High-energy Power Law Research Articles

Intrapulse Spectral Evolution in Photospheric Gamma-Ray Bursts

Photons that decouple from a relativistic jet do so over a range of radii, leading to a spreading in arrival times at the observer. Therefore, changes to the comoving photon distribution across the decoupling zone are encoded in the emitted signal. In this paper, we study such spectral evolution occurring across a pulse. We track the radiation from the deep subphotospheric regions all the way to the observed time-resolved signal, accounting for emission at various angles and radii. We assume a simple power-law photon spectrum injection over a range of optical depths and let the photons interact with the local plasma. At high optical depths, we find that the radiation exists in one of three characteristic regimes, two of which exhibit a high-energy power law. Depending on the nature of the injection, this power law can persist to low optical depths and manifest itself during the rise time of the pulse with a spectral index β ≈ α − 1, where α is the low-energy spectral index. The results are given in the context of a gamma-ray burst jet, but are general to optically thick, relativistic outflows.

Enhancement of fusion reactivity under non-Maxwellian distributions: effects of drift-ring-beam, slowing-down, and kappa super-thermal distributions

Non-Maxwellian distributions of particles are commonly observed in fusion studies, especially for magnetic confinement fusion plasmas. The particle distribution has a direct effect on fusion reactivity, which is the focus of this study. We investigate the effects of three types of non-Maxwellian distributions, namely drift-ring-beam, slowing-down, and kappa super-thermal distributions, on the fusion reactivities of D-T (Deuterium-Trillium) and p-B11 (proton-Boron) using a newly developed program, where the enhancement of fusion reactivity relative to the Maxwellian distribution is computed while keeping the total kinetic energy constant. The calculation results show that for the temperature ranges of interest to us, namely 5–50 keV for D-T and 100–500 keV for p-B11, these non-Maxwellian distributions can enhance the fusion reactivities. In the case of the drift-ring-beam distribution, the perpendicular ring beam velocity leads to decreased enhancement in low temperature range and increased enhancement in high temperature range. This effect is favorable for p-B11 fusion reaction and unfavorable for D-T fusion reaction. This is because the important temperature range for fusion reaction significantly overlaps with the high temperature enhancement range, while the important temperature range for fusion significantly overlaps with the low temperature reduction range. In the slowing-down distribution, the birth speed plays a crucial role in both reactions, and increasing birth speed leads to a shift in the enhancement ranges towards lower temperatures, which is beneficial for both reactions. Finally, the kappa super-thermal distribution results in a relatively large enhancement in the low temperature range with a small high energy power-law index . Overall, this study provides insight into the effects of non-Maxwellian distributions on fusion reactivity and highlights potential opportunities for enhancing fusion efficiency.

Photon scattering in a relativistic outflow having velocity shear: a novel mechanism of generation for high energy power-law spectra

Abstract. We show that an extragalactic jet with a velocity shear gives rise to Fermi like acceleration process for photons scattering withing the shear layers of the jet. Such photons then gain energy to produce a high energy power law. These power law spectra at high energies are frequently observed in several extragalactic objects such as Gamma Ray Bursts (GRBs). We implement the model on GRBs to show that the obtained range of the photon indices are well within their observed values. The analytic results are confirmed with numerical simulations following Monte Carlo approach.

Proton Synchrotron Origin of the Very-high-energy Emission of GRB 190114C

We consider here a proton-synchrotron model to explain the MAGIC observation of GRB 190114C afterglow in the energy band of 0.2–1 TeV, while the X-ray spectra are explained by electron-synchrotron emission. Given the uncertainty of the particle acceleration process, we consider several variations of the model, and show that they all match the data very well. We find that the values of the uncertain model parameters are reasonable: isotropic explosion energy ∼1054.5 erg, ambient density ∼10–100 cm−3, and the fraction of electrons/protons accelerated to a high-energy power law is of a few percent. All these values are directly derived from the observed teraelectronvolt and X-ray fluxes. The model also requires that protons be accelerated to observed energies as high as a few 1020 eV. Further, assuming that the jet break takes place after 106 s gives the beaming-corrected energy of the burst to be ≈1053 erg, which is one to two orders of magnitude higher than usually inferred, because of the small fraction of electrons accelerated. Our modeling is consistent with both late time data at all bands, from optical to X-rays, and with numerical models of particle acceleration. Our results thus demonstrate the relevance of proton-synchrotron emission to the high-energy observations of gamma-ray bursts during their afterglow phase.

Photons’ Scattering in Relativistic Plasma with Velocity Shear: Generation of High Energy Power-law Spectra

A high energy power law is a common feature in the spectra of many astrophysical objects. We show that the photons in an unmagnetized relativistic plasma composed of electrons and protons with a variable Lorentz factor (or a velocity shear) go through repeated scattering with electrons to gain energy. The escaped population of photons naturally produces a power-law-shaped spectrum making it a photon’s analog to the conventional Fermi acceleration mechanism for charged particles. Thus, this mechanism provides a natural alternative to current explanations of high energy power-law spectra via synchrotron or thermal Comptonization. The model is applicable to any relativistic plasma beam with an arbitrary Lorentz factor profile. We implement the theory to the gamma-ray burst prompt phase and show that the obtained range of the photon indices is compatible with the observed values and the results of Monte Carlo simulations that we carry out independently. Therefore, the observed high energy spectral indices provide a unique indicator of the jet structure.

Testing warm Comptonization models for the origin of the soft X-ray excess in AGNs

The X-ray spectra of many active galactic nuclei (AGNs) show a soft X-ray excess below 1–2 keV on top of the extrapolated high-energy power law. The origin of this component is uncertain. It could be a signature of relativistically blurred, ionized reflection or the high-energy tail of thermal Comptonization in a warm (kT ~ 1 keV), optically thick (τ ≃ 10–20) corona producing the optical/UV to soft X-ray emission. The purpose of the present paper is to test the warm corona model on a statistically significant sample of unabsorbed, radio-quiet AGNs with XMM-Newton archival data, providing simultaneous optical/UV and X-ray coverage. The sample has 22 objects and 100 observations. We use two thermal Comptonization components to fit the broadband spectra, one for the warm corona emission and one for the high-energy continuum. In the optical/UV, we also include the reddening, the small blue bump, and the Galactic extinction. In the X-rays, we include a warm absorber and a neutral reflection. The model gives a good fit (reduced χ2 < 1.5) to more than 90% of the sample. We find the temperature of the warm corona to be uniformly distributed in the 0.1–1 keV range, while the optical depth is in the range ~10–40. These values are consistent with a warm corona covering a large fraction of a quasi-passive accretion disk, i.e., that mostly reprocesses the warm corona emission. The disk intrinsic emission represents no more than 20% of the disk total emission. According to this interpretation, most of the accretion power would be released in the upper layers of the accretion flow.

High energy power-law tail in X-ray binaries and bulk Comptonization due to an outflow from a disk

We study the high energy power-law tail emission of X-ray binaries (XRBs) by a bulk Comptonization process which usually observe in the very high soft VHS state of blackhole BH XRBs and the high soft HS state of neutron star (NS) and BH XRBs. Earlier, to generate the power-law tail in bulk Comptonization framework, a free-fall converging flow into BH or NS has been considered as a bulk region. In this work, for a bulk region we consider mainly an outflow geometry from the accretion disk which is bounded by a torus surrounding the compact object. We have a two choice for an outflow geometry i) collimated flow ii) conical flow of opening angle $\theta_b$ and the axis is perpendicular to the disk. We also consider an azimuthal velocity of the torus fluids as a bulk motion where the fluids are rotating around the compact object (a torus flow). We find that the power-law tail can be generated in a torus flow with having large optical depth and bulk speed ($>$ 0.75c), and in conical flow with $\theta_b$ $>$ $\sim$30 degree for a low value of Comptonizing medium temperature. Particularly, in conical flow the low opening angle is more favourable to generate the power-law tail in both state HS and VHS. We notice that when the outflow is collimated, then the emergent spectrum does not have power-law component for a low Comptonizing medium temperature.

Monte Carlo Simulations of Photospheric Emission in Relativistic Outflows

Abstract We study the spectra of photospheric emission from highly relativistic gamma-ray burst outflows using a Monte Carlo code. We consider the Comptonization of photons with a fast-cooled synchrotron spectrum in a relativistic jet with a realistic photon-to-electron number ratio , using mono-energetic protons that interact with thermalized electrons through Coulomb interaction. The photons, electrons, and protons are cooled adiabatically as the jet expands outward. We find that the initial energy distributions of the protons and electrons do not have any appreciable effect on the photon peak energy and the power-law spectrum above . The Coulomb interaction between the electrons and the protons does not affect the output photon spectrum significantly as the energy of the electrons is elevated only marginally. and the spectral indices for the low- and high-energy power-law tails of the photon spectrum remain practically unchanged even with electron-proton coupling. Increasing the initial optical depth results in a slightly shallower photon spectrum below and fewer photons at the high-energy tail, although above and up to ∼1 MeV, independent of . We find that determines the peak energy and the shape of the output photon spectrum. Finally, we find that our simulation results are quite sensitive to , for . For almost all our simulations, we obtain an output photon spectrum with a power-law tail above extending up to ∼1 MeV.

GRB 131014A: A LABORATORY FOR STUDYING THE THERMAL-LIKE AND NON-THERMAL EMISSIONS IN GAMMA-RAY BURSTS, AND THE NEW ${L}_{{\rm{i}}}^{\mathrm{nTh}}-{E}_{\mathrm{peak},{\rm{i}}}^{\mathrm{nTh},\mathrm{rest}}$ RELATION

Evidence has been accumulated on the existence of a thermal-like component during the prompt phase of GRBs. This component, often associated with the GRB jet's photosphere, is usually subdominant compared to a much stronger non-thermal one. The prompt emission of Fermi GRB 131014A provides a unique opportunity to study this thermal-like component. Indeed, the thermal emission in GRB 131014A is much more intense than in other GRBs and a pure thermal episode is observed during the initial 0.16 s. The thermal-like component cools monotonically during the first second while the non-thermal emission kicks off. The intensity of the non-thermal component progressively increases until being energetically dominant at late time. This is a perfect scenario to disentangle the thermal component from the non-thermal one. A low-energy spectral index of +0.6 better fit the thermal component than the typical index value +1 corresponding to a pure Planck function. The non-thermal component is adequately fitted with a Band function whose low and high energy power law indices are ~-0.7 and <~-3, respectively; this is also statistically equivalent to a cutoff power law with a ~-0.7 index. This is in agreement with our previous results. Finally, a strong correlation is observed between the time-resolved luminosity of the non-thermal component, L$_i^{nTh}$, and its corresponding rest frame spectral peak energy, E$_{peak,i}^{rest,nTh}$, with a slope similar to the one reported in our previous articles. Assuming this relation to be universal for all GRBs we estimate a redshift of ~1.55 for GRB 131014A that is a typical value for long GRBs. These observational results are consistent with the models in which the non-thermal emission is produced well above the GRB jet photosphere but they may also be compatible with other scenarios (e.g., dissipative photosphere) that are not discussed in this article.

3C 273 WITHNuSTAR: UNVEILING THE ACTIVE GALACTIC NUCLEUS

We present results from a 244\,ks \textit{NuSTAR} observation of 3C\,273 obtained during a cross-calibration campaign with the \textit{Chandra}, \textit{INTEGRAL}, \textit{Suzaku}, \textit{Swift}, and \textit{XMM-Newton} observatories. We show that the spectrum, when fit with a power-law model using data from all observatories except \textit{INTEGRAL} over the 1--78\,keV band, leaves significant residuals in the \textit{NuSTAR} data between 30--78\,keV. The \nustar\ 3--78\,keV spectrum is well-described by an exponentially cutoff power-law ($\Gamma = 1.646 \pm 0.006$, E$_\mathrm{cutoff} = 202_{-34}^{+51}$\,keV) with a weak reflection component from cold, dense material. There is also evidence for a weak ($EW = 23 \pm 11$ eV) neutral iron line. We interpret these features as arising from coronal emission plus reflection off an accretion disk or distant material. Beyond 80\,keV \textit{INTEGRAL} data show clear excess flux relative to an extrapolation of the AGN model fit to \nustar. This high-energy power-law is consistent with the presence of a beamed jet, which begins to dominate over emission from the inner accretion flow at 30-40 keV. Modeling the jet locally (in the \textit{NuSTAR} + \textit{INTEGRAL} band) as a power-law, we find the coronal component is fit by $\Gamma_\mathrm{AGN} = 1.638 \pm 0.045$, $E_\mathrm{cutoff} = 47 \pm 15$\,keV, and jet photon index by $\Gamma_\mathrm{jet} = 1.05 \pm 0.4$. We also consider \textit{Fermi}/LAT observations of 3C\,273 and here the broad-band spectrum of the jet can be described by a log-parabolic model, peaking at $\sim 2$\,MeV. Finally, we investigate the spectral variability in the \textit{NuSTAR} band and find an inverse correlation between flux and $\Gamma$.

Detection of fundamental and first harmonic cyclotron line in X-ray pulsar Cep X-4

Abstract We report the broad-band spectral properties of the X-ray pulsar Cep X-4 by using a Suzaku observation in 2014 July. The 0.8–70 keV spectrum was found to be well described by three continuum models – Negative and Positive power-law with Exponential cut-off (NPEX), high-energy cut-off power-law and CompTT models. Additional components such as a cyclotron line at ∼28 keV and two Gaussian components for iron lines at 6.4 and 6.9 keV were required in the spectral fitting. Apart from these, an additional absorption feature at ∼45 keV was clearly detected in residuals obtained from the spectral fitting. This additional feature at ∼45 keV was clearly seen in phase-resolved spectra of the pulsar. We identified this feature as the first harmonic of the fundamental cyclotron line at ∼28 keV. The ratio between the first harmonic and fundamental line energies (1.7) was found to be in disagreement with the conventional factor of 2, indicating that the heights of line-forming regions are different or viewed at larger angles. The phase-resolved spectroscopy of the fundamental and first harmonic cyclotron lines shows significant pulse-phase variation of the line parameters. This can be interpreted as the effect of viewing angle or the role of complicated magnetic field of the pulsar.

Relationship between X-ray spectral index and X-ray Eddington ratio for Mrk 335 and Ark 564

We present a comprehensive flux resolved spectral analysis of the bright Narrow line Seyfert I AGNs, Mrk~335 and Ark~564 using observations by XMM-Newton satellite. The mean and the flux resolved spectra are fitted by an empirical model consisting of two Comptonization components, one for the low energy soft excess and the other for the high energy power-law. A broad Iron line and a couple of low energies edges are required to explain the spectra. For Mrk~335, the 0.3 - 10 keV luminosity relative to the Eddington value, L{$_{X}$}/L$_{Edd}$, varied from 0.002 to 0.06. The index variation can be empirically described as $\Gamma$ = 0.6 log$_{10}$ L{$_{X}$}/L$_{Edd}$ + 3.0 for $0.005 < L{_{X}}/L_{Edd} < 0.04$. At $ L_{{X}}/L_{Edd} \sim 0.04$ the spectral index changes and then continues to follow $\Gamma$ = 0.6 log$_{10}$ L$_{{X}}$/L$_{Edd}$ + 2.7, i.e. on a parallel track. We confirm that the result is independent of the specific spectral model used by fitting the data in the 3 - 10 keV band by only a power-law and an Iron line. For Ark~564, the index variation can be empirically described as $\Gamma$ = 0.2 log$_{10}$ L$_{{X}}$/L$_{Edd}$ + 2.7 with a significantly large scatter as compared to Mrk~335. Our results indicate that for Mrk~335, there may be accretion disk geometry changes which lead to different parallel tracks. These changes could be related to structural changes in the corona or enhanced reflection at high flux levels. There does not seem to be any homogeneous or universal relationship for the X-ray index and luminosity for different AGNs or even for the same AGN.

The Properties of the Gamma-ray Bursts with High-energy Spectral Component

Spectral properties of some GRB with presence of high-energy component are discussed. The energy spectra shape of GRBs with high energy emission presence can follows the Band model (or power law or broken power law) up to some tens or hundreds of MeV (as for GRB 100724B and GRB 021008) or contains additional high energy power law component (for example, GRB 050525B and GRB 090902B). Both GRBs types were registered since CGRO mission has begun. The analysis of their energy spectra has shown that the break between low energy spectral part (described by either Band or power law or broken power law etc. models) and additional component was in energy region 2 - 200 MeV. The Fermi/LAT low energy threshold is lower than CGRO/BATSE one and the very low-energy spectral component described by power law with index δ and characterised X-ray emission in the range E<50 keV was introduced for several bursts energy spectra approximation. Moreover, for several GRBs this spectral parameter δ similar to Γ (characterizing gamma-emission in the band E >100 MeV) and the question about formation of wide range emission during GRB due to single mechanism arises again.

Synchrotron cooling in energetic gamma-ray bursts observed by theFermiGamma-Ray Burst Monitor

We study the time-resolved spectra of eight GRBs observed by Fermi GBM in its first five years of mission, with 1 keV - 1 MeV fluence $f>1.0\times10^{-4}$ erg cm$^{-2}$ and signal-to-noise level $\text{S/N}\geq10.0$ above 900 keV. We aim to constrain in detail the spectral properties of GRB prompt emission on a time-resolved basis and to discuss the theoretical implications of the fitting results in the context of various prompt emission models. We perform time-resolved spectral analysis using a variable temporal binning technique according to optimal S/N criteria, resulting in a total of 299 time-resolved spectra. We fit the Band function to all spectra and obtain the distributions for the low-energy power-law index $\alpha$, the high-energy power-law index $\beta$, the peak energy in the observed $\nu F_\nu$ spectrum $E_\text{p}$, and the difference between the low- and high-energy power-law indices $\Delta s=\alpha-\beta$. Using the distributions of $\Delta s$ and $\beta$, the electron population index $p$ is found to be consistent with the "moderately fast" scenario which fast- and slow-cooling scenarios cannot be distinguished. We also apply a physically motivated synchrotron model, which is a triple power-law with constrained power-law indices and a blackbody component, to test for consistency with a synchrotron origin for the prompt emission and obtain the distributions for the two break energies $E_\text{b,1}$ and $E_\text{b,2}$, the middle segment power-law index $\beta$, and the Planck function temperature $kT$. A synchrotron model is found consistent with the majority of time-resolved spectra for these eight energetic Fermi GBM bursts with good high-energy photon statistics, as long as both the cooling and injection break are included and the leftmost spectral slope is lifted either by inclusion of a thermal component or when an evolving magnetic field is accounted for.

Millihertz quasi-periodic oscillations and broad iron line from LMC X-1

We study the temporal and energy spectral characteristics of the persistent black hole X-ray binary LMC X-1 using two XMM-Newton and a Suzaku observation. We report the discovery of low frequency (~ 26-29 mHz) quasi-periodic oscillations (QPOs). We also report the variablity of the broad iron K-alpha line studied earlier with Suzaku. The QPOs are found to be weak with fractional rms amplitude in the ~ 1-2 % range and quality factor Q~2-10 . They are accompanied by weak red noise or zero-centered Lorentzian components with rms variability at the ~ 1-3 % level. The energy spectra consists of three varying components - multicolour disk blackbody (kT_{in} ~ 0.7-0.9 keV), high energy power-law tail (Gamma ~ 2.4 - 3.3) and a broad iron line at 6.4-6.9 keV. The broad iron line, the QPO and the strong power-law component are not always present. The QPOs and the broad iron line appear to be clearly detected in the presence of a strong power-law component. The broad iron line is found to be weaker when the disk is likely truncated and absent when the power-law component almost vanished. These results suggest that the QPO and the broad iron line together can be used to probe the dynamics of the accretion disk and the corona.

PHOTOSPHERIC EMISSION FROM STRATIFIED JETS

We explore photospheric emissions from stratified two-component jets, wherein a highly relativistic spine outflow is surrounded by a wider and less relativistic sheath outflow. Thermal photons are injected in regions of high optical depth and propagated until they escape at the photosphere. Due to the presence of shear in velocity (Lorentz factor) at the boundary of the spine and sheath region, a fraction of the injected photons are accelerated via a Fermi-like acceleration mechanism such that a high energy power-law tail is formed in the resultant spectrum. We show, in particular, that if a velocity shear with a considerable variance in the bulk Lorentz factor is present, the high energy part of observed Gamma-ray Bursts (GRBs) photon spectrum can be explained by this photon acceleration mechanism. We also show that the accelerated photons may also account for the origin of the extra hard power-law component above the bump of the thermal-like peak seen in some peculiar bursts (e.g., GRB 090510, 090902B, 090926A). It is demonstrated that time-integrated spectra can also reproduce the low energy spectrum of GRBs consistently due to a multi-temperature effect when time evolution of the outflow is considered. Finally, we show that the empirical Ep-Lp relation can be explained by differences in the outflow properties of individual sources.

X-RAY SPECTRAL CUTOFF AND THE LACK OF HARD X-RAY EMISSION FROM TWO ULTRALUMINOUS X-RAY SOURCES M81 X-6 AND HOLMBERG IX X-1

We present broadband X-ray spectral study of two ultraluminous X-ray sources (ULXs), M81 X-6 and Holmberg IX X-1 based on Suzaku & XMM-Newton observations. We perform joint broadband spectral analysis of the brightest sources in the field, i.e. the two ULXs and the active galactic nucleus (AGN) in M81, and demonstrate that the X-ray spectra of the ULXs cut off at energies more than about 3keV with negligible contribution at high energies in the Suzaku HXD/PIN band. The 90% upper limit on the 10-30keV band luminosity of an underlying broadband power-law component is 3.5e38 ergs/s for M81 X-6 and 1.2e39ergs/s for Holmberg IX X-1. These limits are more than an order of magnitude lower than the bolometric (0.1-30 keV) luminosity of 6.8e39ergs/s for M81 X-6 and 1.9e40 ergs/s for Holmberg IX X-1. Our results confirm earlier indications of spectral cut-offs inferred from the XMM-Newton observations of bright ULXs and show that there isn't an additional high energy power-law component contributing significantly to the X-ray emission. The spectral form of the two ULXs are very different from those of Galactic black hole X-ray binaries (BHBs) or AGNs. This implies that the ULXs are neither simply scaled-up versions of stellar mass BHBs or scaled-down versions of AGNs.

On the sensitivity of the HAWC observatory to gamma-ray bursts

We present the sensitivity of HAWC to gamma ray bursts (GRBs). HAWC is a very high-energy gamma-ray observatory currently under construction in Mexico at an altitude of 4100m. It will observe atmospheric air showers via the water Cherenkov method. HAWC will consist of 300 large water tanks instrumented with 4 photomultipliers each. HAWC has two data acquisition (DAQ) systems. The main DAQ system reads out coincident signals in the tanks and reconstructs the direction and energy of individual atmospheric showers. The scaler DAQ counts the hits in each photomultiplier tube (PMT) in the detector and searches for a statistical excess over the noise of all PMTs. We show that HAWC has a realistic opportunity to observe the high-energy power law components of GRBs that extend at least up to 30GeV, as it has been observed by Fermi LAT. The two DAQ systems have an energy threshold that is low enough to observe events similar to GRB 090510 and GRB 090902b with the characteristics observed by Fermi LAT. HAWC will provide information about the high-energy spectra of GRBs which in turn could help to understanding about e-pair attenuation in GRB jets, extragalactic background light absorption, as well as establishing the highest energy to which GRBs accelerate particles.

THE CHARACTERISTICS OF GRBs WITH PRESENCE OF HIGH ENERGY COMPONENT IN THEIR SPECTRA

The properties of GRBs with presence of high energy emission in spectra are discussed. The temporal profiles of part of events are similar in various energy bands in prompt phase (as for GRB 080528, GRB 021008) but during some events extended high energy emission was detected (for example, GRB 090902B). For other part of GRBs temporal profiles are quite different in various energy bands during prompt phase (as for GRB 050525B), but for some such events extended high energy emission was observed too – for example, GRB 080514B. Moreover, high energy precursors were registered for several GRBs: some photons in energy band 30 MeV - 30 GeV were detected by AGILE during GRB 080514B. The shape of energy spectra of GRBs with presence of high energy emission can follows the Band model (or power law or broken power law) up to some tens or hundreds of MeV (as for GRB 021008) or contains additional high energy power law component (for example, GRB 050525B and GRB 090902B). Following this criteria it is possible to separate two main subclasses of GRBs with high energy emission. Both types of GRBs observed since CGRO mission beginning. The analysis of their energy spectra has shown that the break between additional high energy component and Band (or power law or broken power law) component was in energy region 2-200 MeV. Both types can have got extended high energy emission including component with E &gt; 500 MeV for some events and low energy precursors. The special features of second class of GRBs by the results of preliminary data analysis are the absence of hard to soft evolution in the low energy band and (or) presence of the high energy precursors for some events.

STUDY OF FOUR YOUNG TeV PULSAR WIND NEBULAE WITH A SPECTRAL EVOLUTION MODEL

We study four young Pulsar Wind Nebulae (PWNe) detected in TeV gamma-rays, G21.5-0.9, G54.1+0.3, Kes 75, and G0.9+0.1, using the spectral evolution model developed and applied to the Crab Nebula in our previous work. We model the evolution of magnetic field and particle distribution function inside a uniformly expanding PWN considering a time-dependent injection from the pulsar and radiative and adiabatic losses. Considering uncertainties in the interstellar radiation field (ISRF) and their distance, we study two cases for each PWN. Because TeV PWNe have a large TeV gamma-rays to X-rays flux ratio, the magnetic energy of the PWNe accounts for only a small fraction of the total energy injected (typically a few x 10^{-3}). The gamma-ray emission is dominated by inverse Compton scattering off the infrared photons of the ISRF. A broken power-law distribution function for the injected particles reproduces the observed spectrum well, except for G0.9+0.1. For G0.9+0.1, we do not need a low energy counterpart because adiabatic losses alone are enough to reproduce the radio observations. High energy power-law indices at injection are similar (2.5 -- 2.6), while low energy power-law indices range from 1.0 to 1.6. The lower limit of the particle injection rate indicates that the pair multiplicity is larger than 10^4. The corresponding upper limit of the bulk Lorentz factor of the pulsar winds is close to the break energy of the broken power-law injection, except for Kes 75.