Blackbody Spectrum Research Articles

Distinct Thermal Emission from GRB 190109A

The gamma-ray bursts (GRBs) with distinct thermal components are rarely detected, especially in cases with thermal components throughout the prompt phase. Recently, Fermi/GBM, Swift/BAT, and Swift/XRT detected the special long-duration GRB 190109A, which has four pulses in the prompt gamma-ray emission, i.e, Pulse I (−4 to 20 s), Pulse II (20–50 s), Pulse III (50–90 s), and Pulse IV (90–120 s). GRB 190109A exhibits a very hard low-energy index (α ∼ 1) in the Band function relative to the typical GRBs (α ∼ − 1). In the whole burst prompt emission, we find distinct thermal emissions in the time-resolved spectra throughout four pulses. The blackbody (BB) temperature kT varies from 24.7 to 8.2 keV for Pulse I to Pulse IV. We also obtain the relation of F ∝ kT −0.40 for the early phase (Pulse I) and F ∝ kT 3.33±0.76 for the late phase (Pulses II–IV), respectively. The significant deviation of the kT − F relation in the early epochs from that in the late epochs likely suggests that the BB spectra origin of the early phase (Pulse I) may have disparate physical processes from those of the late phase (Pulses II–IV). For instance, it may be the transition from cocoon surroundings by a jet to the photosphere of the matter-dominated jet. A jet break is found in the late X-ray afterglow, which is in keeping with the standard external shock afterglow model in the interstellar medium circumburst.

Relativity, scaling, and electromagnetic radiation equilibrium for circular orbits

The radiation emitted by a charged particle moving in a circular orbit requires that the orbital speed of the particle is less than the speed of light in vacuum. This crucial relativistic restriction is lost in any treatment which combines nonrelativistic mechanics with classical electrodynamics through the nonrelativistic Larmor radiation formula or the dipole approximation, which approximations correspond to taking only the lowest power of velocity. A notable example of the resulting failure involves the derivation of the blackbody radiation spectrum within classical physics. Nature contains a smallest electric charge e and a largest speed c. Both these fundamental constants should appear in a classical theory of nature. We connect the assumptions regarding fundamental constants to the scaling aspects of classical theories. Nonrelativistic mechanics exhibits scaling which is entirely different from that found in relativistic classical electrodynamics where only Coulomb potentials are allowed and the constants e and c both appear. The scaling aspects are reflected in the radiation spectra which different theories predict for thermal radiation equilibrium. The Rayleigh–Jeans spectrum reflects the scaling aspects of nonrelativistic classical mechanics whereas the classical electromagnetic zero-point spectrum and the Planck spectrum share the scaling aspects of relativistic classical electrodynamics which includes both e and c.

Design and Simulation of a Circadian Lighting Control System Using Fuzzy Logic Controller for LED Lighting Technology

This paper introduces a fuzzy logic-based circadian lighting control system using flexibility of Light-Emitting Diode (LED) lighting technology to synchronise artificial lighting with circadian (natural) lighting Correlated Colour Temperature (CCT) characteristics. Besides for vision acuity, the Non-Imaging Forming effects of lighting affect human circadian rhythms. Past works in spectrally tuning CCT or Spectral Power Distribution of lighting have used conventional Proportional-Integral-Derivative (PID) control system architecture, where the modelling process of system transfer functions was mathematically complex, especially for nonlinear systems. A methodology of regulating lighting CCT is employed in a 7×5 fuzzy logic rules matrix in a Fuzzy Logic Controller (FLC) system, to closely replicate natural lighting CCT characteristics for indoor lighting. A reference lookup table was devised to store desired CCT values arbitrarily with respect to time mark in a day, which acts as an outdoor circadian stimulus and guides the FLC. The FLC compensates for the lack of CCT in lighting space. Simulation results show acceptable CCT output values conforming to circadian lighting parameters at a time in a day compared to the lookup table targets. Deviation from blackbody curve was within ±0.003 using CCT Duv checking. The system did not produce an overshoot (0.0%) with a steady state (zero error) reached after the fourth iteration. Also, rise time was calculated to be 1 iteration. This approach could be further enhanced to cater for additional custom needs in many built environments. Future works may consider connecting more sensors to capture real-time outdoor CCT values for practical regulation.

A low-dispersion spectral video camera for observing lunar impact flashes

An impact of a meteoroid on the lunar surface at speeds exceeding several kilometers per second generates a light flash generally less than 0.1 s in duration. We made a simple spectral video camera for observing the lunar impact flashes and monitored the waxing crescent Moon’s non-sunlit surface from Oct. 2016 to May 2017. We detected ten flash candidates though there was no report of simultaneous detections by other observers. We obtained low-dispersion spectra in visible wavelengths for nine of them. Six of them show spectra similar to those of the flashes observed during the Geminids meteor activity in Dec. 2018 by the same camera. The spectra are continuous and red. Blackbody spectra fitted to them show temperatures around 3000 K. On the other hand, three of them show continuous blue spectra. Blackbody spectra fitted to them show temperatures of more than 6000 K. Specular reflection of sunlight by space debris might lead to these flashes. However, the impact of a low-density meteoroid not against the fine lunar regolith but solid lunar rocks could cause blue flashes. In this paper, we give full details of the camera and the analytical procedures of the videos. We also discuss recommendations for future spectral observations.Graphical

Radiative thermalization in semiclassical simulations of light-matter interaction

Prediction of the equilibrium populations in quantum dynamics simulations of molecules exposed to black-body radiation has proved challenging for semiclassical treatments, with the usual Ehrenfest and Maxwell-Bloch methods exhibiting serious failures. In this context, we explore the behavior of a recently introduced semiclassical model of light-matter interaction derived from a dissipative Lagrangian [C. M. Bustamante, E. D. Gadea, A. Horsfield, T. N. Todorov, M. C. Gonz\'alez Lebrero, and D. A. Scherlis, Phys. Rev. Lett. 126, 087401 (2021)]. It is shown that this model reproduces the Boltzmann populations for two-level systems, predicting the black-body spectra in approximate agreement with Planck's distribution. In multilevel systems, small deviations from the expected occupations are seen beyond the first excited level. By averaging over fast oscillations, a rate equation is derived from the dissipative equation of motion that makes it possible to rationalize these deviations. Importantly, it enables us to conclude that this model will produce the correct equilibrium populations provided the occupations of the lowest levels remain close to unity, a condition satisfied at low temperature or small excitations.

The coherence time of sunlight in the context of natural and artificial light-harvesting

The suggestion that quantum coherence might enhance biological processes such as photosynthesis is not only of fundamental importance but also leads to hopes of developing bio-inspired ‘green’ quantum technologies that mimic nature. A key question is how the timescale of coherent processes in molecular systems compare to that of the driving light source—the Sun. Across the quantum biology literature on light-harvesting, the coherence time quoted for sunlight spans about two orders of magnitude, ranging from 0.6 to ‘10s’ of femtoseconds. This difference can potentially be significant in deciding whether the induced light-matter coherence is long enough to affect dynamical processes following photoexcitation. Here we revisit the historic calculations of sunlight coherence starting with the black-body spectrum and then proceed to provide values for the more realistic case of atmospherically filtered light. We corroborate these values with interferometric measurements of the complex degree of temporal coherence from which we calculate the coherence time of atmospherically filtered sunlight as 1.12pm {0.04},{hbox { fs}}, as well as the coherence time in a chlorophyll analogous filtered case as 4.87pm {0.21},{hbox { fs}}.

Classical Physics and Blackbody Radiation.

We investigate the properties of the blackbody spectrum by direct numerical solution of the classical equations of motion of a one-dimensional model that contains the essential general features of the field-matter interaction. Our results, which do not rely on any statistical assumption, show that the classical blackbody spectrum exhibits remarkable properties: (i)a quasistationary state characterized by scaling properties, (ii)consistency with the Stefan-Boltzmann law, and (iii)a high-frequency cutoff. Our Letter is a preliminary step in the understanding of statistical properties of infinite-dimensional systems.

CMB as thermal radiation from cosmic dust grains in equilibrium with the redshifted starlight

This paper suggests that the cosmic microwave background radiation (CMB) arises from thermalized cosmic dust grains both in the interstellar medium (ISM) and in the intergalactic medium (IGM) in electron density zones equal to 0.5 el/m3. Otherwise, the thermalization is characterized by higher temperatures in the observed range 15-27 K. Considering that a black body spectrum requires an absorber/re-emitter to take place, starting from the radiative transfer equation, the calculation method applied determines the diameter of the targets in equilibrium with the redshifted starlight necessary to produce a thermal radiation at 2.725 K. The calculated value of the diameter can only correspond to cosmic dust grains in nature with their specific mass density and to nothing else. It is fully consistent with the observed size range of extra-terrestrial cosmic dust within 10-1000 μm. Furthermore, the carbon composition of the grains is capable to describe a black body behaviour as well as the metal composition is in a position to feature the polarization CMB map under the influence of galactic magnetic fields. The results of this inquiry are valid for any observer in the Cosmos.

Full-sky, Arcminute-scale, 3D Models of Galactic Microwave Foreground Dust Emission Based on Filaments

Abstract We present the DustFilaments code, a full-sky model for the millimeter Galactic emission of thermal dust. Our model, composed of millions of filaments that are imperfectly aligned with the magnetic field, is able to reproduce the main features of the dust angular power spectra at 353 GHz as measured by the Planck mission. Our model is made up of a population of filaments with sizes following a Pareto distribution ∝ L a − 2.445 , with an axis ratio between short and long semiaxes ϵ ∼ 0.16 and an angle of magnetic field misalignment with a dispersion rms(θ LH) = 10°. On large scales, our model follows a Planck-based template. On small scales, our model produces spectra that behave like power laws up to ℓ ∼ 4000 or smaller scales by considering even smaller filaments, limited only by computing power. We can produce any number of Monte Carlo realizations of small-scale Galactic dust. Our model will allow tests of how the small-scale non-Gaussianity affects CMB weak lensing and the consequences for the measurement of primordial gravitational waves or relativistic light relic species. Our model also can generate frequency decorrelation on the modified blackbody spectrum of dust and is freely adjustable to different levels of decorrelation. This can be used to test the performance of component separation methods and the impact of frequency spectrum residuals on primordial B-mode surveys. The filament density we paint in the sky is also able to reproduce the general level of non-Gaussianities measured by Minkowski functionals in the Planck 353 GHz channel map.

Relativistic X-Ray Reflection Models for Accreting Neutron Stars

Abstract We present new reflection models specifically tailored to model the X-ray radiation reprocessed in accretion disks around neutron stars, in which the primary continuum is characterized by a single-temperature blackbody spectrum, emitted either at the surface of the star or at the boundary layer. These models differ significantly from those with a standard power-law continuum, typically observed in most accreting black holes. We show comparisons with earlier reflection models and test their performance in the NuSTAR observation of the neutron star 4U 1705−44. Simulations of upcoming missions such as XRISM-Resolve and Athena X-IFU are shown to highlight the diagnostic potential of these models for high-resolution X-ray reflection spectroscopy. These new reflection models xillverNS, and their relativistic counterpart relxillNS, are made publicly available to the community as an additional flavor in the relxill suite of reflection models.

Solar Temperature Variations Computed from SORCE SIM Irradiances Observed During 2003\u2009\u2013\u20092020

NASA’s Solar Radiation and Climate Experiment (SORCE) Spectral Irradiance Monitor (SIM) instrument produced about 17 years of daily average Spectral Solar Irradiance (SSI) data for wavelengths 240 – 2416 nm. We choose a day of minimal solar activity, August 24, 2008 (2008-08-24), during the 2008 – 2009 minimum between Cycles 23 and 24, and compute the brightness temperature (T_{o}) from that day’s solar spectral irradiance (mathit{SSI}_{o}). We consider small variations of T and SSI about these reference values, and derive linear and quadratic analytic approximations by Taylor expansion about the reference-day values. To determine the approximation accuracy, we compare to the exact brightness temperatures T computed from the Planck spectrum, by solving analytically for T, or equivalent root finding in Wolfram Mathematica. We find that the linear analytic approximation overestimates, while the quadratic underestimates, the exact result. This motivates the search for statistical “fit” models “in between” the two analytic models, with minimum root-mean-square-error, RMSE. We make this search using open-source statistical R software, determine coefficients for linear and quadratic fit models, and compare statistical with analytic RMSEs. When only linear analytic and fit models are compared, the fit model is superior at ultraviolet, visible, and near-infrared wavelengths. This again holds true when comparing only quadratic models. Quadratic is superior to linear for both analytic and statistical models, and statistical fits give the smallest RMSEs. Lastly, we use linear analytic and fit models to find an interpolating function in wavelength, useful when the SIM results need adjustment to another choice of wavelengths, to compare or extend to any other instrument. Advantages of the quadratic T over the exact T include ease of interpretation, and computational speed.

Pre-explosion Properties of Helium Star Donors to Thermonuclear Supernovae

Abstract Helium star–carbon-oxygen white dwarf (CO WD) binaries are potential single-degenerate progenitor systems of thermonuclear supernovae. Revisiting a set of binary evolution calculations using the stellar evolution code MESA, we refine our previous predictions about which systems can lead to a thermonuclear supernova and then characterize the properties of the helium star donor at the time of explosion. We convert these model properties to near-UV/optical magnitudes assuming a blackbody spectrum and support this approach using a matched stellar atmosphere model. These models will be valuable to compare with pre-explosion imaging for future supernovae, though we emphasize the observational difficulty of detecting extremely blue companions. The pre-explosion source detected in association with SN 2012Z has been interpreted as a helium star binary containing an initially ultra-massive WD in a multiday orbit. However, extending our binary models to initial CO WD masses of up to 1.2 M ⊙, we find that these systems undergo off-center carbon ignitions and thus are not expected to produce thermonuclear supernovae. This tension suggests that, if SN 2012Z is associated with a helium star–WD binary, then the pre-explosion optical light from the system must be significantly modified by the binary environment and/or the WD does not have a carbon-rich interior composition.

Constraining Cosmic Microwave Background Temperature Evolution With Sunyaev–Zel’Dovich Galaxy Clusters from the Atacama Cosmology Telescope

Abstract The Sunyaev–Zel’dovich (SZ) effect introduces a specific distortion of the blackbody spectrum of the cosmic microwave background (CMB) radiation when it scatters off hot gas in clusters of galaxies. The frequency dependence of the distortion is only independent of the cluster redshift when the evolution of the CMB radiation is adiabatic. Using 370 clusters within the redshift range 0.07 ≲ z ≲ 1.4 from the largest SZ-selected cluster sample to date from the Atacama Cosmology Telescope, we provide new constraints on the deviation of CMB temperature evolution from the standard model α = 0.017 − 0.032 + 0.029 , where T ( z ) = T 0 1 + z 1 − α . This result is consistent with no deviation from the standard adiabatic model. Combining it with previous, independent data sets we obtain a joint constraint of α = −0.001 ± 0.012. Attributing deviation from adiabaticity to the decay of dark energy, this result constrains its effective equation of state w eff = − 0.998 − 0.010 + 0.008 .

Numerical derivation and validation of the angular, hemispherical and normal emissivity and reflectivity of common window glass

The thermal radiative properties of glazing materials are fundamental inputs for evaluating the energetic performance and thermal behaviour of buildings. These properties are required for many practical applications ranging from infrared thermography to building performance simulation and thermal comfort evaluations. Soda–lime–silica glass is the most widely used glass, worldwide, for glazing and the derivation of its thermal and optical properties are the subject of this work. Based on experimentally acquired spectral reference measurement data for soda-lime glass, the complex-valued Fresnel equations are solved and Monte-Carlo integration is carried out over the black-body spectrum, as well as over the hemisphere. These calculations are performed for various radiative temperatures to establish their temperature dependencies, and additionally the temperature-dependent transmittance of soda-lime glass was analysed. By applying a non-linear optimisation algorithm, computationally efficient practical fitting formulae for the angular reflectivity, emissivity and absorptivity are derived. All equations are numerically solved with a high degree of accuracy. The determination of the hemispherical total emissivity for this type of glass confirms the current accepted value (∼0.2%) originally derived by Rubin (1985). A simple yet robust experimental design, based on thermography, is used to validate the results of the numerical reflectivity model. Additionally, we provide angular functions, fitting functions and additional constants that were hitherto unavailable. The practical benefits of the fitting formulae provided are considerable in relation to modelling the reflection of thermal radiation on glazed surfaces, and are demonstrated in two case-study applications in the appendix.

The interpretation of the CMBR

In the popular ΛCDM model, the cosmic microwave background radiation (CMBR) is thought to be the remnant of the early hot universe. An important precondition of this interpretation of CMBR is: after the last scattering surface formed, the high temperature ionized gases in the universe became low temperature neutral gases and so the universe has been completely transparent to the radiation which comes from the hot early universe. However, observations show that today most gases in the universe are still in a high temperature ionized state. The universe is not completely transparent to the radiation which comes from the hot early universe. According to the famous Sunyaev-Zeldovich effect, if the CMBR comes from the early hot universe and follows a perfect blackbody spectrum, the free electrons in the cosmic plasma will distort the perfect blackbody spectrum of the CMBR. In this case, the observed CMBR cannot be of a perfect blackbody spectrum. This is a fatal flaw in the interpretation of CMBR using the ΛCDM model. In order to overcome this fatal flaw, in this paper it is proposed that in the ΛCDM model frame, a better interpretation of CMBR is: The CMBR is a thermal equilibrium product between the high temperature ionized gases and the cosmic radiation field in the local universe space.

Nature of the ultrarelativistic prompt emission phase of GRB 190114C

We address the physical origin of the ultrarelativistic prompt emission (UPE) phase of GRB 190114C observed in the interval 1.9-3.99 s, by the Fermi-GBM in 10 keV-10 MeV . Thanks to high S/N ratio of Fermi-GBM data, a time resolved spectral analysis has evidenced a sequence of similar blackbody plus cutoff power-law spectra, on ever decreasing time intervals during the entire UPE phase. We assume that during the UPE phase, the inner engine of the GRB, composed of a Kerr black hole and a uniform test magnetic field B0, aligned with the BH rotation axis, operates in an overcritical field. We infer an $e^+e^-$ pair electromagnetic plasma in presence of a baryon load, a PEMB pulse, originating from a vacuum polarization quantum process in the inner engine. This initially optically thick plasma self-accelerates, giving rise at the transparency radius to the MeV radiation observed by Ferm-GBM. At trf > 3.99 s, the electric field becomes undercritical, and the inner engine operates in the classical electrodynamics regime and generate the GeV emission. During both the quantum and the classical electrodynamics processes, we determine the time varying mass and spin of the Kerr BH in the inner engine, fulfilling the Christodoulou-Hawking-Ruffini mass-energy formula. For the first time, we quantitatively show how the inner engine, by extracting the rotational energy of the Kerr BH, produces a series of PEMB pulses. We follow the quantum vacuum polarization process in sequences with decreasing time bins. We compute the Lorentz factors, the baryon loads and the radii at transparency, as well as the value of the magnetic field, assumed to be constant in each sequence. The fundamental hierarchical structure, linking the quantum electrodynamics regime to the classical electrodynamics regime, is characterized by the emission of blackholic quanta with a timescale $t=10^{-9}$s, and energy $E=10^{45}$ erg.

Equivalent Analysis of Thermo-Dynamic Blow-Off Impulse under X-ray Irradiation

X-ray thermodynamic effect is an important damage mode for spacecraft. Blow-off impulse as the main thermodynamic damage parameter has been widely studied by combining laboratory and numerical simulations. In this paper, most calculations and analyses have been carried out by using the self-developed software RAMA, including the equivalent calculation of blow-off impulse of monoenergetic and blackbody X-ray, and soft/hard blackbody X-ray irradiated at different incidence angles of LY-12 aluminium target. The results show that the characteristic mono-energetic X-ray can be exploited to simulate the blow-off impulse of the blackbody X-ray under certain conditions as a feasible equivalent method for the equal-flux and equal-impulse relations between mono-energetic and intense pulse blackbody of blow-off impulse. Moreover, the equivalent thermodynamic effect can be achieved between the point source radiation and parallel X-ray of X-ray. Furthermore, the cosine distribution of blow-off impulse is conducive to designing and calculating X-ray radiation load of hard aluminium corresponding to 1–5 keV blackbody spectrum. The mentioned results can be referenced for pulse X-ray simulation source and enhance the fidelity of the thermal-mechanical effect by electron beam. It is noteworthy that the study on the thermodynamic effects of intense pulsed X-ray is of high significance.

Acceleration radiation of an atom freely falling into a Kerr black hole and near-horizon conformal quantum mechanics

An atom falling freely into a Kerr black hole in a Boulware-like vacuum is shown to emit radiation with a Planck spectrum at the Hawking temperature. For a cloud of falling atoms with random initial times, the radiation is thermal. The existence of this radiation is due to the acceleration of the vacuum field modes with respect to the falling atom. Its properties can be traced to the dominant role of conformal quantum mechanics in the neighborhood of the event horizon. We display this effect for a scalar field, though the acceleration radiation has a universal conformal behavior that is exhibited by all fields in the background of generic black holes.

The Blow-Off Impulse Equivalence of Typical Missile Homogeneous Al-Alloy under Multienergy Composite Spectrum Electron Beam and Powerful Pulsed X-ray

The electron beam, one of the most effective approaches to simulate the irradiation effects of powerful pulsed X-ray in the laboratory, plays an important role in simulating the thermodynamic effects of powerful pulsed X-ray. This paper studies the thermodynamics equivalence between multienergy composite spectrum electron beam and blackbody spectrum X-ray, which is helpful to quickly determine the experimental parameters in the simulation experiment. The experimental data of electron beam are extrapolated by numerical calculation, to increase the range of energy flux. Through calculating the blow-off impulse of blackbody spectrum X-ray irradiation, we obtained the curve of X-ray blow-off impulse varying with energy flux, and then found two categories of equivalent relations—equal-energy flux and equal-impulse—by analyzing the calculation results of electron beam and X-ray blow-off impulse. Based on such relations, we could directly or indirectly obtain the results of blackbody spectrum X-ray irradiation blow-off impulse via electron beam experiment.

Simplified derivation of the Kompaneets equation

An isotropic electromagnetic field in a plasma of thermalized electrons undergoes changes in energy as a result of Compton scattering and an Einstein–Hopf drag force on the electrons, eventually approaching a Bose–Einstein photon distribution at the electron temperature. The rate of change of field energy due to the combined effects of Compton scattering and the drag force is shown to be described by the Kompaneets equation for photon diffusion in frequency space. A similarity is noted between this approach and Einstein's derivation of the Planck spectrum based on the recoil of atoms as they absorb and emit radiation.