Possible Wormhole Candidates in Active Galactic Nuclei

Abstract

The hypothesis is considered that the active galactic nuclei (AGNs) are wormhole (WH) mouths rather than supermassive black holes (SMBHs). We study the difference in the physical properties of such objects from those of AGNs with SMBH, as well as the the corresponding difference in observational data. Firstly, the radiative efficiency for some types of WHs (both static and rotating) can be significantly larger than the theoretical maximal value for the Kerr SMBHs. A number of AGNs is presented, for which the observational data can be interpreted as the result of the presence of WHs in them. Secondly, a sufficiently strong gamma radiation with a characteristic spectrum noticeably differing from that of AGNs jets, can be emitted from a static WH as a result of a collision of accreting flows of matter inside the WH.

1. Introduction

In recent years, an interesting hypothesis has been proposed that the active galactic nuclei (AGNs) in the centers of active galaxies are not supermassive black holes (SMBHs), but mouths of primordial macroscopic wormholes (WHs) [1,2,3,4]. This can lead to serious differences in the observational manifestations of such objects from AGNs with SMBHs.

2. Radiative Efficiency of AGNs with WHs

In considering AGNs, one uses such an important parameter as the radiative efficiency, defined as $\epsilon =L_{bol}/\dot{M}{c}^2$, where $L_{bol}$ is the bolometric luminosity of AGN, $\dot{M}$ is the accretion rate, and c is the speed of light. In the case where the SMBH is located in the center of the AGN, $\epsilon$ in a special way depends on the spin (dimensionless angular momentum) of the SMBH $a_{*}=cJ/G{M}_{BH}^2$, where J is the angular momentum and $M_{BH}$ is the mass of the SMBH [5]. Additionally, in particular, the maximum possible value is $\epsilon \approx 0.324$ (at $a_{*}\approx 0.998$) [6].

It was shown in Harko et al. [7], Lobo [8] that, if, instead of the SMBH in the center of the AGN is placed a traversable, rotating WH of the Teo type [9], and the accretion in the form of a geometrically thin, optically thick accretion disk is considered, then the resulting picture will be quite different from the case of SMBH. For example, the radius of the innermost stable circular orbit $R_{ISCO}$, which, in the case of the SMBH, is highly sensitive to the spin and it varies within the range of $G{M}_{BH}/c^2<R_{ISCO}<6G{M}_{BH}/c^2$ (for $a_{*}\ge 0$) [5], in the case of WH, does not depend on the spin and it is equal to the radius $r_{WH}$ of the mouth of the WH (for all wormholes in this paper we take $r_{WH}\approx 2G{M}_{WH}/c^2$). It is especially important that the radiative efficiency $\epsilon$ is also practically independent of spin and equal to about 0.5 (see

Table 1. The results of estimations of radiative efficiency for six popular models (see Section 3). Mass is expressed in $log(M_{BH}/M_{\odot })$, luminosity in $log\left(L_{bol}\right)$, $L_{bol}$ in erg/s, i—in degrees, $l_E$—Eddington ratio.

Object	${\mathit{M}}_{\mathit{BH}}$	i	${\mathit{L}}_{\mathit{bol}}$	${\mathit{l}}_{\mathit{E}}$	${\mathit{\epsilon }}_1$	${\mathit{\epsilon }}_2$	${\mathit{\epsilon }}_3$	${\mathit{\epsilon }}_4$	${\mathit{\epsilon }}_5$	${\mathit{\epsilon }}_6$
NGC 7213	${7.88}_{-0.18}^{+0.13}$	21	44.3	${0.018}_{-0.004}^{+0.009}$	${0.448}_{-0.149}^{+0.149}$	${0.634}_{-0.210}^{+0.212}$	${0.437}_{-0.145}^{+0.146}$	${0.440}_{-0.146}^{+0.146}$	${0.437}_{-0.132}^{+0.128}$	${0.740}_{-0.245}^{+0.247}$
PG 1302-102	${8.90}_{-0.50}^{+0.50}$	32	46.33	${0.179}_{-0.122}^{+0.388}$	${0.397}_{-0.272}^{+0.853}$	${0.352}_{-0.241}^{+0.758}$	${0.242}_{-0.165}^{+0.525}$	${0.244}_{-0.167}^{+0.528}$	${0.179}_{-0.115}^{+0.319}$	${0.411}_{-0.281}^{+0.889}$
Mrk 877	${8.79}_{-0.28}^{+0.15}$	20	45.33	${0.023}_{-0.007}^{+0.021}$	${1.140}_{-0.544}^{+0.460}$	${1.190}_{-0.566}^{+0.490}$	${0.819}_{-0.389}^{+0.341}$	${0.824}_{-0.391}^{+0.336}$	${0.635}_{-0.277}^{+0.228}$	${1.390}_{-0.661}^{+0.570}$
Mrk 6	${8.13}_{-0.43}^{+0.04}$	26	44.56	${0.018}_{-0.001}^{+0.031}$	${0.569}_{-0.360}^{+0.049}$	${0.734}_{-0.464}^{+0.064}$	${0.506}_{-0.320}^{+0.044}$	${0.509}_{-0.322}^{+0.044}$	${0.71}_{-0.277}^{+0.036}$	${0.858}_{-0.542}^{+0.074}$
UGC 3973	${7.85}_{-0.23}^{+0.15}$	19	44.31	${0.019}_{-0.006}^{+0.014}$	${0.426}_{-0.175}^{+0.175}$	${0.601}_{-0.247}^{+0.248}$	${0.414}_{-0.170}^{+0.171}$	${0.417}_{-0.172}^{+0.171}$	${0.417}_{-0.157}^{+0.150}$	${0.702}_{-0.289}^{+0.289}$
Mrk 1018	8.60	45	44.90	0.013	0.785	0.913	0.629	0.633	0.517	1.070
Mrk 1383	${8.97}_{-0.28}^{+0.12}$	30	45.78	${0.043}_{-0.010}^{+0.039}$	${0.906}_{-0.431}^{+0.284}$	${0.870}_{-0.413}^{+0.280}$	${0.600}_{-0.285}^{+0.190}$	${0.603}_{-0.286}^{+0.193}$	${0.440}_{-0.192}^{+0.122}$	${1.020}_{-0.487}^{+0.320}$
Mrk 876	${8.81}_{-0.21}^{+0.14}$	27	45.81	${0.067}_{-0.018}^{+0.041}$	${0.632}_{-0.243}^{+0.240}$	${0.604}_{-0.232}^{+0.230}$	${0.416}_{-0.159}^{+0.158}$	${0.419}_{-0.161}^{+0.159}$	${0.317}_{-0.111}^{+0.106}$	${0.705}_{-0.270}^{+0.269}$

from Harko et al. [7]). It should be noted that this is a fairly significant difference, which is detectable in principle by the existing observational methods.

3. Estimations of Radiative Efficiency

We estimated the value of the radiative efficiency $\epsilon$ from observational data for a number of active galaxies. The list contains 112 Seyfert galaxies of the first, second and intermediate types, with the Eddington ratio $l_E=L_{bol}/L_{Edd}$ ($L_{Edd}=1.5\times {10}^{38}{M}_{BH}/M_{\odot }$ is the Eddington luminosity) lying within the range of $0.01<l_E<0.3$, which allows for us to use a model of a geometrically thin, optically thick accretion disk.

The masses $M_{BH}$, the bolometric luminosities $L_{bol}$, and the angles between the normal to the plane of the accretion disk and the line of sight i were taken from Marin [10].

The estimations was carried out using six popular models that were taken from the literature.

• Du et al. [11]: ${\mu }^{3/2}{l}_E=0.201{\left(\frac{L_{5100}}{{10}^{44}}\right)}^{1.5}{M}_8^{-2}\epsilon \left(a\right)$.
• Trakhtenbrot [12]: ${\mu }^{3/2}{L}_{bol}=1.37\times {10}^{47}{\left(\frac{\lambda L_{\lambda }}{{10}^{45}}\right)}^{3/2}{\left(\frac{\lambda }{5100}\right)}^2{M}_8^{-1}\epsilon \left(a\right),\lambda L_{\lambda }=L_{opt},\lambda =4400\AA$.
• Davis and Laor [13]: ${\mu }^{3/2}{L}_{bol}=1.48\times {10}^{47}{\left(\frac{L_{opt}}{{10}^{45}}\right)}^{1.5}{M}_8^{-1}\epsilon \left(a\right)$.
• Simple Newtonian accretion disk [13]:
  $\epsilon \left(a\right)=0.068\left(\frac{L_{bol}}{{10}^{46}}\right){\left(\frac{L_{opt}}{{10}^{45}}\right)}^{-3/2}{M}_8{\mu }^{3/2}$.
• Raimundo et al. [14]: $\epsilon \left(a\right)=0.063{\left(\frac{L_{bol}}{{10}^{46}}\right)}^{0.99}{\left(\frac{L_{opt}}{{10}^{45}}\right)}^{-1.5}{M}_8^{0.89}{\mu }^{3/2}$.
• Lawther et al. [15]: ${\mu }^{3/2}{L}_{bol}=0.87\times {10}^{47}{\left(\frac{L_{opt}}{{10}^{45}}\right)}^{1.5}{\left(\frac{{\lambda }_{opt}}{4392}\right)}^2\epsilon \left(a\right)M_8^{-1}$.

Definition of $L_{opt}$ is taken from Hopkins et al. [16]:

$\frac{L_{bol}}{L_{opt}}=\frac{L_{bol}}{L_B}=6.25{\left(\frac{L_{bol}}{{10}^{10}{L}_{\odot }}\right)}^{-0.37}+9{\left(\frac{L_{bol}}{{10}^{10}{L}_{\odot }}\right)}^{-0.012},L_B=L\left(4400\text{Å}\right),M_8=\frac{M_{BH}}{{10}^8{M}_{\odot }}$.

$\mu =cosi$, where i is the angle between the normal to the plane of the accretion disk and the line of sight.

Table 1 shows that, for our objects, most methods (and for some objects all methods) give $\epsilon$ values greater than 0.324—the maximal possible value for Kerr BH. Of course, this can be explained, for example, by erroneous determination of the magnitude of the bolometric luminosity or mass. However, the fact that there are a lot of such objects (about 7 % of the total list of 112 objects from [10]), as well as the fact that these objects are not distinguished by other parameters (distance, magnitude, mass, Eddington ratio etc.), speak in favor of the fact that this can be a real physical effect.

4. High Energy Photons from Accretion on a Schwarzschild-like Wormholes

In this section, we show that the existence of traversable wormholes may lead to observable effects even if the former are of simplest non-rotating kind. To this end we consider a traversable wormhole connecting two galactic centers. To make the situation as simple as possible, assume that the wormhole is spherically symmetric, static, and empty everywhere beyond a spherical layer L. Assume further that the gravitational force acting on a radially falling test particle in any point of that wormhole is directed towards the throat. These properties make a wormhole very simple, but, at the same time, none of them look too unrealistic.

An example of a wormhole satisfying all listed requirements is a “Schwarzschild-like wormhole” [17]. Outside of the layer $L\equiv \{r<r_{*}\}$ this wormhole is empty and hence, by Birkhoff’s theorem, Schwarzschild’s (the corresponding mass will be denoted by M). $r_{*}$ stands for some constant greater than (but close to) the throat’s radius.

The matter attracted by mouths of such a wormhole must form two fluxes colliding at the throat. The energy of the collision depends on the form of the wormhole and can, in principle, be arbitrarily high. Note that we are not challenging energy conservation: the collision is powered by the potential energy of the particles falling toward a gravitating body.

Consider, for example, a particle of mass $\mu$ that falls freely from infinity (with zero initial velocity) and in the throat of the wormhole hits head-on exactly the same oncoming particle. The energy—in the center-of-mass system—of such a collision is

$$E_{\mathrm{c}.\mathrm{m}.}\approx 2\mu \mathsf{\Gamma }{c}^2,\mathsf{\Gamma }\equiv max{g}_{00}^{-1/2},$$

(1)

see Equation (12) in [17]. As a result, an external observer will see two spheres (these are the spheres—with radii $r_{*}$—bounding L) of ultra relativistic plasma. The said spheres radiate with a distinctive spectrum, see below, much different from those of jets or accretion disks, which makes it possible to identify the wormhole.

The phenomenon in discussion is rather complex and, to explore it, we will make as much simplifying assumptions as possible. Specifically, we consider a pair of AGNs with the masses $M\approx 4\times {10}^8$ M_⊙ connected by a Schwarzschild-like wormhole with $\mathsf{\Gamma }\approx 10$. Assuming that

• the galactics in question are Narrow-line Seyfert 1 Galaxies (NLS1) [18,19,20,21,22], they have a rather weak gamma radiation, thus, our supposed WH gamma radiation will be less diluted;
• the plasma layer is heated (only) by the collision of the fluxes; and,
• the magnetic field, the interaction of the infalling matter with the outcoming radiation, and the backreaction of the spheres on the metric of the wormhole are negligible.

we can write down the following rough estimates.

The characteristic accretion rates of NLS1 lie [23,24] within the range of $\dot{m}\approx (0.1÷1)M_{\odot }/1$ year, which means in our rough approximation

$$\dot{m}\approx 1M_{\odot }/1\mathrm{year}.$$

(2)

According to estimates of duty cycles of AGNs of type under consideration [25,26,27], this accretion regime should exist for al least ${10}^8$ years. Accordingly, the mass of the plasma spherical layer is at least

$$m\approx {10}^8{M}_{\odot },$$

(3)

twhere the layer’s mass m is understood as the integral of density rather than a characteristic of the wormhole’s metric. By (3), the proton concentration in the accreting plasma is

$$n_{acc}\approx M_{\odot }/(m_{p}4\pi r_{*}^2·\sqrt{g_{*00}}\mathrm{ly}),$$

(4)

where $m_p$ is the proton mass. Substituting our parameters in this expression we obtain the estimate

$$n_{acc}\approx 4\frac{\mathsf{\Gamma }}{{(M/M_{\odot })}^2}·{10}^{27}{\mathrm{cm}}^{-3},$$

(5)

Finally, if we take an AGN mass to be $M\approx 4\times {10}^8$ M_⊙ and $\mathsf{\Gamma }\approx 10$, then $n_{acc}\approx {10}^{11}$ cm⁻³.

On the other side, by Equation (1), the temperature T of the plasma cloud is approximately

$$T\approx \mathsf{\Gamma }{m}_p{c}^2/k\approx {10}^{13}\mathsf{\Gamma }\mathrm{K},$$

(6)

where k is the Boltzmann constant.

The plasma with such a temperature and proton concentration was considered, for example, in Marscher et al. [28]; below, we will use their results. At high temperatures in the plasma the production of ${\pi }^0$ mesons begins [28,29,30]. ${\pi }^0$ mesons decay into two photons with energies $\sim 68$ MeV. For $T=2.5\times {10}^{13}$ K and $T={10}^{14}$ K the gamma-ray production spectra of plasma for this radiation mechanism (in Minkowski space) were found in Marscher et al. [28]. The latter spectrum has a peak value of $log(Q_{\max }(erg$ cm⁻³ s⁻¹) ≈ 13.4 at about 68MeV, where Q is the gamma-ray production value. To find the spectrum of the wormhole (as measured by an observer resting out of the wormhole), we extrapolate Marscher’s result and assume that the peak value in the spectrum is reached at $\sim 68{\mathsf{\Gamma }}^{-1}$MeV (the factor ${\mathsf{\Gamma }}^{-1}$ is due to the red shift experienced by a photon on its way from the throat to infinity) and it is equal to $log\left(Q_{\max }\left(T\right)\right)\approx log\left(Q_{\max }(T={10}^{14}\mathrm{K})\right)+0.25log(T/{10}^{14}\mathrm{K})-log\left(\mathsf{\Gamma }\right)$. The resulting spectrum looks (qualitatively), as shown in Figure 1.

The observed values of the flux from NLS1 is $\sim {10}^{-13}$ ergcm⁻² s⁻¹ and the characteristic distance for observed AGNs of this type is about ${10}^9$ light years. In order for the whole flux to be generated, the volume of the radiating plasma needs to be $\approx {10}^{54}$ cm³.

Further, in [28] the plasma is optically thin, so we consider radiation only from outer layers of plasma cloud with a volume of 10% of the total volume of cloud. Thus, the full cloud volume will be $\sim {10}^{55}$ cm³. Taking into account (5) we obtain the mass of the plasma cloud

$$m=n_{acc}{m}_{p}V\approx {10}^8{M}_{\odot }$$

(7)

When comparing this with (3), we see that the observed accretion rate (2) is sufficiently high for WH radiation to be observable.

5. Conclusions

Summing up we can conclude that:

• Eight AGNs may contain WH instead of SMBH judging from their radiative efficiency.
• A peak at about (0.1–10) MeV range may appear in the spectrum of an AGN with WH. This peak can be quite high, comparable to the observed radiation of NLS1.