Photon Energy Density Research Articles

Repeated Compton scattering in a strong magnetic field

Repeated scatterings of unpolarized photons by non-relativistic electrons in a static and uniform magnetic field are investigated by using the Boltzmann equation with quantum mechanical correction factors for the stimulated scattering effects. The resulting Kompaneets equation depends explicitly on the electron cyclotron frequency and the incidence angle of the incoming photons relative to the direction of the magnetic field. The evolutionary behavior of the photon spectrum and energy density is highly anisotropic with respect to the static external magnetic field. Possible applications of our results to the X-ray emission from compact and massive stellar objects are discussed in detail and those to the interaction of the microwave background radiation with the hot electrons in galactic clusters are discussed briefly.

Subsurface Femtosecond Tissue Alteration: Selectively Photobleaching Macular Degeneration Pigments in Near Retinal Contact

This paper uses advances in the ultrafast manipulation of light to address a general need in medicine for a clinical approach that can provide a solution to a variety of disorders requiring subsurface tissue manipulation with ultralow collateral damage. Examples are age-related macular degeneration (AMD), fungal infections, tumors surrounded by overlying tissue, cataracts, etc. Although lasers have revolutionized the use of light in clinical settings, most lasers employed in medicine cannot address such problems of depth-selective tissue manipulation. This arises from the fact that they are mostly based on one photon based laser tissue interactions that provide a cone of excitation where the energy density is sufficiently high to excite heat or fluorescence in the entire cone. Thus, it is difficult to excite a specific depth of a tissue without affecting the overlying surface. However, the advent of femtosecond (fs) lasers has caused a revolution in multiphoton microscopy (Zipfel et al. Nat. Biotechnol. 2003, 21, 1369-1377; Denk et al. Science 1990, 248, 73-76) and fabrication (Kawata et al. Nature 2001, 412, 697-698). With such lasers, the photon energy density is only high enough for multiphoton processes in the focal volume, and this opens a new direction to address subsurface tissue manipulation. Here we show in an AMD animal model, Ccr2 KO knockout mutant mice, noninvasive, selective fs two-photon photobleaching of pigments associated with AMD that accumulate under and in ultraclose proximity to the overlying retina. Pathological evidence is presented that indicates the lack of collateral damage to the overlying retina or other surrounding tissue.

Uncertainty Relation for Photons

The uncertainty relation for the photons in three dimensions that overcomes the difficulties caused by the nonexistence of the photon position operator is derived in quantum electrodynamics. The photon energy density plays the role of the probability density in configuration space. It is shown that the measure of the spatial extension based on the energy distribution in space leads to an inequality that is a natural counterpart of the standard Heisenberg relation. The equation satisfied by the photon wave function in momentum space which saturates the uncertainty relations has the form of the Schrödinger equation in coordinate space in the presence of electric and magnetic charges.

External photon fields in Fermi bright blazars

The external Compton (EC) model is used to study the high energy emission of some blazars, in which the external photon field is considered to dominate inverse Compton radiation. We explore the properties of the external photon field through analyzing the FERMI LAT bright AGN sample within three months of the start of operations in sky-survey mode. In the sample, assuming the high energy radiation of low synchrotron peaked blazars is from the EC process, we find that the external photon parameter Uext/νext may not be a constant. Calculating synchrotron and inverse Compton luminosity from the quasi-simultaneous broadband spectral energy distributions, we find that they have an approximately linear relation. This indicates that the ratio of external photon and magnetic energy density is a constant in the comoving frame, implying that the Lorentz factor of the emitting blob depends on the external photon field and magnetic field. The result gives a strong constraint on the dynamic jet model.

THE ORIGIN OF GAMMA RAYS FROM GLOBULAR CLUSTERS

Fermi has detected gamma-ray emission from eight globular clusters. We suggest that the gamma-ray emission from globular clusters may result from the inverse Compton scattering between relativistic electrons/positrons in the pulsar wind of MSPs in the globular clusters and background soft photons including cosmic microwave/relic photons, background star lights in the clusters, the galactic infrared photons and the galactic star lights. We show that the gamma-ray spectrum from 47 Tuc can be explained equally well by upward scattering of either the relic photons, the galactic infrared photons or the galactic star lights whereas the gamma-ray spectra from other seven globular clusters are best fitted by the upward scattering of either the galactic infrared photons or the galactic star lights. We also find that the observed gamma-ray luminosity is correlated better with the combined factor of the encounter rate and the background soft photon energy density. Therefore the inverse Compton scattering may also contribute to the observed gamma-ray emission from globular clusters detected by Fermi in addition to the standard curvature radiation process. Furthermore, we find that the emission region of high energy photons from globular cluster produced by inverse Compton scattering is substantially larger than the core of globular cluster with a radius >10pc. The diffuse radio and X-rays emitted from globular clusters can also be produced by synchrotron radiation and inverse Compton scattering respectively. We suggest that future observations including radio, X-rays, and gamma-rays with energy higher than 10 GeV and better angular resolution can provide better constraints for the models.

Photon flux requirements for extreme ultraviolet reticle imaging in the 22- and 16-nm nodes

Extreme UV (EUV)-wavelength actinic microscopy yields detailed information about EUV mask patterns, architectures, defects, and the performance of defect repair strategies without the complications of photoresist imaging.To understand the pattern measurement limits of EUV mask microscopy, we investigate the effects of shot noise on aerial image linewidth measurements in the 22- and 16-nm lithography generations. Using a simple model we probe the influence of photon shot noise on measured, apparent line roughness, and find general flux density requirements independent of the specific EUV microscope configurations. Analysis reveals the trade-offs between photon energy density, effective pixel dimension on the CCD, and image log slope (ILS). We find that shot-noise-induced linewidth roughness (LWR) varies inversely with the square root of the photon energy density and is proportional to the magnification ratio. While high magnification is necessary for adequate spatial resolution, for a given flux density, higher magnification ratios have diminishing benefits. We find that to achieve an LWR (3) value of 5% of linewidth for dense, 88-nm mask features with a 2.52 normalized ILS value (image log-slope, ILS, equal to 28.6/µm) and 13.5-nm effective pixel width (1000 × magnification ratio), a peak photon flux of approximately 1400 photons/pixel per exposure is required.

Non-linear synchrotron self-Compton cooling of relativistic electrons

The broad-band spectral energy distributions (SEDs) of blazars exhibit two broad spectral components which in leptonic emission models are attributed to synchrotron radiation and synchrotron self-Compton (SSC) radiation of relativistic electrons. During high-state phases, the high-frequency SSC component dominates over the low-frequency synchrotron component implying that the inverse Compton SSC losses of electrons are at least equal or greater than the synchrotron losses of electrons. The linear synchrotron cooling, included routinely in radiation models of blazars, then has to be replaced by the SSC cooling. It is shown that the SSC energy-loss rate of electrons calculated in the Thomson limit (SST cooling) depends on an energy integral of the actual electron spectrum, reflecting the dependence of the energy density of the target synchrotron photons on the differential electron energy spectrum. The dependence of the SST loss rate on the initial kinetic energy of injected electrons is a collective effect completely different from the linear synchrotron cooling case. For the illustrative case of instantaneous injection of monoenergetic particles, we solve the non-linear kinetic equation for the intrinsic temporal evolution of the relativistic particles under SST cooling and compare the solution with the standard linear synchrotron cooling solution. For standard blazar emission region parameters, we find that under SST cooling electrons cool much more rapidly than in linear synchrotron cooling. The different cooling behaviour of electrons implies differences for the optically thin synchrotron and SSC radiation intensity and fluence energy spectra. The first difference concerns the duration of the SSC flare at different scattered photon energies. At large SSC photon energies, the SST cooled duration time is much smaller than the synchrotron cooled duration time, whereas at small SSC photon energies the SST cooled flare lasts much longer than the synchrotron cooled flare. Secondly, strong differences in the spectral behaviour of the total SSC fluence occur. At low scattered photon energies, the synchrotron cooled total SSC fluence exhibits a flatter (∝ k s -1/4 ) power-law behaviour than the SST cooled total SSC fluence (∝ k s -3/4 ). Thirdly, the SST cooled total synchrotron fluence exhibits a steeper (by Δα = 1) power-law behaviour [F T (∈) ∝ ∈ -3/2 ] than the synchrotron cooled total synchrotron fluence [F s (∈) ∝ ∈ -1/2 ] below the same exponential cut-off energy. These predictions of spectral behaviour with time and frequency provide conclusive tests for the presence or absence of linear synchrotron cooling or non-linear SST cooling in flaring non-thermal sources.

Photon energy and carrier density dependence of spin dynamics in bulk CdTe crystal at room temperature

Excitation photon energy and carrier density dependence of spin dynamics in bulk CdTe crystal was studied by time resolved pump-probe reflectivity technique at room temperature. The results show that spin relaxation time decreases monotonously. While with increasing excitation carrier density, the time constants increases initially then decreases after reaching a maximum value. Our experimental results reveal that both D’yakonov–Perel’ [M. I. D’yakonov and V. I. Perel’, Sov. Phys. JETP 38, 177 (1974)] and Elliot–Yafet [R. J. Elliott, Phys. Rev. 96, 266 (1954); Y. Yafet, Solid State Phys. 14, 1 (1963)] mechanisms dominate the spin relaxation process in CdTe crystal.

Wavelength-Selectivity in Photochemical Reaction Between 1-Alcohol and Hydrogen-Terminated Silicon

We investigated a wavelength-selectivity in photochemical reaction between 1-alcohol and hydrogen-terminated silicon. Upon irradiation with UV lights with wavelengths shorter than 355 nm, 1-alcohol molecule attached onto the hydrogenated surface of single-side polished silicon (H-Si) to give a surface terminated with alkoxyl monolayer. In contrast, a 380 nm UV-irradiation could not produce an alkoxyl-terminated monolayer. Unlike the case of 1-alcohol, a wavelength-selectivity was not observed on H-Si in the presence of a neat 1-alkene, which was used as a control experiment. In our experiment, all of 1-alcohols and 1-alkenes were treated with sodium sulfate, and were then deoxygenated for at least 30 min through Freeze-Pump-Thaw (FPT) cycles. Both alkoxylation and alkylation of outermost silicon atoms were accelerated with increases in photon energy density of UV lights. We discuss this interesting phenomenon, that is, different photochemical reactivity of 1-alcohol, by the difference in monolayer formation mechanism between 1-alcohol and 1-alkene under UV light illumination.

Undulator background in the final focus test beam experiment with polarized positrons

In the proposed E-166 experiment at SLAC, 50 GeV electrons pass through a helical undulator, and produce circularly polarized photons, which interact with a tungsten target and generate longitudinally polarized positrons. The background is an important issue for an experiment under consideration. To address this issue, simulations were performed with the code GEANT3 to model the production of secondary particles from high-energy electrons hitting an undulator. The energy density of photons generated at the target has been analyzed. Results of the simulations are presented and discussed.

LIMITS ON THE INTEGRATION CONSTANT OF THE DARK RADIATION TERM IN BRANE COSMOLOGY

We consider the constraints from primordial Helium abundances on the constant of integration of the dark radiation term of the brane-world generalized Friedmann equation derived from the Randall–Sundrum single brane model. We found that — using simple, approximate and semi-analytical methods — the constant of integration is restricted to the range between -9.18 and 5.18 which limits the contribution from dark radiation to be approximately between -28% to 16% of the background photon energy density.

A Test of External Compton Models for Gamma‐Ray Active Galactic Nuclei

There is clear evidence that the gamma-ray emission from active galactic nuclei (AGNs) can be attributed to inverse Compton scatterings in the relativistic blobs near the massive black holes. If the soft seed photons are from the regions outside the blobs, a linear relation between (vF(v,gamma)/vF(v,syn)u(*))(1/(1+alpha)) and the Doppler factor delta is expected, where vF(v,gamma) and vF(v,syn) are monochromatic gamma-ray and synchrotron fluxes, respectively, and u(*) is the energy density of soft seed photons. We estimate the soft photon energy density in the relativistic blobs contributed by the broadline regions (BLRs) in these gamma-ray AGNs using their broad-line emission data. The Doppler factors delta are derived from their radio core and X-ray emission data, based on the assumption that the X-ray emission is produced through synchrotron self-Compton (SSC) scatterings. We find two nearly linear correlations: (vF(v,gamma)/vF(opt)u(*))1/(1+alpha) proportional to delta(1.09) and (vF(v,gamma)/vF(IR)u(*))(1/(1+alpha)) proportional to delta(1.20), which are roughly consistent with the linear correlation predicted by the theoretical model for external Compton scatterings. Our results imply that the soft seed photons are predominantly from the BLRs in these gamma-ray AGNs.

The case against primordial nucleosynthesis

It is shown that there is no underlying basic theory which will lead to the idea that the lightest isotopes were produced in an early universe. Everything depends on the choice of the initial ratio of the energy density of photons to baryons that is chosen (originally by Gamow and his colleagues). There is a clear alternative for the origin of the light isotopes. This is that they were generated by hydrogen burning in stars which produces the helium directly while are produced by flare activity in stellar atmospheres. All of this activity takes place in the centers of active galaxies where matter is being created in a cyclic (quasi-steady) state universe.

The Energy Density of Soft Photons at the Jet Center: the Case with Velocity Structures

On the basis of observational facts and theoretical speculation, it has been suggested that bulk velocity structures along and perpendicular to the jet axis are present in relativistic jets. There are some clues that these velocity structures influence the energy density of seed photons from synchrotron emission. In this paper, we adopt a rigorous method to investigate the energy density in the case of continuous velocity structures. As shown by numerical results, the energy densities are similar in accelerating and stationary jets. However, in a decelerating jet or a transversely structured jet the energy density is much higher, sometimes reaching similar to20-200 times the value estimated for a uniform blob. The emitting region that produces most of the observed radiation flux is determined by the location of the dissipation and the area in which the peak bulk Lorentz factor Gamma(p) appears. The inverse Compton radiation in the cases Gamma(0)less than or equal toGamma(p) and Gamma(c)less than or equal toGamma(p) is studied. We think that, in the comoving frame, the inverse Compton scattering process in a structured jet has properties similar to the external Compton (EC) model; i.e., soft photons are injected just from the slower, downstream part. In this regard, the EC models in which seed photons come from outside the jet are not necessary if the velocity structures exist in regions very close to the core and the structure index is suitable. In particular, the jet model in which the two kinds of velocity structures coexist can be applied to TeV blazars, large-scale X-ray jets, and possibly gamma-ray bursts.

Photon localization barrier can be overcome

In contradistinction to a widespread belief that the spatial localization of photons is restricted by a power-law falloff of the photon energy density, Bialynicki-Birula [Phys. Rev. Lett. 80 (1998) 5247] has proved that any stronger – up to an almost exponential – falloff is allowed. We are showing that for certain specifically designed cylindrical one-photon states the localization is even better in lateral directions. If the photon state is built from the so-called focus wave mode, the falloff in the waist cross-section plane turns out to be quadratically exponential (Gaussian) and such strong localization persists in the course of propagation.

A possible feature of thermal matter in relativistic jets of radio-loud quasars

It has been suggested that relativistic jets in quasars may contain a considerable amount of thermal matter. In this paper, we explore the possibility that the K-alpha line from the thermal matter may appear at tens of keV due to a high Doppler blue-shift. In the jet comoving frame, the energy density of photons originally emitted by the accretion disk and reflected off the broad line region clouds dominates over that of photons of other origin. We discuss the photoionization states of the thermal matter and find that the irons elements are neutral. The high metallicity in quasars enhances the possibility to detect the thermal matter in the relativistic jet in some radio-loud quasars. A highly Doppler blue-shifted K-alpha line may be detected. We make a rediction for 3C 273, in which the K-alpha line luminosity might be of the order $3.0\times 10^{44}$ erg/s with an equivalent width of 2.4 keV. Such a line could be detected in a future mission.

Black Hole Masses and Doppler Factors of Gamma‐Ray Active Galactic Nuclei

The sizes of the broad-line regions (BLRs) in $\gamma$-ray active galactic nuclei (AGNs) are estimated from their optical continuum luminosity by using the empirical relation between $R_{\rm BLR}$ and $L_{\lambda,\rm opt}$. Using the broad emission line data, we derive the photon energy density in the relativistic blobs near the massive black holes in AGNs. We calculate the power of the broad-line photons Compton up-scattered by the relativistic electrons in the blobs. Compared with observed $\gamma$-ray emission data, the Doppler factors $\delta$ of the blobs for a sample of 36 $\gamma$-ray AGNs are derived, which are in the range of $\sim 3-17$. We estimate the central black hole masses of these $\gamma$-ray AGNs from the sizes of the BLR and the broad line widths. It is found that the black hole masses are in the range of $\sim 10^{8}-10^{10}M_{\odot}$. A significant correlation is found between the Doppler factor $\delta$ and the core dominance parameter $R$. The results are consistent with the external radiation Compton (ERC) models for $\gamma$-ray emission from AGNs. The soft seed photons are probably from the broad-line regions.

The brightness temperature problem in extreme intra-day variable quasars: a model for PKS 0405-385

I re-examine the brightness temperature problem in PKS 0405-385, which is an extreme intra-day variable radio quasar with an inferred brightness temperature of ∼5 x 10 1 4 K at 5 GHz, well above the Compton catastrophe limit of ∼10 1 1 K that is reached when the synchrotron photon energy density exceeds the energy density of the magnetic field. If one takes into account the uncertainty in the distance to the ionized clouds responsible for interstellar scintillation causing rapid intra-day variability in PKS 0405-385, it is possible that the brightness temperature could be as low as ∼10 1 3 K at 5 GHz, or even lower. The radio spectrum can be fitted by optically thin emission from mono-energetic electrons, or an electron spectrum with a low-energy cut-off such that the critical frequency of the lowest energy electrons is above the radio frequencies of interest. If one observes optically thin emission along a long narrow emission region, the average energy density in the emission region can be many orders of magnitude lower than calculated from the observed intensity if one assumed a spherical emission region. I discuss the physical conditions in the emission region and find that the Compton catastrophe can then be avoided using a reasonable Doppler factor. I also show that MeV to 100-GeV gamma-ray emission at observable flux levels should be expected from extreme intra-day variable sources such as PKS 0405-385.

Observational constraints on dark radiation in brane cosmology

We analyze the observational constraints on brane-world cosmology whereby the universe is described as a three-brane embedded in a five-dimensional anti-de Sitter space. In this brane-universe cosmology, the Friedmann equation is modified by the appearance of extra terms which derive from existence of the extra dimensions. In the present work we concentrate on the “dark radiation” term which diminishes with cosmic scale factor as a −4. We show that, although the observational constraints from primordial abundances allow only a small contribution when this term is positive, a much wider range of negative between the observed primordial 4He and D abundances. We also discuss the possible constraints on this term from the power spectrum of CMB anisotropies in the limit of negligible cosmological perturbation on the brane world. We show that BBN limits the possible contribution from dark radiation just before the e + e − aniihilation epoch to lie between −123% and +11% of the background photon energy density. Combining this with the CMB constraint reduces this range to between −41% and +10.5% at the 2σ confidence level.

Emission of concentrated solutions of organic compounds excited with high-power laser radiation

Specific features of emission of concentrated (C ≤ 1.2·1019 cm–3) solutions of organic molecules (rhodamine 6G, rhodamine C, phenalemine 512, and substituted paraterphenyl (LOC-1)) are investigated as functions of the exciting photon energy (at λexc = 308 and 532 nm) and power density of exciting radiation (up to 1 GW/cm2). One of the observed emission types – band emission – is studied. The intensity of band emission (its short- and long-wavelength maxima) is investigated versus the exciting radiation power density, and its time and polarization characteristics are also analyzed. The results obtained together with the specific features of the emission spectrum of concentrated rhodamine-C solution, measured after passage of sounding radiation with maximum at the wavelength equal to that of the short-wavelength maximum of band emission, demonstrate that the band emission is simply superfluorescence.