arXiv subjects

Judith H. Croston

Publications and source records attributed to Judith H. Croston.

At least 19 recordsLinked to original sources

arXiv2026

Mapping the emission and spectral properties of the FRI radio galaxy 3C 449 with LOFAR and the VLA

The jets and lobes of nearby radio galaxies are ideal laboratories to explore the spectral and dynamical evolution of the radio-emitting plasma that emanates from active galactic nuclei. Here, we present a high-resolution radio continuum study of the low-redshift (z=0.01713), Fanaroff-Riley I (FRI) radio galaxy 3C 449 performed by combining radio data at 145 MHz acquired with the LOw Frequency ARray (LOFAR) and archival Very Large Array (VLA) data at 1365, 1485, 4985, and 8485 MHz. Our LOFAR maps have angular resolutions of 20"x20" and 6.0"x6.0", and show the full extent of the known radio emission at the highest angular resolution to date. Our spectral index maps show the distribution of the spectrum in the 145-8485 MHz frequency range over a region that extends beyond 2.5'. The average 145-8485 MHz spectrum is consistent with a single power law and stays approximately constant over the inner ~50" of both jets. Beyond ~50", on both source sides, the higher-frequency spectrum steepens, indicating no significant downstream sites of particle acceleration. By modelling the spectrum under the assumption of equipartition and of a constant magnetic field across the source, we derive maps of the highest radiative age of the particles. At the outer edges of both the northern tail and southern lobe, the spectral age is ~150 Myr. If the latter age were representative of the dynamical source age, the average expansion speed of both jets during the source lifetime would be supersonic, with Mach numbers of M~4.1 and M~2.8 for the northern and southern jets, respectively. As numerical simulations of FRI jets suggest that the source's current expansion is subsonic, the high Mach numbers might arise either from the source being highly supersonic for a small fraction of its lifetime or from a severe underestimation of the spectral age due to particle acceleration on scales of hundreds of kpc.

astro-ph.HE↗

arXiv2024

Core prominence as a signature of restarted jet activity in the LOFAR radio-galaxy population

(abridged) Characterizing duty cycles of recurrent phases of dormancy and activity in supermassive black holes in active galactic nuclei is crucial in understanding impact of energy released on host galaxies and their evolution. However, identifying sources in quiescent and restarted phases is challenging. Our goal is to identify and characterize a substantial sample of radio galaxies in restarted phase and explore core prominence as a signature of this activity. We expand our prior study from a $30\,\mathrm{deg^2}$ area in Lockman Hole to a larger $424\,\mathrm{deg^2}$ region in Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) field using visually selected core-dominated radio galaxies. We used 144 MHz LOFAR survey images to identify galaxies with restarting jets. By applying selection criteria, including radio core dominance, low surface brightness extended emission, spectral index properties, and morphology, we found 69 candidate restarted radio galaxies. These candidates show diverse intrinsic morphology, spanning FRI, FRII, core-with-halo, and asymmetric forms, suggesting different progenitors. Among these, nine galaxies exhibit ultra-steep spectrum extended emission combined with high radio core prominence, representing previous and current epochs of jet activity. This subset supports a model where the switch-on and switch-off mechanism occurs with fast duty cycle. The restarted candidates span radio luminosities from log$_{10}$(L$_\mathrm{144 MHz}$/$\mathrm{WHz^{-1}}$) = 23.24 to 26.80, with sizes between 88 and 1659 kpc, including 16 giant radio galaxies. Their total stellar content aligns with massive elliptical galaxies. Our findings at $z<0.4$ suggest that many restarting galaxies are not found in rich cluster environments, consistent with broader radio-galaxy population. This study confirms core prominence as an effective parameter for selecting restarted radio sources.

astro-ph.GA↗

arXiv2023

The SPT-Chandra BCG Spectroscopic Survey I: Evolution of the Entropy Threshold for Cooling and Feedback in Galaxy Clusters Over the Last 10 Gyr

We present a multi-wavelength study of the brightest cluster galaxies (BCGs) in a sample of the 95 most massive galaxy clusters selected from South Pole Telescope (SPT) Sunyaev-Zeldovich (SZ) survey. Our sample spans a redshift range of 0.3 < z < 1.7, and is complete with optical spectroscopy from various ground-based observatories, as well as ground and space-based imaging from optical, X-ray and radio wavebands. At z~0, previous studies have shown a strong correlation between the presence of a low-entropy cool core and the presence of star-formation and a radio-loud AGN in the central BCG. We show for the first time that a central entropy threshold for star formation persists out to z~1. The central entropy (measured in this work at a radius of 10 kpc) below which clusters harbor star-forming BCGs is found to be as low as $K_\mathrm{10 ~ kpc} = 35 \pm 4$ keV cm$^2$ at z < 0.15 and as high as $K_\mathrm{10 ~ kpc} = 52 \pm 11$ keV cm$^2$ at z~1. We find only marginal (~1$σ$) evidence for evolution in this threshold. In contrast, we do not find a similar high-z analog for an entropy threshold for feedback, but instead measure a strong evolution in the fraction of radio-loud BCGs in high-entropy cores as a function of redshift. This could imply that the cooling-feedback loop was not as tight in the past, or that some other fuel source like mergers are fueling the radio sources more often with increasing redshift, making the radio luminosity an increasingly unreliable proxy for radio jet power. We also find that our SZ-based sample is missing a small (~4%) population of the most luminous radio sources ($νL_ν > 10^{42}$ erg/s), likely due to radio contamination suppressing the SZ signal with which these clusters are detected.

astro-ph.GA↗

arXiv2019

Investigating the spectral age problem with powerful radio galaxies

The 'spectral age problem' is our systematic inability to reconcile the maximum cooling time of radiating electrons in the lobes of a radio galaxy with its age as modelled by the dynamical evolution of the lobes. While there are known uncertainties in the models that produce both age estimates, `spectral' ages are commonly underestimated relative to dynamical ages, consequently leading to unreliable estimates of the time-averaged kinetic feedback of a powerful radio galaxy. In this work we attempt to solve the spectral age problem by observing two cluster-centre powerful radio galaxies; 3C320 and 3C444. With high-resolution broad-band Karl G. Jansky Very Large Array observations of the radio sources and deep XMM-Newton and Chandra observations of their hot intra-cluster media, coupled with the use of an analytic model, we robustly determine their spectral and dynamical ages. After finding self-consistent dynamical models that agree with our observational constraints, and accounting for sub-equipartition magnetic fields, we find that our spectral ages are still underestimated by a factor of two at least. Equipartition magnetic fields will underestimate the spectral age by factors of up to ~20. The turbulent mixing of electron populations in the radio lobes is likely to be the main remaining factor in the spectral age/dynamical age discrepancy, and must be accounted for in the study of large samples of powerful radio galaxies.

astro-ph.HE↗

arXiv2018

The Cocoon Shocks of Cygnus A: Pressures and Their Implications for the Jets and Lobes

We use 2.0 Msec of Chandra observations to investigate the cocoon shocks of Cygnus A and some implications for its lobes and jet. Measured shock Mach numbers vary in the range 1.18-1.66 around the cocoon. We estimate a total outburst energy of $\simeq 4.7\times10^{60}\rm\ erg$, with an age of $\simeq 2 \times 10^{7}\rm\ yr$. The average postshock pressure is found to be $8.6 \pm 0.3 \times 10^{-10}\rm\ erg\ cm^{-3}$, which agrees with the average pressure of the thin rim of compressed gas between the radio lobes and shocks, as determined from X-ray spectra. However, average rim pressures are found to be lower in the western lobe than in the eastern lobe by $\simeq 20\%$. Pressure estimates for hotspots A and D from synchrotron self-Compton models imply that each jet exerts a ram pressure $\gtrsim$ 3 times its static pressure, consistent with the positions of the hotspots moving about on the cocoon shock over time. A steady, one-dimensional flow model is used to estimate jet properties, finding mildly relativistic flow speeds within the allowed parameter range. Models in which the jet carries a negligible flux of rest mass are consistent with with the observed properties of the jets and hotspots. This favors the jets being light, implying that the kinetic power and momentum flux are carried primarily by the internal energy of the jet plasma rather than by its rest mass.

astro-ph.HE↗

arXiv2017

FR-II radio galaxies at low frequencies II: spectral ageing and source dynamics

In this paper, the second in a series investigating FR II radio galaxies at low frequencies, we use LOFAR and VLA observations between 117 and 456 MHz in addition to archival data to determine the dynamics and energetics of two radio galaxies, 3C452 and 3C223, through fitting of spectral ageing models on small spatial scales. We provide improved measurements for the physical extent of the two sources, including a previously unknown low surface brightness extension to the northern lobe of 3C223, and revised energetics based on these values. We find spectral ages of $77.05^{+9.22}_{-8.74}$ and $84.96^{+15.02}_{-13.83}$ Myr for 3C452 and 3C223 respectively suggesting a characteristic advance speed for the lobes of around one per cent the speed of light. For 3C452 we show that, even for a magnetic field strength not assumed to be in equipartition, a disparity of factor of approximately 2 exists between the spectral age and that determined from a dynamical standpoint. We confirm that the injection index of both sources (as derived from the lobe emission) remains steeper than classically assumed values even when considered on well resolved scales at low frequencies, but find an unexpected sharp discontinuity between the spectrum of the hotspots and the surrounding lobe emission. We suggest that this discrepancy is due to the absorption of hotspot emission and/or non-homogeneous and additional acceleration mechanisms and, as such, hotspots should not be used in the determination of the underlying initial electron energy distribution.

astro-ph.GA↗

arXiv2017

A representative survey of the dynamics and energetics of FRII radio galaxies

We report the first large, systematic study of the dynamics and energetics of a representative sample of FRII radio galaxies with well-characterized group/cluster environments. We used X-ray inverse-Compton and radio synchrotron measurements to determine the internal radio-lobe conditions, and these were compared with external pressures acting on the lobes, determined from measurements of the thermal X-ray emission of the group/cluster. Consistent with previous work, we found that FRII radio lobes are typically electron-dominated by a small factor relative to equipartition, and are over-pressured relative to the external medium in their outer parts. These results suggest that there is typically no energetically significant proton population in the lobes of FRII radio galaxies (unlike for FRIs), and so for this population, inverse-Compton modelling provides an accurate way of measuring total energy content and estimating jet power. We estimated the distribution of Mach numbers for the population of expanding radio lobes, finding that at least half of the radio galaxies are currently driving strong shocks into their group/cluster environments. Finally, we determined a jet power--radio luminosity relation for FRII radio galaxies based on our estimates of lobe internal energy and Mach number. The slope and normalisation of this relation are consistent with theoretical expectations, given the departure from equipartition and environmental distribution for our sample.

astro-ph.GA↗

arXiv2016

FR II radio galaxies at low frequencies I: morphology, magnetic field strength and energetics

Due to their steep spectra, low-frequency observations of FR II radio galaxies potentially provide key insights in to the morphology, energetics and spectrum of these powerful radio sources. However, limitations imposed by the previous generation of radio interferometers at metre wavelengths has meant that this region of parameter space remains largely unexplored. In this paper, the first in a series examining FR IIs at low frequencies, we use LOFAR observations between 50 and 160 MHz, along with complementary archival radio and X-ray data, to explore the properties of two FR II sources, 3C452 and 3C223. We find that the morphology of 3C452 is that of a standard FR II rather than of a double-double radio galaxy as had previously been suggested, with no remnant emission being observed beyond the active lobes. We find that the low-frequency integrated spectra of both sources are much steeper than expected based on traditional assumptions and, using synchrotron/inverse-Compton model fitting, show that the total energy content of the lobes is greater than previous estimates by a factor of around 5 for 3C452 and 2 for 3C223. We go on to discuss possible causes of these steeper than expected spectra and provide revised estimates of the internal pressures and magnetic field strengths for the intrinsically steep case. We find that the ratio between the equipartition magnetic field strengths and those derived through synchrotron/inverse-Compton model fitting remains consistent with previous findings and show that the observed departure from equipartition may in some cases provide a solution to the spectral versus dynamical age disparity.

astro-ph.GA↗

arXiv2015

Centaurus A: constraints on the nature of the giant lobe filaments from XMM-Newton observations

We report on deep XMM-Newton observations of the vertex filament in the southern giant lobe of the Fanaroff-Riley class I radio galaxy Centaurus A. We find no X-ray excess from the filament region and place a 3 sigma upper limit on the 1 keV flux density of the filament of 9.6 nJy. This directly constrains the electron density and magnetic field strength in the filament. For the first time in an individual filament, we show that so long as the particle index >=2, the excess in synchrotron emissivity cannot be produced purely by excess electrons: the filament magnetic field strength must be higher than in the giant lobes as a whole, and close to or above the equipartition value for the filament. The filaments are not significantly overpressured with respect to the surrounding lobe with a pressure provided by relativistic electrons.

astro-ph.GA↗

arXiv2015

The link between accretion mode and environment in radio-loud active galaxies

The interactions between radio-loud AGN and their environments play an important role in galaxy and cluster evolution. Recent work has demonstrated fundamental differences between High and Low Excitation Radio Galaxies (HERGs and LERGs), and shown that they may have different relationships with their environments. In the Chandra Large Project ERA (Environments of Radio-loud AGN), we made the first systematic X-ray environmental study of the cluster environments of radio galaxies at a single epoch (z~0.5), and found tentative evidence for a correlation between radio luminosity and cluster X-ray luminosity. We also found that this relationship appeared to be driven by the LERG sub-population (Ineson et al. 2013). We have now repeated the analysis with a low redshift sample (z~0.1), and found strong correlations between radio luminosity and environment richness and between radio luminosity and central density for the LERGs but not for the HERGs. These results are consistent with models in which the HERGs are fuelled from accretion discs maintained from local reservoirs of gas, while LERGs are fuelled more directly by gas ingested from the intra-cluster medium. Comparing the samples, we found that although the maximum environment richness of the HERG environments is similar in both samples, there are poorer HERG environments in the z~0.1 sample than in the z~0.5 sample. We have therefore tentative evidence of evolution of the HERG environments. We found no differences between the LERG sub-samples for the two epochs, as would be expected if radio and cluster luminosity are related.

astro-ph.GA↗

arXiv2014

New results on the exotic galaxy `Speca' and discovering many more Specas with RAD@home network

We present the first report on an innovative new project named "RAD@home", a citizen-science research collaboratory built on free web-services like Facebook, Google, Skype, NASA Skyview, NED, TGSS etc.. This is the first of its kind in India, a zero-funded, zero-infrastructure, human-resource network to educate and directly involve in research, hundreds of science-educated under-graduate population of India, irrespective of their official employment and home-location with in the country. Professional international collaborators are involved in follow up observation and publication of the objects discovered by the collaboratory. We present here ten newly found candidate episodic radio galaxies, already proposed to GMRT, and ten more interesting cases which includes, bent-lobe radio galaxies located in new Mpc-scale filaments, likely tracing cosmological cluster accretion from the cosmic web. Two new Speca-like rare spiral-host large radio galaxies have also been been reported here. Early analyses from our follow up observations with the Subaru and XMM-Newton telescopes have revealed that Speca is likely a new entry to the cluster and is a fast rotating, extremely massive, star forming disk galaxy. Speca-like massive galaxies with giant radio lobes, are possibly remnants of luminous quasars in the early Universe or of first supermassive black holes with in first masssve galaxies. As discoveries of Speca-like galaxies did not require new data from big telescopes, but free archival radio-optical data, these early results demonstrate the discovery potential of RAD@home and how it can help resource-rich professionals, as well as demonstrate a model of academic-growth for resource-poor people in the underdeveloped regions via Internet.

astro-ph.GA↗

arXiv2014

The impact of a young radio galaxy: clues from the cosmic-ray electron population

In the framework of hierarchical structure formation AGN feedback shapes the galaxy luminosity function. Low luminosity, galaxy-scale double radio sources are ideal targets to investigate the interplay between AGN feedback and star formation. We use VLA and BIMA observations to study the radio continuum emission of NGC 3801 between 1.4 and 112.4 GHz. We find a prominent spectral break at ~10 GHz, where the spectrum steepens as expected from cosmic-ray electron (CRe) ageing. Using the equipartition magnetic field and fitting JP models locally we create a spatially resolved map of the spectral age of the CRe population. The spectral age of tau_int = 2.0 +/- 0.2 Myr agrees within a factor of two with the dynamical age of the expanding X-ray emitting shells. The spectral age varies only little across the lobes, requiring an effective mixing process of the CRe such as a convective backflow of magnetized plasma. The jet termination points have a slightly younger CRe spectral age, hinting at in-situ CRe re-acceleration. Our findings support the scenario where the supersonically expanding radio lobes heat the ISM of NGC 3801 via shock waves, and, as their energy is comparable to the energy of the ISM, are clearly able to influence the galaxy's further evolution.

astro-ph.GA↗

arXiv2013

Mass entrainment and turbulence-driven acceleration of ultra-high energy cosmic rays in Centaurus A

Observations of the FR I radio galaxy Centaurus A in radio, X-ray and gamma-ray bands provide evidence for lepton acceleration up to several TeV and clues about hadron acceleration to tens of EeV. Synthesising the available observational constraints on the physical conditions and particle content in the jets, inner lobes and giant lobes of Centaurus A, we aim to evaluate its feasibility as an ultra-high-energy cosmic-ray source. We apply several methods of determining jet power and affirm the consistency of various power estimates of ~ 1 x 10^43 erg s^-1. Employing scaling relations based on previous results for 3C 31, we estimate particle number densities in the jets, encompassing available radio through X-ray observations. Our model is compatible with the jets ingesting ~ 3 x 10^21 g s^-1 of matter via external entrainment from hot gas and ~ 7 x 10^22 g s^-1 via internal entrainment from jet-contained stars. This leads to an imbalance between the internal lobe pressure available from radiating particles and magnetic field, and our derived external pressure. Based on knowledge of the external environments of other FR I sources, we estimate the thermal pressure in the giant lobes as 1.5 x 10^-12 dyn cm^-2, from which we deduce a lower limit to the temperature of ~ 1.6 x 10^8 K. Using dynamical and buoyancy arguments, we infer ~ 440-645 Myr and ~ 560 Myr as the sound-crossing and buoyancy ages of the giant lobes respectively, inconsistent with their spectral ages. We re-investigate the feasibility of particle acceleration via stochastic processes in the lobes, placing new constraints on the energetics and on turbulent input to the lobes. The same 'very hot' temperatures that allow self-consistency between the entrainment calculations and the missing pressure also allow stochastic UHECR acceleration models to work.

astro-ph.HE↗

arXiv2013

The X-ray Properties of Optically Selected Clusters of Galaxies

We present the results of Chandra and Suzaku X-ray observations of nine moderate-redshift (0.16 < z < 0.42) clusters discovered via the Red-sequence Cluster Survey (RCS). Surface brightness profiles are fitted to beta models, gas masses are determined, integrated spectra are extracted within R2500, and X-ray temperatures and luminosities are inferred. The Lx-Tx relationship expected from self-similar evolution is tested by comparing this sample to our previous X-ray investigation of nine high-redshift (0.6 < z < 1.0) optically selected clusters. We find that optically selected clusters are systematically less luminous than X-ray selected clusters of similar X-ray temperature at both moderate and high-z. We are unable to constrain evolution in the Lx-Tx relation with these data, but find it consistent with no evolution, within relatively large uncertainties. To investigate selection effects, we compare the X-ray properties of our sample to those of clusters in the representative X-ray selected REXCESS sample, also determined within R2500. We find that while RCS cluster X-ray properties span the entire range of those of massive clusters selected by other methods, their average X-ray properties are most similar to those of dynamically disturbed X-ray selected clusters. This similarity suggests that the true cluster distribution might contain a higher fraction of disturbed objects than are typically detected in X-ray selected surveys.

astro-ph.CO↗

arXiv2013

Spectral Properties of X-ray Binaries in Centaurus A

We present a spectral investigation of X-ray binaries in NGC 5128 (Cen A), using six 100 ks Chandra observations taken over two months in 2007. We divide our sample into thermally and non-thermally dominated states based on the behavior of the fitted absorption column, and present the spectral parameters of sources with L >2x10^37 erg/s. The majority of sources are consistent with being neutron star low mass X-ray binaries (NS LMXBs) and we identify three transient black hole (BH) LMXB candidates coincident with the dust lane, which is the remnant of a small late-type galaxy. Our results also provide tentative support for the apparent `gap' in the mass distribution of compact objects between ~2-5 Msol. We propose that BH LMXBs are preferentially found in the dust lane, and suggest this is because of the younger stellar population. The majority (~70-80%) of potential Roche-lobe filling donors in the Cen A halo are >12 Gyr old, while BH LMXBs require donors >1 Msol to produce the observed peak luminosities. This requirement for more massive donors may also explain recent results that claim a steepening of the X-ray luminosity function with age at Lx >= 5x10^38 erg/s for the XB population of early-type galaxies; for older stellar populations, there are fewer stars >1 Msol, which are required to form the more luminous sources.

astro-ph.HE↗

arXiv2012

Gas Sloshing and Radio Galaxy Dynamics in the Core of the 3C449 Group

We present results from a 140 ks Chandra/ACIS-S observation of the hot gas around the canonical FR I radio galaxy 3C 449. An earlier, shorter 30 ks Chandra observation of the group gas showed an unusual entropy distribution and a surface brightness edge in the gas that could be a strong shock around the inner radio lobes. In our deeper data we find no evidence for a temperature increase inside of the brightness edge, but a temperature decrease across part of the edge. This suggests that the edge is a "sloshing" cold front due to a merger within the last ~1.3-1.6 Gyrs. Both the northern and the southern inner jets are bent slightly to the west in projection as they enter their respective lobes, suggesting that the sloshing core is moving to the east. The straight inner jet flares at approximately the position where it crosses the contact edge, suggesting that the jet is entraining and thermalizing some of the hot gas as it crosses the edge. We also detect filaments of X-ray emission around the southern inner radio jet and lobe which we attribute to low entropy entrained gas. The lobe flaring and gas entrainment were originally predicted in simulations of Loken et al. (1995) and are confirmed in our deep observation.

astro-ph.CO↗

arXiv2012

Shocks, Seyferts and the SNR connection: a Chandra observation of the Circinus galaxy

We analyse new Chandra observations of the nearest (D=4 Mpc) Seyfert 2 active galaxy, Circinus, and match them to pre-existing radio, infrared and optical data to study the kpc-scale emission. The proximity of Circinus allows us to observe in striking detail the structure of the radio lobes, revealing for the first time edge-brightened emission both in X-rays and radio. After considering various other possible scenarios, we show that this extended emission in Circinus is most likely caused by a jet-driven outflow, which is driving shells of strongly shocked gas into the halo of the host galaxy. In this context, we estimate Mach numbers M=2.7-3.6 and M=2.8-5.3 for the W and E shells respectively. We derive temperatures of 0.74 (+0.06, -0.05) keV and 0.8-1.8 keV for the W and E shells, and an expansion velocity of ~900-950 km/s. We estimate that the total energy (thermal and kinetic) involved in creating both shells is ~2x10^55 erg, and their age is ~10^6 years. Comparing these results with those we previously obtained for Centaurus A, NGC 3801 and Mrk 6, we show that these parameters scale approximately with the radio power of the parent AGN. The spatial coincidence between the X-ray and edge-brightened radio emission in Circinus resembles the morphology of some SNR shocks. This parallel has been expected for AGN, but has never been observed before. We investigate what underlying mechanisms both types of systems may have in common, arguing that, in Circinus, the edge-brightening in the shells may be accounted for by a B field enhancement caused by shock compression, but do not preclude some local particle acceleration. These results can be extrapolated to other low-power systems, particularly those with late type hosts.

astro-ph.CO↗

arXiv2012

A Transient Sub-Eddington Black Hole X-ray Binary Candidate in the Dust Lanes of Centaurus A

We report the discovery of a bright X-ray transient, CXOU J132527.6-430023, in the nearby early-type galaxy NGC 5128. The source was first detected over the course of five Chandra observations in 2007, reaching an unabsorbed outburst luminosity of 1-2*10^38 erg/s in the 0.5-7.0 keV band before returning to quiescence. Such luminosities are possible for both stellar-mass black hole and neutron star X-ray binary transients. Here, we attempt to characterize the nature of the compact object. No counterpart has been detected in the optical or radio sky, but the proximity of the source to the dust lanes allows for the possibility of an obscured companion. The brightness of the source after a >100 fold increase in X-ray flux makes it either the first confirmed transient non-ULX black hole system in outburst to be subject to detailed spectral modeling outside the Local Group, or a bright (>10^38 erg/s) transient neutron star X-ray binary, which are very rare. Such a large increase in flux would appear to lend weight to the view that this is a black hole transient. X-ray spectral fitting of an absorbed power law yielded unphysical photon indices, while the parameters of the best-fit absorbed disc blackbody model are typical of an accreting ~10 Msol black hole in the thermally dominant state.

astro-ph.HE↗