lecture14_0702updated 07/01, 21:35
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- 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.
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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.
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(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
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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.
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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.
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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.
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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
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• 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
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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-
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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
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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 sha1_base64="G4kR/D/IJSh3Zdj38tTxSb9skT8=">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</latexit>
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 sha1_base64="2nPbZDk7Sa/Jl6+CYSChZ4UYQII=">AAADV3icdVJdb9MwFPVSGKV8tfCIkKxVk3iYqmQUbUh7mDSEkKBiiHWbtJTiuDeZVyeObKdTZfmJX8Mr/Jr9GnDaaqxfV3k4Pvdc++jkRjlnSvv+zYZXuXd/80H1Ye3R4ydPn9Ubz0+VKCSFLhVcyPOIKOAsg65mmsN5LoGkEYezaHhU9s9GIBUT2Yke59BLSZKxmFGiHdWvvwr872/DHRPKFH+yBycH7rx3e+7Xm37LnxReBsEMNNGsjvsNbyscCFqkkGnKiVIXgZ/rniFSM8rB1rbDQkFO6JAkYEh+FYtMK1u7y6ZEX2oh+AJd5IkEGM6RFw5mJAXVM5MoLN52zADHQuLyZjxh564hqVLjNHLK8h212CvJnf8OVqkoySjwBR863u8ZluWFhoxObcQFx1rgMnU8YBKo5mMHCJXMhYHpJZGEavdvauF7cGFJ+OaMCf7BGTdHHQ66bFrzpfPZGpqm1riPaXsr7zhr0xETZoU1YelVyIG9O737pgx9eWK0Rv9jtFp/vU5/vVqfrNMn5VYFizu0DE53W0G79e5ru3nYnu1XFb1EW+g1CtAeOkQf0THqIop+ol/oN/rj3Xh/K5uV6lTqbcxmXqC5qjT+AQaTG4s=</latexit>
5 107 cm3 < n < 5 105 cm3
<latexit sha1_base64="VEdZcL/50dmmmWUWdzx1cc9uJYI=">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</latexit>
<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
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<latexit sha1_base64="HWqxvQMv7r91v69n7eSyFN6amTM=">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</latexit>
- 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
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<latexit sha1_base64="g8jiz5bYIaCH5rdJ9o/DoDCksxI=">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</latexit>
- 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
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`
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nH 6nbary,0 1.5 106 cm3 at T 3 106 K
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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
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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
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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
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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 (kiseon@kasi.re.kr)
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: