A&A 425, 9-14 (2004)
E. Elfgren 1 - F.-X. Désert 2
1 - Department of Physics, Luleå University of Technology, 971 87 Luleå, Sweden
2 - Laboratoire d'Astrophysique, Observatoire de Grenoble, BP 53, 414 rue de la piscine, 38041 Grenoble Cedex 9, France
Received 6 October 2003 / Accepted 13 May 2004
The possibility that population III stars have reionized the Universe at redshifts greater than 6 has recently gained momentum with WMAP polarization results. Here we analyse the role of early dust produced by these stars and ejected into the intergalactic medium. We show that this dust, heated by the radiation from the same population III stars, produces a submillimetre excess. The electromagnetic spectrum of this excess could account for a significant fraction of the FIRAS (Far Infrared Absolute Spectrophotometer) cosmic far infrared background above 700 micron. This spectrum, a primary anisotropy () spectrum times the dust emissivity law, peaking in the submillimetre domain around 750 micron, is generic and does not depend on other detailed dust properties. Arcminute-scale anisotropies, coming from inhomogeneities in this early dust, could be detected by future submillimetre experiments such as Planck HFI.
Key words: cosmology: cosmic microwave background - cosmology: early Universe
More accurate measurements of the cosmic microwave background (CMB) implies a need for a better understanding of the different foregrounds. We study the impact of dust in the very early universe 5<z<15. WMAP data on the CMB polarization, Kogut et al. (2003) provides a strong evidence for a rather large Thomson opacity during the reionization of the Universe: . Although the mechanism of producing such an opacity is not fully understood, Cen (2003,2002) has shown that early, massive population-III (Pop III) stars could ionize the Universe within 5<z<15 (see Figs. 1 and 2). Adopting this hypothesis, we discuss the role and observability of the dust that is produced by the Pop III stars. As we can only conjecture about the physical properties and the abundance of this early dust, we adopt a simple dust grain model with parameters deduced from the Milky Way situation. The dust production is simply linked to the ionizing photon production by the stars through their thermal nuclear reactions. The low potential well of the small pre-galactic halos allows the ejected dust to be widely spread in the intergalactic medium. The ionizing and visible photons from the same Pop III stars heat this dust. There are no direct measurements of this dust, but by means of other results the amount of dust can be estimated. A similar study has been done for a later epoch of the universe, in which data are more readily available, Pei et al. (1999). We use a cosmology with , where , and h = 0.72 as advocated by WMAP, Spergel et al. (2003), using WMAP data in combination with large scale structure observations (2dFGRS + Lyman ). Furthermore, since the universe is matter-dominated. We relate all cosmological parameters to their measurement today so that they have their present-day values throughout our calculations.
We now proceed to compute the abundance and the temperature of this dust. Consequences on the CMB distortions are then to be discussed.
|Figure 1: Total number of ionizing photons produced from Pop III stars per baryon, cf. (Cen 2002, Fig. 14). The dotted line represents a simplified model with a constant photon production, from z=16, of 8 per unit z per baryon. The results are similar.|
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|Figure 2: Production rate of ionizing photons from Pop III stars per baryon, . The odd form between each integer z is not physical but are due to the fact that the redshift z is a nonlinear function of time.|
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Here we assume the dust properties to be similar to what is observed in our galaxy.
we suppose spherical dust grains with radius m and density
The absorption cross section,
between photons and dust can be written as
In the submm and far IR range, the spectral index is constant, and with Q0 = 0.0088 the assumed opacity agrees well with measurements by FIRAS on cirrus clouds in our galaxy, cf. Fixsen et al. (1998); Boulanger et al. (1996); Lagache et al. (1999). In the visible and UV region, the cross section is independent of the frequency because . In the submm region, the cross section is proportional to the mass of the grain.
In order to evaluate the significance of the dust during the reionization, we calculate the amount
of dust present in the universe at a given time.
The co-moving relative dust density is
is the dust density, z is the red-shift,
is the critical density
(H0 and G are Hubble's and Newton's constants, respectively).
The co-moving relative dust density as measured today evolves as:
The Pop III stars produce enough photons for the reionization while
burning H and thus forming metals (Li and higher). These metals are released in
supernovae explosions at the end of the stars short lives (1 Myr),
whereafter they clump together to form dust, Nozawa et al. (2003).
Knowing the production rate of ionizing photons to be
(Fig. 2), we can calculate the total photon energy released from the Pop III stars.
This can be done by supposing that each photon has an effective energy of
is the spectrum of a star with temperature T*.
The energy of the non-ionizing photons is included through
(u is the energy from the star).
A Pop III star has
K (Shioya et al. 2002, p. 9) which gives
Note that for other reasonable star temperatures,
does not vary significantly,
Hence, the total Pop III photon energy production is
per baryon per unit z.
For each consumed nucleon, we assume that a nuclear energy of Er = 7 MeV is released as radiation,
which means that the nucleon consumption rate is
nucleons per baryon per unit z.
is the fraction of the consumed baryon mass that becomes interstellar dust,
(some of the metal atoms will remain with the core after the SN explosion,
some will stay in the close vicinity of the SN and some will never clump together to form dust)
the co-moving dust production rate will be
Solving Eq. (3) gives the dust density evolution
|Figure 3: The co-moving relative dust density evolution , for . The minima at z=6 and 9 for Gyr is due to the fact that is not a constant time interval.|
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If we suppose that most of the metals were ejected as dust (not as gas)
the metallicity comes from the dust grains.
The metallicity is directly obtained through the produced dust. By letting
Gyr is good enough) we find the metallicity:
There are not much metallicity data available for z>5. Metal poor stars in our galaxy are one point of reference, absorption lines in the Ly spectrum from quasars are another one. The lowest metallicities found in stars in the Milky Way are , Depagne et al. (2002). The Ly forest suggests (Songaila & Cowie 2002, Fig. 13) that for assuming that [Fe/H as suggested by (VandenBerg et al. 2000, page 432). This indicates that . However, this might be lower than the actual value, cf. (Pettini et al. 1997, Fig. 4).
In heavy stars, virtually all the helium is consumed, producing metals. For simplicity (and lack of data), we assume that all the ejected metals clump to form dust, . This means that will almost entirely depend on the dust ejection rate in the supernova explosion. In Iwamoto et al. (1998) a detected hypernova of mass seems to have . Furthermore, according to a dust production model by Nozawa et al. (2003), . At the same time, some of the stars will become black holes, not ejecting any metals, Heger & Woosley (2002), decreasing . Currently this decrease is largely unknown.
In summary, the mass fraction of the produced metals in the Pop III stars, having become interstellar dust, should be around . In the following we use the more conservative , in agreement with the Ly forest measurements, unless otherwise stated.
With our model for the dust density evolution, we want to calculate the opacity of the dust, as seen by the CMB. This will tell us how much the CMB spectrum is altered by the passage through the dust.
The dust opacity is given by
The resulting opacity can be seen in Fig. 4. We note that the opacity is small, . The smooth knee is due to the change of at the redshifted , see Sect. 2, but this is not in the spectral range of the CMB. The differential opacity d is plotted in Fig. 5 for mm. We see that with a short dust lifetime, the dust differential opacity falls off almost immediately (in terms of z). However, for longer lifetimes, the early dust could still play a certain role for z<3. This could eventually contribute to dimming of distant objects. We also note the impact of the expansion of the universe in decreasing the dust density and thus the opacity. This is why the increase in Fig. 1, at , is not apparent in the opacity, Fig. 4. Furthermore, the submillimetre effective dust opacity follows a emissivity law.
|Figure 4: Opacity with dust evolution taken into account.|
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|Figure 5: The differential opacity d at mm for different dust lifetimes.|
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However, in our calculations we use the exact Eqs. (11) and (12), while Eq. (14) can be used as a cross-check.
The absorbed power density, P* from the radiation of Pop III stars peaks in the
UV-region and can be approximated by
The energy density of the ionizing photons are compared to the CMB in Fig. 6.
The star energy density is much less
than the CMB energy density at this epoch, and the curve resembles the accumulated
photons in Fig. 1.
Hence, the dust temperature closely follows the CMB temperature, see Fig. 7 and
|Figure 6: Energy density of ionizing photons compared to , where is Stefan-Boltzmann's constant.|
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|Figure 7: The dust temperature is plotted against the CMB temperature with the relative quatity .|
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In Fig. 8, the excess intensity is plotted along with the extragalactic background measured by FIRAS, Fixsen et al. (1998); Lagache et al. (1999); Puget et al. (1996). Depending on the dust destruction rate (parametrized by the dust lifetime ), the computed early dust background can be an important part of the observed background from 400 m up to the mm wave-length. The exact position of will only slightly displace the spectrum, leaving the magnitude unchanged. Most of the far IR background can now be explained by a population of z=0 to z=3 luminous IR galaxies, Gispert et al. (2000). A fraction of the submillimetre part of this background could arise from larger redshift dust emission as suggested by Fig. 8.
|Figure 8: Comparison of the modeled intensity for the early dust emission in excess of the CMB with the observed FIRAS spectrum (dashed red curve) of the cosmic far IR background as detailed by Lagache et al. (1999).|
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In order to check our results, we calculate the co-moving luminosity density of the dust in the submm region and compare it with (Gispert et al. 2000, Fig. 4). We find them compatible.
Just like the Thomson scattering during reionization, early dust will also tend to erase the primordial anisotropies in the CMB. However, due to the much smaller dust opacity (compare and ), this effect will be negligible.
The early dust will also introduce a new type of secondary anisotropies with a typical size of a dark matter filament. Here, we only estimate the order of magnitude of this effect. If the co-moving size of the dark matter filament is L, the angular size is Mpc) arcminutes at z=10which corresponds to multipole number Mpc). Fortunately, this region in -space does not contain any primordial fluctuations because of the Silk damping. However, there are other foregrounds in the same region, see Aghanim et al. (2000). If we suppose a contrast of 10% in the dust intensity between dark matter filaments and the void, we obtain values of (for mm, and Gyr). These anisotropies, pending more accurate calculations, clearly are in the range of expected arcminute secondary anisotropies from other effects. They could be detected by Planck HFI (High Frequency Instrument), Lamarre et al. (2003) and FIRAS-II type of instrument, Fixsen & Mather (2002).
The results of these calculations depend only very weakly on the precise dust model assumptions. We have also tried a different (but similar) shape of the ionizing photon production, Fig. 1, and found that the results do not vary significantly.
Very little is known about the universe during the reionization epoch. Nevertheless, there are several parameters that could be calculated more accurately.
The two most important parameters in the present model are the dust lifetime, and the mass fraction of the produced metals that are ejected as interstellar dust, . The dust lifetime could be determined more precisely by making 3D simulations of the dust production in combination with structure formation. The simulations would also give the inhomogeneous dust density evolution. The result would be a better estimate of the aforementioned secondary anisotropies caused by the variations in the dust opacity. A more refined dust grain model, using e.g. a distribution of grain sizes would also be more realistic. If the dust is long-lived, it could also have a certain impact on measurements in the optical and UV region. Finally, we note that most of the results are proportional to the dust density and thus to . To evaluate more precisely, we need a better understanding of the typical properties of the first generation of stars, see Sect. 3.1, which is currently much debated.