Power-law Electron Distribution Research Articles

Electron Acceleration in Magnetic Islands in Quasi-parallel Shocks

We report new theories and simulations for electron acceleration in magnetic islands generated by magnetic reconnection in the shock turbulence in a quasi-parallel shock, using a 2 and 1/2 dimensional particle-in-cell simulation. When an island is moving, unmagnetized electrons are accelerated by the Hall electric field pointing toward the island center. In a stationary island, some electrons are energized by “island betatron acceleration” due to the induction electric field when the island core magnetic field changes with time. In the simulation, almost all of the high-energy electrons in the shock transition region that show a power-law distribution are accelerated in ion-skin-depth-scale magnetic flux ropes, and about half of them are accelerated by the Hall electric field and island betatron acceleration. These mechanisms can produce a power-law electron distribution, and also inject electrons into the diffusive shock acceleration. The mechanisms are applicable to quasi-parallel shocks with high Alfvén Mach numbers (M A > 10), including planetary bow shocks and shocks in astrophysical objects such as supernova remnants.

Sunyaev-Zeldovich signatures from non-thermal, relativistic electrons using CMB maps

Relativistically energetic, non-thermal population of electrons can give rise to unique CMB spectral distortion signatures which can be significantly different from thermal Sunyaev-Zeldovich signal or y-distortion. These signatures depend upon the spectrum of non-thermal electrons, therefore, a detection can inform us about the existence and abundance of non-thermal electrons in our universe. Using public CMB maps and data, we derive upper limits on non-thermal y-parameter for a relativistic, power-law electron distribution. With future CMB experiments, we may be in a position to detect or put significantly tighter constraints on these signals which can affect our understanding of non-thermal electron distributions in our universe.

A Generic Model for a Persistent Radio Source around Fast Radio Bursts

The repeated fast radio bursts FRB 121102A and FRB 190520B have been reported, along with a spatially coincident, compact, persistent radio emission. In this paper, we present a parameterized one-zone model, with the basic scenario that a relativistic magnetized wind from the pulsar sweeps up the surroundings, e.g., freely expanding supernova ejecta, giving rise to a power-law distribution of electrons between the forward shock and the termination shock. We show that via appropriate adjustment of the model parameters, we can obtain synchrotron radio emission properties from the one-zone model bright enough to account for the observation, simply and analytically fitting the observed spectra well. Through dynamical evolution of the model, we can also obtain time-varying relevant properties. This parameterized model does not depend on concrete physical models such as a central engine; instead, we can constraint the physical model via comparison between parameters and observations, indicating the information about the central engine and surroundings. We also discuss the synchrotron self-Compton emission in our scenario in the end but find no clue about the counterparts at other wave bands.

Internal Shock with a Background Magnetic Field for the Prompt Emission of Gamma-Ray Bursts—A Case Study of GRB 211211A

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.

Understanding the broad-band emission process of 3C 279 through long term spectral analysis

ABSTRACT The long term broad-band spectral study of Flat Spectrum Radio Quasars during different flux states has the potential to infer the emission mechanisms and the cause of spectral variations. To scrutinize this, we performed a detailed broad-band spectral analysis of 3C 279 using simultaneous Swift-XRT/UVOT and Fermi-LAT observations spanning from 2008 August to 2022 June. We also supplement this with the simultaneous NuSTAR observations of the source. The optical/UV, X-ray, and γ-ray spectra were individually fitted by a power law to study the long term variation in the flux and the spectral indices. A combined spectral fit of simultaneous optical/UV and X-ray spectra was also performed to obtain the transition energy at which the spectral energy distribution is minimum. The correlation analysis suggests that the long term spectral variations of the source are mainly associated with the variations in the low energy index and the break energy of the broken power-law electron distribution which is responsible for the broad-band emission. The flux distribution of the source represents a lognormal variability while the γ-ray flux distribution showed a clear double lognormal behaviour. The spectral index distributions were again normal except for γ-ray which showed a double-Gaussian behaviour. This indicates that the lognormal variability of the source may be associated with the normal variations in the spectral index. The broad-band spectral fit of the source using synchrotron and inverse Compton processes indicates different emission processes are active at optical/UV, X-ray, and γ-ray energies.

On the Properties of Inverse Compton Spectra Generated by Upscattering a Power-law Distribution of Target Photons

Relativistic electrons are an essential component in many astrophysical sources, and their radiation may dominate the high-energy bands. Inverse Compton (IC) emission is the radiation mechanism that plays the most important role in these bands. The basic properties of IC, such as the total and differential cross sections, have long been studied; the properties of the IC emission depend strongly not only on the emitting electron distribution but also on the properties of the target photons. This complicates the phenomenological studies of sources, where target photons are supplied from a broad radiation component. We study the spectral properties of IC emission generated by a power-law distribution of electrons on a power-law distribution of target photons. We approximate the resulting spectrum by a broken-power-law distribution and show that there can be up to three physically motivated spectral breaks. If the target photon spectrum extends to sufficiently low energies, (m e and c are electron mass and speed of light, respectively; and are the minimum/maximum energies of target photons and electrons, respectively), then the high-energy part of the IC component has a spectral slope typical for the Thomson regime with an abrupt cutoff close to . The spectra typical for the Klein–Nishina regime are formed above . If the spectrum of target photons features a cooling break, i.e., a change of the photon index by 0.5 at ε br, then the transition to the Klein–Nishina regime proceeds through an intermediate change of the photon index by 0.5 at .

Understanding the very high energy γ-ray excess in nearby blazars using leptonic model

ABSTRACT The availability of simultaneous X-ray and very high energy (VHE) observations of blazars helps to identify the plausible radiative contributors to the VHE emission. Under leptonic scenario, the VHE emission from BL Lacs are attributed to the synchrotron self Compton (SSC) emission. However, many BL Lacerate (BL Lacs) have shown significant hardening at VHE after correction for the extragalactic background light (EBL) attenuation. We study the spectral hardening of two nearby BL Lac objects, Mkn 421 and Mkn 501 having most number of simultaneous X-ray and VHE observations available among all the blazars. These BL Lacs are relatively close and the effect of EBL attenuation is relatively minimal/negligible. We study the scatter plot between the X-ray spectral indices and intrinsic VHE indices to identify the plausible origin of the VHE emission. For Mkn 501, the VHE spectral indices are steeper than X-ray spectra, suggesting the scattering process happening at extreme Klein–Nishina regime. On the other hand, for Mkn 421, the VHE spectra is remarkably harder than the X-ray spectra, which suggests an additional emission mechanism other than the SSC process. We show this hard VHE spectrum of Mkn 421 can be explained by considering the inverse Compton (IC) emission from a broken power-law electron distribution with Maxwellian pileup. The possibility of the hadronic contribution at VHE γ-rays is also explored by modelling the hard spectrum under the photomeson process.

Multiwavelength variability and broad-band SED modelling of BL Lac during a bright flaring period MJD 59000–59943

ABSTRACT We carried out a detailed temporal and spectral study of the BL Lacertae (BL Lac) by using the long-term Fermi-Large Area Telescope (LAT) and Swift-X-ray Telescope (XRT)/Ultraviolet Optical Telescope (UVOT) observations, during the period MJD 59000–59943. The daily-binned γ-ray light curve displays a maximum flux of $1.74\pm 0.09\times 10^{-5} \,\rm photons\, cm^{-2}\, s^{-1}$ on MJD 59868, which is the highest daily γ-ray flux observed from BL Lac. The γ-ray variability is characterized by power spectral density (PSD), rms–flux relation, and flux distribution study. We find that the power-law model fits the PSD with index ∼1, which suggests a long-memory process at work. The observed rms–flux relation exhibits a linear trend, which indicates that the γ-ray flux distribution follows a lognormal distribution. The skewness/Anderson–Darling test and histogram fit reject the normality of flux distribution, and instead suggest that the flux distribution is a lognormal distribution. The fractional variability amplitude shows that the source is more variable in the X-ray band than in optical/ultraviolet/γ-ray bands. In order to obtain an insight into the underlying physical process, we extracted broad-band spectra from different time periods of the light curve. The broad-band spectra are statistically fitted with the convolved one-zone leptonic model with different forms of the particle energy distribution. We found that spectral energy distribution during different flux states can be reproduced well with the synchrotron, synchrotron self-Compton, and external Compton emissions from a broken power-law electron distribution, ensuring equipartition condition. A comparison between the best-fitting physical parameters shows that the variation in different flux states is mostly related to an increase in the bulk Lorentz factor and spectral hardening of the particle distribution.

RAIKOU (来光): A General Relativistic, Multiwavelength Radiative Transfer Code

We present a general relativistic radiative transfer code RAIKOU (来光) for multiwavlength studies of spectra and images including the black hole shadows around Kerr black holes. Important radiative processes in hot plasmas around black holes, i.e., (cyclo-)synchrotron, bremsstrahlung emission/absorption, and Compton/inverse-Compton scattering, are incorporated. The Maxwell–Jüttner and single/broken power-law electron distribution functions are implemented to calculate the radiative transfer via both thermal and nonthermal electrons. Two calculation algorithms are implemented for studies of the images and broadband spectra. An observer-to-emitter ray-tracing algorithm, which inversely solves the radiative transfer equation from the observer screen to emitting plasmas, is suitable for an efficient calculations of the images, e.g., the black hole shadows observed by the Event Horizon Telescope, and spectra without Compton effects. On the other hand, an emitter-to-observer Monte Carlo algorithm, by which photons are transported with a Monte Carlo method including the effects of Compton/inverse-Compton scatterings, enables us to compute multiwavelength spectra, with their energy bands broadly ranging from radio to very high energy gamma-ray. The X-ray black hole shadows, which are formed via synchrotron emission and inverse-Compton scattering processes and will be observed in the future X-ray interferometry missions, can be also computed with this algorithm. The code is generally applicable to accretion flows around Kerr black holes with relativistic jets and winds/coronae with various mass accretion rates (i.e., radiatively inefficient accretion flows, super-Eddington accretion flows, and others). We demonstrate an application of the code to a radiatively inefficient accretion flow onto a supermassive black hole.

The Radio to GeV Afterglow of GRB 221009A

GRB 221009A (z = 0.151) is one of the closest known long γ-ray bursts (GRBs). Its extreme brightness across all electromagnetic wavelengths provides an unprecedented opportunity to study a member of this still-mysterious class of transients in exquisite detail. We present multiwavelength observations of this extraordinary event, spanning 15 orders of magnitude in photon energy from radio to γ-rays. We find that the data can be partially explained by a forward shock (FS) from a highly collimated relativistic jet interacting with a low-density, wind-like medium. Under this model, the jet’s beaming-corrected kinetic energy (E K ∼ 4 × 1050 erg) is typical for the GRB population. The radio and millimeter data provide strong limiting constraints on the FS model, but require the presence of an additional emission component. From equipartition arguments, we find that the radio emission is likely produced by a small amount of mass (≲6 × 10−7 M ⊙) moving relativistically (Γ ≳ 9) with a large kinetic energy (≳1049 erg). However, the temporal evolution of this component does not follow prescriptions for synchrotron radiation from a single power-law distribution of electrons (e.g., in a reverse shock or two-component jet), or a thermal-electron population, perhaps suggesting that one of the standard assumptions of afterglow theory is violated. GRB 221009A will likely remain detectable with radio telescopes for years to come, providing a valuable opportunity to track the full lifecycle of a powerful relativistic jet.

Effects of Fully Relativistic Condition on Electron Cyclotron Maser Emission

The electron cyclotron maser (ECM) instability is a very important nonthermal radiation mechanism. It has been developed by proposing various electron distribution functions as well as the relativistic resonance condition, called the semirelativistic correction. Taking account of the relativistic effects of both the velocity distribution of energetic electrons and the resonance condition, called the fully relativistic correction, the present paper investigates the ECM instability driven by a power-law electron distribution with a low-energy cutoff. The results show that (1) both in the semirelativistic and fully relativistic cases, the growth rate and relative frequency bandwidth of ordinary (O) and extraordinary (X) modes show a positive correlation with cutoff energy E c , i.e., the peak frequency decreases with increasing E c ; (2) the peak frequency ratio (H peak/F peak) of the harmonic and fundamental waves is always ∼2; (3) compared with the semirelativistic case, the fully relativistic case has a larger growth rate (for both the O and X mode) and a smaller peak frequency (only for the O mode) for energy > 50 keV, and there is almost no difference at lower energy for the two cases; (4) the peak frequency of the X1 mode can be higher than its cutoff frequency in a strongly magnetized plasma, implying that the X1 mode emission may escape more easily for a higher E c and stronger magnetic field. These results can be helpful for us to understand better the physics of radio bursts from the Sun and other objects.

Plasma dynamics in the flaring loop observed by RHESSI

Context. Hard X-rays (HXRs) contain the most direct information about the non-thermal electron population in solar flares. The approximation of the HXR emission mechanism (bremsstrahlung), known as the thick-target model, is well developed. It allows one to diagnose the physical conditions within a flaring structure. The thick-target model predicts that in flare foot points, we should observe lowering of HXR sources’ altitude with increasing energy. Aims. The foot point of HXR sources result from the direct interaction of non-thermal electron beams with plasma in the lower part of the solar atmosphere, where the density increases rapidly. Therefore, we can estimate the plasma density distribution along the non-thermal electron beam directly from the observations of the altitude-energy relation obtained for the HXR foot point sources. However, the relation is not only density-dependent. Its shape is also determined by the power-law distribution of non-thermal electrons. Additionally, during the impulsive phase, the plasma density and a degree of ionisation within foot points may change dramatically due to heating and chromospheric evaporation. For this reason, the interpretation of observed HXR foot point sources’ altitudes is not straightforward and needs detailed numerical modelling of the electron precipitation process. Methods. We present the results of numerical modelling of one well-observed solar flare. We used HXR observations obtained by RHESSI. The numerical model was calculated using the hydrodynamic 1D model with an application of the Fokker-Planck formalism for non-thermal beam precipitation. Results. HXR data were used to trace chromospheric density changes during a non-thermal emission burst, in detail. We have found that the amount of mass that evaporated from the chromosphere is in the range of 2.7 × 1013 − 4.0 × 1014 g. This is in good agreement with the ranges obtained from hydrodynamical modelling of a flaring loop (2.3 × 1013 − 3.3 × 1013 g), and from an analysis of observed emission measure in the loop top (3.9 × 1013 − 5.3 × 1013 g). Additionally, we used specific scaling laws which gave another estimation of the evaporated mass around 2 × 1014 g. Conclusions. Consistency between the obtained values shows that HXR images may provide an important constraint for models – a mass of plasma that evaporated due to a non-thermal electron beam depositing energy in the chromosphere. High-energy, non-thermal sources’ (above 20 keV in this case) positions fit the column density changes obtained from the hydrodynamical model perfectly. Density changes seem to be less affected by the electrons’ spectral index. The obtained results significantly improve our understanding of non-thermal electron beam precipitation and allow us to refine the energy balance in solar flare foot points during the impulsive phase.

Exact Analytical Expression for the Synchrotron Radiation Spectrum in the Gaussian Turbulent Magnetic Field

Abstract We demonstrate that the exact solution for the spectrum of synchrotron radiation from an isotropic population of monoenergetic electrons in a turbulent magnetic field with a Gaussian distribution of local field strengths can be expressed in the simple analytic form: , where We use this expression to find the approximate synchrotron spectra for power-law electron distributions with -type high-energy cutoff; the resulting synchrotron spectrum has the exponential cutoff factor with a frequency raised to the 2β/(3β + 4) power in the exponent. For the power-law electron distribution without a high-energy cutoff, we find the coefficient a m as a function of the power-law index, which results in the exact expression for the synchrotron spectrum when using the monochromatic (i.e., each electron radiates at the frequency ) approximation.

Unravelling the unusually curved X-ray spectrum of RGB J0710 + 591 using AstroSat observations

ABSTRACT We report the analysis of simultaneous multiwavelength data of the high-energy-peaked blazar RGB J0710 + 591 from the Large Area X-ray Proportional Counters, Soft X-ray focusing Telescope, and Ultraviolet Imaging Telescope (UVIT) instruments onboard AstroSat. The wide band X-ray spectrum (0.35–30 keV) is modelled as synchrotron emission from a non-thermal distribution of high-energy electrons. The spectrum is unusually curved, with a curvature parameter βp ∼ 6.4 for a log parabola particle distribution, or a high-energy spectral index p2 > 4.5 for a broken power-law distribution. The spectrum shows more curvature than an earlier quasi-simultaneous analysis of Swift–XRT/NuSTAR data where the parameters were βp ∼ 2.2 or p2 ∼ 4. It has long been known that a power-law electron distribution can be produced from a region where particles are accelerated under Fermi process and the radiative losses in acceleration site decide the maximum attainable Lorentz factor, γmax. Consequently, this quantity decides the energy at which the spectrum curves steeply. We show that such a distribution provides a more natural explanation for the AstroSat data as well as the earlier XRT/NuSTAR observation, making this as the first well-constrained determination of the photon energy corresponding to γmax. This in turn provides an estimate of the acceleration time-scale as a function of magnetic field and Doppler factor. The UVIT observations are consistent with earlier optical/UV measurements and reconfirm that they plausibly correspond to a different radiative component than the one responsible for the X-ray emission.

Two Years of Nonthermal Emission from the Binary Neutron Star Merger GW170817: Rapid Fading of the Jet Afterglow and First Constraints on the Kilonova Fastest Ejecta

Abstract We present Chandra and Very Large Array observations of GW170817 at ∼521–743 days post-merger, and a homogeneous analysis of the entire Chandra data set. We find that the late-time nonthermal emission follows the expected evolution of an off-axis relativistic jet, with a steep temporal decay F ν ∝ t − 1.95 ± 0.15 and power-law spectrum F ν ∝ ν − 0.575 ± 0.007 . We present a new method to constrain the merger environment density based on diffuse X-ray emission from hot plasma in the host galaxy and find n ≤ 9.6 × 10 − 3 cm − 3 . This measurement is independent from inferences based on jet afterglow modeling and allows us to partially solve for model degeneracies. The updated best-fitting model parameters with this density constraint are a fireball kinetic energy E 0 = 1.5 − 1.1 + 3.6 × 10 49 erg ( E iso = 2.1 − 1.5 + 6.4 × 10 52 erg ) and jet opening angle θ 0 = 5.9 − 0.7 + 1.0 deg with characteristic Lorentz factor Γ j = 163 − 43 + 23 , expanding in a low-density medium with n 0 = 2.5 − 1.9 + 4.1 × 10 − 3 cm − 3 and viewed θ obs = 30.4 − 3.4 + 4.0 deg off-axis. The synchrotron emission originates from a power-law distribution of electrons with index p = 2.15 − 0.02 + 0.01 . The shock microphysics parameters are constrained to ϵ e = 0.18 − 0.13 + 0.30 and ϵ B = 2.3 − 2.2 + 16.0 × 10 − 3 . Furthermore, we investigate the presence of X-ray flares and find no statistically significant evidence of ≥2.5σ of temporal variability at any time. Finally, we use our observations to constrain the properties of synchrotron emission from the deceleration of the fastest kilonova ejecta with energy E k KN ∝ ( Γ β ) − α into the environment, finding that shallow stratification indexes α ≤ 6 are disfavored. Future radio and X-ray observations will refine our inferences on the fastest kilonova ejecta properties.

Matter effects and coherent effect of neutrinos produced from -ray bursts * * Supported in part by the Natural Science Foundation of China (11675131, 11775038, 11603005, 11847301), and by the Fundamental Research Funds for the Central Universities (2019CDJDWL0005)

Neutrinos produced from -ray bursts (GRBs) carry significant physical information. The electron density in the GRBs outflow is very large. In this study, we calculate the matter effect on neutrinos when they propagate through such a dense region. The average survival probability and the flavor ratio of neutrinos are determined. The ratio of resonant neutrino energy from different spherical shells provides the information of power index N for the power-law distribution of electrons in the hot fireball model. Electron density in the magnetic jet model is sufficiently lower than in the hot fireball model. The matter effect on neutrinos can be used to distinguish these two models. The coherent effect of strongly lensed PeV neutrinos is also discussed. The average survival probability of strongly-lensed electron neutrinos in the normal and inverted hierarchical cases are presented. The results show that this coherent effect can be used to determine the hierarchical mass of neutrinos.

Systematic Physical Characterization of the γ-Ray Spectra of 2FHL Blazars

Abstract We test different physically motivated models for the spectral shape of the γ-ray emission in a sample of 128 blazars with known redshifts detected by the Fermi Large Area Telescope (LAT) at energies above 50 GeV. The first nine years of LAT data in the energy range from 300 MeV to 2 TeV are analyzed in order to extend the spectral energy coverage of the 2FHL blazars in our sample. We compare these spectral data to four leptonic models for the production of γ-rays through Compton scattering by a population of electrons with different spectral shapes. In the first three models we consider Compton scattering in the Thomson regime with different acceleration mechanisms for the electrons. In the fourth model we consider Compton scattering by a pure power-law distribution of electrons with spectral curvature due to scattering in the Klein–Nishina regime. The majority of blazar γ-ray spectra are preferentially fit with either a power law with exponential cutoff in the Thomson regime or a power-law electron distribution with Compton scattering in the Klein–Nishina regime, while a log-parabola with a low-energy power-law and broken power-law spectral shape in the Thomson regime appears systematically disfavored, which is likely a consequence of the restriction to pure Thomson scattering that we imposed on those models. This finding may be an indication that the γ-ray emission from flat-spectrum radio quasars (FSRQs) in the 2FHL catalog is dominated by Compton scattering of radiation from the dusty torus, while in the case of BL Lac objects, it is dominated by synchrotron self-Compton radiation.

Establishing the spectral turnover of blazar PKS 2155−304 as an outcome of radiative losses

Abstract The broad-band optical/UV and X-ray spectra of blazars have been often modelled as synchrotron component arising from a broken power-law distribution of electrons. A broken power-law distribution is expected, since the high-energy electrons undergo radiative losses effectively. The change in the energy index should then be ≈1 and corresponds to a spectral index difference of 0.5. However, one of the long outstanding problems has been that the observed index change is significantly different. On the other hand, recent high-quality observations of blazars suggest that their local spectra may not be a power law, instead have a slight curvature and often represented by a log-parabola model. Using XMM–Newtonobservations spanning over 12 yr for the BL Lac PKS 2155−304, we show that the optical/UV and X-ray spectra can be well represented by a broken log-parabola model. Further, we show that such a spectrum can indicate the energy dependence of the electron escape time-scale from the main acceleration zone. This novel approach, besides addressing the observed difference in the photon spectral indices, also tries to explain the spectral turn over in far-UV/soft X-rays as a result of the radiative losses.

Revisiting gamma-ray burst afterglows with time-dependent parameters

The relativistic external shock model of gamma-ray burst (GRB) afterglows has been established with five free parameters, i.e., the total kinetic energy E, the equipartition parameters for electrons and for the magnetic field , the number density of the environment n and the index of the power-law distribution of shocked electrons p. A lot of modified models have been constructed to consider the variety of GRB afterglows, such as: the wind medium environment by letting n change with radius, the energy injection model by letting kinetic energy change with time and so on. In this paper, by assuming all four parameters (except p) change with time, we obtain a set of formulas for the dynamics and radiation, which can be used as a reference for modeling GRB afterglows. Some interesting results are obtained. For example, in some spectral segments, the radiated flux density does not depend on the number density or the profile of the environment. As an application, through modeling the afterglow of GRB 060607A, we find that it can be interpreted in the framework of the time dependent parameter model within a reasonable range.

The energy distribution of electrons in radio jets

Black-hole and neutron-star X-ray binaries exhibit compact radio jets, when they are in the so called quiescent, hard, or hard intermediate states. The radio spectrum in these states is flat to slightly inverted. It is widely accepted that the energy distribution of the electrons, in the rest frame of the jet, is a power law with index p. A power-law energy distribution of the electrons in the jet is sufficient to explain the flat to slightly inverted spectrum emitted by the jet from radio to near infrared wavelengths, but is it necessary? Contrary to what our thinking was decades ago, now we know that the jets originate in the hot inner flow around black holes and neutron stars. Thus, we have investigated the spectrum that is emitted by a thermal jet with kT in the range 100-250 keV. We have computed the emitted spectrum from radio to near infrared using either a thermal distribution of electrons or a power-law one. We have found that parabolic jets with a thermal distribution of electrons give inverted spectra with alpha in the range 0-0.4, while jets with a power-law distribution of electrons give inverted spectra with alpha in the range 0-0.2. The rest of the parameters are kept the same in the two cases. The break frequency, which marks the transition from optically thick to optically thin synchrotron emission, is comparable for the two electron energy distributions. Our conclusion is that, contrary to common belief, it is not necessary to invoke a power-law energy distribution of the electrons in a jet to explain its flat to slightly inverted radio spectrum. A relativistic Maxwellian produces similar spectra. Thus, the widely invoked corona around black holes in X-ray binaries may actually be the jet.