A Unified Framework for X-shaped Radio Galaxies

In Figure 4, we show the evolution of cold-mode accreting black holes in retrograde configuration whose mass is relatively smaller. Such systems produce weaker jet feedback and thus fail to influence the interstellar medium (ISM), so they have no effect on their accretion flow which persists in cold mode. Time evolution is from bottom panel toward top panel. If these low-power FRIIs accrete near the Eddington limit, they evolve rapidly from high retrograde spin to high prograde spin on a timescale of about 100 million years. Our goal, however, is to explore the jets that are produced on opposite sides of zero spin, the one for low spin but in retrograde mode, and the one for low spin, but in prograde mode, to see if there is a reasonable expectation in the model for a timescale between such jets of order a few million years. We propose that such jets are the ones observed as XRGs.

Figure 4 offers a more detailed version of Figure 2(a) of Garofalo et al. (2018), in the sense that we have included low retrograde and low prograde spin systems, as opposed to showing only the zero-spin panel. For symmetry purposes, Figure 4 displays −0.2 and 0.2 jets, despite the fact that the −0.1 and 0.2 spin jets have the same power (Garofalo et al. 2010). Although the jet turns off strictly speaking only at zero spin, there is some observational threshold below which the jet effectively disappears. At the Eddington limit, we can connect the low retrograde system with the 0.2 prograde system by estimating a timescale on the order of 6 million years, which is compatible with observations (Mezcua et al. 2011). In other words, the Eddington-limited timescale connecting values of spin that correspond to jets strong enough to be visible, happens to be short enough that the secondary jet has not had time to dissipate. It is worth emphasizing that these model features are not ad hoc, and cannot be fine tuned to explain XRGs. Note that as we are describing accretion onto relatively smaller black holes that are found in less-massive dark matter halos, the XRGs described in Figure 4 are associated with isolated field environments.

In Figure 5, we show the time evolution for systems whose black holes are larger on average than those in Figure 4, and therefore produce more powerful and effective jet feedback that (unlike the black holes in Figure 4) eventually affect the accretion flow. The uppermost panel in Figure 5 shows an advection dominated accretion flow (ADAF) that is the result of hot gas flowing into the inner regions. Although the details need to be worked out computationally, there is a basic qualitative picture that we can describe: the original FRII jet increases the entropy of the ISM and suppresses star formation such that before the system ends up as in the a = 0.9 panel, the greater galaxy is already transitioning away from the physical processes that classify it as high excitation, despite the fact that cold gas still fuels the black hole (Garofalo et al. 2010). We argue that these are the XRGs that are classified as low excitation (Gillone et al. 2016), and suggest that an analysis of the distribution of emission lines will reveal weak signatures for the greater galaxy, whereas on nuclear scales emission lines are still present and may be hidden or reprocessed by the hot halo. Note that because these black holes are, on average, more massive than in Figure 4, they live in more massive dark matter halos, which means such XRGs will distribute themselves in both isolated as well as in cluster environments.

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Places where black holes have the largest average masses also have the largest average jet powers and largest average jet feedback on the ISM, a rapid transition to an ADAF and no cold gas state connecting retrograde with prograde systems (Figure 6). As a result of the ADAF phase setting in early while still in retrograde mode, such black holes produce FRII LERG jets at low retrograde spin, and FRI LERG jets at low prograde spins that are separated by an order of a billion years. Hence, these two jets are not simultaneously visible, and no XRGs appear. Figures 4–6 illustrate the reason why XRGs tend to distribute themselves in isolated environments and less so in clusters; they also allow an understanding of why XRGs that inhabit galaxies that are becoming LERGs tend to live in clusters compared with the XRGs living in galaxies that are classified as HERGs. Along the same lines, we can appreciate the reason why the mid-infrared signatures associated with postmerger star formation are stronger in field environments. The weakness of such signatures are part and parcel of the HERG to LERG transition, which increasingly comes into play as we move from Figure 4 to Figures 5 and 6.

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In this section, we explore the physical mechanism for reorientation of the primary jet in the transition through zero black hole spin. The cold gas that accretes onto the black hole is supplied in clumps of mass that roughly satisfy M_d/M_BH < 10⁻³ (King et al. 2008; Nixon et al. 2013), where M_d is the mass of the disk, and M_BH is the black hole mass such that accretion is therefore a sequence of these clumps. Unlike King et al. (2008), however, we argue that the cold gas reservoir has some average angular momentum that each clump of gas that flows toward the black hole respects. This means that each sequence of clumps has angular momentum that is close to the overall average angular momentum of the cold gas reservoir, or in terms of directions, satisfies

$$\begin{eqnarray*}&&{\theta }_{{\rm{d}}}-{\theta }_{\mathrm{CG}}\leqslant 180^\circ \end{eqnarray*}$$

where θ_d, and θ_CG, are the angular directions of the disk and cold gas torus angular momenta, respectively. The bottom line is that chaotic accretion does not occur. When the black hole spins rapidly, the difference in the directions of the angular momenta of the black hole and disk are subject to frame dragging and the Lense–Thirring effect, which brings the angular momenta into alignment or counteralignment (King et al. 2005, 2008); we are interested in the latter. Counteralignment between disk and black hole is stable under restrictive conditions on black hole and disk mass, which makes such systems a minority among the total active galaxy population (Garofalo et al. 2019). This picture amounts to a continuous accretion scenario whereby an initially retrograde accreting black hole continues to spin down toward zero spin and eventually spin up into the prograde direction. However, Lense–Thirring precession depends on the presence of frame dragging which requires a spinning black hole. At zeroth order, frame dragging imparts an angular velocity that is proportional to black hole spin via

$$\begin{eqnarray*}&&\omega =2{{GM}}_{c}a/{c}^{2}{r}^{3},\end{eqnarray*}$$

where G is the gravitational constant, c is the speed of light, a is the dimensionless spin of the black hole, and r is the radial distance from the black hole. Hence, the impetus for alignment or counteralignment of the angular momenta progressively vanishes as the black hole spins down toward zero spin. Therefore, the clumps feeding the black hole near zero spin form thin disks that tend to retain their original θ_CG values, which are the clumps illustrated further out in Figures 7 and 8. We show the details of this in Figures 7 and 8 with a spinning black hole in Figure 7, and a Schwarzschild black hole in Figure 8. In the former we see the Bardeen–Petterson effect (Bardeen & Petterson 1975) aligning (or antialigning) the angular momenta near the black hole, whereas in the latter we see the inner disk forming with the same angular momentum direction as that of the inflowing clumps.

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As a result of the absence of Bardeen–Petterson for zero-spin black holes, a new plane of accretion is generated which produces a new jet direction that becomes visible after a few million years when the spin is about 0.2 and the observational threshold for the jet is crossed.

A number of features drop out of this model. First, notice that because the retrograde jet is more powerful than the prograde jet for a given value of spin (in Figures 4 and 5, the choice is an absolute spin value of 0.2), the earlier jet is more powerful and collimated, hence travels further out into the ISM than the latter prograde jet. This qualitatively explains the observation that the secondary jet extends further than the primary jet in XRGs. However, this is not a dominant effect, as the spin is relatively low, and environment may have a comparably larger effect. In other words, near zero spin, a denser environment can turn an engine generated FRII-like jet into an FRI-like jet. Note that these ideas form the backdrop for the explanation of the Owen–Ledlow diagram (see Section 3.4 of Garofalo et al. 2010).

Second, the possibility of viewing the retrograde and prograde jets at the same time is only possible because cold-mode accretion allows for an evolution from one jet to the other in just a few million years. If ADAF accretion were to replace the thin disk during the transition through zero spin, the timescale between the retrograde and prograde jets would increase dramatically (by at least a factor of 100), and no two jets would be observed. This is due to the fact that the accretion rate in ADAF mode compared with that at the Eddington limit has been theoretically determined to be (dM/dt)_ADAF < 0.01(dM/dt)_Edd. This can be seen in Figure 6, where the ADAF disk sets in early when the black hole is still accreting in retrograde mode. Hence, there is an explanation for why XRGs emerge in systems near the FRII/FRI boundary of the Owen–Ledlow diagram and not in systems that rapidly transition to ADAFs such as those that are connected to the recently identified class of FR0 radio galaxies (Garofalo & Singh 2019). The jet power, in short, must either not be so large that it affects the accretion flow or, it must not affect the accretion state rapidly, allowing the system to transition well into the prograde regime before it becomes an ADAF. Notice that indeed the black hole masses in XRGs appear to be slightly smaller (Joshi et al. 2019). From the model viewpoint, radio morphology gets blurry near zero spin and environment will tend to wash out engine-based signatures. To the extent, therefore, that the secondary is of the FRII type, the Blandford–Znajek and Blandford–Payne jets that give rise to power and collimation are weaker at low retrograde spin than at high retrograde spin so there should be a difference in these features from a model perspective.

Third, XRGs emerge in systems with weak jet feedback in the model which means they tend to be dominant in isolated environments as shown in Figures 4 and 5 although they can exist in clusters as well (Figure 5). The model prediction for XRGs that form in field environments and that continue to accrete to high prograde spin values is a radio-quiet quasar/radio-quiet AGN as shown in the uppermost panel in Figure 4. For those of Figure 5, instead, continued accretion generates FRI radio galaxies. Note that in addition to the recent transition through zero spin for Figure 5 objects, there is an evolution in the state of accretion that is not present in Figure 4. Jet feedback in Figure 5 objects has slowly heated the ISM and shutdown star formation and the hot gas that now permeates the greater galaxy will eventually flow back into the black hole sphere of influence as an ADAF (Figure 5 upper panel). But the primary jet of the XRGs is formed when the spin is still low (Figure 5 for a = 0.2 spin). Hence, although the greater galaxy is transitioning away from the processes associated with strong emission lines, the near black hole disk is still cold. The model therefore prescribes that XRGs classified as low-excitation radio galaxies (LEGs—Gillone et al. 2016), are actually transition objects that until recently still produced strong emission lines. Interestingly, some of the LEG classified XRGs are close to the HEG/LEG boundary (Gillone et al. 2016).

Fourth, the model predicts that the merger that produced the original FRII HERG (Figures 4 and 5) occurred millions of years in the past of the XRGs and that XRGs are therefore not directly related to mergers, which seems compatible with observations (Landt et al. 2010). The model also allows one to recast an old question in a new context (Sansom et al. 1987): what is the connection between the directions of the XRGs jets and the optical axes of the galaxy? There are two directions that emerge from the model: the original direction of the black hole angular momentum and the direction of the angular momentum of the molecular torus that feeds the black hole. These are the directions for the jets in XRGs. Hence, the question of how the jet directions are related to minor and major optical axes in the model reduces to understanding the connection between original black hole angular momentum and the angular momentum of the torus that feeds the black hole and the optical axes.

Finally, we point out that in the model the primary jet of the XRG is an FRI quasar in its youth (Blundell & Rawlings 2001; Kim et al. 2016). If accretion continues in such objects, the system evolves either into a radio-quiet quasar/AGN (Figure 4 upper panel) or into an FRI radio galaxy (Figure 5 upper panel) which explains the dearth of FRI quasars. The answer to the longstanding question of where the FRI quasars are appears here: they form only in a narrow range of spin and tend to come in the form of XRGs. In closing, we point out that some XRGs have been identified with a different origin. Our model cannot account for such objects as the nucleus in our model is fixed. However, we can predict that such XRGs would not be constrained in the same way as the XRGs discussed in this work. For example, there would be no reason for low black hole spins and no preference for isolated environments for such objects.