Here at the risk of being overly phlegmatic are some selected passages from a totally dynamite article in the APJ , It seems that whatever is out there in the Interstellar Medium (ISM), it has an effect on the light that is scattering around out there, or in transite past it.
I am awed by their technical precision and dedication to collecting the data. Drawing conclusions is always a sliperyslope.
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The Astrophysical Journal, 564:52-59, 2002 January 1
© 2002. The American Astronomical Society. All rights reserved. Printed in U.S.A.
The Imprint of Lithium Recombination on the Microwave Background Anisotropies
Matias Zaldarriaga 1 and Abraham Loeb 2
Received 2001 May 19; accepted 2001 August 31
ABSTRACT
Following the 2001 paper of Loeb, we explore the imprint of the resonant 6708 Å line opacity of neutral lithium on the temperature and polarization anisotropies of the cosmic microwave background (CMB) at observed wavelengths of 250350 m (0.91.2 THz). We show that if lithium recombines in the redshift range of z = 400500 as expected, then the standard CMB temperature and polarization anisotropies would be significantly modified in this wavelength band. The lithium signal may be difficult to separate from the contamination by the far-infrared background and galactic foregrounds. We show that in polarization, the signal could be comparable to the expected polarization anisotropies of the far-infrared background on subdegree angular scales ( 100). Detection of the predicted signal can be used to infer the primordial abundance of lithium, and to probe structure in the universe at z 500.
Subject headings: cosmic microwave backgroundcosmology: theory
1 Physics Department, New York University, 4 Washington Place, New York, NY 10003;
matiasz@physics.nyu.edu.
2 Astronomy Department, Harvard University, 60 Garden Street, Cambridge, MA 02138;
aloeb@cfa.harvard.edu.
1. INTRODUCTION
The latest measurements of the anisotropies in the cosmic microwave background (CMB; see Halverson et al. 2001; Lee et al. 2001; Netterfield et al. 2001) imply that the days of "precision cosmology" have already arrived.3 Future ground- and balloon-based experiments, in combination with the satellite missions Microwave Anisotropy Probe (MAP)4 in 2001 and Planck5 in 2007, will test current theoretical models to a subpercent precision at photon wavelengths 500 m.
However, at far-infrared wavelengths of 350 m, Loeb (2001) has recently shown that the drag force between photons and neutral lithium can strongly modify the CMB anisotropy maps through absorption and reemission at the resonant 6708 Å transition of lithium from the ground state. The drag produced by the hydrogen Ly line is small, because on the scales of interest, this line is highly optically thick; the hydrogen Balmer lines have a smaller optical depth, but the occupation probability of the lower level is strongly suppressed by the Boltzmann factor. For helium, the transitions correspond to frequencies too far on the Wien tail of the CMB spectrum to be important. Thus, the lithium transition is the most relevant one (Loeb 2001).
Lithium is expected to recombine in the redshift interval z 400500 (Palla, Galli, & Silk 1995; Stancil, Lepp, & Dalgarno 1996, 1998). Despite the exceedingly low lithium6 abundance produced in the big bang, the resonant optical depth (Sobolev 1946) after lithium recombination is substantial:
for an observed wavelength of (z) = [(6708 Å)(1 + z)] = (335.4 m)[(1 + z)/500]. Here, XLi 3.8 × 10-10 is the latest estimate of the lithium-to-hydrogen number density ratio (Burles, Nollett, & Turner 2001), and f(z) is the neutral fraction of lithium as a function of redshift (Palla et al. 1995; Stancil et al. 1996, 1998). Loeb (2001) argued that resonant scattering would suppress the original anisotropies by a factor of exp(-), but would generate new anisotropies in the CMB temperature and polarization on subdegree scales ( 100), primarily through the Doppler effect. Observations at different far-infrared wavelengths could then probe different thin slices of the early universe.
In this paper, we calculate in detail the effect of neutral lithium on both the polarization and temperature anisotropies of the CMB. Section 2 describes the modifications we have made to the standard code CMBFAST (Seljak & Zaldarriaga 1996) in order to calculate these anisotropies. In § 3 we describe our results and compare them with the foreground noise introduced by the far-infrared emission from galaxies and quasars. Finally, § 4 summarizes the main conclusions of this work.
Throughout the paper, we adopt the low-density cold dark matter (LCDM) cosmological parameters of cdm 0.25, = 0.7, b = 0.05, and H0 70 km s -1 Mpc -1, and units of c = 1.
3 A compilation of all experiments up to date can be found at
http://www.hep.upenn.edu/max/cmb/experiments.html.
4 Available at
http://map.gsfc.nasa.gov/.
5 Available at
http://astro.estec.esa.nl/Planck.
6 Note that by the redshift of interest, all the 7Be produced during big bang nucleosynthesis transforms to 7Li through electron capture, since 7Be starts to recombine well before 7Li, owing to its significantly higher ionization potential.
2. METHOD OF CALCULATION
In order to compute the temperature and polarization fluctuations induced by lithium scattering, we complement the standard Thomson opacity (T) in CMBFAST by a new component (), which is assumed to have a narrow Gaussian shape in conformal time:
---
3. RESULTS
The significance of the new opacity component can be assessed from the visibility function (). This function provides the probability distribution for the time of last scattering of the photons observed today at a conformal time 0,
In Figure 1, we show the visibility functions for some of the models that we consider later.
Fig. 1 Visibility function for models with = 0.5 and LCDM. We show three examples, corresponding to resonant scattering at different redshifts: z = 400, 450, and 500. The present-day value of the conformal time is 0 = 1.39 × 104 Mpc.
The observed anisotropies have two separate contributions, one from the standard last-scattering surface at hydrogen recombination (decoupling), which is suppressed by e, and a second new contribution that is generated by lithium scattering at lower redshifts. In the following subsections, we characterize this new contribution to the temperature and polarization anisotropies.
3.1. Temperature and Polarization Anisotropies
Figures 2 and 3 show the predicted power spectra for the temperature and polarization anisotropies of the CMB at an observed wavelength of = 335.4 m, corresponding to lithium scattering at z = 500. The Stokes parameters are measured in K. The figures compare the spectrum of fluctuations in standard LCDM (no lithium scattering) with two other models, each having a peak in at a redshift of z = 500, but with a total optical depth of either = 0.5 or 2.0. Since at long wavelengths ( 500 m) the LCDM fluctuations are not altered, precise mapping of these fluctuations by the MAP or Planck satellites will provide a reference power spectrum against which the lithium distortion can be measured.
Fig. 2 Temperature power spectra for the standard calculation (LCDM model) and two other models with lithium optical depths of = 0.5 and 2.0 at z = 500, for observations in a narrow band around 335 m. The width of the Gaussian in eq. (2) is / = 0.01.
Fig. 3 Polarization power spectra. Models are the same as in Fig. 2.
Figure 2 shows that for = 0.5, the small-scale fluctuations are dominated by the suppressed anisotropies from recombination, resulting in a power spectrum that is similar in shape to that of the primary anisotropies, but suppressed in amplitude. However, the = 2 case is very different. Here, the anisotropies are actually larger for many l's than those expected without the lithium scattering, having a different functional dependence on l than the standard case. The e suppression of the original anisotropies is sufficient to make them subdominant relative to the newly generated anisotropies at z = 500.
There is an interesting difference between the primary anisotropies and those created by lithium scattering. In order to explain it, we introduce the integral solution for the temperature anisotropies,
where is the cosine of the angle between the wavevector and the direction of observation, and and are the two gravitational potentials defined by the perturbed metric, ds2 = a2()[-(1 + 2)d2 + (1 - 2) dxi dxi]. While the contribution from recombination is dominated by the monopole term (/4 + ), the lithium anisotropies are dominated by the peculiar velocity term (vb) on most scales. We illustrate this in Figure 4, in which we show the monopole and velocity contributions to the anisotropies in both the standard LCDM model and in a model that has a large optical depth = 10 at z = 500. We chose such a large optical depth in order to suppress the original contribution from decoupling. The figure clearly shows that the anisotropies are dominated by the monopole term for the standard LCDM model for almost all values of l, while the opposite is true for the = 10 model. The new anisotropies are dominated by the monopole term only at very low multipoles, l 20.
Fig. 4 Velocity and temperature contribution to anisotropies for LCDM and for a model with = 10 at z = 500. The curves that approach a finite value at low l are the temperature contributions, and the curves that approach zero at low l describe the velocity contributions.
We can easily explain why the monopole no longer dominates for the lithium contribution. After recombination, the monopole term decays by the free streaming of the photons, while the velocity of the baryons continues to grow as they fall into dark matter potential wells. For a perturbation mode of wavevector k, the monopole term at conformal time after recombination, > rec, is approximately given by
where j0(x) is the spherical Bessel function. Equation (9) shows that the monopole term is small for k( - rec) 1 because of the decay in the Bessel function when its argument is large. Figure 1 shows that the new peak of the visibility function occurs at 500 Mpc, while rec 300 Mpc. We can translate the spatial wavenumber k to angular scale using the conformal distance to the new peak in the visibility function, d = (0 - ) 0. We find that k( - rec) 1.6 × 10-2l, which explains why the monopole term is suppressed for l 60.
While the monopole term decays between recombination and the lithium-scattering surface, the velocity grows, and thus produces anisotropies that are larger than those generated at decoupling in the = 2 case.
The physics of the polarization anisotropies is different from that of the temperature anisotropies. Since polarization is generated by the quadrupole moment, there are two competing effects that need to be considered. On the one hand, the quadrupole anisotropies are small at recombination, since they are suppressed relative to the velocity fluctuations by a factor k , where is the width of the last-scattering surface at recombination (Zaldarriaga & Harari 1995). In the new scenario, the quadrupole is able to grow during the free-streaming period between recombination and z 500. This naturally leads to an increase in the polarization signal. The same effect increases the polarization anisotropies on large scales in models with a substantial optical depth to Thomson scattering after the universe reionizes (Zaldarriaga 1997). On the other hand, due to the nature of resonant-line scattering (Hamilton 1947; Chandrasekhar 1960), only 1/3 of the cross section generates polarization out of this quadrupole, while 2/3 produces unpolarized radiation (E1 = 1/3, E2 = 2/3). Although the quadrupole is bigger at z 500 than at recombination, the newly generated polarization is not as large. For example, Figure 3 shows that even for = 2, the polarization at high multipoles, l 1000, is dominated by the suppressed signal from decoupling.
3.3. Comparison with the Far-Infrared Foreground
The main difficulty in measuring the lithium imprint on the CMB anisotropies is the contamination by the far-infrared background (FIB). There has been no detection to date of the anisotropies in this background, and so we have to rely on theoretical estimates (Haiman & Knox 2000; Knox et al. 2001).
In order to properly combine the contributions from the CMB and FIB anisotropies, we express intensities in terms of the equivalent Rayleigh-Jeans temperature, TRJ (in K). We start by comparing the temperature anisotropies. The total fluctuation amplitude is given by
The ratio between the CMB intensity and the central value for the inferred intensity of the FIB (Fixsen et al. 1998; see the central dot-dashed curve in Fig. 2 of Haiman & Knox 2000) is of order unity for a lithium-scattering redshift z 500:
As noted by Loeb (2001), the temperature fluctuations in the Wien tail translate to intensity fluctuations I (in ergs s -1 cm-2 sr-1 Hz-1) of a much larger contrast,
where we have substituted I(T) exp(-h/kT) and T = 2.725 K (Mather et al. 1999). The anisotropy amplitude shown in Figure 7 depends on , but roughly implies (TRJ/TRJ)CMB 3 × 10-4[500/(1 + z)]. Haiman & Knox (2000) and Knox et al. (2001) estimate (TRJ/TRJ)FIB = 0.050.1. The FIB anisotropies peak at an l of a few hundred, but the peak is very broad. The anisotropies in the FIB are relatively large, since they originate from clustering of sources at low redshifts, z 1.
We conclude that if 50% of the lithium ions recombine at z 500, then
(formula that did not transfer)
Since the CMB contribution is subdominant, it is essential to exploit the different frequency dependence of the FIB and CMB anisotropies in order to subtract the FIB contribution with high precision. This might be possible on small angular scales, at which the temperature anisotropies generated by lithium scattering at different redshifts are uncorrelated, as indicated by Figures 5 and 7. Also, since the FIB is produced by point sources, observations with high angular resolution can resolve the sources and remove them individually. Contamination by emission from Galactic dust is also a potential problem. For measurements of the anisotropies in the FIB, it was proposed to look only in the "cleaner" regions of the sky (Knox et al. 2001), which could greatly reduce the contamination. The feasibility of the proposed measurement will only become clear when more is known about the FIB and the sources that produce it. At this stage, it is fair to say that detecting the lithium signal appears to be very difficult.
Depending on the nature of the sources responsible for the FIB and their luminosity function, it may eventually become possible to resolve most of the FIB through high-resolution observations at different wavelengths. This approach is used, for example, in observational studies of the Sunyaev-Zeldovich effect, in which much of the contribution from discrete foreground sources is subtracted out through deep high-resolution observations at either radio or optical-infrared wavelengths. At the present time, there are no available source counts in the wavelength range that we consider here. Closest in wavelength are source counts from the SCUBA instrument (see, e.g., Borys et al. 1999, Fig. 2). If most of the FIB could be resolved, the task of detecting the effect of lithium would become easier, since the overall level of contamination would be drastically reduced. Future studies of the FIB will determine whether this reduction is feasible.
4. CONCLUSIONS
We have shown that if more than half of the lithium ions recombine by z 500, then the temperature and polarization anisotropies of the CMB would be strongly altered at an observed wavelength of 335 m (see Figs. 2 and 3). For high multipoles, l 10, the change is dominated by two contributions: (1) the Doppler anisotropies induced at the sharp lithium-scattering surface; and (2) the uniform exp suppression of the primary anisotropies that were generated at hydrogen recombination (decoupling). Maps taken at wavelengths that are different by only 10% are expected to have significant differences (see Figs. 7 and 8).
The above signals are superimposed on top of the far infrared background (FIB). Our estimates imply that the lithium imprint on the CMB polarization should be comparable to that provided by the FIB (eq. [18]). Detection is more difficult for the temperature anisotropies (eq. [16]).
The wavelength range that we explored overlaps with the highest frequency channel of the Planck mission (352 m), the Balloon-borne Large-Aperture Sub-millimeter Telescope7 (BLAST), which will have 250, 350, and 500 m channels, and the proposed balloon-borne Explorer of Diffuse Galactic Emissions8 (EDGE), which will survey 1% of the sky in 10 wavelength bands between 230 and 2000 m, with a resolution ranging from 6 to 14 (see Table 1 in Knox et al. 2001).
In order to optimize the detection of the lithium signature on the CMB anisotropies, a new instrument design is required, with multiple narrow bands (/ 0.1) at various wavelengths in the range = 250350 m. The experiment should cover a sufficiently large area of the sky so as to determine reliably the statistics of fluctuations on degree scales. In order to minimize contamination from the FIB, the detector should be sensitive to polarization. For reference, the experiment should also measure the anisotropies at shorter wavelengths, at which the FIB dominates. In order to detect the effect of lithium, high signal-to-noise maps of the primordial CMB should be made for the same region of the sky. Most likely, those maps will become available from future CMB missions such as Planck. A strategy for eliminating the contribution from the brightest FIB sources may also be needed.
The resonant optical depth depends sensitively on the primordial lithium abundance and the recombination history of lithium. More detailed calculations of lithium recombination will be done in a forthcoming paper (P. Stancil et al., in preparation). Detection of the lithium signature will also allow calibration of the primordial lithium abundance, which is a sensitive indicator of the mean value and the clumpiness in the baryon abundance during big bang nucleosynthesis. The lithium abundance in nearby stars is subject to large astrophysical uncertainties (Burles et al. 2001, and references therein). We note that values of the lithium opacity that are higher than the ones we have used are potentially possible. As an extreme example, lithium abundance values as high as X 10-8 were suggested by models of inhomogeneous big bang nucleosynthesis (Applegate & Hogan 1985; Sale & Mathews 1986; Mathews, Alcock, & Fuller 1990),
The lithium signature on the CMB anisotropies is the only direct probe proposed so far of structure in the universe at a redshift z 400500. This redshift marks the beginning of the "dark ages," which end only after the first generation of galaxies form at z 20 (see review by Barkana & Loeb 2001).
7 Available at
http://www.hep.upenn.edu/blast.
8 Available at
http://topweb.gsfc.nasa.gov/.
