Proton Energy Density Research Articles

Mechanical structures inside proton with configurational entropy language

The structure of the proton remains a significant challenge within the field of Quantum Chromodynamics, with the origin of its spin and mass still lacking a satisfactory explanation. In this study, we utilize the gravitational form factor of the proton as the foundation for constructing the configurational entropy of the proton energy system. In our approach we choose the holographic QCD model for input thus obtaining a holographic version of the proton energy density. Employing this approach, we are able to determine key mechanical quantities such as the proton's mass radius and pressure distribution. Our analysis yields the root-mean-square mass radius of 〈rM2〉=0.720 fm and scalar radius of 〈rS2〉=1.024 fm for proton, which are found to be in excellent agreement with recent measurements from the Hall-C collaboration group at Jefferson Lab. Additionally, we examine the radial distribution of pressure and shear force within the proton. We provide a new mode for constraining holographic model parameters in the investigation of proton structures.

Assessment of the reliability of deconvolution procedures for RCF spectroscopy of laser-driven ion beams

Laser-driven ion beams are defined by a number of unique features, including a large spread in energy. A stack configuration of radiochromic films (RCF) can be utilized to characterize such beams through measurements of their energy spectra. A spectroscopic procedure is reported that allows the proton energy density within each active layer of a radiochromic film (RCF) stack to be retrieved. This is based upon on a deconvolution algorithm developed through Geant4 Monte Carlo simulations to correct the contributions of energy depositions within a given film layer. Through Monte Carlo calculations, the spectrum retrieved from a simulated film stack can be retrieved and compared with a known energy spectrum, providing an examination of the efficacy of this tool. Application of the developed deconvolution procedure thus offers the potential to correctly reconstruct the incident energy spectrum of a laser-driven proton and ion beam from a stack of irradiated RCF.

Cosmic rays and non-thermal emission in simulated galaxies – III. Probing cosmic-ray calorimetry with radio spectra and the FIR–radio correlation

ABSTRACT An extinction-free estimator of the star formation rate (SFR) of galaxies is critical for understanding the high-redshift universe. To this end, the nearly linear, tight correlation of far-infrared (FIR), and radio luminosity of star-forming galaxies is widely used. While the FIR is linked to massive star formation, which also generates shock-accelerated cosmic-ray (CR) electrons and radio synchrotron emission, a detailed understanding of the underlying physics is still lacking. Hence, we perform three-dimensional magnetohydrodynamical (MHD) simulations of isolated galaxies over a broad range of halo masses and SFRs using the moving-mesh code arepo, and evolve the CR proton energy density self-consistently. In post-processing, we calculate the steady-state spectra of primary, shock-accelerated and secondary CR electrons, which result from hadronic CR proton interactions with the interstellar medium. The resulting total radio luminosities correlate with the FIR luminosities as observed and are dominated by primary CR electrons if we account for anisotropic CR diffusion. The increasing contribution of secondary emission up to 30 per cent in starbursts is compensated by the larger bremsstrahlung and Coulomb losses. CR electrons are in the calorimetric limit and lose most of their energy through inverse Compton interactions with star light and cosmic microwave background (CMB) photons while less energy is converted into synchrotron emission. This implies steep steady-state synchrotron spectra in starbursts. Interestingly, we find that thermal free–free emission flattens the total radio spectra at high radio frequencies and reconciles calorimetric theory with observations while free–free absorption explains the observed low-frequency flattening towards the central regions of starbursts.

Proton fraction in neutron star matter: dynamical mean-field approach

Dynamical mean field theory (DMFT) is used to study neutron matter, both with and without admixture of the proton fraction. The system is approximated by the lattice Hubbard model. The corresponding equation of state as a function of temperature/density/asymmetry is investigated. The results are compared with the standard mean field (MF) approach where the effect of local correlations is neglected. Whereas the influence of the correlations on the properties of a pure neutron matter is found to be moderate, it becomes strong when the proton admixture is taken into account. In particular, we calculate the proton fraction, energy density and pressure in outer core of neutron stars, taking into account the beta equilibrium condition. The DMFT predicts that the proton fraction is several times the MF based calculations, whereas the DMFT results for energy density and pressure are 30%–40% lower than the corresponding MF estimates. Physical implications of our findings for a neutron star dynamics are discussed.

On the significance of relativistically hot pairs in the jets of FR II radio galaxies

ABSTRACT The energetic composition of radio lobes in the FR II galaxies – estimated by comparing their radio luminosities with the powers required to inflate cavities in the external medium – seems to exclude the possibility of their energetic domination by protons. Furthermore, if the jets were dominated by the kinetic energy of cold protons, it would be difficult to efficiently accelerate leptons in the jets’ terminal shocks. Assuming that the relative energy contents of leptons, protons, and magnetic fields are preserved across the shocks, the above implies that the large-scale jets should also be energetically dominated by leptons: Pe,j ≳ Pp,j. On the other hand, previous studies of small-scale jets in blazars and radio cores suggest a pair content (number of electrons and positrons per proton) of the order of ne/np ∼ 20. Assuming further that the particle composition of jets does not evolve beyond the blazar scales, we show that this implies an average random Lorentz factor of leptons in large-scale jets of $\bar{\gamma }_{\rm e,j} \gtrsim 70(1+\chi _{\rm p})(20n_{\rm p}/n_{\rm e})$, and that the protons should be mildly relativistic with χp ≡ (ϵp + pp)/ρpc2 ≲ 2, pp the pressure of protons, ϵp the internal energy density of protons, and ρpc2 the rest-mass energy density of protons. We derive the necessary conditions for loading the inner jets by electron–positron pairs and proton–electron plasma, and provide arguments that heating of leptons in jets is dominated by magnetic reconnection.

A roadmap to hadronic supercriticalities: a comprehensive study of the parameter space for high-energy astrophysical sources

ABSTRACT Hadronic supercriticalities are radiative instabilities that appear when large amounts of energy are stored in relativistic protons. When the proton energy density exceeds some critical value, a runaway process is initiated resulting in the explosive transfer of the proton energy into electron–positron pairs and radiation. The runaway also leads to an increase of the radiative efficiency, namely the ratio of the photon luminosity to the injected proton luminosity. We perform a comprehensive study of the parameter space by investigating the onset of hadronic supercriticalities for a wide range of source parameters (i.e. magnetic field strengths of 1 G−100 kG and radii of 1011−1016 cm) and maximum proton Lorentz factors (103−109). We show that supercriticalities are possible for the whole range of source parameters related to compact astrophysical sources, like gamma-ray bursts and cores and jets of active galactic nuclei. We also provide an in-depth look at the physical mechanisms of hadronic supercriticalities and show that magnetized relativistic plasmas are excellent examples of non-linear dynamical systems in high-energy astrophysics.

World-Universe Model Predictions

In 2013, World-Universe Model (WUM) proposed a principally different way to solve the problem of Newtonian Constant of Gravitation measurement precision. WUM revealed a self-consistent set of time-varying values of Primary Cosmological parameters of the World: Gravitation parameter, Hubble’s parameter, Age of the World, Temperature of the Microwave Background Radiation, and the concentration of Intergalactic plasma. Based on the inter-connectivity of these parameters, WUM solved the Missing Baryon problem and predicted the values of the following Cosmological parameters: gravitation G, concentration of Intergalactic plasma, relative energy density of protons in the Medium, and the minimum energy of photons, which were experimentally confirmed in 2015-2018. Between 2013 and 2018, the relative standard uncertainty of G measurements decreased x6. The set of values obtained by WUM was recommended for consideration in CODATA Recommended Values of the Fundamental Physical Constants 2014.

Measurement of Low-Energy Cosmic Rays via the Neutral Iron Line

There has been little information of Galactic low-energy cosmic rays (LECRs) so far because observations of LECRs in the solar system are affected by solar modulation and there is no effective way of indirect measurement. When LECRs in the MeV energy band collide with neutral iron atoms in the interstellar medium, uorescent X-rays at 6.4 keV are produced via inner-shell ionization of neutral iron atoms. We investigate the 6.4 keV line in supernova remnants (SNRs) as a prime candidate for the Galactic cosmic-ray origin. The line emission is discovered from 11 SNRs. The spectra and morphologies suggest that the 6.4 keV line is produced by LECRs interacting with cold gas. The proton energy density is estimated to be 10–100 eV cm−3. Furthermore, we measure the distribution of the 6.4 keV line emission near the Galactic center. The intensity profile is very similar to that of molecular clouds. The most plausible origin of the enhancement is the LECR proton bombardment. The energy density of MeV protons is estimated to be ∼ 80 eV cm−3. Since the diffusion length of MeV protons is short, they should be produced in situ. Surprisingly, there is no SNR in the vicinity, and thus another mechanism such as the stochastic acceleration would possibly work.

Patterns of variability in supercritical hadronic systems

A unique and often overlooked property of a source loaded with relativistic protons is that it can become supercritical, i.e. it can undergo an abrupt transition from a radiatively inefficient to a radiatively efficient state once its proton energy density exceeds a certain threshold. In this paper, we investigate the temporal variability of hadronic systems in this hardly explored regime. We show that there exists a range of proton densities that prevent the system from reaching a steady state, but drive it instead in a quasi-periodic mode. The escaping radiation then exhibits limit cycles, even if all physical parameters are held constant in time. We extend our analysis to cases where the proton injection rate varies with time and explore the variability patterns of escaping radiation as the system moves in and out from the supercritical regime. We examine the relevance of our results to the variability of the prompt gamma-ray burst emission and show that, at least on a phenomenological level, some interesting analogies exist.

Evidence for a Neutral Iron Line Generated by MeV Protons from Supernova Remnants Interacting with Molecular Clouds

Abstract Supernova remnants (SNRs) have been prime candidates for Galactic cosmic-ray accelerators. When low-energy cosmic-ray protons (LECRp) collide with interstellar gas, they ionize neutral iron atoms and emit the neutral iron line (Fe i Kα) at 6.40 keV. We search for the iron K-shell line in seven SNRs from the Suzaku archive data of the Galactic plane in the region. All of these SNRs interact with molecular clouds. We discover Fe i Kα line emissions from five SNRs (W28, Kes 67, Kes 69, Kes 78, and W44). The spectra and morphologies suggest that the Fe i Kα line is produced by interactions between LECRp and the adjacent cold gas. The proton energy density is estimated to be ≳10–100 eV cm−3, which is more than 10 times higher than that in the ambient interstellar medium.

Cosmic-ray energy densities in star-forming galaxies

The energy density of cosmic ray protons in star forming galaxies can be estimated from π 0 -decay γ -ray emission, synchrotron radio emission, and supernova rates. To galaxies for which these methods can be applied, the three methods yield consistent energy densities ranging from U p ~ 0.1 − 1 eV cm −3 to U p ~ 10 2 − 10 3 eV cm −3 in galaxies with low to high star-formation rates, respectively.

SPECTRUM OF RELATIVISTIC AND SUBRELATIVISTIC COSMIC RAYS IN THE 100 pc CENTRAL REGION

From the rate of hydrogen ionization and the gamma ray flux, we derived the spectrum of relativistic and subrelativistic cosmic rays (CRs) nearby and inside the molecular cloud Sgr B2 near the Galactic Center (GC). We studied two cases of CR propagation in molecular clouds: free propagation and scattering of particles by magnetic fluctuations excited by the neutral gas turbulence. We showed that in the latter case CR propagation inside the cloud can be described as diffusion with the coefficient $\sim 3\times 10^{27}$ cm$^2$ s$^{-1}$. For the case of hydrogen ionization by subrelativistic protons, we showed that their spectrum outside the cloud is quite hard with the spectral index $\delta>-1$. The energy density of subrelativistic protons ($>50$ eV cm$^{-3}$) is one order of magnitude higher than that of relativistic CRs. These protons generate the 6.4 keV emission from Sgr B2, which was about 30\% of the flux observed by Suzaku in 2013. Future observations for the period after 2013 may discover the background flux generated by subrelativistic CRs in Sgr B2. Alternatively hydrogen ionization of the molecular gas in Sgr B2 may be caused by high energy electrons. We showed that the spectrum of electron bremsstrahlung is harder than the observed continuum from Sgr B2, and in principle this X-ray component provided by electrons could be seen from the INTEGRAL data as a stationary high energy excess above the observed spectrum $E_x^{-2}$.

SYNCHROTRON AND COMPTON SPECTRA FROM A STEADY-STATE ELECTRON DISTRIBUTION

Energy densities of relativistic electrons and protons in extended galactic and intracluster regions are commonly determined from spectral radio and (rarely) $\gamma$-ray measurements. The time-independent particle spectral density distributions are commonly assumed to have a power-law (PL) form over the relevant energy range. A theoretical relation between energy densities of electrons and protons is usually adopted, and energy equipartition is invoked to determine the mean magnetic field strength in the emitting region. We show that for typical conditions, in both star-forming and starburst galaxies, these estimates need to be scaled down substantially due to significant energy losses that (effectively) flatten the electron spectral density distribution, resulting in a much lower energy density than deduced when the distribution is assumed to have a PL form. The steady-state electron distribution in the nuclear regions of starburst galaxies is calculated by accounting for Coulomb, bremsstrahlung, Compton, and synchrotron losses; the corresponding emission spectra of the latter two processes are calculated and compared to the respective PL spectra. We also determine the proton steady-state distribution by taking into account Coulomb and pion production losses, and briefly discuss implications of our steady-state particle spectra for estimates of proton energy densities and magnetic fields.

A Micro Direct Formic Acid Fuel Cell with PDMS Fluid Flow Plates

Micro direct formic acid fuel cell (DFAFC) is currently one of the promising technologies to power micro/nano devices and systems. Compared with micro direct methanol fuel cell (DMFC), micro (DFAFC) can have higher proton conductivity and energy density, and crossover of formic acid through Nafion membrane is significantly less than methanol. In this paper, a micro DFAFC has been developed. Polydimethylsiloxane (PDMS) is chosen as the material for fluid flow plates in both cathode and anode of the micro DFAFC in order to simplify its structure and improve its packaging performance. The developed micro DFAFC has been tested and results show that its input concentration of formic acid solution can reach up to 10mol/L with its peak power output of 13.6mW/cm2 and maximum output current of 97.66mA/cm2.

MAGNETIZATION DEGREE AT THE JET BASE OF M87 DERIVED FROM THE EVENT HORIZON TELESCOPE DATA: TESTING THE MAGNETICALLY DRIVEN JET PARADIGM

We explore the degree of magnetization at the jet base of M87 by using the observational data of the event horizon telescope (EHT) at 230~GHz obtained by Doeleman et al. By utilizing the method in Kino et al., we derive the energy densities of magnetic fields ($U_{B}$) and electrons and positrons ($U_{\pm}$) in the compact region detected by EHT (EHT-region) with its full-width-half-maximum size $40~{\rm \mu as}$. First, we assume that an optically-thick region for synchrotron self absorption (SSA) exists in the EHT-region. Then, we find that the SSA-thick region should not be too large not to overproduce the Poynting power at the EHT-region. The allowed ranges of the angular size and the magnetic field strength of the SSA-thick region are $21~{\rm \mu as} \le \theta_{\rm thick}\le 26.3~{\rm \mu as}$ and $50~{\rm G}\le B_{\rm tot}\le 124~{\rm G}$, respectively. Correspondingly $U_{B}\gg U_{\pm} $ is realized in this case. We further examine the composition of plasma and energy density of protons by utilizing the Faraday rotation measurement ($RM$) at 230~GHz obtained by Kuo et al. Then, we find that $U_{B}\gg U_{\pm}+U_{p} $ still holds in the SSA-thick region. Second, we examine the case when EHT-region is fully SSA-thin. Then we find that $U_{B}\gg U_{\pm}$ still holds unless protons are relativistic. Thus, we conclude that magnetically driven jet scenario in M87 is viable in terms of energetics close to ISCO scale unless the EHT-region is fully SSA-thin and relativistic protons dominated.

Estimates of relativistic electron and proton energy densities in starburst galactic nuclei from radio measurements

The energy density of energetic protons, U_p, in several nearby starburst nuclei (SBNs) has been directly deduced from gamma-ray measurements of the radiative decay of neutral pions produced in interactions with ambient protons. Lack of sufficient sensitivity and spatial resolution makes this direct deduction unrealistic in the foreseeable future for even moderately distant SBNs. A more viable indirect method for determining U_p in star-forming galaxies is to use its theoretically based scaling to the energy density of energetic electrons, U_e, which can be directly deduced from radio synchrotron and possibly also nonthermal hard X-ray emission. In order to improve the quantitative basis and diagnostic power of this leptonic method we reformulate and clarify its main aspects. Doing so we obtain a basic expression for the ratio U_p/U_e in terms of the proton and electron masses and the power-law indices that characterize the particle spectral distributions in regions where the total particle energy density is at equipartition with that of the mean magnetic field. We also express the field strength and the particle energy density in the equipartition region in terms of the region's size, mean gas density, IR and radio fluxes, and distance from the observer, and determine values of U_p in a sample of nine nearby and local SBNs.

Counting gamma rays in the directions of galaxy clusters

Emission from active galactic nuclei (AGNs) and from neutral pion decay are the two most natural mechanisms that could establish a galaxy cluster as a source of gamma rays in the GeV regime. We revisit this problem by using 52.5 months of Fermi-LAT data above 10 GeV and stacking 55 clusters from the HIFLUCGS sample of the X-ray brightest clusters. The choice of >10 GeV photons is optimal from the point of view of angular resolution, while the sample selection optimizes the chances of detecting signatures of neutral pion decay, arising from hadronic interactions of relativistic protons with an intracluster medium, which scale with the X-ray flux. In the stacked data we detected a signal for the central 0.25 deg circle at the level of 4.3σ. Evidence for a spatial extent of the signal is marginal. A subsample of cool-core clusters has a higher count rate of 1.9 ± 0.3 per cluster compared to the subsample of non-cool core clusters at 1.3 ± 0.2. Several independent arguments suggest that the contribution of AGNs to the observed signal is substantial, if not dominant. No strong support for the large contribution of pion decay was found. In terms of a limit on the relativistic proton energy density, we derived an upper limit of ≃2% relative to the gas thermal energy density, provided that the spectrum of relativistic protons is hard (s = 4.1 in dN ∝ p−sd3p). This estimate assumes that relativistic and thermal components are mixed. For softer spectra the upper limits are weaker and equal to 3% for s = 4.2, 4% for s = 4.3, and 6% for s = 4.4.

THE EFFECT OF STOCHASTIC RE-ACCELERATION ON THE ENERGY SPECTRUM OF SHOCK-ACCELERATED PROTONS

The energy spectra of particles in gradual solar energetic particle (SEP) events do not always have a power-law form attributed to the diffusive shock acceleration mechanism. In particular, the observed spectra in major SEP events can take the form of a broken (double) power law. In this paper, we study the effect of a process that can modify the power-law spectral form produced by the diffusive shock acceleration: the stochastic re-acceleration of energetic protons by enhanced Alfvenic turbulence in the downstream region of a shock wave. There are arguments suggesting that this process can be important when the shock propagates in the corona. We consider a coronal magnetic loop traversed by a shock and perform Monte Carlo simulations of interactions of shock-accelerated protons with Alfven waves in the loop. The wave-particle interactions are treated self-consistently, so the finiteness of the available turbulent energy is taken into account. The initial energy spectrum of particles is taken to be a power law. The simulations reveal that the stochastic re-acceleration leads either to the formation of a spectrum that is described in a wide energy range by a power law (although the resulting power-law index is different from the initial one) or to a broken power-law spectrum. The resulting spectral form is determined by the ratio of the energy density of shock-accelerated protons to the wave energy density in the shock's downstream region.

HESS J1640-465 - an exceptionally luminous TeV -ray supernova remnant

The results of follow-up observations of the TeV γ-ray source HESS J1640−465 from 2004 to 2011 with the High Energy Stereoscopic System (HESS) are reported in this work. The spectrum is well described by an exponential cut-off power law with photon index Γ = 2.11 ± 0.09stat ± 0.10sys, and a cut-off energy of |$E_{\rm c} = 6.0^{+2.0}_{-1.2}$| TeV. The TeV emission is significantly extended and overlaps with the northwestern part of the shell of the SNR G338.3−0.0. The new HESS results, a re-analysis of archival XMM–Newton data and multiwavelength observations suggest that a significant part of the γ-ray emission from HESS J1640−465 originates in the supernova remnant shell. In a hadronic scenario, as suggested by the smooth connection of the GeV and TeV spectra, the product of total proton energy and mean target density could be as high as WpnH ∼ 4 × 1052(d/10kpc)2 erg cm−3.

Self-consistent neutrino and UHE cosmic ray spectra from Mrk 421

We examine the neutrino and cosmic ray spectra resulting from two models of fitting the spectral energy distribution (SED) of the blazar Mrk 421 using a self-consistent leptohadronic code. The γ-ray emission is attributed to either synchrotron radiation of ultra-high energy protons (LHs model) or to synchrotron radiation from electrons that result from photopion interactions of lower energy protons (LHπ model). Although both models succeed in fitting satisfactorily the SED, the parameter values that they use result in significantly different neutrino and cosmic-ray spectra. For the LHπ model, which requires high proton energy density, we find that the neutrino spectrum peaks at an energy Eν,peak=3.3PeV which falls well within the energy range of recent neutrino observations. While at the same time its peak flux is just under the sensitivity limit of IC-40 observations, it cannot produce ultra-high energy cosmic rays. In the LHs model, on the other hand, neutrinos are far from being detectable because of their low flux and peak energy at Eν,peak≃100PeV. However, the propagation of protons produced by the decay of escaping neutrons results in an ultra-high energy cosmic ray flux close to that observed by Pierre Augere, HiRes and Telescope Array at energies Ep≃30EeV.