Current date: 2026-10-16
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Created/updated limit: 2026-10-09 (7 days ago)
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Scoring abstracts
Number of records retrieved: 189
Keyword score statistics
score 10 -- 1 abstracts
score 8 -- 1 abstracts
score 7 -- 1 abstracts
score 4 -- 2 abstracts
score 3 -- 3 abstracts
score 2 -- 6 abstracts
in total -- 14 abstracts
Articles that appeared on 2026-10-16
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[abstract 1 / 14] Wow! (score: 10)
- Title: mm-JETs in the multi-messenger eraAuthors: Karri I. I. Koljonen, Thomas D. Russell, Britton Jeter, Lauren Rhodes, Alexandra J. Tetarenko, María Díaz Trigo, Talvikki Hovatta, Pau Bosch-Cabot, Mamta Pandey-Pommier, Alessio Marino, Jakob van den Eijnden, Dieu D. Nguyen, Melania Del Santo, Thomas Maccarone, Anna Y. Q. Ho, Maria C. Baglio, Sera Markoff, the ALMA2040 Transient, Time-Domain Astronomy working group,Comments: Part of the ALMA2040 White Paper Series. 10 pages, 2 figuresSubjects: astro-ph.HE astro-ph.IMCreated: 2026-10-14; Updated: 2026-10-16; Datestamp: 2026-10-16
Jets and outflows operate across the full cosmic mass scale from young stellar objects (YSOs) and X-ray binaries (XRBs) to ACTIVE GALACTIC NUCLEi (AGN), GAMMA-RAY BURSTs (GRBs), and tidal disruption events (TDEs), shaping many time-domain and multi-messenger transients. Key questions concern on how JETs are launched, accelerated and collimated; where and how they dissipate energy and accelerate particles; and how they couple to their environments to set electroMAGNETic counterpart diversity and feedback. Millimeter and sub-millimeter observations uniquely address these questions by tracking the evolving SYNCHROTRON turnover for robust calorimetry and Lorentz-factor constraints, providing full-Stokes POLARIZATION and Faraday diagnostics close to the JET base, and enabling high-resolution imaging from Galactic ejecta to event-horizon-scale AGN JET bases via global Very Long Baseline Interferometry (VLBI). We describe the JET and outflow science enabled by ALMA2040, a next-generation mm/sub-mm interferometer combining an order-of-magnitude sensitivity gain with rapid-response observing, simultaneous multi-band coverage, full-Stokes polarimetry, and integration with global VLBI networks. These capabilities will enable statistically controlled, trigger-driven samples spanning XRB outbursts, early GRB afterglows, protostellar disk winds and JET launching, AGN JET bases, and JETted TDEs, establishing mm/sub-mm astronomy as a cornerstone of time-domain and multi-messenger JET physics in the 2040s and beyond.
[abstract 2 / 14] Wow! (score: 8) - Title: FUGUE: A New GPU-accelerated General Relativistic Magnetohydrodynamics Code with Weak-Field Multipole Self-Gravity and Quasi-Stationary Kerr Black Hole EvolutionAuthors: Piotr Plonka, Agnieszka Janiuk,Comments: 25 pages; 19 figures; In press in ApJ Supplement Series; comments welcomeSubjects: astro-ph.HECreated: 2026-10-14; Updated: 2026-10-16; Datestamp: 2026-10-16
We present FUGUE, a new GPU-accelerated code for general RELATIVISTIC MAGNETohydrodynamics (GRMHD). The code supports an optional quasi-stationary update of the Kerr BLACK HOLE mass and spin, as well as weak-field multipole self-gravity computed with a spherical harmonic Poisson solver. The calculations using high-order multipoles in the Poisson solver are expensive, so the self-gravity solver is well suited for GPU acceleration. The code uses shock-capturing methods and a second-order Runge--Kutta (RK2) scheme for time integration. We validate the code with hydrodynamic, MAGNETohydrodynamic, general RELATIVISTIC, and convergence tests for the self-gravity module. We present an application of the code to a simulation of a self-gravitating, Toomre-unstable, MAGNETized accretion disk with a mass of 1,M-Sun around a Kerr BLACK HOLE. In our demonstration model, gravitational instabilities are associated with changes in the mass accretion rate and the Blandford--Znajek luminosity, and may contribute to GAMMA-RAY BURST variability.The performance of the code is equivalent to or exceeds that of the current state-of-the-art GRMHD codes, achieving more than 470 million zone-cycles per second on a single NVIDIA GH200 GPU with linear reconstruction.
[abstract 3 / 14] Wow! (score: 7) - Title: A model for the image structure and spectral energy distribution of RELATIVISTIC JETsAuthors: Dominic W. Pesce, Ramesh Narayan, Yuh Tsunetoe,Comments: 37 pages, 12 figures, submitted for publication in ApJSubjects: astro-ph.HECreated: 2026-10-14; Updated: 2026-10-16; Datestamp: 2026-10-16
Upcoming advances in high-frequency VLBI promise to enable spatially resolved studies of astrophysical JETs across an increasingly large source population. We present here a Python implementation of the semi-analytic model from Tsunetoe et al. (2025) for self-consistently interpreting the spatial and spectral structure of the SYNCHROTRON emission from such JETs. The model is based on an axisymmetric force-free JET solution supplemented with a prescription for nonthermal electron heating, SYNCHROTRON cooling, pitch-angle anisotropy in the electron distribution, and radiative transfer along straight rays. We use this model to explore how the predicted spectral energy distribution depends on the model parameters, identifying approximately self-similar scalings with BLACK HOLE mass, accretion rate, and electron heating efficiency. We also compare the model predictions against observations of M87 and Sgr A*. For M87, a single fiducial parameter set qualitatively reproduces VLBI images across multiple frequencies and matches the observed longitudinal intensity profile, while also yielding a broadband SED that is quantitatively consistent with the observed radio through X-ray measurements. For Sgr A*, a fit to the quiescent-state SED demonstrates that emission from a collimated JET with comparable nonthermal heating efficiency to M87's is quantitatively consistent with the observed radio through X-ray measurements, predicting a compact JET whose radio size decreases inversely with frequency, consistent with VLBI constraints.
[abstract 4 / 14] Yes (score: 4) - Title: The energetic atmosphere of the SunAuthors: Sven Wedemeyer, Mats Kirkaune, Miroslav Barta, Astrid M. Veronig, Stanislav Gunar, Roman Brajsa, Manuela Temmer, Valery Nakariakov, Stephen White, Bart De Pontieu, Maryam Saberi, Atul Mohan, Masumi Shimojo, Davor Sudar, Galina Motorina, Maria Loukitcheva, Paulo Simoes, Stefaan Poedts, Raghavendra Sahai,Comments: Part of the ALMA2040 White Paper SeriesSubjects: astro-ph.IM astro-ph.SRCreated: 2026-10-14; Updated: 2026-10-16; Datestamp: 2026-10-16
Understanding the mechanisms that heat the Sun's chromosphere and corona to temperatures far exceeding those of the solar photosphere below remains one of the central challenges in solar physics. Small-scale, rapidly evolving processes - including shocks, turbulence, MAGNETohydrodynamic waves, RECONNECTion-driven JETs, and nano-flares - are thought to contribute significantly to the heating budget. However, direct observational constraints on their spatial, temporal, and spectral signatures remain hard to obtain. At millimeter wavelengths, optically thick thermal emission provides a comparatively direct measure of gas temperature. While the Atacama Large Millimeter/submillimeter Array (ALMA) already provides unique diagnostic capabilities, offering temperature diagnostics and high-cadence imaging, the current capabilities are still limiting the study of such dynamic, small-scale phenomena. Improved spatial resolution, enhanced uv-coverage, and simultaneous multi-band observations, as proposed for ALMA2040, would enable transformative progress in capturing dynamic processes across multiple heights and enable time-dependent three-dimensional thermal and MAGNETic tomography of the chromosphere. Combined with complementary diagnostics and simulations, these measurements would test how small-scale processes contribute to atmospheric heating.
[abstract 5 / 14] Yes (score: 4) - Title: JWST reveals a highly ionized nebula powered by an ultraluminous X-ray source with a massive BLACK HOLE in the metal-poor galaxy Holmberg IIAuthors: F. A. Fogantini, P. Zeidler, L. M. Oskinova, T. Bao, W. -R. Hamann, P. Marchant, D. M. -A. Meyer, D. Pauli, S. Reyero Serantes, A. A. C. Sander, T. Shenar, R. Soria,Comments: 9 pages, 5 figuresSubjects: astro-ph.GA astro-ph.HECreated: 2026-10-14; Updated: 2026-10-16; Datestamp: 2026-10-16
Recent James Webb Space Telescope (JWST) observations have revealed fine-structure lines of ions with ionization potentials ${\gtrsim}50$\,eV, such as [Ne\,{\sc v}] and [O\,{\sc iv}], in nebular spectra of some low-metallicity galaxies, raising questions about the nature of the ionizing sources. Ultraluminous X-ray sources (ULXs) have been considered as potential contributors, but direct evidence linking individual ULXs to highly ionized nebulae is limited. Here we present JWST IFU spectroscopy of the nebula surrounding the template ULX Ho\,II\,X--1 in the low-metallicity galaxy Holmberg\,II, already known to emit He\,{\sc ii}\,$\lambda4686$ and [O\,{\sc iv}]\,25.89\,$μ$m lines. We resolve the infrared nebula on spatial scales of ${\sim}15-25$\,pc and report the first detections of [Ne\,{\sc v}] and [Ne\,{\sc vi}] in this source. We find anisotropic ionizing conditions: emission from the highest-ionization species arises from compact regions offset from the ULX toward the previously detected radio knots, whereas lower-ionization species trace the wider nebula. The preferential alignment of the highest-ionization emission with the radio axis suggests anisotropic escape of the ionizing continuum and a physical connection with JET-ejection activity. Spectral lines across the nebula are narrow and consistent with the instrumental resolution, indicating kinematically quiescent gas and disfavoring shocks as the dominant ionization mechanism. Together, these results provide direct evidence linking an individual ULX to a highly ionized nebula in a low-metallicity galaxy. These JWST observations of Ho~II~X--1 show that an accreting BLACK HOLE in a low-metallicity galaxy is responsible for the extreme ionization of the surrounding nebula on ${\sim}100$\,pc scales.
[abstract 6 / 14] (score: 3) - Title: FERMI Acceleration Mechanisms Beyond Lorentz SymmetryAuthors: Gilson A. Ferreira, Erick Aguiar, A. A. Araújo Filho, Edson Otoniel, Valdir B. Bezerra, Iarley P. Lobo,Comments: 23 pages. Matches published versionSubjects: gr-qcCreated: 2026-10-14; Updated: 2026-10-16; Datestamp: 2026-10-16
We construct models for first- and second-order FERMI acceleration of particles, incorporating generic frame transformations, dispersion relations, and conservation laws. Within this framework, we study deformations of Lorentz symmetry via the $κ$-Poincaré algebra in the bicrossproduct and classical bases, which respectively deform and preserve the RELATIVISTIC dispersion relation. We also examine explicit Lorentz symmetry violation and compare the results with deformed relativity and special relativity. The energy spectra present different shapes when one considers deformation or violation of Lorentz symmetry in superluminal or subluminal scenarios. One of the possible outcomes is an intense decay of the spectrum for higher energies. We also gather the predictions of all the scenarios considered, comparing the spectra produced at the source in the energy domain, which is the variable in which COSMIC RAY observatories report their measurements.
[abstract 7 / 14] (score: 3) - Title: The impact of nonlinear Landau damping on COSMIC RAY streaming and the role of external turbulenceAuthors: Rouven Lemmerz, Mohamad Shalaby, Ellen Zweibel, Christoph Pfrommer, Timon Thomas,Comments:Subjects: astro-ph.HE astro-ph.GA physics.plasm-phCreated: 2026-10-14; Updated: 2026-10-16; Datestamp: 2026-10-16
Cosmic rays (CRs) streaming faster than the Alfvén speed generate Alfvén waves that scatter them. The saturated wave amplitude is regulated by a damping mechanism. This damping controls the CR scattering rate and drift velocity, and thus the rate at which CRs transfer momentum and energy to the ambient plasma, which sets the strength of CR feedback. In the ionized interstellar medium, nonlinear Landau damping (NLLD) is commonly invoked as the dominant damping mechanism for Alfvén waves. We test this assumption with fluid-PIC simulations in which thermal ions and electrons are modeled as fluids with optional Landau closures, allowing us to compare otherwise identical runs with and without NLLD. When waves are self-generated by monoenergetic CRs, runs with and without Landau closures are indistinguishable: NLLD is inefficient and the CRs isotropize in the wave frame. Once high-amplitude Alfvén waves mimicking external turbulence are seeded, NLLD curbs wave growth and equalizes forward- and backward-propagating waves. We show that the saturated drift velocity, which falls below the Alfvén speed, can be accurately predicted from the wave spectra alone. If the CR distribution is undersampled, a numerical instability corrupts the largest resonant scales: unphysical, unresolved pitch-angle gradients resonantly generate backward-propagating waves, driving an inverse cascade that should be absent from purely streaming-driven waves. While power-law CR distributions may permit stronger NLLD, our results indicate that NLLD is unlikely to be an intrinsic saturation mechanism of the streaming instability; instead, its effectiveness hinges on the interplay of streaming-generated modes with those of external origin.
[abstract 8 / 14] (score: 3) - Title: Understanding cosmic explosionsAuthors: Karri I. I. Koljonen, Tomek Kamiński, Anna Y. Q. Ho, Thomas Maccarone, Aneurin Evans, María Díaz Trigo, Thomas D. Russell, Dieu D. Nguyen, Dirk Petry, Jakob van den Eijnden, Tanmoy Laskar, Laura Chomiuk, the ALMA2040 Transient, Time-Domain Astronomy working group,Comments: Part of the ALMA2040 White Paper Series. 10 pages, 2 figures, 1 tableSubjects: astro-ph.IM astro-ph.HECreated: 2026-10-14; Updated: 2026-10-16; Datestamp: 2026-10-16
Millimeter-wavelength observations provide a uniquely sensitive window into the physics of cosmic explosions, from SUPERNOVAe (SNe) and tidal disruption events (TDEs) to nova eruptions, stellar mergers and electroMAGNETic counterparts to gravitational wave (GW) sources. Over the past decade, discoveries across the transient sky have revealed that many of the most informative phases of shock interaction, particle acceleration and JET formation unfold at frequencies above the traditional cm-wave domain, where SYNCHROTRON self-absorption weakens and thermal, nonthermal and dust components can be disentangled. Upcoming wide-field mm surveys will detect a new population of short-lived transients but will be limited by coarse localization and limited spectral characterization. ALMA2040, with dramatically improved sensitivity, wide instantaneous spectral coverage, rapid-response and sub-arraying modes, polarimetry and extended baselines, is essential for converting these discoveries into robust physical constraints. Here we outline the scientific context, key open questions and the ALMA2040 capabilities required to unlock the full potential of millimeter time-domain astrophysics in the 2040s.
[abstract 9 / 14] (score: 2) - Title: Jittering JETs in stripped-envelope core-collapse SUPERNOVAeAuthors: Nikki Yat Ning Wang, Dmitry Shishkin, Noam Soker,Comments: Accepted for publication in ApJSubjects: astro-ph.HE astro-ph.SRCreated: 2026-10-14; Updated: 2026-10-16; Datestamp: 2026-10-16
We compare the expected explosion time of core-collapse SUPERNOVAe (CCSNe) in the jittering JETs explosion mechanism (JJEM) to that in the neutrino-driven (the delayed neutrino) mechanism, and conclude that for most, but not all, stellar models, even when the neutrino-driven mechanism might have led to an explosion, the JJEM starts to operate before the neutrino mechanism fully revives the stalled shock. To achieve this goal, we conduct comprehensive one-dimensional stellar evolution simulations using the code \textsc{mesa} to determine the expected explosion time according to the JJEM, which corresponds to the time when the inner convective layer of the core is accreted onto the newly born neutron star (NS). We present results for many hydrogen-rich, hydrogen-stripped, and helium+hydrogen-stripped envelope CCSN progenitor models. We find that most, but not all, of our models in the initial mass range of $M_{\rm ZAMS}=12M_\odot$ to $M_{\rm ZAMS}=40M_\odot$, have at least one strong convective zone inside the mass coordinate that is the maximum baryonic mass of an NS, $m \simeq 2.65\ M_\odot$, which can facilitate the JJEM. This study contributes to establishing the JJEM as a viable explosion mechanism of CCSNe.
[abstract 10 / 14] (score: 2) - Title: Analysis of collisional and facility effects in a MAGNETic nozzle plasma expansionAuthors: Manuel Cortés-Hernán, Mario Merino, Diego García-Lahuerta, Eduardo Ahedo,Comments: 36 pages, 10 figuresSubjects: physics.plasm-phCreated: 2026-10-14; Updated: 2026-10-16; Datestamp: 2026-10-16
An axisymmetric, quasineutral three-fluid model is proposed to study the plasma expansion in a MAGNETic nozzle under the presence of neutrals coming either from the plasma source or as an homogeneous background. As a difference with other models, electron cooling in the plume is achieved by treating the electron energy flux as mainly convective and without the need to postulate any anomalous resistivity. Solutions are presented for the electron high-MAGNETization limit, in which the electron main magnitudes can be integrated along MAGNETic lines. Ionization, elastic and charge-exchange collisions with neutrals do not change the main qualitative features of the plasma expansion, known from previous collisionless models. Ionization enhances the plasma flow in the nozzle, and leads to additional electron cooling, which decreases the electric potential fall along the nozzle. The efficiency of the nozzle is quantified in terms of the gain of MAGNETic thrust and the plume divergence angle. Two types of boundary conditions are discussed for the electron flow: local current ambipolarity conditions at the nozzle throat and global current-free conditions at the outer boundary (i.e., metallic vacuum chamber walls). These last ones are shown to be physically more reliable: they introduce the influence of the chamber walls on the plasma expansion by shaping the ambipolar electric field; they permit the extrapolation to undisturbed free space conditions; and they approximate better experimental trends with the background pressure.
[abstract 11 / 14] (score: 2) - Title: Thermochemically Constrained Multiscale Laplace Neural Operator to Learn Stiff Chemical Kinetics with Conditional Diffusion Model SamplingAuthors: Dong Yang, Xiongbo Duan, Min Zhang, Yuqiang Li,Comments: Main text: 14 pages, 13 figures. Supplementary Materials: 3 pages, 3 figuresSubjects: physics.comp-ph physics.flu-dynCreated: 2026-10-09; Updated: 2026-10-16; Datestamp: 2026-10-16
Stiff chemical kinetics is a major computational bottleneck in reacting-flow simulations, while data-driven solvers remain sensitive to training-state coverage and chemical dynamics. This work combines conditional diffusion sampling with a thermochemically constrained multiscale Laplace neural operator (TC-MLNO) for chemistry ODE integration. The diffusion model learns the equivalence-ratio-conditioned joint distribution of temperature and species from low-dimensional flame data, augmenting the state space without independent perturbations. TC-MLNO represents transient, non-periodic responses through pole-residue Laplace layers and assigns fast, medium, and slow species to separate branches. Thermochemical constraints are imposed through losses for mass and elemental conservation and heat release rate. The framework is evaluated in 1D premixed flames, a 2D developing JET, and a 3D turbulent burner flame. With equal-sized datasets, diffusion sampling reduces the 95th-percentile distance to the base flame manifold by up to 37.5% and the a posteriori full-species macro-average error by up to 92.7% versus random sampling, especially for minor species and radicals. TC-LNO yields smaller errors than the DeepONet baseline for 84.9% of retained modes and reduces the 95th-percentile error for the most attenuated modes from 0.372 to 0.081. In multidimensional flames, TC-MLNO better preserves reaction-zone locations, heat-release structures, and chemically sensitive species than DeepONet. Errors of representative radical and nitrogen-containing species in the 3D flame decrease by 88.0%-88.9%. Compared with direct CVODE integration, TC-MLNO reduces mean chemistry and total solution times by 90.1% and 62.6%, respectively. These results show that distribution-aware sampling and Laplace neural operator learning provide an accurate and efficient alternative for stiff chemical ODE integration.
[abstract 12 / 14] (score: 2) - Title: On MAGNETic-field consistency in the sideways force calculation of Phys. Plasmas 27, 012508 (2020)Authors: Denis Mironov,Comments: 10 pages, 2 figuresSubjects: physics.plasm-phCreated: 2026-10-09; Updated: 2026-10-16; Datestamp: 2026-10-16
We examine the consistency of the equilibrium MAGNETic field $\mathbf{B}_0$ used in the analytical calculation of the sideways wall force by A. A. Martynov and S. Yu. Medvedev [Phys. Plasmas 27, 012508 (2020)] and the subsequent reformulation presented in [Phys. Plasmas 27, 054702 (2020)]. In these attempts, the current density $\mathbf{j}_0 = \nabla \times \mathbf{B}_0$ must vanish in the vacuum regions adjacent to the wall, making $\mathbf{B}_0$ curl-free as a complement to the natural $\nabla \cdot \mathbf{B}_0 = 0$. Since the cited works incorporate selected toroidal corrections without explicitly specifying the corresponding differential operators, we test $\mathbf{B}_0$ adopted in these models against Maxwell's equations using both toroidal and quasi-cylindrical formulations. We show that the divergence-free requirement is violated in the toroidal interpretation, while the curl-free condition is not satisfied in the quasi-cylindrical limit. The reformulation likewise fails to define a self-consistent equilibrium field with toroidal effects because the accompanying field corrections required for consistency with Maxwell's equations are not specified. Since the sideways force calculations are built upon these inconsistent field prescriptions, their analytical derivations are consequently compromised. The resulting arguments therefore cannot serve as a valid basis for revising either the earlier results established by D. V. Mironov and V. D. Pustovitov [Phys. Plasmas 24, 092508 (2017)] or those obtained within the single-harmonic analysis [Phys. Plasmas 22, 052502 (2015)].
[abstract 13 / 14] (score: 2) - Title: The Impact of High-Mass Clusters on the Binary Black Hole Merger Rate over Cosmic TimeAuthors: Aidan Mai, Kyle Kremer, Fulya Kıroğlu,Comments: 16 pages, 11 figures. Submitted to ApJ. Comments welcome!Subjects: astro-ph.GA astro-ph.HECreated: 2026-10-14; Updated: 2026-10-16; Datestamp: 2026-10-16
We present a cosmological calculation of the binary BLACK HOLE merger rate from dense star clusters, using a $\texttt{Cluster Monte Carlo}$ ($\texttt{CMC}$) model grid spanning the full observed parameter space of cluster mass, metallicity, and virial radius. For the first time, we incorporate $N=10^{7}$-particle $\texttt{CMC}$ models into this calculation, including a new solar-metallicity model, extending the $\texttt{CMC Cluster Catalog}$ to the most massive clusters observed in the local Universe. Using an analytic cluster formation model which convolves the cluster formation rate with delay-time distributions from our model suite, we find that the local cluster BBH merger rate is dominated by low-mass ($M_1 \lesssim 20\,M_\odot$) mergers originating from recently formed, high-metallicity clusters. While high-mass clusters are the primary sites of hierarchical (second-generation and higher) mergers, their contribution to the overall merger rate is suppressed by the exponential cutoff of the cluster initial mass function. The hierarchical merger rate is therefore highly sensitive to the exact value of the Schechter mass, $M_S$, suggesting that gravitational wave constraints on the hierarchical merger fraction can independently constrain the high-mass end of the cluster initial mass function. Our cluster formation model reproduces the observed present-day GC number density without fine tuning, and we find $M_S = 10^7\,M_\odot$ provides the best match to the observed Virgo GC mass distribution. For this value, $27\%$ of local dynamical mergers are hierarchical, compared to $18\%$ for the canonical value of $M_S = 10^{6.26}\,M_\odot$. Our merger weights, which we make publicly available, can be used for direct comparison with LVK distributions and other formation models.
[abstract 14 / 14] (score: 2) - Title: Wandering intermediate-mass BLACK HOLEs and off-nuclear tidal disruption events from early star clustersAuthors: Claire E. Williams, Smadar Naoz, Yihao Zhou, Tatsuya Akiba-Lewis, Mark Vogelsberger, Blakesley Burkhart, Naoki Yoshida, Avi Chen, Kyle Kremer, William Lake, Federico Marinacci, Shyam H. Menon,Comments: 27 pages, 11 figuresSubjects: astro-ph.GA astro-ph.HECreated: 2026-10-14; Updated: 2026-10-16; Datestamp: 2026-10-16
Off-nuclear tidal disruption events (TDEs) reveal evidence for massive BLACK HOLEs outside galactic centers, but the origins of this wandering population remain uncertain. We investigate wandering intermediate-mass BLACK HOLEs (IMBHs) formed through runaway stellar collisions in dense, high-redshift star clusters and predict their TDE signatures across cosmic time. Our semi-analytic model samples clusters associated with low-mass subhalos at $7
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