https://orcid.org/0000-0003-3725-6096
ABSTRACT
The excess radio background seen at |${\simeq}0.1\rm{-}10\, {\rm GHz}$| has stimulated much scientific debate in the past years. Recently, it was pointed out that the soft photon emission from accreting primordial black holes may be able to explain this signal. We show that the expected ultraviolet photon emission from these accreting black holes would ionize the universe completely at z > 6 and thus wash out the 21-cm absorption signature at z ≃ 20 as well as be in tension with existing cosmic microwave background anisotropy and average spectral distortion limits. We discuss possible augmentations of the model; however, it seems that an explanation of radio excess by accreting primordial black holes is not well-justified.
1 INTRODUCTION
The detection of a bright radio monopole at ≃0.1–10 GHz (Fixsen et al. 2011; Dowell & Taylor 2018) with an intensity larger than the standard cosmic microwave background (CMB), and known galactic and extragalactic radio sources (Protheroe & Biermann 1996) is one of the outstanding problems in current astrophysics and cosmology. On top of this, the possible detection of an unexpectedly-strong 21-cm absorption feature at z ≃ 20 (Bowman et al. 2018) further adds to this deepening mystery, although recent independent efforts to verify this measurement have resulted in a null detection (Singh et al. 2022). The reader is referred to Singal et al. (2018) for a detailed review of possible explanations for radio excess and future experimental efforts to verify its detection. Most explanations invoke unresolved extragalactic radio contributions, but also galactic contribution could be relevant (Subrahmanyan & Cowsik 2013).
One possible cosmological explanation of the radio excess could be dark matter haloes hosting unresolved radio sources (Holder 2014). This naturally implies that the background is anisotropic, as the haloes are clustered and have finite sizes. However, it was shown that the expected anisotropic signal violates the observed limits unless the radio emitting sources are extended over ≳Mpc scale and are located at redshifts z > 5 (Holder 2014).
Other explanations for radio excess include Comptonized photon injection distortions (Chluba 2015; Bolliet, Chluba & Battye 2021), annihilating axion-like dark matter (Fraser et al. 2018), dark photons (Pospelov et al. 2018; Caputo et al. 2022), supernova explosion of population III stars (Jana, Nath & Biermann 2019), superconducting cosmic strings (Brandenberger, Cyr & Shi 2019), decay of relic neutrinos to sterile neutrinos (Chianese et al. 2019), thermal emission of quark nugget dark matter (Lawson & Zhitnitsky 2019), bright luminous galaxies (Mirocha & Furlanetto 2019), and accreting astrophysical black holes (Ewall-Wice et al. 2018; Ewall-Wice, Chang & Lazio 2020). Many of these works were stimulated by the EDGES measurements and thus simultaneously attempt to explain the large 21-cm absorption feature.
One interesting possibility for testing the presence of an extragalactic radio background proposes to use the up-scattering of the photon field when crossing clusters of galaxies (Holder & Chluba 2021; Lee, Chluba & Holder 2022). This effect, coined radio-SZ effect, is the radio background analogue of the Sunyaev–Zeldovich effect (Zeldovich & Sunyaev 1969), and might be observable at |${\lesssim}3\, {\rm GHz}$| using experiments such as MeerKAT or LOFAR. Along another route, the interaction of cosmic rays with the radio background could produce ultra-high-energy photons from pair-production that could test the origin of the radio excess (Gelmini, Kalashev & Semikoz 2022).
Recently, Mittal & Kulkarni (2022) studied the possibility of explaining the radio monopole with a population of accreting supermassive primordial black holes (PBH) with masses |$M=10^5\rm{-}10^{12}{\rm M}_{\odot }$|. In this, it is crucial to have a relation between the radio and X-ray luminosity of the PBHs. Previous works (Ricotti, Ostriker & Mack 2008; Ali-Haïmoud & Kamionkowski 2017; Hektor et al. 2018; Mena et al. 2019; Yang 2021) have studied accretion on to PBHs (though they restrict themselves to |$M\lesssim 10^4{\rm M}_{\odot }$|), and derived constraints on their abundance using the CMB anisotropy and global 21-cm signature. These limits were derived by deducing the X-ray luminosity under the assumptions that the accretion process is spherical, which adds some level of uncertainty. Instead, the authors in Mittal & Kulkarni (2022) use the parametric relation between radio and X-ray luminosity of Lusso et al. (2010) observed at low redshifts. Using well motivated astrophysical parameters and a reasonable estimate of PBH abundance, it was shown in Mittal & Kulkarni (2022) that radio emission from these PBHs could explain the radio excess of Fixsen et al. (2011), Dowell & Taylor (2018).
Accretion on to black holes will not only result in radio and X-ray emission but also UV/optical emission (Shakura & Sunyaev 1973). Energetic photons with E > 13.6 eV can ionize neutral hydrogen and heat the baryonic gas. Therefore, one has to study the possibility that the over-abundance of ionizing photons can reionize the universe much before z ≃ 6. This would also heat the gas sufficiently such that we may not see any 21-cm absorption signature, which can be computed using standard methods (Pritchard & Loeb 2012).
In this paper, we use a parametric relation between UV and X-ray luminosity (Lusso et al. 2015) similar to the relation used in Mittal & Kulkarni (2022) to study the effect of UV emission from accreting PBHs on the ionization and thermal history of the Universe. We show that the fiducial parameters used in Mittal & Kulkarni (2022) predict too many energetic photons which can ionize the Universe before z ≃ 6 and thereby wash out any 21-cm absorption signal at z ≃ 20. In addition, the changes to the ionization history induce modifications to the CMB temperature and polarization anisotropies that are ruled out by Planck (Planck Collaboration et al. 2016). Finally, we highlight that a large part to the required PBH population has already been ruled out by COBE/FIRAS . Therefore, an explanation of the radio excess by accreting PBHs alone seems to run into significant constraints. Using a simple conservative estimate, we show that the abundance of PBHs has to be orders of magnitude smaller than what has been assumed in Mittal & Kulkarni (2022).
2 PHOTON EMISSION FROM ACCRETING PBHS
2.1 Radio background from PBHs
We illustrate the build-up of radio background as a function of redshift in Fig. 1. The authors in Mittal & Kulkarni (2022) argue that by choosing fduty, λ, fBH, X, and keeping fPBH unchanged, it is possible to make.T|1.4GHz ≃ 0.5K, which can explain the radio excess of Fixsen et al. (2011), Dowell & Taylor (2018). In Fig. 2, we show the expected 21-cm absorption signal from accreting PBHs (see Section 2.3 for details of the 21-cm modelling). One can see that with a further boost factor of 2–3, it may indeed be possible to explain EDGES result (Bowman et al. 2018). However, we are going to show that the associated UV photon emission, assuming the fiducial values is enough to ionize the Universe much before reionization. This effect was ignored in the computation of the 21-cm signal but does modify it significantly.
Comoving intensity of radio background as a function of redshift at 1.4 GHz as the PBHs accrete and the background builds up. We have converted the comoving intensity to temperature using equation (8).
The 21-cm distortion as a function of redshift for various values of fPBH. The fiducial parameters are fBH, X = λ = 0.1 and fduty = 0.01. We have ignored any modification to thermal history of Universe such as changes in electron fraction and matter temperature. We also show the case where we fix fPBH to 10−4 but tune fBH, X, λ, and fduty such that radio luminosity is boosted by a factor of 20. With a further boost of a factor 2–3, the parameters could help explain the ARCADE excess.
2.2 UV luminosity from PBHs
2.3 Global 21-cm signal modelling
Finally, the collisional coupling coefficient xc can be calculated using the recombination history from Recfast++ (Chluba & Thomas 2011), and spin-exchange rate coefficients tabulated in literature: Zygelman (2005) and Furlanetto et al. (2006) for neutral hydrogen collisions, Furlanetto & Furlanetto (2007a) for electron-hydrogen collisions, and Furlanetto & Furlanetto (2007b) for proton-hydrogen collisions. The rates are interpolated for intermediate values of TM on a log–log scale.
To also account for the possible modifications of the background photon field at low frequencies due to the PBHs emission in equation (17), we replace TCMB with the brightness temperature evaluated at the 21-cm rest frame frequency (see Fig. 1). This allows us to estimate the net 21-cm signal with respect to the enhanced background.
2.4 Reionization model
For our purposes, we use a fiducial set of parameters (Nion, f⋆, fesc, fα, fX) = (40000, 0.1, 0.1, 1.0, 1.0). All values but the one for Nion are commonly used in the literature (see, e.g. Furlanetto et al. 2006; Pritchard & Loeb 2012; Cohen et al. 2017). For Nion, a higher value was adopted since with the (physically-motivated) extra factors of (1 − xH ii) and (fHe − xHe ii), reionization process did not complete at z ≲ 6 in the standard scenario. However, this part of the evolution does not affect the results discussed here significantly.
3 MODIFICATION TO IONIZATION AND THERMAL HISTORY OF UNIVERSE
Baryon density (in black) and ionizing photon number density (red) which is |$\dot{N}(z)\Delta t$| with |$\Delta t=\frac{1}{(1+z)H(z)}$|. The parameters used are for fPBH = 10−4 with fBH, X = λ = 0.1, fduty = 0.01.
Evolution of xe as a function of redshift for a few different fPBH.
In Fig. 5, we plot the temperature of baryonic gas for fPBH as shown in Fig. 4 using CosmoTherm (Chluba & Sunyaev 2012). There is big deviation of gas temperature from CMB at z > 100 for fPBH = 10−4, which is expected to wash out the 21-cm absorption signal. For smaller fPBH, adiabatic cooling plays an important part and gas temperature falls below CMB temperature. We also plot the 21-cm distortion temperature as a function of redshift in Fig. 6. For fPBH = 10−4 and even for 10−6, the absorption feature is completely washed out at z ≈ 10–20. As mentioned in Section 2.3, the WF coupling could be induced earlier due the Lyα contribution from the PBHs, which has been neglected in our calculations. This would not have any effect at redshifts z > 100 since collisional coupling to TM is strong enough. For lower redshifts, the effect in case of fPBH = 10−4 would be to further strengthen the emission signal. In the case of fPBH = 10−6, the absorption signal in z ≈ 50–100 range will be more pronounced, but there would still be an emission signal at z ≃ 20. We can obtain a conservative constraint on fPBH by requiring that we see 21-cm signal in absorption (i.e TM < TCMB) at z ≃ 20. In that case, constraints on fPBH turns out to be ≲10−6. This number can be further tightened by using detailed astrophysical modelling. Therefore, we see that fPBH = 10−4, as used in Mittal & Kulkarni (2022) to explain the radio excess today may run into severe constraints when the UV photon emission from PBHs are taken into account.
Evolution of baryon temperature as a function of redshift for a few fPBH as in Fig. 4.
21-cm distortion in temperature for the cases in figures above including the radio background from the accreting PBH themselves.
3.1 Limits from CMB anisotropies
Changes to the ionization history affect the CMB temperature and polarization anisotropies (Peebles, Seager & Hu 2000; Chen & Kamionkowski 2004). Since the latter have been accurately measured using Planck (Planck Collaboration et al. 2014, 2016, 2020), one can directly convert the changes to the ionization history into a limit on fPBH by using an xe principal component projection method (Farhang, Bond & Chluba 2012; Farhang et al. 2013; Hart & Chluba 2020).
We refer the reader to Hart & Chluba (2020) for details of the projection method, but in brief, given the PBH model parameters, we can compute ξ(z) = Δxe/xe with respect to the standard ionization history. The ξ(z) response can then be projected on to the first three xe-modes, Ei(z) to obtain the relevant mode amplitudes2|$\mu _i=\int E_i(z)\, \xi (z)\, {\rm d}z$|. Assuming that the responses in the μi are linear3 in fPBH, and using the Planck constraints from Hart & Chluba (2020), we then find fPBH ≲ 3 × 10−6 (95 per cent c.l.). This limit falls into a similar regime as the one obtained in Ali-Haïmoud & Kamionkowski (2017) for PBHs with |$M\lesssim 10^4{\rm M}_{\odot }$|. Performing a simple extrapolation of the constraint contour in fig. 14 of Ali-Haïmoud & Kamionkowski (2017) to |$M = 10^5{\rm M}_{\odot }$|, we see that the weakest constraint from collisional ionization is also of the order of fPBH ≈ 10−6. Therefore, our calculations rules out the model proposed in Mittal et al. (2022).
We should point out that we actually constrain the total UV luminosity from black holes, which is proportional to the product fduty fX λ fPBH, only when we choose a particular value of astrophysical parameters, we obtain a constraint on fPBH. We remind the reader that Mittal & Kulkarni (2022) fixed fPBH at 10−4, and boosted the combination of fduty, fXλ, fPBH by a factor of 20 to explain the ARCADE excess. According to the parametric relation used in Mittal & Kulkarni (2022) and in this work, the radio emissivity is proportional to X-ray luminosity, which in turn is proportional UV luminosity. Therefore, if we fix fPBH and choose the value of astrophysical parameters to tune radio emissivity to match the radio excess observation we still run into strong CMB anisotropy constraints.
In these calculations, we have assumed that the UV photons escape to the intergalactic medium (IGM) and lead to uniform ionization and heating of the universe. If instead we are able to trap these photons locally close to black holes, it may be possible to avoid CMB anisotropies constraints. The most energetic X-ray photons can still escape to the IGM and propagate large distance before ionizing and heating the medium. We plan to perform a detailed calculation in a future paper. Alternatively, the PBH luminosity may not follow the parametric relation used in this calculation and may be radio-loud by at least a factor of hundred. This may be a possible explanation for ARCADE and EDGES excess without running in the CMB anisotropy constraints. However, there are stringent constraints on the PBH abundance from CMB spectral distortions, as we show now.
3.2 Limits from COBE/FIRAS
Allowed Aζ from y and μ-distortion constraint (Fixsen et al. 1996).
We show the constraints on the abundance of PBHs from CMB spectral distortions in Fig. 8. We see that the μ-distortion constraint essentially excludes any PBHs in the mass range of |$10^4\rm{-}10^{12}{\rm M}_{\odot }$|. The large density fluctuation forms in the exponential tail of the assumed Gaussian initial power spectrum. Due to the strong μ-distortion limit, the width of Gaussian is reduced, which renders high-density fluctuations extremely unlikely.
Constraint on fPBH from y and μ-distortion constraints (Fixsen et al. 1996) as a function of PBH mass. The excluded region is shown in filled lines.
The constraints are model-dependent and do vary if the initial conditions of the universe are non-Gaussian. In the case, the probability for PBH formation at a given level of the curvature perturbation can be significantly enhanced over the Gaussian case. Depending on these details, one can evade the CMB spectral distortion constraints (Nakama, Suyama & Yokoyama 2016) or obtain constraints, which are orders of magnitude stronger than the CMB anisotropy limits obtained in this paper (Nakama, Carr & Silk 2018). There is even a possibility to start with smaller mass PBHs (|${\lesssim}10^4{\rm M}_{\odot }$|) which can then accrete and become supermassive at the redshifts that we are interested in. This regime of PBH masses could be directly constrained by future CMB spectral distortion measurements (Chluba et al. 2021), which promise improved limits on μ by many orders of magnitude.
We also mention the direct y-distortion constraint. The late heating of the Universe by the X-ray and UV photons that lead to early reionization will exceed the COBE/FIRAS limit of y ≲ 1.5 × 10−5 (95 per cent c.l.) once fPBH ≳ 3 × 10−4. In a similar way as the μ-distortion, the y-distortion limit can furthermore be used to place a constraint on Aζ (Chluba et al. 2012a). Looking at Fig. 7, we find that one can obtain a stronger limit for PBHs with mass |${\gtrsim}10^{13}{\rm M}_{\odot }$| from y-distortion. These constraints are orders of magnitude stronger than other constraints in this mass range (Carr, Kühnel & Visinelli 2021). Aside from the fact that we have never encountered BHs of this size, this is reassuring.
4 DISCUSSION AND CONCLUSIONS
In this paper, we have used the empirical relations between radio, X-ray and UV luminosities to show that it is unlikely that accretion on PBHs is able to explain the observed radio excess seen by Fixsen et al. (2011) and Dowell & Taylor (2018). The required abundance of PBHs that can explain the radio excess results in the emission of too many ionizing photons, which can ionize the universe much before reionization, which can be ruled out by Planck (see Section 3.1). Ionization of neutral hydrogen also results in gas heating, which can raise the temperature of gas to ≈104K. We obtain strong CMB anisotropy and spectral distortions constraints on PBH abundance, which are much lower than the assumed fPBH = 10−4 in Mittal & Kulkarni (2022), which would reduce the radio emissivity and the corresponding radio background as seen today.
Previously, the authors in Hektor et al. (2018), Mena et al. (2019), Yang (2021) have obtained constraints on accreting PBHs by studying their effect on 21-cm signal in the mass range |$M\lesssim 10^4{\rm M}_{\odot }$|. They computed the luminosity of black holes assuming a theoretical model of accretion on to the black holes. However, we do not use any such model, but use the empirical relation between luminosity at different frequency bands. This relation is assumed to hold at all redshifts. Radio emission from accreting astrophysical black holes, their implication in the context of EDGES result (Bowman et al. 2018) and impact of UV and X-ray emission on reionization was carried out in Ewall-Wice et al. (2018) [see also Ewall-Wice et al. (2020)]. As opposed to primordial black holes, astrophysical black holes form only at z ≲ 30, and accretion was assumed to stop by z ≃ 15 in their work.
In comparison, the primordial black holes can accrete over a much broader range of redshifts. Also in the case of astrophysical black holes, it is assumed that only a fraction (fBH, esc) of ionizing photons is able to escape to intergalactic medium, which can then ionize neutral hydrogen. Typically the value of fBH, esc is within 0.01–0.1, but it can be highly uncertain (Ma et al. 2015). This effectively reduces the UV luminosity of astrophysical black holes. However, no such criteria exists for primordial black holes and no such factors of fBH, esc are assumed while deriving the constraints on PBH abundance in the aforementioned works. Therefore, we expect to find stronger constraints on the abundance of PBHs as compared to astrophysical black holes for same intrinsic UV luminosity.
While we obtain a conservative estimate on abundance of supermassive PBHs – the primary motivation for our work – one can obtain more accurate constraints on fPBH with detailed calculations of ionization history and 21-cm signal at z ≃ 20 including astrophysical Lyα and X-ray modelling. We defer this work to the future, expecting that the general conclusion remains.
Since, as we argued, for extremely radio-loud PBHs, it may still be possible to evade the CMB anisotropy constraint, it would be very important to study the physics of the atmospheres of the PBHs in more detail. In addition, future CMB spectral distortion limits in combination with astrophysical limits could help close existing loopholes that could lead to an early formation of super-massive PBHs at z ≳ 100–200.
ACKNOWLEDGEMENTS
SKA would like to thank Shikhar Mittal, Girish Kulkarni, and Rishi Khatri for discussions. This work was supported by the ERC Consolidator Grant CMBSPEC (No. 725456). JC was furthermore supported by the Royal Society as a Royal Society University Research Fellow at the University of Manchester, UK (No. URF/R/191023).
DATA AVAILABILITY
The data underlying in this article are available in this article.
Footnotes
We would like to clarify that ν2keV and ν2500Å; corresponds to the frequency at the corresponding energy or wavelength and there is no additional conversion factor involved. Same applies for |$L_{2 \rm keV}$| and L2500 Å, which is the luminosity per frequency ν corresponding to 2keV/2500 Å;.
For fPBH = 10−6, we obtain μ1 ≈ 0.051, μ2 ≈ −0.026, and μ3 ≈ 0.170.
We confirmed this statment for fPBH ≲ few × 10−6.
