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In this contribution, we introduce the multiplicative Jacobi polynomials that arise as one of the solutions of the multiplicative Sturm-Liouville equation \begin{equation*} \frac{d^*}{dx}\left( e^{(1-x^2)\omega(x)}\odot \frac{d^*y}{dx} \right)\oplus \left(e^{ n(n+\alpha+\beta+1)\omega(x)}\odot y\right)=1, \ x\in[-1,1], \end{equation*} where $\omega(x)=(1-x)^{\alpha}(1+x)^{\beta}$ with $\alpha, \beta >-1$ real numbers and $n$ is a non-negative integer number. We extend some properties of classical Jacobi polynomials to the multiplicative case. In particular, we present several properties of multiplicative Legendre polynomials and multiplicative Chebyshev polynomials of first and second kind. We also prove that every real and positive function can be expressed as a multiplicative Jacobi-Fourier series and show that such functions can be approximated by the corresponding partial products of these series. We illustrate the obtained results with some examples., Comment: 34 pages, 10 figures

The mechanisms that drive disk winds are a window into the physical processes that underlie the disk. Stellar-mass black holes are an ideal setting in which to explore these mechanisms, in part because their outbursts span a broad range in mass accretion rate. We performed a spectral analysis of the disk wind found in six Chandra/HETG observations of the black hole candidate 4U~1630$-$472, covering a range of luminosities over two distinct spectral states. We modeled both wind absorption and extended wind re-emission components using PION, a self-consistent photoionized absorption model. In all but one case, two photoionization zones were required in order to obtain acceptable fits. Two independent constraints on launching radii, obtained via the ionization parameter formalism and the dynamical broadening of the re-emission, helped characterize the geometry of the wind. The innermost wind components ($r \simeq {10}^{2-3}$ $GM/{c}^{2}$) tend towards small volume filling factors, high ionization, densities up to $n \simeq {10}^{15-16} {\text{cm}}^{-3}$, and outflow velocities of $\sim 0.003c$. These small launching radii and large densities require magnetic driving, as they are inconsistent with numerical and analytical treatments of thermally driven winds. Outer wind components ($r \simeq {10}^{5}$ $GM/{c}^{2}$) are significantly less ionized and have filling factors near unity. Their larger launching radii, lower densities ($n \simeq {10}^{12} {\text{cm}}^{-3}$), and outflow velocities ($\sim 0.0007c$) are nominally consistent with thermally driven winds. The overall wind structure suggests that these components may also be part of a broader MHD outflow and perhaps better described as magneto-thermal hybrid winds., Comment: 27 pages, 13 figures

This paper details the methodology and results of the EmotioNet challenge. This challenge is the first to test the ability of computer vision algorithms in the automatic analysis of a large number of images of facial expressions of emotion in the wild. The challenge was divided into two tracks. The first track tested the ability of current computer vision algorithms in the automatic detection of action units (AUs). Specifically, we tested the detection of 11 AUs. The second track tested the algorithms' ability to recognize emotion categories in images of facial expressions. Specifically, we tested the recognition of 16 basic and compound emotion categories. The results of the challenge suggest that current computer vision and machine learning algorithms are unable to reliably solve these two tasks. The limitations of current algorithms are more apparent when trying to recognize emotion. We also show that current algorithms are not affected by mild resolution changes, small occluders, gender or age, but that 3D pose is a major limiting factor on performance. We provide an in-depth discussion of the points that need special attention moving forward.

The degree to which the thin accretion disks of black hole X-ray binaries are truncated during hard spectral states remains a contentious open question in black hole astrophysics. During its singular observed outburst in 2009–2010, the black hole X-ray binary XTE J1752−223 spent ∼1 month in a long-stable hard spectral state at a luminosity of ∼0.02–0.1 LEdd. It was observed with 56 RXTE pointings during this period, with simultaneous Swift-XRT daily coverage during the first 10 days of the RXTE observations. While reflection modeling has been extensively explored in the analysis of these data, there is disagreement surrounding the geometry of the accretion disk and corona implied by the reflection features. We reexamine the combined, high signal-to-noise, simultaneous Swift and RXTE observations, and perform extensive reflection modeling with the latest relxill suite of reflection models, including newer high disk density models. We show that reflection modeling requires that the disk be within ∼5 RISCO during the hard spectral state, while weaker constraints from the thermal disk emission imply higher truncation (Rin = 6–80 RISCO). We also explore more complex coronal continuum models, allowing for two Comptonization components instead of one, and show that the reflection features still require only a mildly truncated disk. Finally we present a full comparison of our results to previous constraints found from analyses of the same data set.

We report on a spectroscopic analysis of the X-ray emission from IGR J17062−6143 in the after-math of its June 2020 intermediate duration Type I X-ray burst. Using the Neutron Star Interior Composition Explorer, we started observing the source three hours after the burst was detected with MAXI/GSC, and monitored the source for the subsequent twelve days. We observed the tail end of the X-ray burst cooling phase, and find that the X-ray flux is severely depressed relative to its historic value for a three day period directly following the burst. We interpret this intensity dip as the inner accretion disk gradually restoring itself after being perturbed by the burst irradiation. Superimposed on this trend we observed a 1.5 d interval during which the X-ray flux is sharply lower than the wider trend. This drop in flux could be isolated to the non-thermal components in the energy spectrum, suggesting that it may be caused by an evolving corona. Additionally, we detected a 3.4 keV absorption line at 6.3σsignificance in a single 472 s observation while the burst emission was still bright. We tentatively identify the line as a gravitationally redshifted absorption line from burning ashes on the stellar surface, possibly associated with 40Ca or 44Ti.

Ultra-luminous X-ray pulsars (ULXPs) provide a unique opportunity to study persistent super-Eddington accretion. Here we present the results of a long-term monitoring campaign of ULXP NGC 7793 P13, focusing on the pulse period evolution and the determination of the orbital ephemeris. Over our four year monitoring campaign with Swift, XMM-Newton, and NuSTAR, we measure a continuous spin-up with an average value of ̇P≈−3.8×10−11s s−1. We find that the strength of the spin-up is independent of the observed X-ray flux, indicating that despite a drop in observed flux in 2019, accretion onto the source has continued at largely similar rates. The source entered an apparent off-state in early 2020, which might have resulted in a change of the accretion geometry as no pulsations were found in observations in July/August 2020.We use the long-term monitoring to update the orbital ephemeris, as well as the periodicities seen in both the observed optical/UV and X-ray fluxes. We find that the optical/UV period is very stable over the years, with PUV=63.75+0.17−0.12d. The best-fit orbital period determined from our X-ray timing results is 64.86±0.19 d, almost a day longer than previously implied, and the X-ray flux period is65.21±0.15 d, slightly shorter than measured previously. The physical origin of these different flux periods is currently unknown. We study the hardness ratio of the XMM-Newton and NuSTAR data between 2013–2020 to search for indications of spectral changes. We find that the hardness ratios at high energies are very stable and not directly correlated with the observed flux. At lower energies we observe a small hardening with increased flux, which might indicate increased obscuration through outflows at higher luminosities. Comparing the changes in flux with the observed pulsed fraction, we find that the pulsed fraction is significantly higher at low fluxes. This seems to imply that the accretion geometry already changed before the source entered the deep off-state. We discuss possible scenarios to explain this behavior, which is likely driven by a precessing accretion disk.

1ES 1927+654 is a nearby active galactic nucleus (AGN) which underwent a changing-look event in early 2018, developing prominent broad Balmer lines which were absent in previous observations. We have followed up this object in the X-rays with an ongoing campaign that started in May 2018, and that includes 265 NICER (for a total of 678 ks) and 14 Swift/XRT (26 ks) observations, as well as three simultaneous XMM-Newton/NuSTAR (158/169 ks) exposures. In the X-rays, 1ES 1927+654 shows a behaviour unlike any previously known AGN. The source is extremely variable both in spectral shape and flux, and does not show any correlation between X-ray and UV flux on timescales of hours or weeks/months. After the outburst the power-law component almost completely disappeared, and the source showed an extremely soft continuum dominated by a blackbody component. The temperature of the blackbody increases with the luminosity, going from kT ∼ 80 eV (for a 0.3–2 keV luminosity of L(0.3−2) ∼ 10^(41.5) erg/s) to ∼ 200 eV (for L(0.3−2) ∼ 10^(44) erg/s). The spectra show evidence of ionized outflows, and of a prominent feature at ∼ 1 keV, which can be reproduced by a broad emission line. The unique characteristics of 1ES 1927+654 in the X-ray band suggest that it belongs to a new type of changing-look AGN. Future X-ray surveys might detect several more objects with similar properties.