are they? - DLAs can be thought of as gravitationally bound
protogalaxies, containing gas
(and associated dark matter), but which haven’t yet been effective
at converting gas into stars.
- However, the lower column density absorption lines in the Lyman
alpha forest, which are vastly more numerous than the DLAs, cannot
be associated with individual gravitationally bound gas clouds.
Densities in the Lyman alpha forests are simply not dense enough to
represent
gravitationally collapsed, virialized systems with a high neutral
fraction of hydrogen. Instead, the absorption lines of the Lyman
alpha forests are likely produced from highly
ionized regions of gas that are broadened primarily by the Hubble
flow.
- The Lyman alpha forest shouldn’t be thought as resulting from
discrete clouds along the line of sight to a quasar. Instead, Lyman
alpha forests are more likely to be caused by a smoothly
fluctuating
density field along the line of sight.
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• The Lyman alpha absorption systems are generally associated with
galaxies, but not always. - For instance, 3C 273 lies behind the
Virgo cluster of galaxies, and has a couple of
absorbers in the cluster's redshift range, but they cannot be
clearly identified in position and redshift with specific galaxies
in the Virgo cluster.
- At low redshift, many of the galaxies that are responsible for
the DLA absorbers can be directly identified. These galaxies are a
heterogeneous population. They are not just the most luminous
galaxies, but include dwarf and low surface brightness galaxies.
There are even cases where no galaxy has been identified to
sensitivity limits.
9
-20
-16
-12
Fig. 2.— The column density distribution of Ly! clouds, f(N(H i),
roughly follows a power law over ten or- ders of magnitude; there
are many more weak lines than strong lines. The column density
regions for the three cat- egories of systems are shown: Ly!
forest, Lyman limit, and damped Ly!. The term “Ly! forest” has at
times been used to refer to metal–free Hydrogen clouds, perhaps
those with N(H i) < 1016 cm!2, but now metals have been found
associated with weaker systems down to the detec- tion limit.
tion at !obs = 2870 A due to the presence of C iv in the absorbing
gas at that same redshift. Like many of the strongest metal lines
seen in quasar spectra, C iv is a resonant doublet tran- sition due
to transitions from 2S1/2 energy lev- els to the 2P1/2 and to the
2P3/2 energy levels. (The left superscript “2” represents the
number of orientations of the electron spin, the letter S or P
represents the total orbital angular momen- tum, L, and the right
subscript represents the to- tal angular momentum, J .) Doublet
transitions are easy to identify. The dichotomy between rest
wavelength and redshift is resolved because the observed wavelength
separation of the doublet members increases as 1 + z.
Table 1 lists some of the metal lines that are commonly detected
for intervening absorption systems. Many of these are only strong
enough to be observable for quasar lines of sight that pass through
the higher N(H i) regions of galaxies.
Table 1: Common Transitions
Transition !rest [A] LL . . . . . . . . . . . . . ! 912 Ly" . . . .
. . . . . . . . 972.537 Ly# . . . . . . . . . . . . 1025.722 Ly$ .
. . . . . . . . . . . 1215.670 Si iv 1393 . . . . . . . 1393.755 Si
iv 1402 . . . . . . . 1402.770 C iv 1548 . . . . . . . 1548.195 C
iv 1550 . . . . . . . 1550.770 Fe ii 2382 . . . . . . . 2382.765 Fe
ii 2600 . . . . . . . 2600.173 Mg ii 2796 . . . . . . 2796.352 Mg
ii 2803 . . . . . . 2803.531
2. History, Surveys, and Revolutionary
Progress in the 1990’s
The history of quasar absorption lines began within a couple of
years of the identification of the first quasar in 1963. In 1965,
Gunn and Peterson considered the detection of flux blue- ward of
the Ly$ emission line in the quasar 3C 9, observed by Schmidt, and
derived a limit on the amount of neutral Hydrogen that could be
present in intergalactic space. In that same year, Bahcall and
Salpeter predicted that inter- vening material should produce
observable dis- crete absorption features in quasar spectra. Such
features were detected in 1967 in the quasar PKS 0237 " 23 by
Greenstein and Schmidt, and in 1968 in PHL 938 by Burbidge, Lynds,
and Stockton. By 1969 many intervening systems had been discovered,
and Bahcall and Spitzer proposed that most with metals were
produced by the halos of normal galaxies. As more data ac-
cumulated, the sheer number of Ly$ forest lines strongly supported
the idea that galactic and in- tergalactic gas, and not only
material intrinsic to the quasar, is the source of most quasar
absorp- tion lines.
In the 1980’s many more quasar spectra were
3
• Column density distribution - There are many more weak lines than
strong
lines. - The column density distribution roughly follows
a power-law.
Typical spectrum of a quasar
• Typical spectrum of a quasar, showing the quasar continuum and
emission lines, and the absorption lines produced by galaxies and
IGM that lie between the quasar and the observer. - The Ly forest,
absorption produced by various intergalactic clouds, is apparent at
wavelengths blueward
of the Ly emission line.
- The two strongest absorbers, due to galaxies, are a damped Ly
absorber at = 0.86 ( ) and a Lyman limit system at = 1.15 (
).
- The damped Ly absorber produces a Lyman limit break at ~ 1700 (
).
- The Lyman limit system: a partial Lyman limit break at ~ 1960 ( )
since the neutral Hydrogen column density is not large enough for
it to absorb all ionizing photons.
z (1 + 0.86) × 1216 = 2262Å z (1 + 1.15) × 1216 = 2614Å
(1 + 0.86) × 912 = 1696Å
(1 + 1.15) × 912 = 1961Å
0
1
2
3
4
5
Fig. 1.— Typical spectrum of a quasar, showing the quasar continuum
and emission lines, and the absorption lines produced by galaxies
and intergalactic material that lie between the quasar and the
observer. This spectrum of the z = 1.34 quasar PKS0454 + 039 was
obtained with the Faint Object Spectrograph on the Hubble Space
Telescope. The emission lines at ! 2400 A and ! 2850 A are Ly! and
Ly". The Ly" forest, absorption produced by various intergalactic
clouds, is apparent at wavelengths blueward of the Ly" emission
line. The two strongest absorbers, due to galaxies, are a damped
Ly" absorber at z = 0.86 and a Lyman limit system at z = 1.15. The
former produces a Lyman limit break at ! 1700 A and the latter a
partial Lyman limit break at ! 1950 A since the neutral Hydrogen
column density is not large enough for it to absorb all ionizing
photons. Many absorption lines are produced by the DLA at z = 0.86
(C iv ##1548, 1550, for example, is redshifted onto the red wing of
the quasar’s Ly" emission line).
depth, ! , of the break is given by the product N(H i)", where the
cross section for ionization of Hydrogen, " = 6.3 ! 10!18(E!/13.6
eV)!3 cm2, (and the flux is reduced by the factor e!" ). The energy
dependence of " leads to a recovery of the Lyman limit break at
higher energies (shorter wavelengths), unless N(H i) " 1017.2 cm!2
(see Figure 1).
The curve of growth describes the relationship between the
equivalent width of an absorption line, W , (the integral of the
normalized profile) and its column density, N . Figure 3 shows that
for small N(H i) the number of absorbed pho- tons, and therefore
the flux removed, increases in direct proportion to the number of
atoms. This is called the linear part of the curve of growth. As N
is increased the line saturates so that photons are only absorbed
in the wings of
the lines; in this regime the equivalent width is sensitive to the
amount of line broadening (char- acterized by the Doppler parameter
b), but does not depend very strongly on N(H i). This is the flat
part of the curve of growth. Finally, at N(H i) > 1020.3 cm!2,
there are enough atoms that the damping wings of the line become
pop- ulated and the equivalent width increases as the square root
of N(H i), and is no longer sensitive to b.
In addition to the Ly# (1s # 2p) and higher order (1s # np) Lyman
series lines, quasar spec- tra also show absorption due to di!erent
ioniza- tion states of the various species of metals. Fig- ure 1
illustrates that the damped Ly# system at z = 0.86 that is
responsible for the Ly# absorp- tion line at $obs = 2260 A and a
Lyman limit break at $obs = 1700 A also produces absorp-
2
λLyα rest = 1216Å
λLyβ rest = 1026Å
Evolution of Ly Absorption Systems
• The Ly absorption component evolves strongly with cosmic time. -
We see dramatically more absorbers toward
higher redshifts.
- However, they have not completely disappeared at low redshifts.
When the launch of HST provided the first capability of measuring
Ly at low redshifts to the required accuracy, it was found that a
few of these absorbers remain in the local Universe.
• The evolution of the Ly forest may be intimately connected with
the history of galaxy formation.
• This dramatic evolution in the number of forest clouds is mostly
due to the expansion of the Universe, with a modest contribution
from the cosmic structure growth.
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Ly ! absorption 7
Figure 4. Evolution of the number of lines within a given range of
column density from numerical simulations of Theuns et al. (1998b)
compared with observations. Open and filled circles show simulation
results for the reference model S (described in the text) run at
di!erent numerical resolutions. The large open pentagon shows a
reanalysis of the simulation at z = 0.5 but imposing the
photoionizing background appropriate to z = 2. The observational
data points are as follows: Kim et al. 1997 (open and filled
triangles); Bahcall et al. 1993 (filled squares); Impey et al. 1996
(open squares); Lu et al. 1996 (filled pentagon); Williger et al.
1994 (long dashed line).
divided by a factor of 2 to match the observed optical depth in HI
absorption. This model reproduces the observed column density
distribution accurately over the col- umn density range 1012.5 cm!2
<
! NHI < ! 1015 cm!2 (see Figure 2 of Theuns et al.
1998b) and, as Figure 4 shows, also reproduces the observed rates
of evolution as a function of column density. In particular, the
decrease in the rate of evolution of the Ly! lines found from HST
observations arises from the steep decline in the photoionizing
background at z <
! 2 caused by the rapid drop in quasar numbers at low
redshift.
(c) Reconstruction of the matter power spectrum
Equations (2.1) and (3.1) can be combined to write the observed
transmitted flux in terms of fluctuations in the baryon
density,
F = exp !
"A("b/"b) ! "
Article submitted to Royal Society
Evolution of the number of lines within a given range of column
density obtained from numerical simulations and observations
(Efstathiou et al.)
Ly ! absorption 7
Figure 4. Evolution of the number of lines within a given range of
column density from numerical simulations of Theuns et al. (1998b)
compared with observations. Open and filled circles show simulation
results for the reference model S (described in the text) run at
di!erent numerical resolutions. The large open pentagon shows a
reanalysis of the simulation at z = 0.5 but imposing the
photoionizing background appropriate to z = 2. The observational
data points are as follows: Kim et al. 1997 (open and filled
triangles); Bahcall et al. 1993 (filled squares); Impey et al. 1996
(open squares); Lu et al. 1996 (filled pentagon); Williger et al.
1994 (long dashed line).
divided by a factor of 2 to match the observed optical depth in HI
absorption. This model reproduces the observed column density
distribution accurately over the col- umn density range 1012.5 cm!2
<
! NHI < ! 1015 cm!2 (see Figure 2 of Theuns et al.
1998b) and, as Figure 4 shows, also reproduces the observed rates
of evolution as a function of column density. In particular, the
decrease in the rate of evolution of the Ly! lines found from HST
observations arises from the steep decline in the photoionizing
background at z <
! 2 caused by the rapid drop in quasar numbers at low
redshift.
(c) Reconstruction of the matter power spectrum
Equations (2.1) and (3.1) can be combined to write the observed
transmitted flux in terms of fluctuations in the baryon
density,
F = exp !
"A("b/"b) ! "
Article submitted to Royal Society
• At low redshift, 3C 273 shows only a handful Ly absorbers,
including the strong and broad absorption from its light
intercepting the disk of a foreground spiral galaxy (ours). Our
galaxy also produces absorption in the C IV lines around 1550 ,
which appear at 1337 in the quasar's emitted frame.
• Hundreds of lines can be identified in the spectrum of 1422+2309,
with the densest concentration near the quasar redshift. The strong
and broad emission peak is Ly, which is almost chopped in half by
the onset of the Ly forest in the high-redshift quasar.
• This is a very general feature showing how the density of Ly
absorbers decreases with cosmic time (lower z).
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zz • This figure compares two
quasars at very different redshifts, 3C 273 at = 0.158 and
1422+2309 at = 3.62.
• The spectra were shifted to a common scale in emitted
wavelength.
z z
1216Å /(1 + 0.158) = 1050Å 1550Å /(1 + 0.158) = 1338Å
• Illustration of structure evolution of intergalactic gas from
high to low redshift. - Higher redshift quasars show a much thicker
forest of Ly lines.
• The right-hand panels show slices through N-body/hydrodynamic
simulation results at two epochs = 3 and = 1. - Three contour
levels are shown : (dotted lines), (solid lines) and
(thick solid lines). - Evolution proceeds so that the voids become
more empty and even lower column density material
is found in filamentary structures at low redshifts.
z z 1011 cm−2 1012 cm−2 1013 cm−2
13
PG1634+706
z=3.63
z=1.33
Q1422+2309
z=3
z=1
Fig. 9.— Illustration of structure evolution of intergalactic gas
from high to low redshift. The upper spectrum of a z = 3.6 quasar
is a Keck/HIRES observation, while the lower spectrum is a FOS/HST
observations of a z = 1.3 quasar. Higher redshift quasars show a
much thicker forest of Ly! lines. Slices through
N–body/hydrodynamic simulation results at the two epochs z = 3 and
z = 1 are shown in the right–hand panels. Three contour levels are
shown: 1011 cm!2 (dotted lines), 1012 cm!2 (solid lines) and 1013
cm!2 (thick solid lines). Evolution proceeds so that the voids
become more empty so that even the low column density material is
found in filamentary structures at low redshifts.
ble power law with ! ! 2 for 1.8 < z < 4.5 and ! ! 0.2 for z
< 1.8. Help in understand- ing the physical picture has come
from sophis- ticated N–body/hydrodynamic simulations that
incorporate the gas physics and consider cosmo- logical expansion
of the simulation box. The dy- namical evolution of the H i gas can
be described as outflow from the centers of voids to their sur-
rounding shells, and flows along these sheets to- ward their
intersections where the densest struc- tures form. This picture is
consistent with ob- servational determinations of the “sizes” of
Ly" structures. It is di!cult to obtain direct mea- surements of
sizes except in some special cases to use “double lines of sight”,
close quasar pairs, either physical or apparent due to
gravitational lensing. If the spectra of the two quasars both have
a Ly" absorption line at the same wave-
length that implies a “structure” which covers both lines of sight.
From these studies, it is found that “structures” are at least
hundreds of kpc in extent.
At redshifts z = 5 to z = 2 dN/dz for Ly" for- est absorption is
quite large, but it is declining very rapidly over that range. This
dramatic evo- lution in the number of forest clouds is mostly due
to the expansion of the universe, with a modest contribution from
structure growth. At z < 2, the extragalactic background
radiation field is falling, and Ly" structures are becom- ing more
neutral. Therefore, the more numerous, smaller N(H) structures are
observed at a larger N(H i) and this will counteract the e"ect of
ex- pansion, thus slowing the decline of the forest.
The high redshift Ly" forest was once thought
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Correlation between Density and Temperature • Density versus
Temperature in the intergalactic gas
- In simulations of the evolution of intergalactic gas, it is found
that there is a tight correlation between density and temperature
at T < 105 K. The origin of this correlation lies in the balance
between heating and cooling (adiabatic
cooling due to the expansion of the universe) Heating: With only
hydrogen present, heating is done by the electrons ejected during
the
photoionization of hydrogen. The volumetric heating rate is:
Cooling: The regions that give rise to low column density Ly lines
will cool mainly through adiabatic cooling as the universe expands.
During adiabatic expansion, the thermal energy density has the
dependence (V = volume of a gas element). The volumetric cooling
rate is then:
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= the average kinetic energy of an ejected electron. We need to use
the Case A recombination rate coefficient in a highly ionized
hydrogen gas, responsible to the Lyman alpha forests.
hEi
Gpi n2
We then obtain
• Optical Depth versus Density in the intergalactic gas - The
balance equation between the photoionization and radiative
recombination is
given by
After the epoch of reionization z ~ 8, the neutral fraction will be
smaller than one. In this limit, the solution for the neutral
fraction is
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<latexit
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pi
Using the Case A recombination rate coefficient, , we find
that
- The optical depth for Ly absorption at a given redshift is
proportional to the number density of neutral hydrogen.
Properly normalizing, we obtain the relation between the density
and optical depth:
The constant depends on the assumed cosmology as well as on the
amount of ionizing radiation present.
The above equation is referred to as the fluctuating Gunn-Peterson
approximation.
16
T
Warm-Hot Intergalactic Medium • The Warm-Hot Intergalactic Medium
(WHIM)
- The WHIM is at temperature , and has a density in the range
- These low densities and relatively high temperatures account for
the difficulty of observing the WHIM.
• Missing baryon problem - The baryonic density has been fairly
well known from Big Bang Nucleosynthesis and
from early observations of the CMB by the COBE satellite. -
However, the density in easily detected baryons — stars,
interstellar gas, and X-ray
emitting gas in clusters — was only . - It is believed that the
unobserved baryons are in a low-density gas spread through
intergalactic space.
<latexit
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5 107 cm3 < n < 5 105 cm3
<latexit
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<latexit
sha1_base64="DverNEJqWtvttBcEpcGUPYtYBTY=">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</latexit>
Simulations of the WHIM • Much of what we know about the WHIM comes
from numerical cosmological
simulations that include gas dynamics. - Davé et al. (2001, ApJ,
552, 473) have performed, for the first time, simulations of
the
intergalactic medium, and found that baryons in the universe reside
in four broad phases, defined by their over density and temperature
. Diffuse IGM: . Photoionized intergalactic gas that gives rise to
Lyman
alpha absorption. Condensed: . Stars and cool galactic gas. Hot
intracluster medium: . Gas in galaxy clusters and large groups.
Warm-Hot: . The “warm-hot intergalactic medium.”
T
10.1 Simulations 241
Diffuse ICM T<l0 5 K Warm-Hot ICM 105<T<l0 7 K
Figure 10.1: Left: Distribution of diffuse intergalactic gas (T
< 105 K) at z = 0. Right: Distribution of warm-hot intergalactic
gas (10 5 K < T < 107 K) at z = 0. The color code runs from
green at a density n = l 0nbary,o to red at n = l 04 nbary,o·
[Renyue Cen]
present. At z = 4, shortly after reionization is complete, nearly
all the baryonic gas in the universe was in the form of
photoionized gas with T < l 05 K. However, as structure went
nonlinear and collapsed, more and more of the baryonic gas became
shock-heated to temperatures 105 K < T < 107 K. This
component, indicated by the solid line labeled "Warm-Hot" in Figure
10.2, grew steadily with time until it composed 30 to 40% of the
baryonic matter today (according to the simulations examined here).
"Condensed" gas, shown as the dotted line in Figure 10.2,
represents galaxies containing stars, interstellar gas, and
circumgalactic gas; "hot" gas, shown as the dot-dashed line, is the
intracluster gas at T > 107 K. (Caveat: the amount of condensed
gas is sensitive to the details of star formation assumed, and the
amount of hot gas is sensitive to the effects of cosmic
variance.)
Focusing solely on the warm-hot intergalactic medium, Figure 10.3
shows the distribution of gas in the density- temperature plane. In
the WHIM temperature range of 105 K to 107 K, the density is
positively correlated with temperature
(Left) Distribution of diffuse intergalactic gas at z = 0. (Right)
Distribution of warm-hot intergalactic gas at z = 0.
green : red:
n/n 1
• Summary: - At z = 4, shortly after reionization is
complete,
nearly all the baryonic gas was in the form of photo-ionized gas
with T < 105 K.
- As structure went nonlinear and collapsed, more and more of the
baryonic gas became shock- heated to temperatures 105 K < T <
107 K (WHIM).
- The WHIM grew steadily with time until it composed 30-40% of the
baryonic matter today.
- “Condensed” gas represents galaxies containing stars,
interstellar gas, and circumgalactic gas.
- “Hot” gas is the intracluster gas at T > 107 K.
• Difference between the DIM & WHIM - The diffuse intergalactic
medium (DIM) is
smoothly distributed. - The WHIM is found primarily in long
filaments. As
it flows along filaments to the clusters, the WHIM is shocked and
heated to higher temperatures than the photo-ionized DIM.
19
1 1 -Warm - Hot ,,,, /
- - Diffus e ,.. /
--- Hot ,1/ / /
00 - ·- --- 0 -
1 2 3 4 0 1 2 3 4 z z
1 1 /.
Eo.4 / 0.4 / / / / ..... / . . .,-
0.2 0.2 ,,
00 1 2 3 4 00 1 2 3 4 z z
Figure 10.2: Redshift evolution of the fraction of baryonic matter
in each of four components. The results of four simulations are
shown, with different handling of gas physics and different spatial
resolutions. [Dave et al. 2001]
(not inversely correlated, so there is not a pressure equilibrium).
The solid line in Figure 10.3 shows the scaling
n (IO.I)
where 20n 6ary,o 5 x 10- 6 cm- 3 . The temperature range of the
warm-hot inter- galactic medium embraces the temperature T ~ I 06 K
that is typical of the hot interstellar medium in our galaxy, and
of the corona of the Sun. However, the density nwhim ~ 5 x 1 o-6
cm- 3 of the warm-hot intergalactic medium is smaller by 3 orders
of magnitude than the density nhim ~ 4 x 10- 3 cm- 3 of the hot
interstellar medium, which in turn is 12 orders of magnitude
smaller than the density at the base of the Sun's corona.
Another striking difference between the warm-hot intergalactic
medium and the hot ionized medium of our galaxy is the much lower
metallicity of the WHIM compared to the HIM. Simulations indicate
that the metallicity of intergalactic
Evolution of the fraction of baryonic matter in each of four
components. Four simulation results are shown, with different gas
physics and different spatial resolutions.
[Fig 10.2, Ryden; Dave et al. 2001]
• Density-Temperature of the WHIM - The density is positively
correlated with temperature
(so there is no pressure equilibrium).
• Metallicity - The metallicity of intergalactic gas reaches
primarily in dense virialized clusters, contaminated with gas
ejected by supernovae.
- Along the WHIM filaments, a metallicity is more typical.
- At the low metallicity of the WHIM, bremsstrahlung dominates the
cooling down to a temperature as low as T ~ 106 K.
- The WHIM has a temperature that is typical of the hot
interstellar medium of our Galaxy. However, the WHIM has densities
that are smaller by 3 orders of magnitude than the HIM ( ).
Z > 0.3Z
p/<pb>
Figure 10.3: The distribution of warm-hot intergalactic gas in the
density- temperature plane at z = 0. The contours contain 90%, 50%,
and 10% of the baryons, from the outermost contour inward. The
straight line is a p ex: T fit. [Dave et al. 2001]
gas reaches Z > 0.32 0 primarily in dense virialized clusters,
contaminated with gas ejected by supernovae. Along the filaments
where the WHIM exists, a metal- licity Z ~ 10- 3 Z0 is more
typical. As shown in Figure 10.4, the cooling function in the
temperature range 10 5 K < T < l 07 K is highly sensitive to
metallicity. In the hot ionized medium of our own galaxy, the
metallicity is near the solar value. We saw in Section 5.3 that
cooling in the HIM is dominated by the emission lines of carbon,
oxygen, and iron until temperatures as high as T ~ 2 x 107 K are
reached, and bremsstrahlung takes over. At the low metallicity of
the warm-hot intergalactic medium, however, bremsstrahlung
dominates the cooling down to a temperature as low as T ~ l 06
K.
The bremsstrahlung luminosity density (normalized to the properties
of the WHIM) is
( kT )112 n 2 eff:::::::5.4x10- 35 ergcm- 3 s- 1 k ( 3 ) 0.1 eV 5 x
10- cm- (10.2)
Compare this to equation (8.23) for the luminosity density in the
hotter, denser
The distribution of WHIM in the density-temperature plane at z = 0.
The contours contain 90%, 50%, and 10% of the baryons, from the
outermost contour inward.
[Fig 10.3, Ryden; Dave et al. 2001]
n
20nbary,0 =
T
<latexit
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<latexit
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- Observing bremsstrahlung emission from the WHIM is “challenging”
(impossible).
- Note that, in our Galaxy, seeing bremsstrahlung emission from hot
bubbles other than the Local Bubble is impossible.
• Lines from highly ionized heavy elements. - Consider oxygen, for
instance, the most abundance element heavier than helium. : O V and
O VI become important. : The dominant ionization state of oxygen is
helium-like O VII. : O VIII and fully ionized O IX become
important.
21
kT
kT
2
<latexit
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<latexit
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- O VI emission line: The WHIM at T ~ 3x106 K has a low hydrogen
number density:
For the metallicity , the abundance ratio is . This leads to a
number density of oxygen:
Even at its maximum relative abundance, at T ~ 3x106 K, O VI
accounts for only 25% of all the oxygen:
Since the WHIM is concentrated along filaments of the cosmic web, a
line of sight passing through a single filament, whose thickness is
~ 1 Mpc, will contribute a column density:
Measuring a emission line from column density is difficult.
22
20nbary,0 =
T
<latexit
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<latexit
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`
<latexit
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nH 6nbary,0 1.5 106 cm3 at T 3 106 K
<latexit
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- O VI absorption line: Danforth & Shull (2008), in the study
of UV absorption lines (HST and FUSE) toward bright
AGNs, found O VI absorption systems with column densities:
The strongest absorption systems, with had an average Doppler
broadening parameter , corresponding to .
They concluded that the WHIM in the temperature range of , where O
VI absorption is strongest, provides ~ 10% of the baryonic material
in the universe.
This still leaves a large amount of “missing” baryons in the
IGM.
23
<latexit
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<latexit
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<latexit
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Nonequilibrium ionization effects may alter the postshock ioni-
zation fractions (N. Rajan & J. M. Shull 2008, in preparation).
Because N v lies intermediate in ionization potential between the
two other Li-like ions, it should be a good WHIM tracer as well.
However, the solar nitrogen abundance ismore than 5 times lower
than oxygen, and nitrogen is often observed to be underabun- dant
in Galactic high-velocity clouds (HVCs; Gibson et al. 2001; Richter
et al. 2001; Collins et al. 2003; Tripp et al. 2003; Fox et al.
2004). Until now, N v absorption is largely an unknown quantity in
the low-z IGM.
The UV lines of Si iv kk1393.755, 1402.770, Si iii k1206.500, C iii
k977.020, and Fe iii k1122.526 are all strong transitions of
abundant metals, with production ionization potentials below 3 ryd
(40.8 eV) and expected to probe photoionized, metal-
enriched material. In these lines, we also have two sets of ad-
jacent ionization levels (C iii /iv and Si iii /iv), which may help
to define the ionization state of the absorbers, independent of
ele- mental abundance ratios. Highly ionized metals were the
primary focus of this survey, and singly ionized species were not
explicitly studied. However, low-ion absorption exists in some Ly!
IGM systems (Tripp et al. 2008) and inmany ionizedHVCs (Sembach et
al. 1999; Collins et al. 2003, 2007). We examine the behavior of Si
ii, C ii, Fe ii, and similar species in the IGM and give further
analysis options in adjacent ionization stages (Si ii/iii/iv, C
ii/iii/iv, Fe ii /iii) in a subsequent paper (C. W. Danforth et al.
2008, in preparation).
We examined all 13 transitions for each IGM absorber; Fig- ures 1
and 2 show examples. In each case, we measured the line
Fig. 1.—IGM absorption in the z ! 0:06808 absorber toward PG
0953+414 showing typical, normalized FUSE and STIS/E140M data. Ly!
and Ly" show strong, consistent profiles (WLy! ! 284 " 13m8 andWLy"
! 128 " 16m8). C iii is detected, but Si iii and Fe iii are
nondetections. High ions are depicted in the right panels: O vi
k1032 and both N v lines are detected with consistent profiles. The
O vi k1038 line is blended with a strong H2 transition and is not
shown. C iv shows noisy but consistent detections in both bands of
the doublet as well. The two Si iv transitions are not shown. Each
panel is centered at the redshifted wavelength of the transition
and covers "500 km s#1 in either direction. Other detected features
in the data are identified. The ‘‘g:’’ prefix denotes a Galactic
absorption line, while a numerical suffix denotes the redshift of
an IGM line. The source channel (e.g., STIS/E140M or FUSE LiF2a) is
indicated in the lower right.
LOW-z INTERGALACTIC MEDIUM. III. 197No. 1, 2008
Nonequilibrium ionization effects may alter the postshock ioni-
zation fractions (N. Rajan & J. M. Shull 2008, in preparation).
Because N v lies intermediate in ionization potential between the
two other Li-like ions, it should be a good WHIM tracer as well.
However, the solar nitrogen abundance ismore than 5 times lower
than oxygen, and nitrogen is often observed to be underabun- dant
in Galactic high-velocity clouds (HVCs; Gibson et al. 2001; Richter
et al. 2001; Collins et al. 2003; Tripp et al. 2003; Fox et al.
2004). Until now, N v absorption is largely an unknown quantity in
the low-z IGM.
The UV lines of Si iv kk1393.755, 1402.770, Si iii k1206.500, C iii
k977.020, and Fe iii k1122.526 are all strong transitions of
abundant metals, with production ionization potentials below 3 ryd
(40.8 eV) and expected to probe photoionized, metal-
enriched material. In these lines, we also have two sets of ad-
jacent ionization levels (C iii /iv and Si iii /iv), which may help
to define the ionization state of the absorbers, independent of
ele- mental abundance ratios. Highly ionized metals were the
primary focus of this survey, and singly ionized species were not
explicitly studied. However, low-ion absorption exists in some Ly!
IGM systems (Tripp et al. 2008) and inmany ionizedHVCs (Sembach et
al. 1999; Collins et al. 2003, 2007). We examine the behavior of Si
ii, C ii, Fe ii, and similar species in the IGM and give further
analysis options in adjacent ionization stages (Si ii/iii/iv, C
ii/iii/iv, Fe ii /iii) in a subsequent paper (C. W. Danforth et al.
2008, in preparation).
We examined all 13 transitions for each IGM absorber; Fig- ures 1
and 2 show examples. In each case, we measured the line
Fig. 1.—IGM absorption in the z ! 0:06808 absorber toward PG
0953+414 showing typical, normalized FUSE and STIS/E140M data. Ly!
and Ly" show strong, consistent profiles (WLy! ! 284 " 13m8 andWLy"
! 128 " 16m8). C iii is detected, but Si iii and Fe iii are
nondetections. High ions are depicted in the right panels: O vi
k1032 and both N v lines are detected with consistent profiles. The
O vi k1038 line is blended with a strong H2 transition and is not
shown. C iv shows noisy but consistent detections in both bands of
the doublet as well. The two Si iv transitions are not shown. Each
panel is centered at the redshifted wavelength of the transition
and covers "500 km s#1 in either direction. Other detected features
in the data are identified. The ‘‘g:’’ prefix denotes a Galactic
absorption line, while a numerical suffix denotes the redshift of
an IGM line. The source channel (e.g., STIS/E140M or FUSE LiF2a) is
indicated in the lower right.
LOW-z INTERGALACTIC MEDIUM. III. 197No. 1, 2008
An example spectrum of O VI absorption line in the z = 0.06808
absorber toward PG 0953+414.
Fig 1, Danforth & Shull (2008, ApJ, 679, 194)
105 K < T < 106 K
<latexit
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- The hotter WHIM in the range is more difficult. The ion O VII has
an X-ray line at λ = 21.6
(0.57 keV). However, this is not a strong line, and has been found
only at a relatively low significance level along a few lines of
sight.
The right figure shows a simulation of intervening O VII absorption
lines at four redshifts along the line of sight to an X-ray bright
AGN for a 700 ksec observation (~ 8.1 days) with the Chandra
transmission grating instrument.
Observations have been very challenging and the results are
controversial.
- The “missing” baryons aren’t missing: they just need
high-throughput X-ray spectrographs with high energy resolution to
get their message across to us.
24
<latexit
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OVII I z=0.12
23.5 24.0 24.5 25.0 Wavelength [A]
Figure 10.5: Simulated 700 ksec Chandra LETG/HRC spectrum of B2
1721 +34 showing predicted WHIM O vn Ka absorption at redshifts of
0.11, 0.12, 0.14, and 0.16. [Data provided by A. Gupta & S.
Mathur, OSU]
As we saw when considering O VI absorption lines toward local white
dwarfs, measuring column densities N (0 VI) < 1013 cm- 2 is
difficult.
Danforth & Shull, in a study of UV absorption lines toward
bright AGN, found O VI absorption systems with column densities
ranging from N ~ 8 x 1012 cm- 2 to N ~ 5 x 1014 cm- 2 • The
strongest absorption systems, with N > 1014 cm- 2, had an
average Doppler broadening parameter b ~ 40kms- 1, corre- sponding
to T ~ 106 K. The conclusion of Danforth & Shull was that
warm-hot intergalactic gas in the temperature range 105 K < T
< l 06 K, where O VI absorp- tion is strongest, provides ~ 10%
of the baryonic material in the universe. This still leaves a large
amount of "missing" baryons in the intergalactic medium.
Detecting the hotter WHIM, in the range 106 K < T < l 07 K,
is more difficult. The ion Ovn has an x-ray line at A= 21.6A (hv =
0.57keV). It is not a strong line, however, and has been found only
at a relatively low significance level along a few lines of sight.
Figure 10.5 shows a simulation of intervening O vn absorption lines
at four redshifts along the line of sight to an X-ray bright AGN
for a 700 ksec observation (~8.1 days!) with the Chandra
transmission grating instrument.
Observations attempted to date have been very challenging and the
results
Simulated 700 ksec Chandra LETG/HRC spectrum of B2 1721+34 showing
predicted WHIM O VII K absorption at redshifts of 0.11, 0.12, 0.14,
and 0.16.
[Fig 10.5, Ryden]
Final Exams (Take-Home)
(1) Take pictures or scan (2) email me (
[email protected])
26Chapter 29 Please do not copy, scan, or photograph. 49
Chapter 29. H I Clouds: Observations
29.1 Suppose the H I gas to be in a plane-parallel slab geometry,
with full thickness 6 1020 cm2, and take the velocity distribution
be Gaussian with a one-dimensional velocity dispersion V = 10 km
s1. Neglect the effects of Galactic rotation.
(a) If the spin temperature is Tspin = 100K, for what galactic
latitudes is the line-center optical depth < 0.5, as seen from a
point in the mid-plane?
(b) If the full-thickness of the H I disk is 300 pc, out to what
radius (in the plane) can it be observed with line-center optical
depth < 0.5?
(c) What is the maximum N(H I) that can be observed with < 0.5
at all radial velocities?
29.2 Let dN(H I)/du u be the column density of H I in the radial
velocity interval u. Show that the optical depth in the 21-cm line
can be written
= 3
1020 cm2/( km s1) .
29.3 Suppose we observe a background radio continuum point source
through a layer of “foreground” H I with dN(H I)/du = 3 1020
cm2
/(20 km s1), where u is the radial velocity. If the measured flux
density of the background continuum source changes by less than 1%
on-line to off-line, what can be said about the spin temperature of
the H I? Assume the beamsize is very small. You may use the result
from problem 29.2:
= 0.552
100K
Tspin
Q1 (Lecture 5)
Chapter 15 Please do not copy, scan, or photograph. 29
Chapter 15. Photoionized Gas
15.1 A O9V star has luminosity L = 104.77 L, emits h > 13.6 eV
photons at a rate Q0 = 1048.06 s1, and emits h > 24.6 eV photons
at a rate Q1 = 0.0145Q0 (see Table 15.1). The star is surrounded by
a steady-state H II region.
(a) If the ionized region has a uniform density nH = 102 cm3 and
temperature T = 104 K, estimate the neutral fraction n(H0)/nH at a
distance r = 0.9RH II from the star, where RH II is the radius of
the zone where H is ionized. Assume that the gas is pure hydrogen,
and that dust is negligible.
(b) Now assume that the gas has He/H0.1 by number. What will be the
ratio RHe II/RH II, where RHe II
is the radius of the zone where helium is ionized? An answer
accurate to 10% is OK – don’t worry over details. State your
assumptions.
15.2 Hydrogen 166↵ (i.e., 167`!166`0) and He 166↵ (i.e.,
1s167`!1s166`0) recombination lines are observed from an H II
region. Assume that the telescope beamwidth is much larger than the
nebula. The strengths of the lines are in the ratio T (He)/T (H) =
0.032, i.e.,
Z d
Z d
H166↵ Id .
(a) Using Table 15.1, estimate the temperature of the exciting star
for the H II region, assuming it to be of luminosity class V.
Assume that all h > 24.6 eV photons are absorbed by He. Assume
↵B(H) 2.54 1013 cm3 s1 for HII and ↵B(He) 2.72 1013 cm3 s1 for
HeII.
(b) The observed recombination lines have full widths at
half-maximum (FWHM) of 23.5 and 15.3 km s1 for H and He
respectively, as observed with a receiver with an instrumental line
width (FWHM) of 5 km s1. Assume that the only motions are from
thermal motions plus turbulence with an unknown velocity disper-
sion.
• What is the kinetic temperature T in the nebula? • What is the
one-dimensional velocity dispersion turb of the turbulence?
[You may assume that both the instrumental response function and
the thermal and turbulent velocity distribution functions are
gaussians. The convolution of a gaussian with a gaussian yields a
gaussian with variance equal to the sum of the variances of the
original two gaussians.]
15.3 Consider a spherically-symmetric stellar wind with mass-loss
rate Mw = 104 M yr1. and wind speed
vw = 20 km s1. Suppose the mass-loss continues steadily for tw =
103 yr and then stops, with the wind continuing to “coast”
outwards. Suppose that after a time t, the central star suddenly
becomes an ionizing source emitting hydrogen-ionizing photons at a
rate Q0, creating a “protoplanetary nebula”.
(a) After time t, the outflowing wind has a spherical outer surface
and a spherical inner “hole”. What is the density just inside the
outer surface?
(b) What is the density just outside the inner hole? (c) Ignoring
expansion of the nebula during the ionization process, what is the
minimum value of Q0 required
to ionize the H throughout the nebula? (d) What is the
recombination time just inside the outer surface? Compare this to
the 103 yr dynamical age.
15.4 Consider a runaway O star, of spectral type O8V, traveling
through a diffuse region with nH 0.2 cm3.
(a) What is the Stromgren radius RS0 if the photoionized gas has T
= 104 K? (b) If the star is traveling at v? = 100 km s1, compare
the time required for the star to travel a distance equal
to the Stromgren radius to the recombination time. (c) Very briefly
discuss the implications of the comparison in item (b).
Q2 (Lecture 6)
38 Please do not copy, scan, or photograph. Chapter 21
Chapter 21. Interstellar Dust: Observed Properties
21.1 Suppose that dust produced extinction A() directly
proportional to the frequency of the light. What would be the value
of RV ?
21.2 If the extinction were to vary as a power law, A / , what
power-law index would give RV = 3.1?
Q3 (Lecture 9)
27Chapter 5 Please do not copy, scan, or photograph. 9
Chapter 5. Energy Levels of Molecules
5.1 Both H2 and HD have similar internuclear separation r0 0.741 A.
Assume that the molecules can be approx- imated as rigid
rotors.
(a) Calculate [E(v=0, J)E(v=0, J=0)]/k for H2 for J=1, J=2, and
J=3.
(b) Calculate [E(v=0, J)E(v=0, J=0)]/k for HD for J=1, J=2, and
J=3.
(c) Because H2 has no electric dipole moment, J = ±1 transitions
are forbidden, and instead the only radiative transitions are
electric quadrupole transitions with J=0,±2. Calculate the
wavelengths of the J=2 ! 0 and J=3 ! 1 transitions of H2
(d) Because HD has a (small) electric dipole moment, it has (weak)
electric dipole transitions. What is the longest-wavelength
spontaneous decay for HD in the v = 0 vibrational level?
5.2 Why doesn’t H2 in the ground electronic state X 1+
g have hyperfine splitting?
5.3 Most interstellar CO is 12C16O. The J = 1 ! 0 transition is at
= 115.27GHz, or = 0.261 cm, and the v = 1 ! 0 transition is at =
4.61µm (ignoring rotational effects).
(a) Estimate the frequencies of the J = 1 ! 0 transitions in 13C16O
and 12C17O.
(b) Estimate the wavelengths of the v = 1 ! 0 transitions in 13C16O
and 12C17O. Ignore rotational effects.
(c) Suppose that the 13C16O J=1 0 line were mistaken for the 12C16O
J=1 0 line. What would be the error in the inferred radial velocity
of the emitting gas?
(d) What is E/kB , where E is the difference in “zero-point energy”
between 12C16O and 13C16O, and kB is Boltzmann’s constant?
Q4 (Lecture 11)
Chapter 32 Please do not copy, scan, or photograph. 53
Chapter 32. Molecular Clouds: Observations
32.1 The mass distribution of GMCs in the Galaxy is given by [eq.
(32.1) in the textbook]:
dNGMC
103 M < MGMC < Mu
with Mu 6 106 M, Nu 63, and ↵ 0.6 (Williams & McKee 1997,
Astrophys. J. 476, 166 ).
(a) Calculate the total mass in GMCs in the Galaxy.
(b) Calculate the number of GMCs in the Galaxy with M > 106
M.
Q6 (Lecture 12)
Chapter 9 Please do not copy, scan, or photograph. 15
(c) Given your result from (b) on the upper bound for N(Si II 2P o
3/2), what limit can be placed on the elec-
tron density ne in the intervening galaxy if the kinetic
temperature is assumed to be 104 K? The Ein- stein A coefficient is
A( 2P o
3/2 ! 2P o 1/2) = 2.13 104 s1, and the electron collision strength
is
( 2P o 3/2,
2P o 1/2) = 4.45 (see Table F1 on p. 496). (Ignore the existence of
the 2S1/2 state in this and
(d) below; i.e., treat the two fine-structure states as a two-level
system. Assume the interstellar radiation field in the intervening
galaxy to be not too wildly dissimilar to that in our
Galaxy.)
(d) Can any useful limit be placed on ne if the kinetic temperature
is assumed to be 102 K rather than 104 K?
9.6 An unconventional interpretation of the observations described
above (in problem 9.5) is that the Si II absorption is produced in
a cloud of gas which has been shot out of the quasar with a
velocity c (relative to the quasar) which gives it a redshift (as
seen from the quasar) zGQ satisfying (1 + zG)(1 + zGQ) = (1 + zem),
where zG = 1.36 and zem = 2.22. Thus (1 + zGQ) = (1 + zem)/(1 + zG)
= 1.364.
The velocity c of the cloud relative to the QSO is then given by
the relativistic Doppler shift formula
1.364 = 1 + zGQ = 1 +
(1 + zGQ)2 + 1 = 0.301 .
Suppose the quasar to be emitting (isotropically) a power per unit
frequency (evaluated in the rest frame of the quasar) P =
(L0/0)(/0)↵, where L0 = 1013 L and 0 = 1015 Hz, and the exponent ↵
is of order unity.
At a distance D from the QSO, in a frame at rest relative to the
QSO, the energy density is
u = P
4D2c =
L0/0
4D2c
↵
.
A little bit of special-relativistic reasoning leads to the
conclusion that a “cloud” observer receding from the QSO at
velocity GQc will find that the energy density at frequency G
(measured in the gas cloud frame) is given by
(u)G = 1
↵
.
(a) For the moment consider only transitions between the 2P o 1/2
and 2P o
3/2 levels. What is the minimum value of D which is consistent with
the observed upper limit on the ratio N(Si II 2P o
3/2)/N(Si II 2P o 1/2)?
(Assume ne = 0). (b) Now consider pumping of the 2P o
3/2 level via the 2S1/2 level. What is the probability per time for
an Si II ion in the 2P o
1/2 state to be excited to the 2S1/2 level by absorbing a UV
photon? Give your answer as a function of D.
(c) What fraction of the Si II excitations to the 2S1/2 state will
lead to population of the 2P o 3/2 state?
(d) Suppose the absorbing cloud to be a spherical shell around the
quasar. If the Si/H ratio in the gas does not exceed the Si/H ratio
in our Galaxy (Si/H=4105), and the gas has He/H = 0.1, what is the
minimum kinetic energy of this expanding shell? (This extreme
energy requirement has been used in arguing against this
interpretation of absorption line systems.)
9.7 An absorption line is observed in the spectrum of a quasar at
an observed wavelength = 5000. A. The absorp- tion is produced by
an intergalactic cloud of gas somewhere between us and the quasar.
The observer measures an equivalent width W = 1.0102 A. The
absorption line is resolved, with an observed FWHM = 0.50 A.
The line is assumed to be H I Lyman↵, with rest wavelength 0 =
1215.7 A and oscillator strength f`u = 0.4164.16 Please do not
copy, scan, or photograph. Chapter 9
(a) What is the redshift z of the absorber?
(b) What is the column density of H I in the absorbing cloud?
(c) In the rest frame of the cloud, the H I has a one-dimensional
velocity distribution / e (v/b)2 . What is
the value of b for this cloud?
9.8 The spectrum of a quasar has absorption lines at observed
wavelengths = 5000.0 A and 5008.4 A, with observed equivalent
widths W = 0.020 A and W = 0.010 A, respectively. Both lines are
resolved, each with observed FWHM = 0.40 A.
The lines are interpreted as being produced by C IV, with rest
wavelengths 0 = 1548.20 A and 1550.77 A, and oscillator strengths
f`u = 0.190 and 0.096.
(a) What is the redshift z of the absorber?
(b) What is the column density of C IV in the absorbing
cloud?
(c) In the rest frame of the cloud, the H I has a one-dimensional
velocity distribution / e (v/b)2 . What is
the value of b for this cloud?
9.9 The CH+ molecule has an absorption line at = 4233 A with an
oscillator strength f`u = 0.0060 out of the ground state `. An
absorption line is observed at this wavelength with an equivalent
width W = 0.010 A, and a FWHM of 10 km s1. What is the column
density of ground-state CH+ on this line-of-sight? Single-digit
accuracy is sufficient.
9.10 High-resolution spectra of a quasar show absorption by H
Lyman↵ (rest-frame wavelength 1215.6 A) at an observed wavelength =
3890.2 A and a C IV absorption doublet (rest-frame wavelengths
1548.2, 1550.8 A) at = 4954.2 A and = 4962.6 A. Suppose that all
three lines are optically thin, with Gaussian line profiles. The
line at 3890.2 A has observed full-width-at-half-maximum FWHMH =
0.3168 A. The line at = 4954.2 A has observed FWHMC IV = 0.2196 A.
Recall that if a variable x has a Gaussian distribution, FWHMx
=
p 8 ln 2 x = 2.355x.
(a) What is the redshift z of the absorbing gas?
(b) What is the one-dimensional velocity dispersion v,H of the
hydrogen atoms (in the absorption system rest frame)? Give your
answer in km s1.
(c) What is the one-dimensional velocity dispersion v,C IV of the C
IV ions (in the absorption system rest frame)? Give your answer in
km s1
(d) Assume that the H and C IV are in gas with temperature T and
turbulence with one-dimensional turbulent velocity dispersion turb,
so that the one-dimensional velocity dispersion of a particle of
mass M is given by the sum (in quadrature) of the thermal and
turbulent velocity dispersions:
2 v =
2 turb
For the absorption line system, what is T (in degrees K) and turb
(in km s1)? 9.11 Suppose that an H atom in the 3p level is at rest
in an H I cloud of density n(H) = 20 cm3 and kinetic
temperature T = 100K. Assume that the motions of the other H atoms
in the cloud are purely thermal. Assume the cloud to be infinite in
extent, and pure H (no dust, etc.).
If the H(3p) emits a Lyman photon, what is the mean free path of
this photon before it is absorbed by another H atom? The wavelength
of Lyman is 1025.7A. The oscillator strength for the Lyman
transition is f1s,3p = 0.0791.
Q8 (Lecture 13 & Lecture 5)
Q7 (Lecture 12)
Consider a spherical cloud with a total mass M and a radius R.
Assume that the cloud has a radial density profile of . The
gravitational potential energy can be expressed as follows: