Oxygen Pumping: Probing Intergalactic Metals at the Epoch of Reionization

We consider the pumping of the 63.2 mm fine-structure line of neutral O i in the high-redshift intergalactic medium (IGM), in analogy with the Wouthuysen-Field effect for the 21 cm line of cosmic H i. We show that the soft UV background at ∼1300 can affect the population levels, and if a significant fraction of the IGM volume is filled Å with “fossil H ii regions” containing neutral O i, then this can produce a nonnegligible spectral distortion in the cosmic microwave background (CMB). O i from redshift z is seen in emission at mm, and in the range (1 z)63.2 produces a mean spectral distortion of the CMB with y p (10 9 to 3 # 10 )(Z/10 3 Z,)(IUV), where 7 ! z ! 10 Z is the mean metallicity of the IGM and IUV is the UV background at 1300 in units of ergs s 1 Hz 1 cm 2 20 Å 10 sr . A measurement of this signature can trace the metallicity at the end of the dark ages, prior to the completion of cosmic reionization, and is complementary to cosmological 21 cm studies. While future CMB experiments such as Planck could constrain the metallicity to the 10 2 Z, level, specifically designed experiments could potentially achieve a detection. Subject headings: cosmic microwave background — cosmology: theory — intergalactic medium — ISM: abundances The first sources of light that ended the cosmic dark ages are expected to have reionized the intergalactic medium (IGM) and polluted it with metals (e.g., Loeb & Barkana 2001). To use the metal enrichment as a potential probe of the reionization epoch, recent studies have concentrated on the neutral oxygen (O i) produced by the first massive stars (Oh 2002; Basu et al. 2004). The ionization potential of O i is only 0.2 eV higher than that of hydrogen (H i), and the two species are in charge exchange equilibrium. Therefore, oxygen is likely to be highly ionized in regions of the IGM where hydrogen is ionized. However, the recombination time for oxygen (as for hydrogen) is shorter than the Hubble time at , indicating that oxygen z 6 can be neutral even in regions where H has been ionized but where short-lived ionizing sources have turned off, allowing the region to recombine (Oh 2002). Numerical simulations that do not resolve the first generation of “minihalos” find a small volume filling factor of such “fossil” H ii regions (Iliev et al. 2007; McQuinn et al. 2006; Ricotti et al. 2002). However, Oh & Haiman (2003) argued, in a semianalytical model, that minihalos are more susceptible to negative feedback and that they can produce fossil H ii regions that occupy 150% of the volume of the IGM prior to reionization. More generally, the distribution of metals around early galaxies is poorly understood, but they may preferentially occupy denser regions around galaxies, where recombination time is short (Theuns et al. 2002; Miralda-Escudé et al. 2000; Cen & Ostriker 1999). Moderate wind velocities (10–100 km s ) suffice to pollute a significant fraction of the IGM volume, in principle (Haiman 2003), although the metal escape can be hindered by large-scale structures around the small galaxies. In fact, Becker et al. (2006) claim to have found evidence for significant O i absorption in quasar spectra corresponding to highly ionized patches of the IGM at . If correctly interpreted, then the trend in their z 1 6 1 Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104; [email protected], [email protected], [email protected]. 2 Department of Astronomy, Columbia University, New York, NY 10027; [email protected]. 3 Instituto de Fı́sica Teórica, UAM/CSIC, Universidad Autónoma de Madrid, Madrid, Spain. data suggests that O i abundance may even increase at earlier stages of reionization. Previous work has proposed exploiting the scattering of UV photons by O i, and the corresponding absorption features in the spectra of quasars: the O i forest (Oh 2002), analogous to the lower redshift H i Lya forest (e.g., Becker et al. 2006). In the case of H i, another interesting signature from the highredshift IGM is the 21 cm hyperfine-structure line, which is made detectable by UV pumping by the Lya background (the so-called Wouthuysen-Field effect; see Field 1958 or Furlanetto et al. 2006 for a recent review). Here we examine whether a similar effect occurs for O i, and demonstrate that there exist O i lines with the required features: the fine-structure lines of the electronic ground state, 44.1, 63.2, and 145.5 mm, can be pumped by 1300 photons produced by the first stars or black Å holes, via the Baa line of O i. We compute the spectral distortion in the CMB created by this effect, and find that it can be as high as if ZO i at , just prior to reionization, 7 y ∼ 10 z ∼ 7 is ∼10 2.5 Z,. Values for the metal abundance of the order of 10 3 Z, in (slightly increasing with redshift) have z [1, 4] been observed (Schaye et al. 2003), and since there is less than 1 Gyr between and 7, from now on we take ZO i p 10 3 z p 4 Z, as our fiducial value. This distortion could be detectable with future CMB experiments and opens the possibility of performing tomography of the reionization epoch using this effect. In combination with 21 cm studies, it could yield direct measurements of the abundance and spatial distribution of metals in the high-redshift IGM. The basic criteria for a line of a metal species or their 0 ↔ 1 ions to produce an effect analogous to the Wouthuysen-Field pumping of the H i 21 cm line are as follows: (1) abundant metals in the IGM in the required ionization state; (2) the transition at a frequency suitable for detection, with 0 ↔ 1 Einstein coefficients small enough to allow the line to deviate from equilibrium with the CMB; (3) the upper and lower states 4 Metals will likely be dispersed into the IGM and will not be retained inside the shallow gravitational potential wells of the earliest galaxies (Mac Low & Ferrara 1999). Furthermore, any residual oxygen trapped inside galaxies would be either ionized or in dense, optically thick clumps and would not contribute to the signal. L86 HERNÁNDEZ-MONTEAGUDO ET AL. Vol. 660 Fig. 1.—Schematic representation of the transitions of neutral oxygen considered here. Note the analogy with the 21 cm transition of H i. In the 21 cm transition the relevant line corresponds to a hyperfine transition, while for O i it corresponds to a fine-structure transition. The 21 cm line is pumped by H i Lya photons, while the O i line is pumped by O i Baa photons. should be connected via allowed transitions to another state (hereafter called state 2), so that they can be “pumped” in a two-step process; (4) a large enough background flux at the wavelength corresponding to the and l ≈ l 0 ↔ 2 1 ↔ 2 02 12 transitions. In particular, the last criterion imposes the constraint on the wavelength of the UV pumping photons ̊ l 1215 A 02 before reionization, since neutral H i depletes the background at shorter wavelengths (Haiman et al. 2000). We selected oxygen for our study because it can be relatively abundant at high redshifts and because of the similarity of its ionization potential to that of hydrogen. The ground state of neutral oxygen is split into the three fine-structure levels of the outermost electrons in the shell, hereafter denoted as 0, n p 2 1a, and 1b. We found that among the electronic states of oxygen, these are the only ones that satisfy all of the criteria above and give rise to photons observable in the CMB frequency band. The states 0–1a and 1a–1b are connected by magnetic dipolar transitions [O i] at 63.2 mm and 3 3 P r P 2 1 at 145.5 mm, respectively, and the states 0–1b are con3 3 P r P 1 0 nected by an electric quadrupolar transition at 44.1 mm. 3 3 P r P 2 0 We consider only lines involving the 0 state as the lower P2 level for the transition, since the CMB ambient field is practically unable to populate the state and the 145.5 mm line will be P1 suppressed. Since these transitions are forbidden, the spontaneous-emission Einstein coefficients ( , 10 A p 1.34 # 10 44.1 mm , s ) are much 5 5 1 A p 8.91 # 10 A p 1.75 # 10 63.2 mm 145.5 mm smaller than the typical values for electric dipole transitions (∼108 s ), a property shared by the hydrogen 21 cm line with s . 15 1 A p 2.85 # 10 H 21 The states 0 and 1a, 1b are connected to the excited electronic state in the shell (hereafter denoted by 2) by means S n p 3 1 of the absorption of an O i Baa photon with wavelength . A schematic level diagram is shown in ̊ l ≈ l ≈ 1300 A 20 21 Figure 1. In the absence of a UV field, O i is in thermal equilibrium with the CMB and, as shown in Basu et al. (2004), resonant scattering is more important than collisionally induced emission, except at extremely large overdensities. For this transition, we obtain that the collisions become important at overdensities 10. However, if the first stars or black holes generated a UV background at 1300 , then the relative Å populations of the fine-structure states 0 and 1 are modified by the two-step “pumping” transitions and . 0 r 2 r 1 1 r 2 r 0 For simplicity we start by considering only one fine-structure transition and address the combined effect later. In what follows we use the indices i, j to denote the two levels in the fundamental state, with i referring to the lowest one. For example, for the 63.2 mm transition (i, j) corresponds to (0, 1a) (see Fig. 1). The steady state solution for the level population reads UV n P B I g T j ij ij n j , ji p { exp . (1) ( ) UV n P B I A g T i ji ji n ji i S, ji This equation defines the spin temperature . Here is T T S, ji , ji the equivalent temperature of the transition [T , ji { hnji/ i ↔ j kB 231(63.2 mm/lji) K, with kB the Boltzmann constant]; , , and are the Einstein coefficients for spontaneous A B B ji ji ij emission, induced emission and absorption, respectively; UV Pji and denote the UV de-excitation and excitation rates; UV P I ij n denotes the specific intensity at the resonant frequency of the transition; and , , and are the dei ↔ j g p 3 g p 1 g p 5 1a 1b 0 generacy factors. It is useful to define the UV color temperature in terms of the ratio of the UV de-excitation and excitation TUV, ji rates, UV UV P /P { (g /g ) exp ( T /T ), (2) ij ji j i , ji UV, ji which represents the spin temperature reached in the limit of strong pumping. Following Field (1958), these pumping rates can be written as 2 g A c I 2 2i n UV P p A , (3) ji 2j ( ) ( ) 3 g 2hn A j n 2m m 2j 2 g A c I 2 2j n UV P p A . (4) ij 2i ( ) ( ) 3 g 2hn A i n 2m m 2i Here and the subscript denotes evaluation at g p 3 n n p 2 pq , i.e., at the frequency of the transition connecting states p npq and q. The sum over m takes into account the five possible downward transitions from the upper state 2, obtained from the NIST data base. From the definition of the UV excitation and de-excitation rates, it is easy to see that their ratio is proportional to the ratio of the quantity evaluated at two slightly different 2 3 c I /(2hn ) n frequencies: and . It follows then that the color temperature n n 2j 2i can be approximated by T 1 T 2i T p , (5) UV log n / nF n 3 a n n ji s 2j where is proportional to the number of photons with 3 n { I /n n n 5 See http://physics.nist.gov/PhysRefData/ASD/lines_form.html. No. 2, 2007 OXYGEN PUMPING L87 Fig. 2.—Solid lines: Relative departure of the spin temperature from the TS CMB temperature as a function of the background intensity at the Baa frequency of O i. Note that these intensities are within the range of amplitudes required for reionization (∼10 photons per H atom; Haiman et al. 2000). Dashed lines: CMB distortion parameter . In both cases, 63.2 mm y { DI /B (T ) n n CMB thick lines refer to , thin lines to . z p 7 z p 10 frequency n, and is the logarithmic slope a { d log I /d log n s n of the background spectrum near the O i Baa line. We have assumed that . For a different aplog n / nF ≈ log n / nF n n n n 2j 2i proach, see Chuzhoy & Shapiro (2006). If is small log n / nF n n2j and negative then the pumping mechanism will be more effective in the transition than in , and as a result the level i i r 2 j r 2 will be relatively depopulated. In particular, the photons j r i will be seen in emission if , which will generally be T 1 T UV CMB the case since T2i ∼ 10 K k TCMB. The amplitude and shape of the UV photon field at 1300 at the beginning of reionization is uncertain. Unlike at the Å H i Lya frequency of 1215 , however, the high-z IGM should Å be optically thin at 1300 (see discussions of the shape of Å the soft UV background in Haiman et al. 1996, 2000). Therefore, the relevant background at redshift z should reflect the intrinsic spectrum of the dominant sources over the ≈27% redshift range (1 z) ! (1 zsource) ! (1 z)nH i Lyb/nO i Baa p 1.27(1 z). Over the 0.2% fractional difference between n2j and , we then expect a relative decrement of of ∼0.2%(3 n n 2i n as) throughout , or a decrement of order ∼1% for sources nji with . For our calculations, we adopted a fiducial choice a ∼ 2 s of ∼1%, but in practice, our results are insensitive to this value (see below). Given the specific intensity , the steady state solution for In the level population provides the following expression for the spin temperature : TS, ji UV 2 3 ( ) ( ) 1 A /P 1 I c /2hn [ ] ji ji n n T ji , ji p log . ( ) UV 2 3 ( ) ( ) T exp ( T /T ) A /P I c /2hn S, ji UV ji ji n nji