Astrophysical Journal最新文献

{"title":"On the Contribution of Coronal Mass Ejections to the Heliospheric Magnetic Flux Budget on Different Time Scales","authors":"Réka M. Winslow, Camilla Scolini, Noé Lugaz, Nathan A. Schwadron, Antoinette B. Galvin","doi":"10.3847/1538-4357/ad02f2","DOIUrl":"https://doi.org/10.3847/1538-4357/ad02f2","url":null,"abstract":"Abstract Coronal mass ejections (CMEs) contribute closed magnetic flux to the heliosphere while they are connected at both ends to the Sun and play a key role in adding magnetic flux to the heliosphere. Here, we discuss how the type of magnetic reconnection that opens CME field lines in the inner heliosphere, i.e., interchange (IC) and/or interplanetary (IP) reconnection, determines the length of time CMEs contribute to the heliospheric flux budget. This distinction has not been taken into account in past studies that estimate the CME flux opening timescale. We outline key criteria to aid in distinguishing IC reconnection from IP reconnection based on in situ spacecraft data and highlight these through two example events. Studying the manner in which CMEs reconnect and open in the inner heliosphere yields important insights not only into CMEs’ role in the heliospheric flux budget but also the evolution of CME complexity, connectivity, and topology.","PeriodicalId":50735,"journal":{"name":"Astrophysical Journal","volume":"25 3-4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135614958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Phase-resolved View of the Low-frequency Quasiperiodic Oscillations from the Black Hole Binary MAXI J1820+070","authors":"Qing C. Shui, S. Zhang, Shuang N. Zhang, Yu P. Chen, Ling D. Kong, Peng J. Wang, Jing Q. Peng, L. Ji, A. Santangelo, Hong X. Yin, Jin L. Qu, L. Tao, Ming Y. Ge, Y. Huang, L. Zhang, Hong H. Liu, P. Zhang, W. Yu, Z. Chang, J. Li, Wen T. Ye, Pan P. Li, Zhuo L. Yu, Z. Yan","doi":"10.3847/1538-4357/acfc42","DOIUrl":"https://doi.org/10.3847/1538-4357/acfc42","url":null,"abstract":"Abstract Although low-frequency quasiperiodic oscillations (LFQPOs) are commonly detected in the X-ray light curves of accreting black hole X-ray binaries, their origin still remains elusive. In this study, we conduct phase-resolved spectroscopy in a broad energy band for LFQPOs in MAXI J1820+070 during its 2018 outburst, utilizing Insight-HXMT observations. By employing the Hilbert–Huang transform method, we extract the intrinsic quasiperiodic oscillation (QPO) variability, and obtain the corresponding instantaneous amplitude, phase, and frequency functions for each data point. With well-defined phases, we construct QPO waveforms and phase-resolved spectra. By comparing the phase-folded waveform with that obtained from the Fourier method, we find that phase folding on the phase of the QPO fundamental frequency leads to a slight reduction in the contribution of the harmonic component. This suggests that the phase difference between QPO harmonics exhibits time variability. Phase-resolved spectral analysis reveals strong concurrent modulations of the spectral index and flux across the bright hard state. The modulation of the spectral index could potentially be explained by both the corona and jet precession models, with the latter requiring efficient acceleration within the jet. Furthermore, significant modulations in the reflection fraction are detected exclusively during the later stages of the bright hard state. These findings provide support for the geometric origin of LFQPOs and offer valuable insights into the evolution of the accretion geometry during the outburst in MAXI J1820+070.","PeriodicalId":50735,"journal":{"name":"Astrophysical Journal","volume":"32 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135372012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Shock Enhanced [C ii] Emission from the Infalling Galaxy Arp 25 ^∗","authors":"Dario Fadda, Jessica S. Sutter, Robert Minchin, Fiorella Polles","doi":"10.3847/1538-4357/acfca1","DOIUrl":"https://doi.org/10.3847/1538-4357/acfca1","url":null,"abstract":"Abstract We present SOFIA observations with HAWC+ and FIFI-LS of the peculiar galaxy Arp 25, also known as NGC 2276 or UGC 3740, whose morphology is deformed by its impact with the intragroup medium of the NGC 2300 galaxy group. These observations show the first direct proof of the enhancement of [C ii ] emission due to shocks caused by ram pressure in a group of galaxies. By comparing the [C ii ] emission to UV attenuation, dust emission, PAH, and CO emission in different regions of the galaxy, we find a clear excess of [C ii ] emission along the impact front with the intragroup medium. We estimate that the shock due to the impact with the intragroup medium increases the [C ii ] emission along the shock front by 60% and the global [C ii ] emission by approximately 25% with respect to the predicted [C ii ] emission assuming only excitation caused by stellar radiation. This result shows the danger of interpreting [C ii ] emission as directly related to star formation since shocks and other mechanisms can significantly contribute to the total [C ii ] emission from galaxies in groups and clusters.","PeriodicalId":50735,"journal":{"name":"Astrophysical Journal","volume":"43 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135372415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Polarized Anisotropic Synchrotron Emission and Absorption and Its Application to Black Hole Imaging","authors":"Alisa Galishnikova, Alexander Philippov, Eliot Quataert","doi":"10.3847/1538-4357/acfa77","DOIUrl":"https://doi.org/10.3847/1538-4357/acfa77","url":null,"abstract":"Abstract Low-collisionality plasma in a magnetic field generically develops anisotropy in its distribution function with respect to the magnetic field direction. Motivated by the application to radiation from accretion flows and jets, we explore the effect of temperature anisotropy on synchrotron emission. We derive analytically and provide numerical fits for the polarized synchrotron emission and absorption coefficients for a relativistic bi-Maxwellian plasma (we do not consider Faraday conversion/rotation). Temperature anisotropy can significantly change how the synchrotron emission and absorption coefficients depend on observing angle with respect to the magnetic field. The emitted linear polarization fraction does not depend strongly on anisotropy, while the emitted circular polarization does. We apply our results to black hole imaging of Sgr A* and M87* by ray tracing a GRMHD simulation and assuming that the plasma temperature anisotropy is set by the thresholds of kinetic-scale anisotropy-driven instabilities. We find that the azimuthal asymmetry of the 230 GHz images can change by up to a factor of 3, accentuating ( T ⊥ > T ∥ ) or counteracting ( T ⊥ < T ∥ ) the image asymmetry produced by Doppler beaming. This can change the physical inferences from observations relative to models with an isotropic distribution function, e.g., by allowing for larger inclination between the line of sight and spin direction in Sgr A*. The observed image diameter and the size of the black hole shadow can also vary significantly due to plasma temperature anisotropy. We describe how the anisotropy of the plasma can affect future multifrequency and photon ring observations. We also calculate kinetic anisotropy-driven instabilities (mirror, whistler, and firehose) for relativistically hot plasmas.","PeriodicalId":50735,"journal":{"name":"Astrophysical Journal","volume":"81 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135411685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Existence of Subsonic Solitary Waves Associated with Reconnection Jets in Earth’s Magnetotail","authors":"Kuldeep Singh, Steffy Sara Varghese, Frank Verheest, Ioannis Kourakis","doi":"10.3847/1538-4357/acfe6d","DOIUrl":"https://doi.org/10.3847/1538-4357/acfe6d","url":null,"abstract":"Abstract The Magnetospheric Multiscale Spacecraft (MMS) has detected the signature of electrostatic solitary waves (ESWs) occurring in the reconnection jet site of the Earth’s magnetotail (Liu et al.). These observations have motivated us to explore the mechanism underlying the formation of fast- and slow-mode ion-acoustic solitary waves in the magnetotail region. To this end, we have formulated a three-component magnetized plasma model consisting of nonthermal electrons and two cold ion beams streaming parallel and antiparallel to the magnetic field, respectively. In this work, we have examined the existence conditions for ion-acoustic subsonic waves in a suprathermal space plasma comprising two counterstreaming (drifting) ion beams interacting with a suprathermal electron background. An exact (nonperturbative) nonlinear technique has been adopted to examine the role of the beam velocity and the spectral index on the evolution of subsonic waves. Linear analysis reveals that subsonic waves are unstable when the beam velocity is lower than a threshold value; hence in this regime, only conventional supersonic (fast) waves are formed. On the other hand, when the beam velocity exceeds the threshold, either supersonic or subsonic waves may exist. The combined impact of the beam velocity and electron superthermality on the characteristics of subsonic solitary waves has been analyzed. Our results are shown to be in good agreement with observations of slow ESWs by the MMS spacecraft. Our findings will help to unfold the so-far unexplored dynamical characteristics of subsonic waves that may occur in the reconnection site of Earth’s magnetotail.","PeriodicalId":50735,"journal":{"name":"Astrophysical Journal","volume":"33 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135412375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Internal Shock with a Background Magnetic Field for the Prompt Emission of Gamma-Ray Bursts—A Case Study of GRB 211211A","authors":"Li Zhou, Da-Bin Lin, Xing Yang, Guo-Yu Li, Kuan Liu, Jing Li, En-Wei Liang","doi":"10.3847/1538-4357/acfede","DOIUrl":"https://doi.org/10.3847/1538-4357/acfede","url":null,"abstract":"Abstract It is proposed that the synchrotron emission from an internal shock with a decaying shock-generated magnetic field can account for the prompt emission of gamma-ray bursts (GRBs). Generally, a jet from the central engine of a GRB is launched with a significant magnetization, and thus there would be a background magnetic field, rather than only the shock-generated magnetic field, in the emission region. In this paper, we study the synchrotron emission of internal shocks with both a decaying shock-generated magnetic field and a nondecaying background magnetic field. It is found that a shoulder with spectral index −1/2 appears in the low-energy regime of the radiation spectrum. The shoulder becomes dominant by increasing the ratio of the background magnetic field energy to the initial value of the shock-generated magnetic field energy f B . Correspondingly, a radiation spectrum with two bumps or a plateau around the peak of the ν F ν − ν spectrum may appear. Owing to the decay of the shock-generated magnetic field, the radiation spectral morphology in the high-energy regime is not a power-law function even though a power-law distribution of electrons is injected. We apply our model to GRB 211211A, of which the hard main emission is suggested to originate from the synchrotron emission. Compared with the spectral fitting results with a Band function and the synchrotron emission from the standard straightforward internal shocks, our model presents a perfect fitting to the observations. The fitting results show that f B is around 0.41–0.99 for the hard main emission of this burst.","PeriodicalId":50735,"journal":{"name":"Astrophysical Journal","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135456360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Maximum Energy of Shock-accelerated Cosmic Rays","authors":"Rebecca Diesing","doi":"10.3847/1538-4357/ad00b1","DOIUrl":"https://doi.org/10.3847/1538-4357/ad00b1","url":null,"abstract":"Abstract Identifying the accelerators of Galactic cosmic ray (CR) protons with energies up to a few PeV (10 15 eV) remains a theoretical and observational challenge. Supernova remnants (SNRs) represent strong candidates because they provide sufficient energetics to reproduce the CR flux observed at Earth. However, it remains unclear whether they can accelerate particles to PeV energies, particularly after the very early stages of their evolution. This uncertainty has prompted searches for other source classes and necessitates comprehensive theoretical modeling of the maximum proton energy, <?CDATA ${E}_{max }$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:msub> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>max</mml:mi> </mml:mrow> </mml:msub> </mml:math> , accelerated by an arbitrary shock. While analytic estimates of <?CDATA ${E}_{max }$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:msub> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>max</mml:mi> </mml:mrow> </mml:msub> </mml:math> have been put forward in the literature, they do not fully account for the complex interplay between particle acceleration, magnetic field amplification, and shock evolution. This paper uses a multizone, semianalytic model of particle acceleration based on kinetic simulations to place constraints on <?CDATA ${E}_{max }$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:msub> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>max</mml:mi> </mml:mrow> </mml:msub> </mml:math> for a wide range of astrophysical shocks. In particular, we develop relationships between <?CDATA ${E}_{max }$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:msub> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>max</mml:mi> </mml:mrow> </mml:msub> </mml:math> , shock velocity, size, and ambient medium. We find that SNRs can only accelerate PeV particles under a select set of circumstances, namely, if the shock velocity exceeds ∼10 4 km s −1 and escaping particles drive magnetic field amplification. However, older and slower SNRs may still produce observational signatures of PeV particles due to populations accelerated when the shock was younger. Our results serve as a reference for modelers seeking to quickly produce a self-consistent estimate of the maximum energy accelerated by an arbitrary astrophysical shock. 1 1 Presented as a thesis to the Department of Astronomy and Astrophysics, The University of Chicago, in partial fulfillment of the requirements for a Ph.D. degree.","PeriodicalId":50735,"journal":{"name":"Astrophysical Journal","volume":"7 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135510260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"oMEGACat. I. MUSE Spectroscopy of 300,000 Stars within the Half-light Radius of ω Centauri","authors":"M. S. Nitschai, N. Neumayer, C. Clontz, M. Häberle, A. C. Seth, T.-O. Husser, S. Kamann, M. Alfaro-Cuello, N. Kacharov, A. Bellini, A. Dotter, S. Dreizler, A. Feldmeier-Krause, M. Latour, M. Libralato, A. P. Milone, R. Pechetti, G. van de Ven, K. Voggel, Daniel R. Weisz","doi":"10.3847/1538-4357/acf5db","DOIUrl":"https://doi.org/10.3847/1538-4357/acf5db","url":null,"abstract":"Abstract Omega Centauri ( ω Cen) is the most massive globular cluster of the Milky Way and has been the focus of many studies that reveal the complexity of its stellar populations and kinematics. However, most previous studies have used photometric and spectroscopic data sets with limited spatial or magnitude coverage, while we aim to investigate it having full spatial coverage out to its half-light radius and stars ranging from the main sequence to the tip of the red giant branch. This is the first paper in a new survey of ω Cen that combines uniform imaging and spectroscopic data out to its half-light radius to study its stellar populations, kinematics, and formation history. In this paper, we present an unprecedented MUSE spectroscopic data set combining 87 new MUSE pointings with previous observations collected from guaranteed time observations. We extract spectra of more than 300,000 stars reaching more than 2 magnitudes below the main-sequence turnoff. We use these spectra to derive metallicity and line-of-sight velocity measurements and determine robust uncertainties on these quantities using repeat measurements. Applying quality cuts we achieve signal-to-noise ratios (S/Ns) of 16.47/73.51 and mean metallicity errors of 0.174/0.031 dex for the main-sequence stars (18 mag <mag F 625 W < 22 mag) and red giant branch stars (16 mag <mag F 625 W < 10 mag), respectively. We correct the metallicities for atomic diffusion and identify foreground stars. This massive spectroscopic data set will enable future studies that will transform our understanding of ω Cen, allowing us to investigate the stellar populations, ages, and kinematics in great detail.","PeriodicalId":50735,"journal":{"name":"Astrophysical Journal","volume":"14 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135510383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Discovery of an X-Ray Photoionized Optical Nebula and a Radio Nebula Associated with the ULX NGC 4861 X-1","authors":"Hang Gong, Ryan Urquhart, Alexandr Vinokurov, Yu Bai, Antonio Cabrera-Lavers, Sergei Fabrika, Liang Wang, Jifeng Liu","doi":"10.3847/1538-4357/acf8c3","DOIUrl":"https://doi.org/10.3847/1538-4357/acf8c3","url":null,"abstract":"Abstract We have conducted long-slit spectroscopic observations and analyzed archival radio data for the ultraluminous X-ray source (ULX) NGC 4861 X-1. Our spectral line analysis unveils NGC 4861 X-1 as the fourth ULX situated within an X-ray photoionized nebula, following three previous findings made approximately two decades ago. Remarkably, we discover NGC 4861 X-1 also possesses a radio nebula emitting optically thin synchrotron radiation, which contradicts its X-ray photoionization and raises doubts about the four ULXs being a mere coincidence. Instead of gradually accumulating from different bands bit by bit, our multiband discovery is made all at once. Moreover, we tentatively perceive a faint continuum spectrum of the optical nebula. Further observations are needed to ascertain its radio structures and verify the optical continuum.","PeriodicalId":50735,"journal":{"name":"Astrophysical Journal","volume":"5 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135516414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Radio Plateaus in Gamma-Ray Burst Afterglows and Their Application in Cosmology","authors":"Xiao Tian, Jia-Lun Li, Shuang-Xi Yi, Yu-Peng Yang, Jian-Ping Hu, Yan-Kun Qu, Fa-Yin Wang","doi":"10.3847/1538-4357/acfed8","DOIUrl":"https://doi.org/10.3847/1538-4357/acfed8","url":null,"abstract":"Abstract The plateau phase in radio afterglows has been observed in very few gamma-ray bursts (GRBs), and in this paper, 27 radio light curves with plateau phases were acquired from the published literature. We obtain the related parameters of the radio plateau, such as temporal indexes during the plateau phase ( α 1 and α 2 ), break time ( T b,z ), and the corresponding radio flux ( F b ). The two-parameter Dainotti relation between the break time of the plateau and the corresponding break luminosity ( L b,z ) in the radio band is &lt;?CDATA ${L}_{{rm{b}},{rm{z}}}propto {T}_{{rm{b}},{rm{z}}}^{-1.20pm 0.24}$?&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"&gt; &lt;mml:msub&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;L&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"normal\"&gt;b&lt;/mml:mi&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mi mathvariant=\"normal\"&gt;z&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:msub&gt; &lt;mml:mo&gt;∝&lt;/mml:mo&gt; &lt;mml:msubsup&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;T&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"normal\"&gt;b&lt;/mml:mi&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mi mathvariant=\"normal\"&gt;z&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;−&lt;/mml:mo&gt; &lt;mml:mn&gt;1.20&lt;/mml:mn&gt; &lt;mml:mo&gt;±&lt;/mml:mo&gt; &lt;mml:mn&gt;0.24&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;/mml:msubsup&gt; &lt;/mml:math&gt; . Including the isotropic energy E γ ,iso and peak energy E p,i , the three-parameter correlations for the radio plateaus are written as &lt;?CDATA ${L}_{{rm{b}},{rm{z}}}propto {T}_{{rm{b}},{rm{z}}}^{-1.01pm 0.24}{E}_{gamma ,mathrm{iso}}^{0.18pm 0.09}$?&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"&gt; &lt;mml:msub&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;L&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"normal\"&gt;b&lt;/mml:mi&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mi mathvariant=\"normal\"&gt;z&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:msub&gt; &lt;mml:mo&gt;∝&lt;/mml:mo&gt; &lt;mml:msubsup&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;T&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"normal\"&gt;b&lt;/mml:mi&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mi mathvariant=\"normal\"&gt;z&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;−&lt;/mml:mo&gt; &lt;mml:mn&gt;1.01&lt;/mml:mn&gt; &lt;mml:mo&gt;±&lt;/mml:mo&gt; &lt;mml:mn&gt;0.24&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;/mml:msubsup&gt; &lt;mml:msubsup&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;E&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;γ&lt;/mml:mi&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mi&gt;iso&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mn&gt;0.18&lt;/mml:mn&gt; &lt;mml:mo&gt;±&lt;/mml:mo&gt; &lt;mml:mn&gt;0.09&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;/mml:msubsup&gt; &lt;/mml:math&gt; and &lt;?CDATA ${L}_{{rm{b}},{rm{z}}}propto {T}_{{rm{b}},{rm{z}}}^{-1.18pm 0.27}{E}_{{rm{p}},{rm{i}}}^{0.05pm 0.28}$?&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"&gt; &lt;mml:msub&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;L&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"normal\"&gt;b&lt;/mml:mi&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mi mathvariant=\"normal\"&gt;z&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:msub&gt; &lt;mml:mo&gt;∝&lt;/mml:mo&gt; &lt;mml:msubsup&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;T&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"normal\"&gt;b&lt;/mml:mi&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mi mathvariant=\"normal\"&gt;z&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;−&lt;/mml:mo&gt; &lt;mml:mn&gt;1.18&lt;/mml:mn&gt; &lt;mml:mo&gt;±&lt;/mml:mo&gt; &lt;mml:mn&gt;0.27&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;/mml:msubsup&gt; &lt;mml:msubsup&gt; ","PeriodicalId":50735,"journal":{"name":"Astrophysical Journal","volume":"28 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135764440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}