trying to understand Lyman-alpha forest

[Widdekind]

OOPS -- Lyman-alpha forest "clouds" are large (~1Mly) (omitted baryon mass fraction)

According to Mo & van den Bosch' Galaxy Formation & Evolution, from direct observations, Lyman-alpha forest "clouds" are large (~1Mly). "Clouds" cluster, and dis-cluster, on larger scales (~100Mly). Inexpertly, "clouds" are fully ionized for column densities <10¹⁴cm^-2; strongly ionized for column densities <10¹⁸cm^-2. "Clouds" seem associated with the peripheries of galactic structures. Separately, DLAs are weakly ionized for column densities of ~10¹⁹cm^-2; and increasingly neutral for column densities >10²⁰cm^-2. DLAs seem associated with emerging spiral galaxy disks.

 

For a characteristic "cloud" of (say) N ~ 10¹⁶cm^-2, f_N ~ 10^-4, R ~ 1Mly:

[math]N(HI) \approx f_N n R[/math]

 

[math]n \approx \frac{N(HI)}{f_N R} \approx 10^{-4}cm^{-3}[/math]

At redshift (z~5), critical density was (equivalent to) about 10^-3cm^-3. Separately, the hot halo of the Milky Way contains most of a hundred billion solar masses, in a volume most a million light-years across; from which numbers i calculate an average space density of 10^-4cm^-3. If so, then "clouds" resemble galaxy hot halos.

 

Given those recent observations, of a vast circumgalactic halo of hot x-ray emitting gas, enveloping the Milky Way, most of 1Mly across; i understand, that low neutral density "clouds" could correspond to sightlines threading through circum-galactic hot halos; and DLAs to sightlines threading through the denser proto-galaxies themselves. Over billions of years, from (z~3-0), halos became heated, and increasingly ionized. Please ponder a sightline threading through our Local (Virgo) Cluster; absorption features from heating halos ("clouds") and proto-galaxies (DLAs) would clearly cluster together within emerging Cosmic Structure, and dis-cluster from emerging Cosmic Voids:

 

 

 

 

Simplistically, Quasar spectra are emitted "blue", and "redden" as they propagate through space & time, to earth today. As their spectra propagate whilst reddening, they occasionally encountered "clouds" containing neutral hydrogen. Those clouds absorbed out (some) photons near 1215A in the local rest frame ("their, then"). But the photons absorbed had "reddened into" (redshifted into) the 1215A near-UV band, from "bluer" higher-energies in the farther-UV. Then, once imprinted into a Quasar spectrum, the absorption lines are also redshifted out to ever longer wavelengths. Successive encounters, with a series of such "clouds", so results in a series of absorption "lines", from wavelengths near that of the Quasar's own 1215A emission peak (redshifted to 1215A x (1+z_Q)), towards ever shorter wavelengths (redshifted to 1215A x (1+z_c), where z_c < z_Q).

 

Now, at short cosmological ranges, proper distances are (approximately) proportional to the difference in redshift, i.e. Hubble's Law:

dL = c dz / H(z)

= c dz / H

₀

h(z)

= c T

₀

dz / h(z)

= D

₀

dz / h(z)

 

h(z) = 2/3 (1+z)

^3/2

And the redshift of, and between, "clouds" is implied by the differences between their redshifted originally-1215A wavelengths:

w = 1215A x (1+z)

dw = 1215A x dz

dz = dw/1215A

 

(1+z) = w/1215A

And so,

dL = 1.5 D

₀

dz / (1+z)

^3/2

= 20Gly x dz / (1+z)

^3/2

The only freely-available internet images of the spectrum of QSO 1425-6039 seems to be provided by CalTech. The following figure is reproduced in Dan Moaz' Astrophysics in a Nutshell (pg.227):

(EDIT: Johan Hidding has also posted a webpage, providing a picture, of the same spectrum.)

From the figure, "clouds" cluster, and dis-cluster, across changes in wavelength of ~50A, near wavelengths of ~4800A, corresponding to estimated distance scales of:

dz ~ 1/25

(1+z) ~ 4

 

dL ~ 20Gly x (1/25) / 4

^3/2

= 0.1Gly

=

100Mly

So, at that distant region, at that ancient epoch (z~3), the local "space weather" was "cloudy" and "clear", on proper distance scales, of about 100Mly. Are these calculations correct?

 

According to Dan Maoz' seemingly cogent & clear cosmology book, the "clouds" are warm (T ~ 10⁴K) and nearly ionized (neutral fraction f ~ 10^-4), whilst the "clearings" are hot (T ~ 10^5-6) and fully ionized. According to Hyron Spinrad's Galaxy Formation & Evolution (pg.11), the "clouds" have neutral column densities of 10^14-18cm^-2, and spatial densities a hundred times the cosmic average. The latter translates into about one particle per cubic centimeter (at redshift z~5). With a neutral fraction of one ten thousandth, and so neutral space densities of one ten thousandth neutral particle per cubic centimeter, the calculated column densities demand sizes of 1 to 10,000 ly, i.e. from protostellar nebulae to globular star clusters to dwarf galaxies. Are these calculations correct?

EDIT: The calculated sizes, and estimated total space densities, imply masses ranging from 0.001 to 1 billion M_sun, also suggesting protostellar nebulae to globular star clusters to dwarf spheroidal galaxies.

 

---

Damped Lyman-alpha Absorbers (DLAs)

According to Spinrad, DLAs have neutral column densities of 10^20-23cm^-2, and spatial densities scaling commensurately from 10^2-5 times the cosmic average. The latter translates into about 1-1000 particles per cubic centimeter (at redshift z~5). DLAs are a different kind of "cloud", having higher column densities, densities, and metallicities. So, assuming a neutral fraction of one, and so neutral space densities also of 1-1000 particles per cubic centimeter, the calculated column densities, and estimated space densities, all demand sizes of 100 ly; and imply masses of 1000 to 1 million M_sun; all suggesting globular star clusters; and consistent with the cold component of the Interstellar Medium (ISM). However, if DLAs have lower neutral fractions (f ~ 10^-4), then they would be much bigger (1Mly), and implausibly more massive (10^15-18M_sun). If DLAs had intermediate neutral fractions (f ~ 10^-2), then they would be bigger (10Kly), and plausibly more massive (10^9-12M_sun). DLAs are commonly associated to spiral galaxy disks (perhaps because of their higher metallicities, Z ~ 0.01-10 Z_sun, similar to spiral galaxy disks, having ongoing star-formation), favoring the intermediate model, which is consistent with the warm (and most common) component of the ISM (cp. Jedamzik & Prochaska, "velocity width dispersion favors large & thick disks with small neutral gas fraction").

 

---

physical picture -- protogalaxies & halo clusters ?

i understand, that Lyman-alpha clouds correspond to star clusters & dwarf galaxies; whereas DLAs correspond to large spirals. In the following figure, freely available on the internet from Atlas of the Universe, the large spiral galaxies in our Local Group (Andromeda, Milky Way, Triangulum) could have generated DLA absorption features in ancient Quasar spectra; whereas all of their satellite globular star clusters & dwarf galaxies could have generated Lyman-alpha cloud features, in such spectra:

Is my understanding consistent with current cosmologist consensus?

 

---

Quasar accretion disks ?

From the formula for Doppler Shift, the relative broadening of the Quasar's 1215A emission implies the velocity dispersion, of the emitting neutral hydrogen:

[math]\frac{\Delta f}{f_0} \approx \frac{\Delta \lambda}{\lambda_0} \approx \frac{v}{c}[/math]

For QSO 1425-6039:

[math]\frac{\Delta \lambda}{\lambda_0} \approx \frac{1}{25}[/math]

Assuming the emitting neutral hydrogen was swirling around a central SMBH, within an emerging "growing" protogalaxy, then the gas was orbiting with speeds around ~10,000 km/s. Such speeds, assuming a mass for said SMBH, imply the size of the assumed accretion disk:

[math]\left(\frac{v}{c}\right)^2 \approx \frac{G M}{c^2 R} \approx \frac{R_S}{R}[/math]

 

[math]\approx 10^{-4}[/math]

For SMBH masses of a million to a billion solar masses, implied accretion disk radii range from 100AU to 1ly, from larger than our solar system, to nearly the distance from earth to the nearest star. Is this interpretation of the Quasar's broad Lyman-alpha emission peak appropriate? If the Quasar (jets) is aimed at earth, then the accretion disk would be seen face on, and evidence no radial, Doppler-shift-inducing, motion. If so, then actual space speeds might be higher by an inverse sin or cos function.

(EDIT: The only clear & cogent picture explaining Quasars easily available on the internet comes from CalTech. Quasars are observed off-jet-axis by about 30 degrees.)

Edited November 15, 2012 by Widdekind

[Widdekind]

OOPS -- Lyman-alpha forest "clouds" are large (~1Mly) (omitted baryon mass fraction)

According to Mo & van den Bosch' Galaxy Formation & Evolution, from direct observations, Lyman-alpha forest "clouds" are large (~1Mly). "Clouds" cluster, and dis-cluster, on larger scales (~100Mly). Inexpertly, "clouds" are fully ionized for column densities <10¹⁴cm^-2; strongly ionized for column densities <10¹⁸cm^-2. "Clouds" seem associated with the peripheries of galactic structures. Separately, DLAs are weakly ionized for column densities of ~10¹⁹cm^-2; and increasingly neutral for column densities >10²⁰cm^-2. DLAs seem associated with emerging spiral galaxy disks.

 

For a characteristic "cloud" of (say) N ~ 10¹⁶cm^-2, f_N ~ 10^-4, R ~ 1Mly:

[math]N(HI) \approx f_N n R[/math]

 

[math]n \approx \frac{N(HI)}{f_N R} \approx 10^{-4}cm^{-3}[/math]

At redshift (z~5), critical density was (equivalent to) about 10^-3cm^-3. Separately, the hot halo of the Milky Way contains most of a hundred billion solar masses, in a volume most a million light-years across; from which numbers i calculate an average space density of 10^-4cm^-3. If so, then "clouds" resemble galaxy hot halos.

 

For a maximal DLA of N ~ 10²³cm^-2, f_N ~ 1, R ~ 1Mly:

[math]N(HI) \approx f_N n R[/math]

 

[math]n \approx \frac{N(HI)}{f_N R} \approx 10^{-1}cm^{-3}[/math]

Thus, the estimated densities and temperatures (~10⁴K) of DLAs resemble the warm (and most common) component of the Milky Way's ISM.

 

Given those recent observations, of a vast circumgalactic halo of hot x-ray emitting gas, enveloping the Milky Way, most of 1Mly across; i understand, that low neutral density "clouds" could correspond to sightlines threading through circum-galactic hot halos; and DLAs to sightlines threading through the denser proto-galaxies themselves. Over billions of years, from (z~3-0), halos became heated, and increasingly ionized. Please ponder a sightline threading through our Local (Virgo) Cluster; absorption features from heating halos ("clouds") and proto-galaxies (DLAs) would clearly cluster together within emerging Cosmic Structure, and dis-cluster from emerging Cosmic Voids:

Paradoxically, "growing" galaxies, the site of ongoing star-formation, and (hence) sources of ionizing photons, were also the last bastions of neutral hydrogen in our universe.