Cosmic-ray Luminosity Research Articles

Revealing the Production Mechanism of High-energy Neutrinos from NGC 1068

The detection of high-energy neutrino signals from the nearby Seyfert galaxy NGC 1068 provides us with an opportunity to study nonthermal processes near the center of supermassive black holes. Using the IceCube and latest Fermi-LAT data, we present general multimessenger constraints on the energetics of cosmic rays and the size of neutrino emission regions. In the photohadronic scenario, the required cosmic-ray luminosity should be larger than ∼1%−10% of the Eddington luminosity and the emission radius should be ≲15R S in low-β plasma and ≲3R S in high-β plasma. The leptonic scenario overshoots the NuSTAR or Fermi-LAT data for any emission radii we consider, and the required gamma-ray luminosity is much larger than the Eddington luminosity. The beta-decay scenario also violates not only the energetics requirement but also gamma-ray constraints, especially when the Bethe–Heitler and photomeson production processes are consistently considered. Our results rule out the leptonic and beta-decay scenarios in a nearly model-independent manner and support hadronic mechanisms in magnetically powered coronae if NGC 1068 is a source of high-energy neutrinos.

Gamma-rays and neutrinos from giant molecular cloud populations in the galactic plane

The recent IceCube detection of significant neutrino flux from the inner Galactic plane has provided us valuable insights on the spectrum of cosmic rays in our Galaxy. This flux can be produced either by a population of Galactic point sources or by diffused emission from cosmic ray interactions with the interstellar medium or by a mixture of both. In this work, we compute diffused gamma-ray and neutrino fluxes produced by a population of giant molecular clouds (GMCs) in our Galaxy, assuming different parametrizations of the Galactic diffused cosmic ray distribution. In particular, we take into account two main cases: (I) constant cosmic ray luminosity in our Galaxy, and (II) space-dependent cosmic ray luminosity, based on the supernovae distribution in our Galaxy. For Case-I, we found that the neutrino flux from GMCs is a factor of ∼ 10 below compared to π 0 and KRA γ best-fitted models of IceCube observations at 105 GeV. Instead, for Case-II the model can explain up to ∼ 90 % of the neutrino flux at that energy. Moreover, for this last scenario IceCube detector could be able to detect neutrino events from the Galactic centre regions. We then calculated gamma-ray and neutrino fluxes from individual GMCs and noticed that several current and future Cherenkov telescopes and neutrino observatories have the right sensitivities to study these objects. In particular, very neutrino-bright region such as Aquila Rift is favourable for detection by the IceCube-Gen2 observatory.

The role of supernovae inside AGN jets in UHECR acceleration

Context. Jets of active galactic nuclei are potential accelerators of ultra high-energy cosmic rays. Supernovae can occur inside these jets and contribute to cosmic ray acceleration, particularly of heavy nuclei, but that contribution has been hardly investigated so far. Aims. We carried out a first dedicated exploration of the role of supernovae inside extragalactic jets in the production of ultra high-energy cosmic rays. Methods. We characterized the energy budget of supernova-jet interactions, and the maximum possible energies of the particles accelerated in those events, likely dominated by heavy nuclei. This allowed us to assess whether these interactions can be potential acceleration sites of ultra high-energy cosmic rays, or at least of their seeds. For that, we estimated the cosmic ray luminosity for different galaxy types, and compared the injection rate of cosmic ray seeds into the jet with that due to galactic cosmic ray entrainment. Results. Since the supernova is fueled for a long time by the luminosity of the jet, the energy of a supernova-jet interaction can be several orders of magnitude greater than that of an isolated supernova. Thus, despite the low rate of supernovae expected to occur in the jet, they could still provide more seeds for accelerating ultra high-energy particles than cosmic ray entrainment from the host galaxy. Moreover, these interactions can create sufficiently efficient accelerators to be a source of cosmic rays with energies ≳10 EeV. Conclusions. Supernova-jet interactions can contribute significantly to the production of ultra high-energy cosmic rays, either directly by accelerating these particles themselves or indirectly by providing pre-accelerated seeds.

High-energy neutrino astronomy — the neutrino connections to the cosmic-ray origin: present and future

High-energy neutrino astronomy has been blooming. In addition to the possible identification of the blazar and Seyfert II galaxies as neutrino emitters, the present neutrino data has indicated some hints to characterize or constrain the origin of cosmic rays. Being motivated by the observational fact that the astrophysical neutrino background energy flux is comparable to that of ultrahigh-energy (UHE) cosmic rays, we derive the generic requirements that a major fraction of UHE cosmic ray sources must meet, if they are also responsible for the ∼ 100 TeV-energy cosmic neutrino background radiation. The source parameters characterizing the cosmic ray – neutrino unified scheme, such as the photon radiation luminosity and the cosmic ray luminosity density, suggest that the yet-unidentified cosmic ray and neutrino origins can be transient objects visible in the optical/NIR wavelength band. We propose a viable scheme of multimessenger observations to identify the sources using the neutrino multiplet detections.

The Role of Jet–Cocoon Mixing, Magnetization, and Shock Breakout in Neutrino and Cosmic-Ray Emission from Short Gamma-Ray Bursts

Abstract We perform general relativistic magnetohydrodynamic and relativistic magnetohydrodynamic simulations of weakly and highly magnetized gamma-ray burst (GRB) jets propagating in binary neutron star (BNS) merger ejecta. Using the simulations, we first find that mixing between the jet and cocoon, which is present in all types of jets, inhibits the formation of subphotospheric collisionless shocks. However, we show that a mild magnetization may lead to the formation of collisionless subshocks, which allow efficient proton acceleration. We consider shear acceleration and diffusive shock acceleration at collimation shocks, internal shocks, shock breakout, and external shocks to provide the first estimate for neutrino and cosmic-ray (CR) signals from self-consistent simulations of GRBs in BNS mergers. We find that short GRBs do not produce detectable neutrino signals with current-day facilities. Shock breakout yields ∼10 PeV neutrinos at viewing angles ∼20°, independent of the jet magnetization. However, a neutrino signal from shock breakout is well below the detection limits of current detectors. Such a signal would allow a coincident neutrino–γ-ray detection, providing a testable prediction for shock breakout as a neutrino production site. Using the numerical modeling that fits GW 170817 afterglow emission, we find that blast waves in BNS mergers can account for 5%–10% of the Galactic CR luminosity in the PeV–EeV energy range. Based on these estimates, the observed level of CR anisotropy places a constraint on the distance of the latest Galactic BNS merger to ≲3 kpc.

The diffuse gamma-ray emission toward the Galactic mini starburst W43

In this paper we report the Fermi Large Area Telescope (Fermi-LAT) detection of the γ-ray emission toward the young star forming region W43. Using the latest source catalog and diffuse background models, the extended γ-ray excess is detected with a significance of ~16σ. The γ-ray emission has a spectrum with a photon index of 2.3 ± 0.1. We also performed a detailed analysis of the gas content in this region by taking into account the opacity correction to the HI gas column density. The total cosmic-ray (CR) proton energy is estimated to be on the order of 1048 erg, assuming the γ-rays are produced from the interaction of the accelerated protons and nuclei with the ambient gas. Comparing this region to the other star formation regions in our Galaxy, we find that the CR luminosity is better correlated with the wind power than the star formation rate (SFR). This result suggests that CRs are primarily accelerated by stellar wind in these systems.

Radio and X-ray connection in radio mini-halos: Implications for hadronic models

Context. A large fraction of cool-core clusters are known to host diffuse, steep-spectrum radio sources, called radio mini-halos, in their cores. Mini-halos reveal the presence of relativistic particles on scales of hundreds of kiloparsecs, beyond the scales directly influenced by the central active galactic nucleus (AGN), but the nature of the mechanism that produces such a population of radio-emitting, relativistic electrons is still debated. It is also unclear to what extent the AGN plays a role in the formation of mini-halos by providing the seeds of the relativistic population. Aims. In this work we explore the connection between thermal and non-thermal components of the intra-cluster medium in a sample of radio mini-halos and we study the implications within the framework of a hadronic model for the origin of the emitting electrons. Methods. For the first time, we studied the thermal and non-thermal connection by carrying out a point-to-point comparison of the radio and the X-ray surface brightness in a sample of radio mini-halos. We extended the method generally applied to giant radio halos by considering the effects of a grid randomly generated through a Monte Carlo chain. Then we used the radio and X-ray correlation to constrain the physical parameters of a hadronic model and we compared the model predictions with current observations. Results. Contrary to what is generally reported in the literature for giant radio halos, we find that the mini-halos in our sample have super-linear scaling between radio and X-rays, which suggests a peaked distribution of relativistic electrons and magnetic field. We explore the consequences of our findings on models of mini-halos. We use the four mini-halos in the sample that have a roundish brightness distribution to constrain model parameters in the case of a hadronic origin of the mini-halos. Specifically, we focus on a model where cosmic rays are injected by the central AGN and they generate secondaries in the intra-cluster medium, and we assume that the role of turbulent re-acceleration is negligible. This simple model allows us to constrain the AGN cosmic ray luminosity in the range ∼1044−46 erg s−1 and the central magnetic field in the range 10–40 μG. The resulting γ-ray fluxes calculated assuming these model parameters do not violate the upper limits on γ-ray diffuse emission set by the Fermi-LAT telescope. Further studies are now required to explore the consistency of these large magnetic fields with Faraday rotation studies and to study the interplay between the secondary electrons and the intra-cluster medium turbulence.

Gamma-Ray Production in the Extended Halo of the Galaxy and Possible Implications for the Origin of Galactic Cosmic Rays

Various studies have implied the existence of a gaseous halo around the Galaxy extending out to 100 kpc. Galactic cosmic rays (CRs) that propagate to the halo, either by diffusion or by convection with the possibly existing large-scale Galactic wind, can interact with the gas therein and produce gamma-rays via proton-proton collision. We calculate the cosmic ray distribution in the halo and the gamma-ray flux, and explore the dependence of the result on model parameters such as diffusion coefficient, CR luminosity, CR spectral index. We find that the current measurement of isotropic gamma-ray background at $\lesssim$TeV with Fermi Large Area Telescope already approaches a level that can provide interesting constraints on the properties of Galactic cosmic ray (e.g., with CR luminosity $L_{CR}\leq 10^{41}$erg/s). We also discuss the possibilities of the Fermi bubble and IceCube neutrinos originating from the proton-proton collision between cosmic rays and gas in the halo, as well as the implication of our results for the baryon budget of the hot circumgalactic medium of our Galaxy. Given that the isotropic gamma-ray background is likely to be dominated by unresolved extragalactic sources, future telescopes may extract more individual sources from the IGRB, and hence put even more stringent restriction on the relevant quantities (such as Galactic cosmic ray luminosity and baryon budget in the halo) in the presence of a turbulent halo that we consider.

Pevatron at the Galactic Center: multi-wavelength signatures from millisecond pulsars

Diffuse TeV emission has been observed by H.E.S.S. in the Galactic Center region, in addition to the GeV gamma rays observed by Fermi. We propose that a population of unresolved millisecond pulsars located around the Galactic Center, suggested as possible candidates for the diffuse Galactic Center excess observed by Fermi, accelerate cosmic rays up to very high energies, and are thus also responsible for the TeV excess. We model analytically the diffusion of these accelerated protons and their interaction with the molecular clouds, producing gamma rays. The spatial and spectral dependences of the gamma rays produced can reproduce the H.E.S.S. observations, for a population of ∼ 104–105 millisecond pulsars above the cosmic-ray luminosity 1034 erg s−1, with moderate acceleration efficiency. More precise measurements at the highest energies would allow us to constrain the properties of the pulsar population, such as the magnetic field or initial spin distributions.

Ultrahigh-energy cosmic ray production by turbulence in gamma-ray burst jets and cosmogenic neutrinos

We propose a novel model to produce ultrahigh-energy cosmic-rays (UHECRs) in gamma-ray burst jets. After the prompt gamma-ray emission, hydrodynamical turbulence is excited in the GRB jets at or before the afterglow phase. The mildly relativistic turbulence stochastically accelerates protons. The acceleration rate is much slower than the usual first-order shock acceleration rate, but in this case it can be energy-independent. The resultant UHECR spectrum is so hard that the bulk energy is concentrated in the highest energy range, resulting in a moderate requirement for the typical cosmic ray luminosity of $\sim 10^{53.5}~\mbox{erg}~\mbox{s}^{-1}$. In this model, the secondary gamma-ray and neutrino emissions initiated by photopion production are significantly suppressed. Although the UHECR spectrum at injection shows a curved feature, this does not conflict with the observed UHECR spectral shape. The cosmogenic neutrino spectrum in the $10^{17}$--$10^{18}$ eV range becomes distinctively hard in this model, which may be verified by future observations.

ISOTROPY CONSTRAINTS ON POWERFUL SOURCES OF ULTRAHIGH-ENERGY COSMIC RAYS AT 1019 eV

ABSTRACT Anisotropy in the arrival direction distribution of ultrahigh-energy cosmic rays (UHECRs) produced by powerful sources is numerically evaluated. We show that nondetection of significant anisotropy at ≈ 10 19 ?> eV at present and in future experiments imposes general upper limits on UHECR proton luminosity of steady sources as a function of source redshifts. The upper limits constrain the existence of typical steady 10 19 ?> eV UHECR sources in the local universe and limit their local density to ≳ 10 − 3 ?> Mpc − 3 , ?> assuming average intergalactic magnetic fields less than 10 − 9 ?> G. This isotropy, being stronger than that measured at the highest energies, may indicate the transient generation of UHECRs. Our calculations are applied for extreme high-frequency-peaked BL Lacertae objects 1ES 0229+200, 1ES 1101–232, and 1ES 0347–121, to test the UHECR-induced cascade model, in which beamed UHECR protons generate TeV radiation in transit from sources. While the magnetic-field structure surrounding the sources affects the required absolute cosmic-ray luminosity of the blazars, the magnetic-field structure surrounding the Milky Way directly affects the observed anisotropy. If these magnetic fields are weak enough, significant UHECR anisotropy from these blazars is detectable by the Pierre Auger Observatory unless the maximum energy of UHECR protons is below 1019 eV. Furthermore, if these are the sources of UHECRs above 1019 eV, a local magnetic structure surrounding the Milky Way is needed to explain the observed isotropy at ∼ 10 19 ?> eV, which may be incompatible with large magnetic structures around all galaxies for the UHECR-induced cascade model to work with reasonable jet powers.

Luminosity of ultrahigh energy cosmic rays and bounds on magnetic luminosity of radio-loud active galactic nuclei

We investigate the production of magnetic flux from rotating black holes in active galactic nuclei (AGNs) and compare it with the upper limit of ultrahigh energy cosmic ray (UHECR) luminosities, calculated from observed integral flux of GeV-TeV gamma rays for nine UHECR AGN sources. We find that, for the expected range of black hole rotations (0.44<a<0.80), the corresponding bounds of theoretical magnetic luminosities from AGNs coincides with the calculated UHECR luminosity. We argue that such result possibly can contribute to constrain AGN magnetic and dynamic properties as phenomenological tools to explain the requisite conditions to proper accelerate the highest energy cosmic rays.

Angular correlation of cosmic neutrinos with ultrahigh-energy cosmic rays and implications for their sources

Cosmic neutrino events detected by the IceCube Neutrino Observatory with energy 0≳ 3 TeV have poor angular resolutions to reveal their origin. Ultrahigh-energy cosmic rays (UHECRs), with better angular resolutions at 0>6 EeV energies, can be used to check if the same astrophysical sources are responsible for producing both neutrinos and UHECRs. We test this hypothesis, with statistical methods which emphasize invariant quantities, by using data from the Pierre Auger Observatory, Telescope Array and past cosmic-ray experiments. We find that the arrival directions of the cosmic neutrinos are correlated with 0≥ 10 EeV UHECR arrival directions at confidence level ≈ 90%. The strength of the correlation decreases with decreasing UHECR energy and no correlation exists at energy 0∼ 6 EeV . A search in astrophysical databases within 3̂ of the arrival directions of UHECRs with energy 0≥ 10 EeV, that are correlated with the IceCube cosmic neutrinos, resulted in 18 sources from the Swift-BAT X-ray catalog with redshift z≤ 0.06. We also found 3 objects in the Kühr catalog of radio sources using the same criteria. The sources are dominantly Seyfert galaxies with Cygnus A being the most prominent member. We calculate the required neutrino and UHECR fluxes to produce the observed correlated events, and estimate the corresponding neutrino luminosity (25 TeV–2.2 PeV) and cosmic-ray luminosity (500 TeV–180 EeV), assuming the sources are the ones we found in the Swift-BAT and Kühr catalogs. We compare these luminosities with the X-ray luminosity of the corresponding sources and discuss possibilities of accelerating protons to 0≳ 10 EeV and produce neutrinos in these sources.

Upper limits on the total cosmic-ray luminosity of individual sources

In this paper, upper limits on the total luminosity of ultra-high-energy cosmic-rays (UHECR) E > 1018 eV) are determined for five individual sources. The upper limit on the integral flux of GeV--TeV gamma-rays is used to extract the upper limit on the total UHECR luminosity of individual sources. The correlation between upper limit on the integral GeV--TeV gamma-ray flux and upper limit on the UHECR luminosity is established through the cascading process that takes place during propagation of the cosmic rays in the background radiation fields, as explained in reference [1]. Twenty-eight sources measured by FERMI-LAT, VERITAS and MAGIC observatories have been studied. The measured upper limit on the GeV--TeV gamma-ray flux is restrictive enough to allow the calculation of an upper limit on the total UHECR cosmic-ray luminosity of five sources. The upper limit on the UHECR cosmic-ray luminosity of these sources is shown for several assumptions on the emission mechanism. For all studied sources an upper limit on the ultra-high-energy proton luminosity is also set.

Photo-disintegration of heavy nuclei at the core of Cen A

Fermi LAT has detected gamma ray emissions from the core of Cen A.More recently, a new component in the gamma ray spectrum from the core has been reported in the energy range of 4 GeV to tens of GeV.We show that the new component and the HESS detected spectrum of gamma rays from the core at higher energy have possibly a common origin in photo-disintegration of heavy nuclei. Assuming the cosmic rays are mostly Fe nuclei inside the core and their spectrum has a low energy cut-off at 52 TeV in the wind frame moving with a Doppler factor 0.25 with respect to the observer on earth, the cosmic ray luminosity required to explain the observed gamma ray flux above 1 GeV is found to be 1.5 × 1043 erg/sec.

An upper limit on the cosmic-ray luminosity of individual sources from gamma-ray observations

Different types of extragalactic objects are known to produce TeV gamma-rays. Some of these objects are the most probable candidates to accelerate cosmic rays up to 1020 eV. It is very well known that gamma-rays can be produced as a result of the cosmic ray propagation through the intergalactic medium. These gamma-rays contribute to the total flux observed in the direction of the source. In this paper we propose a new method to derive an upper limit on the cosmic-ray luminosity of an individual source based on the measured upper limit on the integral flux of GeV-TeV gamma-rays. We show how it is possible to calculate an upper limit on the cosmic-ray luminosity of a particular source and we explore the parameter space in which the current GeV-TeV gamma-ray measurements can offer a useful determination. We study in detail two particular sources, Pictor A and NGC 7469, and we calculate the upper limit on the proton luminosity of each source based on the upper limit on the integral gamma-ray flux measured by the H.E.S.S. telescopes.

Model-Dependent High-Energy Neutrino Flux from Gamma-Ray Bursts

The IceCube Collaboration recently reported a stringent upper limit on the high energy neutrino flux from gamma-ray bursts (GRBs), which provides a meaningful constraint on the standard internal shock model. Recent broadband electromagnetic observations of GRBs also challenge the internal shock paradigm for GRBs, and some competing models for γ-ray prompt emission have been proposed. We describe a general scheme for calculating the GRB neutrino flux, and compare the predicted neutrino flux levels for different models. We point out that the current neutrino flux upper limit starts to constrain the standard internal shock model. The dissipative photosphere models are also challenged if the cosmic ray luminosity from GRBs is at least 10 times larger than the γ-ray luminosity. If the neutrino flux upper limit continues to go down in the next few years, then it would suggest the following possibilities: (i) the photon-to-proton luminosity ratio in GRBs is anomalously high for shocks, which may be achieved in some dissipative photosphere models and magnetic dissipation models; or (ii) the GRB emission site is at a larger radius than the internal shock radius, as expected in some magnetic dissipation models such as the internal collision-induced magnetic reconnection and turbulence model.

BLAZARS AS ULTRA-HIGH-ENERGY COSMIC-RAY SOURCES: IMPLICATIONS FOR TeV GAMMA-RAY OBSERVATIONS

The spectra of BL Lac objects and Fanaroff–Riley I radio galaxies are commonly explained by the one-zone leptonic synchrotron self-Compton (SSC) model. Spectral modeling of correlated multiwavelength data gives the comoving magnetic field strength, the bulk outflow Lorentz factor, and the emission region size. Assuming the validity of the SSC model, the Hillas condition shows that only in rare cases such sources accelerate protons to much above 1019 eV, so ≳ 1020 eV ultra-high-energy cosmic rays (UHECRs) are likely to be heavy ions if powered by this type of radio-loud active galactic nuclei (AGNs). Survival of nuclei is shown to be possible in TeV BL Lacs and misaligned counterparts with weak photohadronic emissions. Another signature of hadronic production is intergalactic UHECR-induced cascade emission, which is an alternative explanation of the TeV spectra of some extreme non-variable blazars such as 1ES 0229+200 or 1ES 1101−232. We study this kind of cascade signal, taking into account effects of the structured extragalactic magnetic fields in which the sources should be embedded. We demonstrate the importance of cosmic-ray deflections on the γ-ray flux, and show that required absolute cosmic-ray luminosities are larger than the average UHECR luminosity inferred from UHECR observations and can even be comparable to the Eddington luminosity of supermassive black holes. Future TeV γ-ray observations using the Cerenkov Telescope Array and the High Altitude Water Cerenkov detector array can test for UHECR acceleration by observing >25 TeV photons from relatively low redshift sources such as 1ES 0229+200, and ≳TeV photons from more distant radio-loud AGNs.

Detectability of ultrahigh energy cosmic-ray signatures in gamma-rays

The injection of ultra-high energy cosmic rays in the intergalactic medium leads to the production of a GeV-TeV gamma-ray halo centered on the source location, through the production of a high electromagnetic component in the interactions of the primary particles with the radiation backgrounds. This paper examines the prospects for the detectability of such gamma ray halos. We explore a broad range of astrophysical parameters, including the inhomogeneous distribution of magnetic fields in the large scale structure as well as various possible chemical compositions and injection spectra; and we consider the case of a source located outside clusters of galaxies. With respect to the gamma-ray flux associated to synchrotron radiation of ultra-high energy secondary pairs, we demonstrate that it does not depend strongly on these parameters and conclude that its magnitude ultimately depends on the energy injected in the primary cosmic rays. Bounding the cosmic ray luminosity with the contribution to the measured cosmic ray spectrum, we then find that the gamma-ray halo produced by equal luminosity sources is well below current or planned instrument sensitivities. Only rare and powerful steady sources, located at distances larger than several hundreds of Mpc and contributing to a fraction > 10% of the flux at 10^19 eV might be detectable. We also discuss the gamma-ray halos that are produced by inverse Compton/pair production cascades seeded by ultra-high energy cosmic rays. This latter signal strongly depends on the configuration of the extragalactic magnetic fields; it is dominated by the synchrotron signal on a degree scale if the filling factor of magnetic fields with B > 10^(-14) G is smaller than a few percents. Finally, we discuss briefly the case of nearby potential sources such as Centaurus A.

SELF-CONSISTENT EVOLUTION OF GAS AND COSMIC RAYS IN CYGNUS A AND SIMILAR FR II CLASSICAL DOUBLE RADIO SOURCES

In Cygnus A and other classical FR II double radio sources, powerful opposing jets from the cores of halo-centered galaxies drive out into the surrounding cluster gas, forming hotspots of shocked and compressed cluster gas at the jet extremities. The moving hotspots are sandwiched between two shocks. An inner-facing shock receives momentum and cosmic rays from the jet and creates additional cosmic rays that form a radio lobe elongated along the jet axis. An outer-facing bow shock moves directly into the undisturbed group or cluster gas, creating a cocoon of shocked gas enclosing the radio lobe. We describe computations that follow the self-consistent dynamical evolution of the shocked cluster gas and the relativistic synchrotron-emitting gas inside the lobes. Relativistic and non-relativistic components exchange momentum by interacting with small magnetic fields having dynamically negligible energy densities. The evolution of Cygnus A is governed almost entirely by cosmic ray energy flowing from the hotspots. Mass flowing into hotspots from the jets is assumed to be small, greatly reducing the mass of gas flowing back along the jet, common in previous calculations, that would disrupt the spatial segregation of synchrotron-loss ages observed inside FR II radio lobes. We compute the evolution of the cocoon when the velocity and cosmic ray luminosity of the hotspots are constant and when they vary with time. If cosmic rays mix with cluster gas in hotspots before flowing into the radio lobe, the thermal gas is heated to mildly relativistic temperatures, producing an unobserved pressure inside the lobe.