Search

Superluminal propagation is an intrinsic problem in the diffusion equation and has not been effectively addressed for a long time. In this work, a rigorous solution to this issue is obtained under the assumption that particles undergo a random flight process, where they move isotropically at a constant speed while experiencing random scatterings. We validate this solution by comparing it with comprehensive simulations of the random flight process and find that it significantly deviates from the solution derived from the J\"{u}ttner propagator. This solution is broadly applicable to various diffusion phenomena, such as cosmic-ray propagation. We emphasize that our rigorous solution is particularly crucial in scenarios involving burst-like particle injection, where previous phenomenological approaches to the superluminal diffusion problem may not yield accurate results., Comment: 8 pages, 4 figures

The recently discovered stellar system, Ursa Major III/UNIONS 1, may be the faintest and densest dwarf spheroidal satellite galaxy of the Milky Way. Owing to its close proximity and substantial dark matter (DM) component, Ursa Major III emerges as a highly promising target for DM indirect detection. It is known that electrons and positrons originating from DM annihilation can generate a broad radio spectrum through the processes of synchrotron radiation and inverse Compton scattering within galaxies. In this study, we investigate the potential of the Square Kilometre Array (SKA) in detecting radio signatures arising from DM annihilation in Ursa Major III over a 100 hour observation period. Our analysis indicates that the SKA has strong capabilities in detecting these signatures. For instance, the SKA sensitivity to the DM annihilation cross section is estimated to reach $\mathcal{O}(10^{-30})-\mathcal{O}(10^{-28})\; \rm cm^{3} s^{-1}$ in the DM mass range from several GeV to $\sim100$ GeV for the $e^+e^-$ and $\mu^+\mu^-$ annihilation channels. The precise results are significantly influenced by various astrophysical factors, such as the strength of magnetic field, the diffusion coefficient, and the DM density profile in the dwarf galaxy. We discuss the impact of the uncertainties associated with these factors, and find that the SKA sensitivities have the potential to surpass the current constraints, even when considering these uncertainties., Comment: 20 pages, 6 figures

The recent AMS-02 measurements of cosmic-ray (CR) deuteron fluxes suggest the presence of primary deuterons in quantities far exceeding predictions from Big Bang nucleosynthesis. This poses a significant challenge to modern astrophysics, as no known processes can account for such large amounts of deuterons without violating existing constraints~\cite{Epstein:1976hq}. In contrast, it is recently proposed that the AMS-02 measurements can be explained by a purely secondary origin when contributions from heavier nuclei are considered. In this study, we recalculate the secondary deuteron flux using production cross sections updated with the latest collider data. We find that some of the deuteron production cross sections are overestimated in the widely-used calculation tools for CR propagation, and a primary deuteron component is still necessary. We then propose a novel process for generating primary deuterons at CR sources through a fusion mechanism, which is naturally unique to deuterons. This model could explain the observed deuteron excess while maintaining consistency with other CR measurements., Comment: 8 pages, 8 figures

Observations of the velocity dispersion indicate a severe dark matter (DM) deficit in the ultra-diffuse galaxy, NGC1052-DF4 (DF4). The ultra-deep images obtained with the Gemini telescope, which has the deepest imaging data till now, confirm the presence of tidal tails in DF4, suggesting its tidal formation. To enhance tidal effects, we consider the self-interaction among DM particles. Using an N-body simulation in the scenario of self-interacting dark matter (SIDM), we reproduce a DM-deficient galaxy that is consistent with all observational data of DF4. Specifically, our simulation result yields an extremely low DM-to-star mass ratio and a radial surface brightness profile very similar to that from deep images, showing accurate tidal features. By performing simulations with similar tidal effects and various cross-sections of SIDM, we show a significant impact of SIDM on the DM-to-star mass ratio in the central region of the galaxy. Our work confirms the tidal formation of DF4 in theory., Comment: 9 pages, 6 figures

The interaction between axion-like particles (ALPs) and photons induces ALP-photon oscillations in astrophysical magnetic fields, leading to spectral distortions in the $\gamma$-ray spectrum of blazars. The primary uncertainty of this phenomenon may originate from the magnetic field within the jet of the blazar. While many studies have explored the effects of ALP-photon oscillations using typical values for jet magnetic field parameters, it is important to recognize that these parameters can be constrained by multi-wavelength observations. In this study, we utilize the high energy $\gamma$-ray spectrum of Mrk 421 obtained from MAGIC and Fermi-LAT observations. By employing multi-wavelength fitting with a one-zone synchrotron self-Compton model, we derive the parameters characterizing the magnetic field model within the jet, and investigate their impacts on the ALP constraints., Comment: 9 pages, 7 figures

The recently discovered satellite dwarf galaxy Ursa Major III provides a promising opportunity to explore the signatures resulting from dark matter (DM) annihilation, due to its proximity and large J-factor. Owing to the absence of an excess of $\gamma$-ray signatures originating from Ursa Major III, observations of $\gamma$-rays, such as those from Fermi-LAT, can be utilized to set constraints on the DM annihilation cross section. In this study, we determine the DM density profile, and consider the relationship between DM density and velocity dispersion at different locations within Ursa Major III through Jeans analysis. We calculate the J-factor of Ursa Major III for s-wave annihilation, along with the effective J-factors for p-wave and Sommerfeld enhanced annihilation scenarios. Utilizing these derived J-factors, we set stringent constraints on DM annihilation cross sections in three scenarios. Given the substantial impact of member star identification on the J-factor of Ursa Major III, we further calculate J-factors with the condition of excluding the largest velocity outlier. Our analysis reveals a notable reduction in the median value and an increase in the deviation of J-factors, thereby leading to considerably weaker constraints.

In recent astronomical observations, an almost dark galaxy, designated as Nube, has unveiled an intriguing anomaly in its stellar distribution. Specifically, Nube exhibits an exceptionally low central brightness, with the 2D half-light radius of its stars far exceeding the typical values found in dwarf galaxies, and even surpassing those observed in ultra-diffuse galaxies (UDGs). This phenomenon is difficult to explain within the framework of cold dark matter (CDM). Meanwhile, due to its ultralight particle mass, fuzzy dark matter (FDM) exhibits a de Broglie wavelength on the order of kiloparsecs under the typical velocities of galaxies. The interference between different modes of the FDM wave gives rise to fluctuations in the gravitational field, which can lead to the dynamical heating of stars within galaxies, resulting in an expansion of their spatial distribution. In this paper, we aim to interpret the anomalous stellar distribution observed in Nube as a consequence of the dynamical heating effect induced by FDM. Our findings suggest that a FDM particle mass around $1-2\times 10^{-23}$ eV can effectively account for this anomaly. And we propose that the FDM dynamical heating effect provides a new insight into understanding the formation of field UDGs., Comment: 13 pages, 4 figures

Recently LHAASO Collaboration gives precise measurements of cosmic rays (CR) all particle energy spectrum and mean logarithmic mass $\left \langle \ln A \right \rangle$ from 0.3 PeV to 30 PeV. Combining the CR measurements by AMS-02 and DAMPE in space and that by LHAASO and Auger on the ground we construct a model to recover all these measurements from tens of GeV to tens of EeV. We find the LHAASO measurement is crucial in the model construction by connecting the Galactic component to the extragalactic component. The precise measurements of CR spectra for individual species by AMS-02 and DAMPE together with the newest LHAASO results clearly indicates three Galactic CR components, that is, a soft low energy background, a hard high energy component, and a local source contribution. However, the LHAASO data show that above $\sim 10^{16}$ eV a nonnegligible extragalactic component must be included. Combining the Auger results and the LHAASO results we figure out the extragalactic CRs which need at least two components at lower and higher energies. Thanks to the precise measurements by LHAASO the constraints on the model parameters are quite stringent. The spectra features and mass measurements in all energy range are all well reproduced in the model., Comment: 11 pages, 2 figures, 4 tables

Observations have revealed a significant dark matter deficit in the ultra-diffuse galaxy NGC1052-DF2 (DF2). It is widely accepted that the formation of this unique galaxy can be attributed to the tidal stripping of its host galaxy, NGC1052. In this study, we simulate the evolution of a satellite system containing globular clusters (GCs) within an accreting host halo in the framework of self-interacting dark matter (SIDM). Our simulation results suggest that the heightened tidal stripping resulting from DM self-interactions can give rise to the transformation of a conventional dwarf galaxy into a dark matter deficit galaxy resembling DF2. By comparing the simulation results with identical initial conditions in both the standard cold dark matter (CDM) and SIDM models, we find that the latter is more likely to replicate the properties of DF2. Furthermore, we demonstrate that a DF2 analog can also be produced on an orbit with a greater pericenter distance by increasing the strength of DM self-interactions. This suggests that the issue of extreme orbital parameters can be mitigated by implementing the SIDM model. The distributions of the GC population derived in our SIDM simulation are consistent with the observed characteristics of DF2. For comparison, we also explored the potential for achieving GC distributions in the context of CDM., Comment: 12 pages, 7 figures

The excesses in the electron and positron spectra observed by many experiments, such as PAMELA and AMS-02, have sparked significant theoretical investigation. It is not easy to distinguish the two primary hypotheses dark matter annihilation/decay and pulsars from the spectral features. Should pulsars be the source of this excess, the expected variability in their distribution may introduce distinct irregularities in the positron energy spectrum. In this study, we use an irregularity estimator to detect these potential features in the positron energy spectrum of AMS-02. Our analysis of the current AMS-02 data reveals these spectral irregularities with a statistical significance of $1.75\sigma$. However, our projection indicates that, with AMS-02 data collected over a period of 20 years, such irregularities could be identified with a confidence level of $3\sigma$ level in 71\% of our simulations., Comment: 6 pages, 6 figures

The Be isotopic measurements preliminarily reported by the AMS-02 Collaboration have reached an unprecedented energy of 12 GeV/$n$. As secondary cosmic rays (CRs), the Be isotopes include both stable and unstable species, which are crucial for constraining the propagation parameters of Galactic CRs. However, uncertainties in their production cross sections can skew the interpretation of the CR data, especially when cross-section measurements are of significantly lower quality than CR measurements. In this work, we consider the uncertainties of the cross sections to interpret the Be isotopic data by adopting a cross-section parametrization that fully utilizes the available experimental data. Owing to the high-quality measurements of the $^7$Be production cross section, we innovatively employ $^7$Be instead of $^9$Be to constrain propagation parameters. Notably, the diffusion halo thickness is constrained to $5.67\pm0.76$~kpc, representing a moderate value compared to previous analogous works. Combining the well-constrained CR propagation model and the precise CR measurements of $^9$Be, we conversely constrain the major production cross section of $^9$Be and find that it ought to be remarkably lower than previously thought. Our analysis also questions the reliability of certain cross sections measured by some experiments, potentially marking the first time CR data has been used to identify dubious nucleon production cross sections. The method presented in this work holds promise for analyzing upcoming isotopic data from other nuclei., Comment: 15 pages, 9 figures

High-energy photons may oscillate with axion-like particles (ALPs) when they propagate through the Milky Way's magnetic field, resulting in an alteration in the observed photon energy spectrum. The ultra-high energy gamma-ray spectra, measured by the Large High Altitude Air Shower Observatory (LHAASO) up to $\mathcal{O}(1)~\mathrm{PeV}$, provide a promising opportunity to investigate the ALP-photon oscillation effect. In this study, we utilize the gamma-ray spectra of four Galactic sources measured by LHAASO, including the Crab Nebula, LHAASO J2226+6057, LHAASO J1908+0621, and LHAASO J1825-1326, to explore this effect. We employ the $\rm CL_s$ method to set constraints on the ALP parameters. Combing the observations of the four sources, our analysis reveals that the ALP-photon coupling $g_{a\gamma}$ is constrained to be smaller than $1.4\times10^{-10}$ ${\rm GeV}^{-1}$ for the ALP mass of $\sim 4\times10^{-7} ~\mathrm{eV}$ at the 95\% C.L. By combing the observations of the Crab Nebula from LHAASO and other experiments, we find that the ALP-photon coupling could be set to be about $7.2\times10^{-11}$ ${\rm GeV}^{-1}$ for the ALP mass $\sim 4 \times10^{-7}~\mathrm{eV}$ , which is in close proximity to the CAST constraint.

In some quantum gravity (QG) theories, Lorentz symmetry may be broken above the Planck scale. The Lorentz invariance violation (LIV) may induce observable effects at low energies and be detected at high energy astrophysical measurements. The Large High Altitude Air Shower Observatory(LHAASO) has detected the onset, rise, and decay phases of the afterglow of GRB 221009A, covering a wide energy range of photons approximately from $0.2$ to $18$ TeV. This observation provides an excellent opportunity to study the Lorentz invariance violation effect. In this study, we simultaneously utilize the data from the KM2A and WCDA detectors of LHAASO, and apply two event by event methods, namely the pair view method and maximum likelihood method, to investigate LIV. We obtain stringent constraints on the QG energy scale. For instance, through the maximum likelihood method, we determine the 95$\%$ confidence level lower limits to be $E_{QG,1} > 14.7 (6.5)\times 10^{19}$GeV for the subluminal (superluminal) scenario of $n = 1$, and $E_{QG,2} > 12.0 (7.2)\times 10^{11}$GeV for the subluminal (superluminal) scenario of $n = 2$. We find that the rapid rise and slow decay behaviors of the afterglow can impose strong constraints on the subluminal scenario, while the constraints are weaker for the superluminal scenario., Comment: 11 pages, 6 figures.Accepted for publication in JCAP

The LHAASO collaboration recently reported the measurement of the gamma-ray spectra of GRB 221009A, which is the brightest burst ever, covering an energy range from 0.3 $\mathrm{TeV}$ to about 10 $\mathrm{TeV}$. Based on the observation, we investigate the ALP-photon oscillation effect in the host galaxy of GRB 221009A and the Milky Way. The ${\rm CL_s}$ method is applied to set constraints on the ALP parameters in this study. Given the uncertain magnetic field configuration in the host galaxy, we use three different models: a homogeneous magnetic field model, a magnetic field model identical to that of the Milky Way, and a model constructed from the HST observations of the host galaxy. We find that the constraints derived using these three host galaxy magnetic field models are comparable. Our results are complementary in the small ALP mass regions compared with other experiments., Comment: 8 pages, 13 figures

Numerous simulations indicate that a large number of subhalos should be hosted by the Milky Way. The potential existence of a nearby subhalo could have important implications for our understanding of dark matter (DM) annihilation. In this study, we investigate the hypothetical presence of a nearby subhalo and set the upper limits on the DM annihilation cross section by analyzing the cosmic-ray antiproton spectrum. By presenting the ratios of annihilation cross section limits for scenarios with and without a nearby subhalo, we can quantitatively evaluate the potential impact of the nearby subhalo on the limits of the DM annihilation cross section. The impacts of the concentration model and the subhalo probability distribution have been considered. We explore the antiproton contribution of the potential nearby DM subhalo accounting for the DAMPE $e^\pm$ spectrum at $\sim 1.4$ TeV and find that the current AMS-02 antiproton results do not place the constraint on this contribution., Comment: 8 pages, 5 figures

Axion-like particles (ALPs) may undergo mixing with photons in the presence of astrophysical magnetic fields, leading to alterations in the observed high energy $\gamma$-ray spectra. In this study, we investigate the ALP-photon oscillation effect using the spectra of the blazar Mrk 421 over 15 observation periods measured by Major Atmospheric Gamma Imaging Cherenkov Telescopes (MAGIC) and Fermi Large Area Telescope (Fermi-LAT). Compared with previous studies, we generate mock data under the ALP hypothesis and employ the ${\rm CL_s}$ method to set constraints on the ALP parameters. This method is widely utilized in high energy experiments and avoids the exclusion of specific parameter regions where distinguishing between the null and ALP hypotheses is challenging. We find that the ALP-photon coupling $g_{a\gamma}$ is constrained to be smaller than $\sim 2\times10^{-11}$ GeV$^{-1}$ for ALP masses ranging from $10^{-9}$ eV to $10^{-7}$ eV at the 95\% confidence level. We also present the constraints derived from the TS distribution under the null hypothesis, which is commonly utilized in previous astrophysical ALP studies. Our results reveal that the combined constraints of all the periods obtained from both methods are consistent. However, the ${\rm CL_s}$ method remains effective in cases where the latter method fails to provide constraints for specific observation periods., Comment: 10 pages, 27 figures

The diffusion coefficients around the pulsar $\gamma$-ray halos are highly suppressed compared with the value in the interstellar medium. It is suggested in the literature that the $\gamma$-ray halos can be explained by a ballistic-diffusive (BD) propagation without slow diffusion. However our calculation shows that the BD propagation can not account for the $\gamma$-ray halo profile well. Furthermore the transfer efficiency of the pulsar spin down energy to the high energy electrons and positrons is even larger than 1 in the BD scenario. Therefore slow diffusion is necessary to account for the pulsar $\gamma$-ray halos. Taking the slow diffusion into account the contribution of positron flux originated from nearby pulsars to the AMS-02 data is reexamined. We may also expect a slow diffusion disk of the Milky Way as many such slow diffusion regions exist. The positron contribution to the AMS-02 data from dark matter annihilation in the new propagation model is also reexamined. We find that the dark matter scenario satisfies all the $\gamma$-ray limits in the new propagation model., Comment: 10 pages, 8 figures. Proceedings of the 38th International Cosmic Ray Conference (ICRC2023) in Nagoya, Japan

The positron excess in cosmic rays has stimulated a lot of interests in the last decade. The dark matter origin of the extra positrons has attracted great attention. However, the $\gamma$-ray search set very stringent constraints on the dark matter annihilation/decay rate, which leads to great disfavor of the dark matter scenario. In the work, we incorporate the recent progress in cosmic rays propagation and reexamine the dark matter scenario accounting for the positron excess. Recent observations indicate that cosmic rays propagation in the Milky Way may be not uniform and diffusion in the Galactic disk should be slower than that in the halo. In the spatial-dependent propagation model, the positrons/electrons are more concentrated in the disk and lead to smaller dark matter annihilation/decay rate to account for the positron excess and also a smaller deficit in the background positron flux. Especially for the $\mu^+\mu^-$ channel the positron spectrum fit the AMS-02 latest data perfectly and the annihilation rate satisfies all the present constraints from $\gamma$-ray and CMB observations., Comment: 11 pages, 4 figures

Precise measurements of the spectra of secondary and primary cosmic rays are crucial for understanding the origin and propagation of those energetic particles. The High Energy cosmic-Radiation Detection (HERD) facility onboard China`s Space Station, which is expected to operate in 2027, will push the direct measurements of cosmic ray fluxes precisely up to PeV energies. In this work, we investigate the potential of HERD on studying the propagation of cosmic rays using the measurements of boron, carbon, and oxygen spectra. We find that, compared with the current results, the new HERD measurements can improve the accuracy of the propagation parameters by 8\% to 40\%. The constraints on the injection spectra at high energies will also be improved., Comment: 10 pages, 4 figures

Anisotropic diffusion is one of the potential interpretations for the morphology of the Geminga pulsar halo. It interprets the observed slow-diffusion phenomenon through a geometric effect, assuming the mean magnetic field direction around Geminga is closely aligned with the line of sight toward it. However, this direction should not extend further than the correlation length of the turbulent magnetic field $L_c$, which could be $100$ pc or less. We first revisit the $L_c=\infty$ scenario and show that the halo asymmetry predicted by this scenario is mainly contributed by the electrons located beyond the ``core" section around Geminga, which has a length of $100$ pc. Then, considering the directional variation of the magnetic field beyond the core section, we take one magnetic field configuration as an example to investigate the possible halo morphology. The predicted morphology has some different features compared to the $L_c=\infty$ scenario. The current experiments may already be able to test these features. In addition, we use a semi-analytical method to solve the anisotropic propagation equation, which offers significant convenience compared to numerical approaches., Comment: 15 pages, 7 figures

Recent studies on cosmic rays (CRs) have reported the possibility of an excess in the antiproton flux around $10-20$ GeV. However, the associated systematic uncertainties have impeded the interpretation of these findings. In this study, we conduct a global Bayesian analysis to constrain the propagation parameters and evaluate the CR antiproton spectrum, while comprehensively accounting for uncertainties associated with interstellar CR propagation, production cross sections for antiprotons and other secondaries, and the charge and energy dependent effects of solar modulation. We establish that the most recent AMS-02 $\bar{p}$ spectrum is in agreement with a pure secondary origin. Based on this, we establish upper limits on dark matter (DM) annihilation. We also determine that the AMS-02 data favors the empirical hadronic interaction models over phenomenological ones. Finally, we find that the latest AMS-02 antiproton data from 2011 to 2018 disfavors the antiproton excess at $\mathcal{O}$(10) GeV and the corresponding DM interpretation that can simultaneously account for the Galactic Center excess in the gamma-ray observation., Comment: 11 pages, 7 figures

The multi-messenger anomalies, including spectral hardening or excess for nuclei, leptons, ratios of $\bar p/p$ and B/C, and anisotropic reversal, were observed in past years. AMS-02 experiment also revealed different spectral break for positron and electron at 284 GeV and beyond TeV respectively. It is natural to ask whether all those anomalies originate from one unified physical scenario. In this work, the spatially-dependent propagation (SDP) with a nearby SNR source is adopted to reproduce above mentioned anomalies. There possibly exists dense molecular cloud(DMC) around SNRs and the secondary particles can be produced by pp-collision or fragmentation between the accelerated primary cosmic rays and DMC. As a result, the spectral hardening for primary, secondary particles and ratios of $B/C$ and $\bar p/p$ can be well reproduced. Due to the energy loss at source age of 330 kyrs, the characteristic spectral break-off for primary electron is at about 1 TeV hinted from the measurements. The secondary positron and electron from charged pion take up $5\%$ energy from their mother particles, so the positron spectrum has a cut-off at $\sim$250 GeV. Therefore, the different spectral break for positron and electron together with other anomalies can be fulfilled in this unified physical scenario. More interesting is that we also obtain the featured structures as spectral break-off at 5 TV for secondary particles of Li, Be, B, which can be served to verify our model. We hope that those tagged structures can be observed by the new generation of space-borne experiment HERD in future., Comment: 16 pages, 12 figures

Precise measurements of the boron-to-carbon and boron-to-oxygen ratios by DAMPE show clear hardenings around $100$ GeV/n, which provide important implications on the production, propagation, and interaction of Galactic cosmic rays. In this work we investigate a number of models proposed in literature in light of the DAMPE findings. These models can roughly be classified into two classes, driven by propagation effects or by source ones. Among these models discussed, we find that the re-acceleration of cosmic rays, during their propagation, by random magnetohydrodynamic waves may not reproduce sufficient hardenings of B/C and B/O, and an additional spectral break of the diffusion coefficient is required. The other models can properly explain the hardenings of the ratios. However, depending on simplifications assumed, the models differ in their quality in reproducing the data in a wide energy range. The models with significant re-acceleration effect will under-predict low-energy antiprotons but over-predict low-energy positrons, and the models with secondary production at sources over-predict high-energy antiprotons. For all models high-energy positron excess exists., Comment: 14 pages, 7 figures. Published version

We propose that the interaction between the axionlike particles (ALPs) and photons can be a possible origin of optical circular polarization (CP) in blazars. Given that there is no definite detection of optical CP at $\sim0.1\%$ level, a rough limit on ALP-photon coupling can be obtained, specifically $g_{a\gamma}\cdot B_\mathrm{T0}\lesssim7.9\times10^{-12}~\mathrm{G\cdot GeV}^{-1}$ for $m_{a}\lesssim 10^{-13}~\mathrm{eV}$, depending on the magnetic field configuration of the blazar jet. Obviously, for the blazar models with a larger magnetic field strength, such as hadronic radiation models, this constraint could be more stringent. We also perform a dedicated analysis of the tentative observations of optical CP in two blazars, namely 3C 66A and OJ 287, and we find that these observations could be explained by the ALP-photon mixing with $g_{a\gamma} \sim 10^{-11}~\mathrm{GeV}^{-1}$. As an outlook, our analysis can be improved by further research on the radiation models of blazars and high-precision joint measurements of optical CP and linear polarization., Comment: 15 pages, 9 figures, 4 tables

The stable secondary-to-primary flux ratios of cosmic rays (CRs), represented by the boron-to-carbon ratio (B/C), are the main probes of the Galactic CR propagation. However, the fluorine-to-silicon ratio (F/Si) predicted by the CR diffusion coefficient inferred from B/C is significantly higher than the latest measurement of AMS-02. This anomaly is commonly attributed to the uncertainties of the F production cross sections. In this work, we give a careful test to this interpretation. We consider four different cross-section parametric models. Each model is constrained by the latest cross-section data. We perform combined fits to the B/C, F/Si, and cross-section data with the same propagation framework. Two of the cross-section models have good overall goodness of fit with $\chi^2/n_{d.o.f.}\sim1$. However, the goodness of fit of the cross-section part is poor with $\chi^2_{\rm{cs}}/n_{\rm{cs}}\gtrsim2$ for these models. The best-fitted F production cross sections are systematically larger than the measurements, while the fitted cross sections for B production are systematically lower than the measurements. This indicates that the F anomaly can hardly be interpreted by neither the random errors of the cross-section measurements nor the differences between the existing cross-section models. We then propose that the spatially dependent diffusion model could help to explain B/C and F/Si consistently. In this model, the average diffusion coefficient of the Ne-Si group is expected to be larger than that of the C-O group., Comment: 13 pages, 7 figures

Gamma-ray pulsar halos are ideal indicators of cosmic-ray propagation in localized regions of the Galaxy and electron injection from pulsar wind nebulae. HESS~J1831$-$098 is a candidate pulsar halo observed by both H.E.S.S. and HAWC experiments. We adopt the flux map of the H.E.S.S. Galactic plane survey and the spectrum measurements of H.E.S.S. and \textit{Fermi}-LAT to study HESS~J1831$-$098. We find that HESS~J1831$-$098 meets all the criteria for a pulsar halo. The diffusion coefficient inside the halo and the conversion efficiency from the pulsar spin-down energy to the electron energy are both similar to the Geminga halo, a canonical pulsar halo. The injection spectrum can be well described by an exponentially-cutoff power law. However, the needed power-law term is very hard with $p\lesssim1$ if the diffusion coefficient is spatially and temporally independent. Considering the possible origins of the slow-diffusion environment, we adopt the two-zone diffusion model and the time-delayed slow-diffusion model. Both the models can interpret the H.E.S.S. and \textit{Fermi}-LAT results with a milder $p$. A modified injection time profile may have a similar effect., Comment: 15 pages (one column), 4 figures, 1 table

Recently, the CDF collaboration reported a new measurement of the $W$ boson mass $M_W = 80.4335 \pm 0.0094$ GeV, which shows a $\sim 7\sigma$ deviation from the standard model prediction $80.3545 \pm 0.0057$ GeV obtained by the electroweak (EW) global fit. This deviation can be explained by new physics generating moderate EW oblique parameters $S$, $T$, and $U$. In this work, we use the loop corrections induced by some extra EW multiplets to explain the CDF $M_W$ anomaly. The lightest neutral particle in the multiplets can also serve as a candidate of cold dark matter (DM). We consider two such models, namely singlet-triplet scalar DM and singlet-doublet fermionic DM models, and perform numerical scans to find the parameter points accounting for the $M_W$ anomaly. The constraints from the correct DM thermal relic density and direct detection are also taken into account. We find the parameter points simultaneously interpreting the $M_W$ anomaly and satisfying the DM requirements in the former model, but do not find such parameter points in the latter model., Comment: 23 pages, 5 figures; v3: matches version accepted for publication in Phys. Rev. D

The gamma-ray halo around Geminga is formed owing to the slow diffusion of the electrons released by the Geminga PWN. The latest HAWC and HESS observations exhibit complex features in the TeV gamma-ray spectrum of the Geminga halo. We first show that the new results cannot be interpreted by the commonly used simple model, where a single power-law injection spectrum and an energy index of $\delta=1/3$ for the diffusion coefficient are assumed. We then propose a two-population electron injection model based on the x-ray observations of the Geminga PWN, which consists of a population of freshly accelerated electrons escaping from the PWN through rapid outflows and a population trapped longer inside the PWN before escaping. The two-population model interprets the HAWC and HESS data well, and the goodness of fit improves significantly compared with the single power-law injection model. It also predicts a different energy dependency of the gamma-ray profile from the single power-law model, which could be tested by LHAASO in the coming future. We note that a $\delta$ slightly larger than 1 is needed to fit the HAWC and HESS data consistently. We also discuss the possible improvements by adopting the two-zone diffusion model., Comment: 15 pages, 4 figures

The DArk Matter Particle Explorer (DAMPE) is well suitable for searching for monochromatic and sharp $\gamma$-ray structures in the GeV$-$TeV range thanks to its unprecedented high energy resolution. In this work, we search for $\gamma$-ray line structures using five years of DAMPE data. To improve the sensitivity, we develop two types of dedicated data sets (including the BgoOnly data which is the first time to be used in the data analysis for the calorimeter-based gamma-ray observatories) and adopt the signal-to-noise ratio optimized regions of interest (ROIs) for different DM density profiles. No line signals or candidates are found between 10 and 300 GeV in the Galaxy. The constraints on the velocity-averaged cross section for $\chi\chi \to \gamma\gamma$ and the decay lifetime for $\chi \to \gamma\nu$, both at 95% confidence level, have been calculated and the systematic uncertainties have been taken into account. Comparing to the previous Fermi-LAT results, though DAMPE has an acceptance smaller by a factor of $\sim 10$, similar constraints on the DM parameters are achieved and below 100 GeV the lower limits on the decay lifetime are even stronger by a factor of a few. Our results demonstrate the potential of high-energy-resolution observations on dark matter detection., Comment: 14 pages, 8 figures. Update the content to keep up with the published version

New physics could be explored through loop effects by the precision measurements at the Circular Electron Positron Collider due to its clean collision environment and high luminosity. In this work, we focus on two dark matter models that involve additional electroweak fermionic multiplets. We calculate their one-loop corrections to five processes, i.e. $e^+e^- \to \mu^+\mu^-, ~Zh, ~ZZ, ~W^+W^-$, and $Z\gamma$, and investigate the corresponding signatures at CEPC with the projected sensitivity. We find that the detectable parameter regions of these processes are complementary. The combined analysis shows that the mass of dark matter $m_{\chi^0_1}$ in these two models can be probed up to $ \sim 150~\mathrm{GeV}$ and $\sim 450$ GeV at a 95\% confidence level, respectively., Comment: 15 pages, 5 figures

The large gap between a galactic dark matter subhalo's velocity and its own gravitational binding velocity creates the situation that small subhalos can be evaporated before dark matter thermalize with baryons due to the low binding velocity. In case dark matter acquires an electromagnetic dipole moment, the survival of low-mass subhalos requires stringent limits on the photon-mediated soft scattering. The current stringent direct detection limits indicate for a small dipole moment, which lets DM decouple early and allows small subhalos to form. We calculate the DM kinetic decoupling temperature in the Early Universe and evaluate the smallest protohalo mass. In the late Universe, low-mass subhalos can be evaporated via soft collision by ionized gas and accelerated cosmic rays. We calculate the subhalos evaporation rate and show that subhalos lighter than $10^{-5}M_{\odot}$ in the gaseous inner galactic region are subject to evaporation via dark matter's effective electric and magnetic dipole moments below current direct detection limits, which potentially affects the low-mass subhalos distribution in the galactic center., Comment: 11 pages, 6 figures, published version in EPJC

We explore the axion-like particle (ALP)-photon oscillation effect in the $\gamma$-ray spectra of the blazars Markarian 421 (Mrk 421) and PG 1553+113, which are measured by the Major Atmospheric Gamma Imaging Cherenkov Telescopes (MAGIC) and Fermi Large Area Telescope (Fermi-LAT) with high precision. We investigate the constraints on the ALP parameter space using the Mrk 421 and PG 1553+113 observations of 15 and 5 phases, respectively. We find that the combined analysis with all the 15 phases improves the limits from the Mrk 421 observations. The combined limit set by the Mrk 421 observations has excluded the ALP parameter region with the ALP-photon coupling of $g_{a\gamma} \gtrsim 2 \times 10^{-11} \, \rm GeV^{-1}$ for the ALP mass of $\sim 8\times 10^{-9}\, {\rm eV} \lesssim m_a \lesssim 2\times 10^{-7}\rm \, eV$ at 95% $\rm C.L.$ We also find that the ALP hypothesis can slightly improve the fit to the PG 1553+113 results in some parameter regions, and do not set the limit in this case., Comment: 10 pages, 6 figures

The energy spectra of primary and secondary cosmic rays (CR) generally harden at several hundreds of GeV, which can be naturally interpreted by propagation effects. We adopt a spatially dependent CR propagation model to fit the spectral hardening, where a slow-diffusion disk (SDD) is assumed near the Galactic plane. We aim to constrain the propagation parameters with the Bayesian parameter estimation based on a Markov chain Monte Carlo sampling algorithm. The latest precise measurements of carbon spectrum and B/C ratio are adopted in the Bayesian analysis. The $\rm{^{10}Be/^{9}Be}$ and Be/B ratios are also included to break parameter degeneracies. The fitting result shows that all the parameters are well constrained. Especially, the thickness of the SDD is limited to 0.4-0.5 kpc above and below the Galactic plane, which could be the best constraint for the slow-diffusion region among similar works. The $\bar{p}/p$ ratio and amplitude of CR anisotropy predicted by the SDD model are consistent with the observations, while the predicted high-energy electron and positron fluxes are slightly and significantly lower than the observations, respectively, indicating the necessity of extra sources., Comment: 14 pages, 16 figures

As a well-motivated dark matter candidate, axions can be detected through the axion-photon resonant conversion in the magnetospheres of magnetic white dwarf stars or neutron stars. In this work, we utilize Omega Centauri, which is the largest globular cluster in the Milky Way and is suggested to be the remnant core of a dwarf galaxy, to probe the axion dark matter through radio signals that originate from all the neutron stars and magnetic white dwarf stars in it. With 100 hours of observation, the combination of SKA phase 1 and LOFAR can effectively probe the parameter space of the axion-photon coupling $g_{a\gamma}$ up to $10^{-14}\sim 10^{-15}~\text{GeV}^{-1}$ for the axion mass range of $0.1\sim 30 ~\mu\text{eV}$. Depending on the choice of neutron star evolution model, this limitation is two or three and a half orders of magnitude higher than that of the single neutron star or magnetic white dwarf., Comment: 22 pages, 8 figs, and 2 tables; Phys Rev D accepted version

It was suggested that the $\gamma$-ray halo around Geminga might not be interpreted by slow-diffusion. If the ballistic regime of electron/positron propagation is considered, the Geminga halo may be explained even with a large diffusion coefficient. In this work, we examine this effect by taking the generalized J\"uttner propagator as the approximate relativistic Green's function for diffusion and find that the morphology of the Geminga halo can be marginally fitted in the fast-diffusion scenario. However, the recently discovered $\gamma$-ray halo around PSR J0622$+$3749 at LHAASO cannot be explained by the same effect and slow diffusion is the only solution. Furthermore, both the two pulsar halos require a conversion efficiency from the pulsar spin-down energy to the high energy electrons/positrons much larger than 100\%, if they are interpreted by this ballistic transport effect. Therefore, we conclude that slow diffusion is necessary to account for the $\gamma$-ray halos around pulsars., Comment: 11 pages, 8 figures; version accepted by APJ

LHAASO J0621$+$3755 is a TeV gamma-ray halo newly identified by LHAASO-KM2A. It is likely to be generated by electrons trapped in a slow-diffusion zone around PSR J0622$+$3749 through inverse Compton scattering. When the gamma-ray spectrum of LHAASO-KM2A is fitted, the GeV fluxes derived by the commonly used one-zone normal diffusion model for electron propagation are significantly higher than the upper limits (ULs) of Fermi-LAT. In this work, we respectively adopt the one-zone superdiffusion and two-zone normal diffusion models to solve this conflict. For the superdiffusion scenario, we find that a model with superdiffusion index $\alpha\lesssim1.2$ can meet the constraints of Fermi-LAT observation. For the two-zone diffusion scenario, the size of the slow-diffusion zone is required to be smaller than $\sim50$ pc, which is consistent with theoretical expectations. Future precise measurements of the Geminga halo may further distinguish between these two scenarios for the electron propagation in pulsar halos., Comment: 13 pages (one column), 4 figures, 1 table

The precise measurements of energy spectra and anisotropy could help us uncover the local cosmic-ray accelerators. Our recent works have shown that spectral hardening above $200$ GeV in the energy spectra and transition of large-scale anisotropy at $\sim 100$ TeV are of local source origin. Less than $100$ TeV, both spectral hardening and anisotropy explicitly indicate the dominant contribution from nearby sources. In this work, we further investigate the parameter space of sources allowed by the observational energy spectra and anisotropy amplitude. To obtain the best-fit source parameters, a numerical package to compute the parameter posterior distributions based on Bayesian inference, which is applied to perform an elaborate scan of parameter space. We find that by combining the energy spectra and anisotropy data, the permissible range of location and age of local source is considerably reduced. When comparing with the current local SNR catalog, only Geminga SNR could be the proper candidate of the local cosmic-ray source., Comment: 9 pages, 9 figures, 2 tables

The Tibet ASgamma experiment just reported their measurement of sub-PeV diffuse gamma ray emission from the Galactic disk, with the highest energy up to 957 TeV. These gamma-rays are most likely the hadronic origin by cosmic ray interaction with interstellar gas in the Galaxy. This measurement provides direct evidence to the hypothesis that the Galactic cosmic rays can be accelerated beyond PeV energies. In this work, we try to explain the sub-PeV diffuse gamma-ray spectrum within cosmic rays diffusive propagation model. We find there is a tension between the sub-PeV diffuse gamma rays and the local cosmic ray spectrum. To describe the sub-PeV diffuse gamma-ray flux, it generally requires larger local cosmic-ray flux than measurement in the knee region. We further calculate the PeV neutrino flux from the cosmic ray propagation model. Even all of these sub-PeV diffuse gamma rays originate from the propagation, the Galactic neutrinos only account for less than ~15% of observed flux, most of which are still from extragalactic sources., Comment: 8 pages, 5 figures

As a basic characteristic of cosmic ray (CR) propagation, the diffusive halo can advance our understanding of many CR-related studies and indirect dark matter. The method to derive the halo size usually has degeneracy problems thus affected by large uncertainties. The diffusion gamma ray from high-latitude clouds might shed light on the halo size independently. Since the spatially dependent propagation (SDP) model has a better agreement with the observed CRs, compared with conventional propagation model, in this work, we investigate the halo thickness based on SDP model with Fermi-LAT $\rm\gamma$-ray observation on the high- and intermediate-velocity clouds. As a result, in order not to exceed the relative $\gamma$-ray emissivity in the high-latitude clouds, halo thickness should be in the range of $\rm ~3.3\sim9~ kpc$. Moreover, the spatial morphology of $\rm\gamma$-rays estimated based on SDP model under different values of halo thickness are distinctive, which provides us a tool to determine the halo size. We hope that our model could be tested and tuned by multi-wavelength observations in the future., Comment: 5 pages, 3 figures

The spatial-dependent propagation (SDP) model with a nearby source works well to reproduce the co-evolving features of both cosmic ray (CR) nuclei spectra and anisotropy. However, it is well known that the Sun is offset from the Galactic plane. This will lead to a dominating anisotropy in perpendicular direction, which is discrepant with observations. Thus it is necessary to reboot further investigation into the effect of the solar offset. In this work, for the first time the combined studies of the solar offset, nuclei spectra and anisotropy are performed based on the SDP model. As a result, to reproduce CR spectra and anisotropy, the thickness of the halo $\rm (\xi z_h)$ increases linearly with the displacement of the Sun. When the offset is $\rm \sim8~pc$ as estimated from the matter-borne methods, $\rm \xi z_h$ is about 0.9 kpc, which is a much thicker halo than usually. Moreover, the PeV anisotropy could estimate the value of diffusion coefficient, thus breaking the degeneracy of diffusion coefficient and halo thickness. Therefore it is a good messenger to constrain the halo thickness. On the other hand, the anisotropy in PeV energy region, as a new probe, might also shed new light to constrain the solar offset. We hope that the anisotropy at the energies of $\rm \sim TeV$ to $\rm PeV$ can be finely measured by LHAASO experiment, leading to a better understanding about the thick halo., Comment: 7 pages, 7 figures

Axion as one of the promising dark matter candidates can be detected through narrow radio lines emitted from the magnetic white dwarf stars. Due to the existence of the strong magnetic field, the axion may resonantly convert into the radio photon (Primakoff effect) when it passes through a narrow region in the corona of the magnetic white dwarf, where the plasma frequency is equal to the axion mass. We show that for the magnetic white dwarf WD 2010+310, the future experiment SKA phase 1 with 100 hours of observation can effectively probe the parameter space of the axion-photon coupling $g_{a\gamma}$ up to $\sim 10^{-12}~ \text{GeV}^{-1}$ for the axion mass range of $0.2 \sim 3.7~ \mu$eV. Note that in the low mass region ($m_a \lesssim 1.5 ~\mu\text{eV}$), the WD 2010+310 could give greater sensitivity than the neutron star RX J0806.4-4123., Comment: 15 pages, 2 figures, and 2 tables. v3: some parts of the paper have been revised, 1 new figure is added, accepted for publication in PRD

The TeV $\gamma$-ray halo around the Geminga pulsar is an important indicator of cosmic-ray (CR) propagation in the local zone of the Galaxy as it reveals the spatial distribution of the electrons and positrons escaping from the pulsar. Considering the intricate magnetic field in the interstellar medium (ISM), it is proposed that superdiffusion model could be more realistic to describe the CR propagation than the commonly used normal diffusion model. In this work, we test the superdiffusion model in the ISM around the Geminga pulsar by fitting to the surface brightness profile of the Geminga halo measured by HAWC. Our results show that the chi-square statistic monotonously increases as $\alpha$ decreases from 2 to 1, where $\alpha$ is the characteristic index of superdiffusion describing the degree of fractality of the ISM and $\alpha=2$ corresponds to the normal diffusion model. We find that model with $\alpha<1.32$ (or $<1.4$, depending on the data used in fit) is disfavored at 95\% confidence level. Superdiffusion model with $\alpha$ close to 2 can well explain the morphology of the Geminga halo, while it predicts much higher positron flux on the Earth than the normal diffusion model. This has important implication for the interpretation of the CR positron excess., Comment: 11 pages, 4 figures, 1 table

We investigate the solar modulation effect with the long time cosmic ray proton and helium spectrum measured by AMS-02 on the time scale of a Bartels rotation (27 days) between May 2011 and May 2017. The time-span covers the negative heliospheric magnetic field polarity cycle, the polarity reversal period and the positive polarity cycle. The unprecedented accuracy of AMS-02 observation data provide a good opportunity to improve the understanding of the time dependent solar modulation effect. In this work, a two-dimensional solar modulation model is used to compute the propagation of cosmic rays in the heliosphere. Some important ingredients of the model which reflect the global heliospherical environment are taken from the observations. The propagation equation is numerically solved with the pubic Solarprop code. We find that the drift effect is suppressed during the high solar activity period but nearly recovered in the first half of 2017. The time-dependent rigidity dependence of the mean free path is critical to reproduce the observations between August 2012 and October 2015., Comment: 23 pages, 3 tables, 8 figures

In this work, we investigate the axion-like particle (ALP)-photon oscillation effect in the spectra of the blazar Markarian 421 (Mrk 421) using 4.5 years of the Astrophysical Radiation with Ground-based Observatory at YangBaJing (ARGO-YBJ) and Fermi Large Area Telescope (Fermi-LAT) data. These data are collected during the common operation time, which cover ten activity phases of Mrk 421. No significant ALP-photon oscillation effect is confirmed. On the other hand, not all the observations of the ten phases can be individually used to set the 95% confidence level ($\rm C.L.$) constraint on the ALP parameter space. However, the constraint can be significantly improved if the analyses for the ten phases are combined. We find that the upper limit at 95% $\rm C.L.$ on the ALP-photon coupling $g_{a\gamma}$ set by the ARGO-YBJ and Fermi-LAT observations of Mrk 421 is within $\sim [2\times 10^{-11}, \ 6\times 10^{-11}] \rm \, GeV^{-1}$ for the ALP mass of $\sim 5\times 10^{-10}$ eV $\lesssim m_a \lesssim 5\times 10^{-7}\, \rm eV$., Comment: 10 pages, 8 figures

Radiative energy losses are very important in regulating the cosmic ray electron and/or positron (CRE) spectrum during their propagation in the Milky Way. Particularly, the Klein-Nishina (KN) effect of the inverse Compton scattering (ICS) results in less efficient energy losses of high-energy electrons, which is expected to leave imprints on the propagated electron spectrum. It has been proposed that the hardening of CRE spectra around 50 GeV observed by Fermi-LAT, AMS-02, and DAMPE could be due to the KN effect. We show in this work that the transition from the Thomson regime to the KN regime of the ICS is actually quite smooth compared with the approximate treatment adopted in some previous works. As a result, the observed spectral hardening of CREs cannot be explained by the KN effect. It means that an additional hardening of the primary electrons spectrum is needed. We also provide a parameterized form for the accurate calculation of the ICS energy-loss rate in a wide energy range., Comment: 5 pages, 3 figures, 1 table, author-edited version

Recently the AMS-02 reported the precise measurements of the energy spectra of medium-mass compositions (Neon, Magnesium, Silicon) of primary cosmic rays, which reveal different properties from those of light compositions (Helium, Carbon, Oxygen). Here we propose a nearby source scenario, together with the background source contribution, to explain the newly measured spectra of cosmic ray Ne, Mg, Si, and particularly their differences from that of He, C, O. Their differences at high energies can be naturally accounted for by the element abundance of the nearby source. Specifically, the abundance ratio of the nearby source to the background of the Ne, Mg, Si elements is lower by a factor of $\sim1.7$ than that of the He, C, O elements. Such a difference could be due to the abundance difference of the stellar evolution of the progenitor star or the acceleration process/environment, of the nearby source. This scenario can simultaneously explain the high-energy spectral softening features of cosmic ray spectra revealed recently by CREAM/NUCLEON/DAMPE, as well as the energy-dependent behaviors of the large-scale anisotropies. It is predicted that the dipole anisotropy amplitudes below PeV energies of the Ne, Mg, Si group are smaller than that of the He, C, O group, which can be tested with future measurements., Comment: 6 pages, 3 figures; accepted for publication in Frontiers of Physics

The hardening and softening features in the DAMPE proton spectrum are very likely to be originated from a nearby supernova remnant (SNR). The proton spectrum from the nearby SNR is required to be very hard below $\approx10$ TeV. To reproduce this feature, we illustrate that anomalously slow-diffusion zone for cosmic rays (CRs) must be existed in the local interstellar medium (ISM) after also taking the dipole anisotropy of CRs into account. Assuming that the diffusion coefficient is homogeneous in the nearby ISM, we show that the diffusion coefficient is constrained to the magnitude of $10^{26}$ cm$^2$ s$^{-1}$ when normalized to 1 GeV, which is about 100 times smaller than the average value in the Galaxy. We further discuss the spatial distribution of the slow diffusion and find two distinct possibilities. In one case, the SNR is several hundred of parsecs away from the solar system, meanwhile both the SNR and the solar system are required to be included in a large slow-diffusion zone. The homogeneous diffusion belongs to this case. In the other case, the SNR is very close with a distance of $\sim50$ pc and the slow-diffusion zone is only limited around the SNR. The required diffusion coefficient is further smaller in the latter case. This work provides a new way of studying the CR diffusion in the local ISM., Comment: 8 pages, 5 figures, 1 table

We investigate the axion like particle (ALP)-photon oscillation effect in the high energy $\gamma$-ray spectra of PG 1553+113 and PKS 2155-304 measured by Fermi-LAT and H.E.S.S.. The choice of extragalactic background light (EBL) model, which induces the attenuate effect in observed $\gamma$-ray spectra, would affect the ALP implication. For the ordinary EBL model that prefers a null hypothesis, we set constraint on the ALP-photon coupling constant at 95% C.L. as $g_{a\gamma}\lesssim 5\times 10^{-11} ~\rm{GeV}^{-1}$ for the ALP mass $\sim 10$ neV. We also consider the CIBER observation of the cosmic infrared radiation, which shows an excess at the wave wavelength of $\sim 1~\mu$m after the substraction of foregrounds. The high energy gamma-rays from extragalactic sources at high redshifts would suffer from a more significant attenuate effect caused by this excess. In this case, we find that the ALP-photon oscillation would improve the fit to the observed spectra of PKS 2155-304 and PG 1553+113 and find a favored parameter region at 95% C.L.., Comment: 8 pages, 7 figures, 1 table

The observation of cosmic sub-PeV gamma-rays from the Crab Nebula opens up the possibility of testing cosmic ray photon transparency at the multi-hundred TeV scale. Assuming no deviation from a source gamma-ray emission due to accelerated electron inverse-Compton scattering, higher event energies can extend constraints on the effects of new physics; We consider oscillation between gamma-rays and axions/dark photons, plus attenuation effects from gamma-ray absorption in the case of dark photon dark matter. Combining the recent AS$\gamma$ and HAWC sub-PeV data with earlier MAGIC and HEGRA data, axion-like particles are most constrained in the $10^{-7}-10^{-6}$ eV mass range, where the coupling $g_{a\gamma}$ is constrained to be below ${1.8}\times 10^{-10}$ GeV$^{-1}$. In comparison, gamma ray flux attenuation due to oscillation with a dark photon leads to a very weak constraint on the mixing parameter; $\epsilon\lesssim$ 0.2 for dark photon mass between $10^{-7}$ and $10^{-6}$ eV. Direct scattering from dark photon dark matter limits $\epsilon\lesssim$ 0.01 for masses between $6$ and $400$ eV., Comment: 8 pages, 5 figures, 1 table