Populations of Magnetized Filaments in the Intracluster Medium and the Galactic Center

Figure 1 displays a comparison of the filamentary structures associated with the radio jet of 3C 40B and three morphologically similar groups of filaments identified in the GC (Yusef-Zadeh et al. 2022b). 3C 40B is a radio galaxy at a distance of ∼75.5 Mpc, embedded in the poor cluster environment Abell 194 (A194; Knowles et al. 2022), which has recently been studied in detail (Rudnick et al. 2022). Two remarkable filaments emerge from a deviated region of the jet and run parallel to each other as they bend together with two different curvatures leading to diffuse ends. The angular spacing between the filaments is ∼30'' (∼11 kpc), their widths range between 0.85 and 2.8 kpc, and both have an extent of ∼220 kpc (Rudnick et al. 2022). The filaments show signs of physical interaction with a region of the jet that is highly bent, suggesting a scenario in which a cloud is crossing the jet and the filaments are then dragged from the interaction site (Rudnick et al. 2022).

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The Snake has a length of ∼30' (∼70 pc), is one of the longest in the Galactic center, and is characterized by two kinks and three different curvatures along its length. Another two examples of GC filaments are the groups known as the Flamingo and the Eyebrow. The Flamingo shows multiple filaments with similar curvatures and the Eyebrow consists of two parallel filaments with the same curvature suggesting that they are associated with each other.

The morphology of the four filament groups shown in Figure 1 is similar to each other to the extent that it is difficult to distinguish which one is in a galaxy cluster based on appearance alone. The systems of filaments in the GC and 3C 40B have similar morphologies, surface brightnesses, length-to-width ratios, and angular spacings. What is remarkable is that the ICM filaments in 3C 40B are ∼7000 times longer than nonthermal filaments (a.k.a. NTFs) in the GC with a coherent magnetic structure, steepening spectral index, and streaming cosmic-ray particles over such a large distance (Rudnick et al. 2022), and yet they show similar physical characteristics.

The ranges of the spectral indices are α = [−0.60, −0.79] for the Snake, α = [−0.80, −1.05] for the Flamingo, α = [−0.51, −0.76] for the Eyebrow (Yusef-Zadeh et al. 2022b). These estimates of the spectral index are made along individual filaments. The GC spectral index values are all flatter than the spectral indices of the filaments in 3C 40B, which have a mean value of α ∼ − 2 and steepen from −1.3 to −2.5 with distance from the jet.

The equipartition magnetic field of GC filaments ranges between 20 and 100 μG (for a cosmic-ray proton to electron ratio of p/e = 1), which is much higher than that of 3C 40B with the magnetic field of 2–7 μG. The equipartition magnetic field of the Snake has a maximum of ∼0.1 mG and decreases away from the Galactic plane (Yusef-Zadeh et al. 2022a). Furthermore, the direction of the magnetic field runs along the 3C 40B and the Snake filaments. (The magnetic field directions of the Flamingo and Eyebrow are unknown).

IC 4296 is a low-luminosity elliptical galaxy in cluster A3566 at a distance of 50 Mpc (Condon et al. 2021), as shown in Figure 2. A sensitive radio image of this galaxy shows a remarkable group of three filaments with an angular spacing of ∼20'' (called threads in Condon et al. 2021) that appear to converge to a point (Figure 2, left), as showin in Figure 2. The projected lengths and widths of the filaments are ∼50 and ∼2 kpc, respectively, with a surface brightness of ∼0.1 mJy per ∼76 beam (Condon et al. 2021; Figure 2, left panel). This group of filaments lies to the south of the western radio jet where the jet shows a wiggle, thought to be due to Kelvin–Helmholtz (KH) instability (Condon et al. 2021). These authors suggest that relativistic electrons escape from the jet where there is KH instability along the radio jets (Condon et al. 2021). There is also a single isolated filament with a different position angle that arises from the eastern jet. One puzzle is that the spectral index of the filaments steepens from α ∼ −1 to −1.5 closer to the injection point of the radio jet.

The GC grouping of the comet tail consists of six linear structures that resemble a fragmented comet tail (Figure 2, right panel). Some of the filaments branch out into fainter components. The spectral index of individual filaments varies and shows steep spectra in the range [−1, −1.8]. There is a trend where the GC filaments with steeper spectral indices lie at high latitudes (Yusef-Zadeh et al. 2022a). The comparison indicates similar morphology and steep spectral indices in both the comet tail and IC 4296 filaments.

Figure 3(a) shows a radio image of the core of the A3562 galaxy cluster at a distance of ∼200 Mpc (Giacintucci et al. 2022). A linearly polarized filament with a length of 50 kpc runs perpendicular to the end of the tail of the radio galaxy J1333–3141. The filament that arises from the region where the jet terminates is distorted before it splits into two components (Giacintucci et al. 2022). The splitting occurs 60 kpc away from the radio tail. The mean spectral index of the filament is α ∼ −1.5.

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For comparison we show in Figure 3(b), a striking GC filament, the Feather, which splits into a two-pronged forked filament with the junction at the location of a compact source G359.416–0.706 with a possible stellar counterpart detected at IR (Yusef-Zadeh et al. 2022a, 2022b). The compact source is suggested to be an obstacle that splits the bright filament into two parallel, fainter components with steeper spectral index values. The comparison noted in Figure 3 provides another example that radio filaments in both classes of Galactic and extragalactic filaments break up into multiple components, suggestive of a flow along the filaments that splits into two components as it runs into an obstacle.

Figure 4(a) shows a remarkable group of filaments linked to the radio lobes of ESO 137–006, a luminous radio galaxy in the Norma galaxy cluster at 70 Mpc from us (Ramatsoku et al. 2020). The wide-angle tail morphology of this radio galaxy includes multiple straight and bent filaments extending from the eastern lobe toward the western lobe. The longest straight filaments act as a bridge connecting the two radio lobes. In addition, a number of semiregularly spaced filaments are noted to the south of the lobes. The length and width of the longest filament are 80 kpc and 1.2 kpc, respectively, with an aspect ratio (length:width) of 67 (Ramatsoku et al. 2020). The mean spectral index of the filaments, α ≃ −2, is similar to the spectral indices of the lobe from which they emerge. The western half of the galaxy is completely surrounded by diffuse X-ray emission. The western lobe is also highly distorted where diffuse and filamentary structures are present. The filaments bridging the lobes, with similar morphology to the above three examples, arise from a region where the jet is expanding into the lobe.

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G359.484+0.1122 consists of five regularly spaced filaments with the appearance of a bent harp (Thomas et al. 2020; Yusef-Zadeh et al. 2022b). A trend was noted between the length of the filaments and their brightness as well as with the steepening of the spectral index in the range between [−1.3,−1.0] (Yusef-Zadeh et al. 2022b).

The longest and straightest filament in ESO 137–006 (bridging the radio lobes) appears like many straight GC filaments running perpendicular to the Galactic plane (Yusef-Zadeh et al. 2022b). The Bent Harp is one group of GC filaments with a resemblance to the ICM structures in ESO 137–006. Unlike the filaments of ESO 137+006, the Bent Harp is not connected to any obvious sources of cosmic rays.

We compare the measurements and estimates of the physical characteristics of the two populations of filaments at the GC and in the ICM of galaxy clusters, as tabulated in Table 1, to explore the implications for the formation of the magnetic structures and the source of the ultrarelativistic electrons responsible for the observed radio emission. While the filament length scales and magnetic field strengths differ by orders of magnitude, it is their respective dimensionless ratios of timescales and length scales that should be compared. This allows us to examine whether the underlying physical mechanisms responsible for the creation of the two populations are similar. In particular, we are interested in the mechanisms responsible for creating magnetized filaments and for accelerating the relativistic electrons.

First, the morphological parameters of the two populations of filaments are similar: the aspect ratios are ∼30:1, there are multiple parallel filaments, splitting into a two-pronged fork, and bending and spacing between the filaments. The filaments appear in parallel bundles or to converge toward a point in both populations with a spacing of a few filament widths. These similarities are hardly surprising, given that the motivation behind making this comparison is that structures show a remarkable resemblance in the two environments, as shown in Figures 1–4.

Second, the filaments' magnetic fields are estimated to be of order 100 and 3 μG in the GC and ICM, respectively. Their corresponding magnetic energy densities, B²/8π ≈ 3 × 10⁶ and 3 × 10³ cm⁻³ K, are comparable with or lower than the thermal pressure of the medium in which they are embedded. These characteristics suggest that the filaments are confined by the thermal pressure of the external medium. This is supported in the case of the filaments in A194 and IC 4296 (Condon et al. 2021; Rudnick et al. 2022), where the X-ray surface brightness of the intracluster medium is reduced along the filament, consistent with the exclusion of hot gas from the filament's interior. In the case of GC filaments, high external cosmic-ray energy density inferred from ${{\rm{H}}}_{3}^{+}$ measurements contributes to the confinement of the GC filaments (Yusef-Zadeh & Wardle 2019).

Third, the spectral index values are steeper for ICM filaments than the mean spectral index of the GC filaments, as given in Table 1. Both systems of filaments also show steepening of the spectral index along individual filaments. The relativistic electron populations responsible for the observed synchrotron emission at 1.2 GHz have steep spectral indices and show a high percentage of linear polarization based on sensitive observations for both the GC and ICM filament populations.

For the equipartition field strengths mentioned above, the characteristic energy of the electrons dominating the emission at 1.2 GHz is $E={(4\pi {m}_{e}c\nu /3{eB})}^{1/2}\,{m}_{e}{c}^{2}\approx 0.9$ and 5 GeV, respectively. The synchrotron power radiated by an ultrarelativistic electron of energy E = γ m_e c² is $\dot{E}=2{\sigma }_{T}c{\gamma }^{2}{B}^{2}/4\pi$, where for simplicity we have assumed a 90° pitch angle. Then, the synchrotron loss timescale ${t}_{s}=E/\dot{E}\approx 0.9$ or 200 Myr for the GC or IC filaments, respectively. As electron acceleration mechanisms tend to produce electrons with an E⁻² energy spectrum and hence a ν^−0.5 synchrotron spectrum, the steepness of the observed spectra implies that the filament ages are longer than the synchrotron lifetimes given above. In addition, the ages cannot be too much more than this because the filaments would rapidly become faint. Thus, the synchrotron lifetimes give a rough idea of the age of the filaments and impose a requirement on the cosmic-ray electron transport mechanism that must be able to distribute relativistic electrons along the observed filament lengths on this timescale.

The disparate synchrotron loss timescales need to be placed in context. For source models involving acceleration or injection of relativistic electrons at a localized site, they impose a requirement to be able to transport the electrons via diffusion or streaming from the injection site throughout the observed filament lengths L ∼ 30 pc and 100 kpc for the GC and ICM populations, respectively.

If transport is by diffusion, then the diffusion timescale L²/κ ≲ t_s so the diffusion coefficient κ ≳ L² t_s ∼ 3 × 10²⁶ and 2 × 10³¹ cm² s⁻¹, respectively, implying mean free paths l = 3c/κ ∼ 0.01 and 570 pc. The required diffusion is plausible for GC filaments with L ≲ 30 pc but seems rather large in the case of the ICM filaments (Rudnick et al. 2022) as well as GC filaments, such as the Snake, with lengths L ≳ 30 pc. (see Figure 1).

The alternative to diffusion is that the cosmic-ray pressure is sufficient to allow them to stream along the magnetic field lines, in which case scattering by self-generated waves limits the streaming to the Alfvén speed, v_A . The requirement to populate the entire filament length then implies that L/v_A ≲ t_s , i.e., v_A ≳ L/t_s ∼ 30 and ∼600 km s⁻¹ for the GC and ICM filaments, respectively. The density of the ionized thermal plasma present within the filaments is unknown, but we can usefully estimate the maximum density able to yield the required Alfvén speeds, using the characteristic field magnetic strengths B ∼ 100 and 3 μG for the two populations. This implies that the thermal electron density n_e ≲ 3 × 10¹¹ and 8 × 10⁵ cm⁻³ for the GC and ICM filaments, respectively. These upper limits clearly exceed any plausible value in each of the environments by orders of magnitude, so we can conclude another similarity in parameter space between the two populations that streaming would be able to transport electrons from their injection site along the entire length of the observed filaments.

Models of ICM filaments benefit from the fact that there is an obvious reservoir of cosmic-ray particles in jets, lobes, and mini radio halos (Brunetti & Jones 2014) that can be injected into filaments. For example, the filaments of the radio galaxy IC 4296 are thought to originate where helical KH instability disrupts the flow of the radio jet followed by the relativistic particles feeding the filaments (Condon et al. 2021). One puzzle is why the spectrum flattens instead of steepening while moving away from the presumed injection point at the end of the cometary structure's tail toward the convergence point of the filaments. One possible explanation for this is that the injected particles' pitch angle would tend to increase to conserve the magnetic moment p_⊥/B as they spiral along the converging field lines. This mechanism relies on the initial pitch angle of the injected particles being anticorrelated with energy and the pitch-angle scattering to be ineffective in isotropizing the pitch-angle distribution.

In the case of the A3562 galaxy cluster, it has been suggested that the tail of the radio galaxy is interacting with a tangential wind blown in the direction along the filaments (Giacintucci et al. 2022). An alternative to this picture is a scenario in which the cosmic-ray electrons injected from the tail feed cluster magnetic field lines (Giacintucci et al. 2022). In another model, cosmic-ray electrons associated with two parallel filaments of 3C 40B are injected from a region where the jet is highly distorted (Rudnick et al. 2022). In particular, an impact between a moving dense cloud and the jet is expected to distort the shape of the jet as the magnetic field lines are dragged away from the site of the interacting jet (Rudnick et al. 2022). Another remarkable object is source C in A2256 with its extremely narrow and long tail. This unusual source is considered to be a one-sided radio jet. However, it has a very similar morphology to GC radio filaments. Lastly, the collimated synchrotron filaments in ESO 137–006 could be due to the interaction of the magnetic fields of the radio lobes with the magneto-ionic plasma of the intracluster medium (Ramatsoku et al. 2020).

In GC and ICM populations, there are two broad scenarios that could potentially explain how magnetic filaments are formed. Both scenarios posit the amplification and organization of an initially weak magnetic field in the surrounding medium. In the first scenario, the filaments are formed by an initially weak field that is amplified and structured by subsonic turbulent motions in a weakly magnetized medium, a scenario that has been proposed both for GC (Boldyrev & Yusef-Zadeh 2006) and the ICM environments (Porter et al. 2015; Vazza et al. 2018; Rudnick et al. 2022). The challenge in this picture is that simulations show the overall orientation of most filaments is random (Porter et al. 2015; Vazza et al. 2018). The GC filaments are mainly directed in the direction away from the Galactic plane. It is possible that the alignment of GC filaments is generated by cosmic-ray-driven wind running away from the Galactic plane, thus creating a velocity shear in the turbulent medium that aligns the filaments.

In the second scenario, the filaments are created by the subsonic flow of a weakly magnetized medium past an obstacle. The passing flow drapes the obstacle with field lines that are then compressed and stretched back into a comet-like tail, creating a magnetic filament with magnetic pressure of order the thermal ram pressure in the medium. The obstacle could be any relatively dense ionized clump that creates a bow shock in the flow such as a stellar wind bubble, a red giant, an expanding H ii region, wind tubes associated with red giants in AGN relativistic bubbles (Chugai et al. 2011), or a disturbed region along jets or lobes showing size scales similar to the separation between parallel filaments. In this picture, the magnetized filaments are produced at the interaction sites of a large-scale driven wind outflowing away from the Galactic plane and embedded stellar wind bubbles (Rosner & Bodo 1996; Shore & LaRosa 1999; Yusef-Zadeh & Wardle 2019). The large-scale radio bubble filled with X-ray gas in the GC is considered to be arising from cosmic-ray-driven outflow (Yusef-Zadeh & Wardle 2019). In this picture, the obstacle sets the length scale of the separation between the filaments. This is analogous to the interaction of fast-moving mass-losing stars whose winds interact with the ISM and create cometary tails (Martin et al. 2007). In addition to the cometary model, numerous other models have been proposed in the past to explain the origin of the GC filaments and the sources in which cosmic-ray electrons are accelerated. Unlike ICM filaments, it is not clear what feeds cosmic-ray electrons into filaments (Nicholls & Le Strange 1995; Rosner & Bodo 1996; Shore & LaRosa 1999; Bicknell & Li 2001; Dahlburg et al. 2002; Yusef-Zadeh 2003; Boldyrev & Yusef-Zadeh 2006; Ferrière 2009; Banda-Barragán et al. 2016; Yusef-Zadeh & Wardle 2019; Sofue 2020; Thomas et al. 2020; Coughlin et al. 2021).

In the context of the ICM filaments, the relative motion with the external medium is created by the orbital motion of the obstacle or a head–tail radio galaxy through the ICM around the center of the cluster. An additional contribution for slow-moving galaxies close to the center of the cluster could be moving through denser ICM (Toniazzo & Schindler 2001; Douglass et al. 2008). Other sources of external pressure could be due to "weather" motion within the ICM (Brunetti & Jones 2014). On the other hand, in the Galactic center ISM, there is a contribution due to the large-scale nuclear wind generated by high cosmic-ray pressure (Yusef-Zadeh & Wardle 2019).

One interesting aspect of this picture when applied to ICM filaments is that the filaments are linked to jets or lobes of radio galaxies. The locations where the filaments cross radio galaxies are highly distorted and cosmic-ray particles are likely to escape from the jet (Condon et al. 2021). This supports the picture in which there is a concentration of cosmic-ray particles in the jet or the lobe that injects relativistic plasma into the ICM filaments. As described in Section 4.3, the origin of filamentation is interaction with an obstacle and splitting of the filament into multiple filaments. Another possibility for the origin of the filamentation is synchrotron cooling instability formed as a result of the interaction of cosmic rays generated by the winds (e.g., Simon & Axford 1967). The mean spacing and the mean width of the filaments are expected to be similar to each other (Yusef-Zadeh et al. 2022a). In the case of ICM filaments, the spacing is estimated to be the product of the cooling timescale and the Alfvén speed which is of the order of kiloparsecs.

Assuming that the GC and ICM filaments are formed with the same mechanism in the context of an origin involving an obstacle collimating the magnetized wind, the lack of compact radio sources associated with some of the GC filaments is likely to be related to the lifetime of the obstacle. In particular, if an obstacle is an expanding H ii region or a planetary nebula, then it may have already dissipated as simulations of cloud–wind interactions indicate (Banda-Barragán et al. 2016). Another possibility is that the source of injection has a very steep spectrum and would be visible only at very low frequencies.

The above cometary and turbulent models are technically different than a scenario in which there is a strong pre-existing organized field dominating the region, with only some field lines being lit up by an injected population of cosmic-ray electrons. This model was one of the first models proposed for the GC, which was originally thought to be threaded by a milligauss poloidal field (Morris 2007). However, the diffuse radio emission from the inner few hundred parsecs of the galaxy suggests a much weaker global field, ∼10–20 μG (Yusef-Zadeh et al. 2013). This scenario is also inapplicable to the ICM environment in which the field strengths are much less than several microgauss inferred for the magnetized filaments.