pronounced, indicating an increase by ∼100 km s −1 . Remarkably, we observed at the epoch of the sudden magnetic field increase (indicated by the red triangle) that the radial velocity of all spectral lines dropped by several 10 km s −1 . To better highlight the observed changes in radial velocities, we show in Fig. 9 the radial velocity shift correlations between the lines belonging to different elements. Figure 7. Radial velocities measured for different spectral lines in the observations obtained between 2014 and 2018. Figure 8. Radial velocities measured for different spectral lines in the observations obtained between 2017 and 2018. Figure 9. Radial velocity correlations for hydrogen and He i lines. The observed dispersion of the radial velocity measurements in these figures is probably related to β Cephei-like pulsations. The atmospheric parameters presented by Castro et al. ( 2015 ) suggest that HD 54879 has already slightly evolved from the ZAMS and is passing through the β Cephei instability strip. As mentioned above, Järvinen et al. ( 2017 ) were not able to detect significant velocity shifts in high-resolution HARPSpol observations of HD 54879, most likely due to much longer exposure times, of the order of 1–3 h. During the long HARPSpol exposures, any spectral variability is smeared over the pulsation cycle and difficult to detect. In contrast, FORS 2 observations carried out using an 8 m telescope have a duration of only 10–20 min and are expected to be more strongly affected by the β Cephei-like pulsations. According to Telting et al. ( 2006 ), at least half of the late-O to early-B solar-neighbourhood stars that are located in the β Cephei instability strip are actually pulsating in radial and/or non-radial modes. With respect to the remarkable change of the spectral appearance of HD 54879 during the sudden magnetic field increase, it is important to mention that a recent study of the most strongly magnetized O-type star NGC 1624-2 using UV observations with HST /COS revealed similar dramatic variations in the resonance line profiles between rotation phases when looking nearly at the magnetic pole and those when looking nearly at the magnetic equator (see fig. 1 in David-Uraz et al. 2018 ). Similar to our observations of HD 54879, these line profiles show at these two rotation phases very different characteristics including the line intensity, line shape and width, and radial velocity. It should however be noted that the variability of the UV resonance lines in massive stars is usually related to the stellar wind or to the magnetosphere, while for HD 54879 we observe line profile changes in the photospheric lines. It cannot be excluded that the observed changes in radial velocity are caused by an invisible wide companion. Indeed, Castro et al. ( 2015 ) compared their radial velocity measurement from one HARPSpol spectrum with other measurements in the literature and concluded that HD 54879 could be a member of a long-period

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O B-CelestialObject I-CelestialObject O O O O O O B-Model O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Instrument O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O B-Instrument I-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O B-Wavelength O O B-Telescope B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O B-Instrument O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O


The two transonic trajectories with are shown in pink. Green lines show two subsonic trajectories with and and two supersonic trajectories with and . The trajectories that are discontinuous across position are shown in yellow for the same set of constants, , but represent different branches. 3 HAMILTONIAN DESCRIPTION Hamilton’s principle for a conservative system is where the difference of the kinetic and potential energies is the Lagrangian, . This may be generalized for a fluid with internal energy, U (Herivel 1955 ), In non-dimensional units, the Lagrangian for the BP flow is the same as the steady-state equation ( 6 ), where the non-dimensional terms, (log | u | + 2 log | x |), which derive from the dimensional pressure term in equation ( 1 ), are the internal energy. If we define the functional gradient as the directional derivative, for any variation, η, and constant, ε, then the necessary condition of Euler–Lagrange for x to be a critical function of J [ x ] is that the first variation is zero, where the velocity . Since the right-hand side is equivalent to the equation of motion ( 5 ) as can be verified by substitution, then 〈∇ J [ x ]〉 = 0, and the steady-state solution, , is the solution of stationary action toward which the time-dependent solutions evolve. This description is similar to the simple physics problem in which the Lagrangian determines the parabolic trajectory of a particle in a gravitational field and the exact trajectory is determined from the end points as a boundary value problem (BVP) or alternatively from the initial velocities as an IVP. However, the Lagrangian for the BP flow includes the internal energy of the fluid as a function of the density–pressure gradient that is constrained by the conservation equation. Therefore, it is not always possible to find an energy conserving trajectory between two arbitrary velocities. Considered as a BVP, not all boundary conditions are consistent with a steady-state solution. As in Lagrangian mechanics, the energy serves as a Lyapunov function for the stability. The definiteness in sign of the second variation evaluated at the steady state implies at least linear stability (Arnol’d 1965 , 1989 ). Equivalently, the integrand of the second variation, must be definite in sign for every non-zero variation η. Since the middle term with mixed partial derivatives is zero, and This is easily verified for the range x > 0 allowed for BP flows. This implies that the steady-state solution, including all the subsonic, transonic, and supersonic trajectories in the family, is at least linearly stable. The existence of a steady-state solution, a critical point in Lagrangian mechanics, is required for stability. An arbitrary IVP can evolve to the steady state, but the boundary conditions in a BVP must be consistent with the conservation of energy to allow a stable solution. This requirement itself does not determine the steady-state solution or its stability. For example, the derivation of

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-TextGarbage I-TextGarbage O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O B-TextGarbage I-TextGarbage O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


these models demonstrate that banded clouds are easily able to explain the level of polarization measured in Luhman 16A. Considering the disagreement between the measurements and the homogeneous oblate polarization model, we conclude that cloud banding is the dominant source of the measured polarization in Luhman 16A. For Luhman 16B, we can neither rule out nor confirm the presence of banded clouds; the measurements could be explained as due to oblateness alone with clouds thinner than in the f sed = 1 models, or by a combination of oblateness and banded clouds. Although we model the bands and fit the polarization as constant over longitude and time, there is the possibility of variability with amplitudes below our sensitivity limits. Indeed, the bands of Jupiter display variability, yet the bulk features remain relatively constant over time (Ge et al. 2019 ). Similar variability superimposed on the bands discovered here may account for the previously detected photometric variability seen in Luhman 16A. 4.3. Spin Axis Orientations from the Angle of Linear Polarization The angle of polarization for Luhman 16A and B differs by ∼105° (or equivalently, ∼75°, because of a 180° degeneracy in the definition of the angle of polarization). For each object, the angle of polarization could be aligned either parallel or perpendicular to the position angle of the projected on-sky spin axis, as discussed in Section 4.2 . The misalignment of the angle of polarization immediately suggests a misalignment of the two components’ spin axes of either ∼15° or ∼75°, depending on the source of polarization of Luhman 16B. Neither component has an angle of polarization aligned parallel or perpendicular to the longitude of the ascending node of the binary orbit, Ω = 13012 ± 012 (Garcia et al. 2017 ). Luhman 16A’s polarization is at best ∼20° misaligned, and Luhman 16B is ∼40°–60°, indicating that neither object has a spin axis aligned with the orbital plane, regardless of the oblateness or banded interpretation. The misalignment may imply that the two objects did not form alone together within the same disk, but instead may have instead experienced a more raucous dynamical history such as having originally been formed in a triple system (Reipurth Mikkola 2015 ). To the best of the authors’ knowledge, this is the first measurement of the projected spin axis for any brown dwarf (albeit with a 90° degeneracy). Given the low-S/N detection of Luhman 16B, we consider any interpretation of its position angle to be tentative. 5. Total Intensity Variability Interpretation We were unable to measure absolute photometric variability, but the flux ratio of the two objects exhibits quasi-periodic variations, with a period of 1.64 hr. We attribute this signal to Luhman 16B alone ( H -band variability has never been detected in A; e.g., Biller et al. 2013 ; Buenzli et al. 2015b ) and suggest that it may represent a similar three-band scenario to that inferred for other L/T

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in the F125LP image shown in Figure 1 (top left). The FUV bow shock appears to be asymmetric, being thicker and brighter east of the pulsar. We measure the apex distance (from the pulsar to the leading edge of the bow shock) to be ≈25, consistent with the measurements in H α by Brownsberger Romani ( 2014 ), Gaensler et al. ( 2002 ). To extract the bow-shock flux, we defined the source and two background regions, “inside” and “outside” of the bow shock, shown in Figure 1 (top right). The background regions were selected based on the F125LP image, in which the bow shock was most clearly detected. The regions are close to the bow-shock extraction region to mitigate effects from the inhomogeneous detector background while excluding the pulsar. Because of the larger apparent thickness of the east side of the bow shock, more space was left between the bow-shock extraction region and the background regions. We took the background variations into account by selecting background regions on both sides of the bow shock: one “inside” and one “outside” the bow shock. These regions were used for flux measurements in both F125LP and F140LP. A combined background from the two regions was extracted. The net source count rate was calculated similarly to the pulsar, with the area A b being the combined area of the “outside” and “inside” background regions. The F125LP and F140LP count rates and their uncertainties are given in Table 2 . From the measured count rates we calculated the absorbed fluxes in the F125LP and F140LP wavelength ranges: F (1250–2000 Å) = (8.1 ± 0.4) × 10 −15 erg s −1 cm −2 and F (1350–2000 Å) = (7.0 ± 0.7) × 10 −15 erg s −1 cm −2 , for a flat f λ spectrum. The unabsorbed luminosity can be estimated as L (1250–2000 Å) ≈ 1.9 × 10 29 erg s −1 , for E ( B − V ) = 0.03, and d = 410 pc. The bow shock is not detected in the F475X images (see Figure 8 ). Because of the apparent non-uniformities in the background, which significantly exceed the statistical fluctuations, we chose to measure the upper limits by sampling the background counts from ten different regions in the vicinity of the bow shock and calculating the standard deviation from the mean value. The areas of the background regions were equal to that of the bow-shock region used for FUV flux measurements. The standard deviation can be considered as a conservative 1 σ upper limit. The corresponding 3 σ upper limit on the bow-shock flux in the area of 52 arcsec 2 is F (3750–6000 Å) ≈ 2.9 × 10 −15 erg s −1 cm −2 , for a flat f λ spectrum and E ( B − V ) = 0.03. Figure 8. UVIS/F475X image with the bow-shock extraction regions (the same as in Figure 1 ), used for the data analysis. The pulsar and the direction of its proper motion are shown with a circle and an arrow, respectively. Similar to our analysis of the FUV bow shock around J0437 (Rangelov et al. 2016 ), we measured the ratio of the count rates in F125LP and F140LP filters for the J2124 bow shock. We obtained a ratio of C 125 / C 140

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grains (Fujiya et al. 2013 ; Jadhav et al. 2013 ; Liu et al. 2014 ). Stellar evolution theory predicts that, besides the H-ingesting He-shell flash convection on white dwarfs, the i process may also occur in metal-poor low-mass thermally pulsing AGB stars (Lugaro et al. 2012 ), during a He-core flash in metal-poor RGB stars (Campbell, Lugaro Karakas 2010 ), in super-AGB stars (Jones et al. 2016 ), and in Population-III massive stars when their H- and He-burning shells merge (Banerjee Qian Heger 2018 ; Clarkson, Herwig Pignatari 2019 ). In this work, we investigate the robustness of the weak i-process elemental abundances and their ratios that are proposed to contribute to the anomalous chemical composition of the star HD94028. The predicted abundances are affected by uncertainties of the (n,γ) reaction rates for the unstable isotopes involved in this nucleosynthesis. By ‘weak’ with typical neutron exposure τ ∼ 1 we mean an i process that, in spite of having a high neutron density, does not reach a large neutron exposure (time-integrated neutron flux), e.g. because it is terminated by the violent, global, non-radial instability that can be induced by H ingestion into the He-shell convection (Herwig et al. 2014b ), as probably happened in Sakurai’s object Herwig et al. ( 2011 ). As a result of this ‘weakness’ (a low neutron exposure), only the first n-capture peak elements (those with the neutron number close to the magic one N = 50) are produced in a significant amount by the weak i process. We employ the same computational methods and analysis tools that Denissenkov et al. ( 2018 ; hereafter, Paper I ) used in a similar study of i process producing the first peak elements observed in Sakurai’s object. Unlike in Paper I , we do not know the i-process site that contributed to the composition of HD94028. Therefore, we have to use a site-independent one-zone model with the temperature T , density ρ, and initial chemical composition adjusted to mimic the i-process physical conditions appropriate for this case, like it was done by Roederer et al. ( 2016 ). We also deploy constant neutron–density equilibrium models that are independent of the neutron-source reactions. 2 METHODS 2.1 The benchmark simulation For the one-zone simulations of the i-process nucleosynthesis, we use the NuGrid code ppn (Pignatari et al. 2016 ) with the same fixed temperature T = 2 × 10 8 K and density as in Paper I . The initial chemical composition is prepared using the Solar system abundances of Asplund et al. ( 2009 ) scaled to the metallicity of the star HD94028 ([Fe/H] =−1.6), assuming that the α-element abundances are enhanced with the mean value of [α/Fe] equal to +0.4. The initial mass fraction of 12 C is increased to X ( 12 C) = 0.5 to be close to the values found in He-flash convective zones. We also reduce the initial hydrogen abundance to the value of X ( 1 H) = 0.2 adjusted to guarantee that the neutron density will reach the values of N n = 10 13 –10 16 cm −3

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[Ba/Fe]=+0.13 that is significantly above the pristine [Ba/Fe] dex enrichment in Fig. 6 . This suggests that HD 26749 should have a degenerate companion and should have experienced a former epoch of wind accretion. The observable depletion of lithium qualitatively supports this scenario, but for a quantitative argument one would at least need to know the exact amount of the accreted mass. In this context, it is interesting to note that HD 26749 is currently in its subgiant stage of evolution and appears to be 1 or 2 Gyr younger than one might expect for an ancient Population II star. The excess of mass involved amounts to a few hundredths of a solar mass, a reasonable value for wind accretion, but this also depends on a parallax that would need to account for potential orbital motion. While this parallax may be possible with the Gaia DR3 release, it may be worthwhile to observe HD 26749 with high-contrast direct imaging that may disclose the degenerate candidate companion. 4.1.10 HD 34297 Two Hipparcos -based astrometric orbits by Goldin Makarov ( 2006 ) provide an orbital period of about 2 yr for this double-lined spectroscopic binary. The quantitative composite modelling of our Δ v r (Aa–Ab) =+28.9 km s −1 well-resolved 2017 November 28 spectrum of HD 34297 leads to a photometric contrast Δ m V ≃ 0.5 mag, a Population II chemistry [Fe/H]≃ −0.65 and [Fe/Mg]≃ −0.37, and effective temperatures T eff, Aa ≃ 5660 K and T eff, Ab ≃ 5440 K. The surface gravities, log g Aa ≃ 4.43 and log g Ab ≃ 4.53, follow from the Gaia DR2 parallax. Fig. 1 gives an example of the synthetic line formation for the Fe I line λ6200.321. With reference to the bolometric magnitudes M bol, Aa ≃ 4.96 and M bol, Ab ≃ 5.43 and VandenBerg et al. ( 2006 ) evolutionary tracks, the Aa primary, with a stellar radius R Aa ≃ 0.92 R ⊙ and mass M Aa ≃ 0.82 M ⊙ , is already approaching its turnoff position. The Ab secondary is still close to the main sequence at R Ab ≃ 0.80 R ⊙ and M Ab ≃ 0.79 M ⊙ . Our single-epoch radial velocities, and km s −1 , then provide a systemic velocity γ = +27.64 ± 0.27 km s −1 . 4.1.11 HD 51929 This is a known astrometric and spectroscopic binary (Wielen et al. 1999 ; Nordström et al. 2004 ; Makarov Kaplan 2005 ; Frankowski et al. 2007 ); our single-epoch radial velocity, km s −1 (2017 November 28), deviates by 3.73 km s −1 from the Nordström et al. ( 2004 ) velocity. The Ab companion was recently uncovered through direct imaging at ρ = 0.72 arcsec by Kane et al. ( 2019 ), who assess this to be a faint red dwarf, which we do confirm, since the Aa primary displays the pristine [Ba/Fe] dex enrichment (cf. Table 3 and Fig. 6 below). 4.1.12 HD 65721 For this astrometric and spectroscopic binary (Wielen et al. 1999 ; Nordström et al. 2004 ), Hipparcos -based orbital solutions were first presented in Goldin Makarov ( 2006 , 2007 ). In spite of their preliminary character with d and , the eccentricity appears indeed high, for HD 65721 presents an

B-Formula O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset I-Dataset O O O O O O O B-CelestialObject I-CelestialObject O B-ObservationalTechniques I-ObservationalTechniques I-ObservationalTechniques O O O O O O O O B-CelestialObject I-CelestialObject O B-Telescope O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O B-CelestialObject I-CelestialObject O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O B-Formula I-Formula O B-Formula I-Formula O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O B-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula O O O B-Dataset I-Dataset O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O B-CelestialObject I-CelestialObject O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Formula I-Formula I-Formula O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Telescope O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O


CO(3–2) and HCO(4–3) lines with the ASTE telescope, aiming at studying in detail the spatial distribution and physical characteristics of the molecular gas associated with the nebula. To analyze the properties of the dust in the nebula and its surroundings we use images from the ATLASGAL and Herschel databases. To account for the interaction between the ionized and molecular gas and to determine the evolutionary status of the H ii region, we use radio continuum data from the NVSS archives. This analysis also allows us to identify spots of dense molecular gas and dust where the massive star formation is developing, particularly the central region corresponding to the source IRAS 18139-1842, where star formation processes seem to be very active. In addition, we look for signatures of star formation in the surroundings using archival photometric data and we investigate a probable scenario of triggered star formation at the border of the nebula. We also study the characteristics of an identified stellar cluster projected onto the border of the bubble using new IR data. This provides some additional information that helps us to better understand the star formation activity in the nebula. N5 is an open IR bubble of about 8 in diameter centered at RA, Dec(J2000) = 181702, 184019, coincident with the H ii region Sh2-39, and located at a distance of 4.1 kpc ( Bronfman et al. 1996 ; Faúndez et al. 2004 ). In Fig. 1 we present a 8.28 m (MSX-A) emission image of the nebula, which has a typical arc-shaped morphology in the mid-IR wavelengths. At wavelengths of about 8 m most of the emission originates in strong features of PAH molecules, which are considered to be good tracers of warm UV-irradiated photodissociation regions (PDR; Hollenbach Tielens 1997 ). Since these complex molecules are destroyed inside the ionized gas of an H ii region, they indicate the limits of the ionization front and delineate the boundaries of the bubble nebula, giving a glimmer of the location of the parental molecular gas against which N5 is likely expanding. The open morphology of the IR nebula suggests that Sh2-39 is the classical H ii region density bounded toward the outer side (eastward) and ionization bounded toward the molecular cloud (westward). The nebula is believed to be linked to the IR sources IRAS 18139-1842 and IRAS 18139-1839, which both have characteristics of massive young stellar objects (see Sect. 6). The CS(2–1)line was detected by Bronfman et al. (1996) at a velocity 1 of 40.2 km s in the direction of IRAS 18139-1842. NH line and HO maser emission, which are believed to be excellent indicators of early stages of massive star formation, were also detected toward this IRAS source ( Sunada et al. 2007 ; Urquhart et al. 2011 ), while radio recombination line observations (H87 and H88) show emission at the same position at a velocity of 41 km s (Lockman, 1989 , see Fig. 1 ), which indicates the existence of high density ionized gas at the same radial velocity

B-Wavelength O B-Wavelength O O O B-Telescope I-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Database O B-Database I-Database O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O B-Archive I-Archive O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O B-Wavelength O O O O O O O O B-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion O O O O O O B-CelestialObject O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Wavelength I-Wavelength B-Telescope O O O O O O O O O O O O O B-Wavelength O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O B-CelestialObject O O O O O O O O B-Wavelength O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O B-Wavelength O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O B-Wavelength O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O


of the ejecta, the luminosity of this radioactivity-powered AIC optical emission cannot be much higher than ∼10 41 erg s −1 , even though the synthesization of 56 Ni in the ejecta is very efficient. In principle, the AIC NSs could sometimes (but may not always) be converted into magnetars, as these NSs can initially rotate very rapidly and differentially. Following this consideration, it has been suggested that the rapid spin-down of the magnetars can substantially affect the AIC optical transient, e.g., by providing an extra energy source to heat the AIC ejecta (Yu et al. 2015 , 2019 ). In more detail, the energy released from the magnetars can be initially in the form of a Poynting flux, which could eventually transform into a relativistic electron-positron wind. Then, questions arise as to what kind of emission can be produced by the pulsar wind (PW) and how energy is transferred from the PW to the AIC ejecta. It is expected that the PW emission, if detected, can help to identify AIC candidates in the future. Basically, PW emission could be mainly determined by the collisions of the PW with the AIC ejecta and, in particular, with the companion star. An illustration of these interactions is presented in Figure 1 . Considering the fact that the spin-down luminosity of a magnetar can be as high as ∼10 45 erg s −1 , the companion could be completely evaporated by the PW in a few days, because the gravitational binding energy of the companion is probably not much higher than ∼10 48 erg. The evaporated companion material (ECM) would finally form a torus due to the orbital motion, which surrounds the magnetar and blocks the PW in the orbital plane. The formation of such an ECM torus and its interaction with the PW are investigated in Section 2 . Meanwhile, the termination shock (TS) of the PW due to its interaction with the AIC ejecta is calculated in Section 3 . Both of these PW emission components can penetrate the AIC ejecta and become detectable as long as the ejecta becomes transparent for X-rays. A summary of our calculations is given in Section 4 . In Section 5 , we discuss the possible application of the AIC model in explaining the multi-wavelength emission of a recently discovered fast-evolving luminous optical transient: AT 2018cow. Figure 1. Illustration of a post-AIC system (not to scale), including the stages before and after the breakdown of an ECM torus. 2. The Interaction of a PW with a Companion 2.1. The Evaporation of a Companion Some NSs formed from AIC events are considered to rotate very rapidly and possibly differentially. In this case, the magnetic fields of the NSs can be significantly amplified through magnetorotational instability (Duncan Thompson 1992 ; Dessart et al. 2007 ; Cheng Yu 2014 ). However, in practice, it is still difficult to assign a fiducial value to the spin periods and the magnetic fields of the NSs, because these parameter values are highly dependent on the properties of progenitor WDs. In principle,

O O O O O O O O B-Model B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model B-Wavelength O O O O O O O O O O O B-Model O B-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O B-Wavelength O B-CelestialObject I-CelestialObject O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


resulting in the gray eclipse. Also, no significant pulsations in maximum light are present in the historical light curve of MASTER OT J095310.04+335352.8, which also speaks in favor of the cold dust disk. Of course, the edge-on disk orientation is not the only possibility to explain this system, and further study of this system will clarify this question. The spectral energy distribution (SED) of the system was very similar in the all our spectra despite the great difference in continuum fluxes. The main contributor to the SED is a red giant in eclipse as well as after eclipse, and the TiO bands of the red giant are the most prominent absorption features in the spectra. The spectrum obtained in eclipse also exhibits some faint emission lines against the TiO bands (see Sect. 2.2). We neglect the interstellar reddening because the system is above the Galactic plane and there is not any sufficient continuum distortion. The spectrum obtained in eclipse (February 10, 2013) includes the red region, allowing us to estimate the spectral type of the partially eclipsed red giant by means of [TiO] spectral index ( Kenyon Fernandez-Castro 1987 ). The star is an M1-type giant (0.5 subclass). Differences between the observed spectrum and standard SEDs of M0III and M1III do not exceed in the red part of spectrum, but for M2III the difference are about . There are not any signs of CaH absorption bands in any of our spectra, therefore, the luminosity class of the star cannot be (MS star). Another luminosity criterion is a relative intensity of FeI 5250 Å and CaI 5269 Å. According to this criterion the star is a giant (III class) rather than supergiant ( class). We note that the SED in the red region is nearly the same as that of a standard M1-type giant, but in the blue region the situation is quite different; see Figs. 2 and 5. The continuum fluxes are nearly 20% higher than the standard M1III SED. The second spectrum was obtained after eclipse and does not include the red region and, therefore, we cannot trace the emission lines evolution. The main difference between two spectra is that after eclipse the observed SED is similar to a standard M1 SED even in the blue region; see Fig. 4 . A difference between the SED observed in eclipse and a standard M1III SED is shown in Fig. 5 . A SED of the difference characterizes a sufficiently hot source because its continuum flux grows from the visual to blue region. The emission of this source was visible only during eclipse (when the contribution of the red giant to the total flux was greatly diminished). Without the eclipse, the SED is the pure contribution from the M1III-type star. The SED of the hot component corresponds poorly to a SED of any standard hot star with spectral class earlier than F5 and does not correspond to SEDs of later stars (thick line in Fig. 5 is a standard B6V SED); we tried to approximate the observed hot component spectrum by means of SEDs for MK standard stars for spectral classes

O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


mode of HDO at 1475 cm is not clearly visible as a result of the signal-to-noise (S/N) level. The bending mode is at least four times weaker than the stretching mode, which is not detectable for the S/N achieved here ( Oba et al. 2014 ). This means that the produced OD radicals either form DO or abstract an H-atom from CH. The availability of D atoms on the surface results in the barrierless deuteration of a CH radical. Since the D atoms are abundant and diffuse quickly, other radical-radical reactions are prevented. The CHOD or CH yields lie below the sensitivity of our RAIRS technique, that is, reactions R7 and R8 are not relevant here. Note that the abstraction reaction between HO and CH has a barrier of K ( Aguilera-Iparraguirre et al. 2008 ), and we therefore exclude any CH radical production via this route. Furthermore, none of the control experiments (numbers 2–4) resulted in the detection of CHD. This means that the CHD detected in experiment 1 is not the cause of contamination (follows from experiment 2) nor the result of H-abstraction from CH by D atoms directly (follows from control experiments 3 and 4). In other words, in our experimental setup, the reaction between CH and the D atom does not proceed within our experimental sensitivity. Since the same setup is used for experiments 1, 3, and 4, essentially for identical conditions, we conclude that the reaction CH + OD is more efficient and the only one responsible for the formation of the observed CHD. This result can be rationalized by realizing that the reaction CH + H CH + H has a high barrier of 69407545 K ( Nyman et al. 2007 ; Corchado et al. 2009 ), making it highly unlikely to be competitive at the low temperatures considered here, even if it were to occur via tunneling. Indeed, the (bimolecular) rate constants calculated on several PES at 300 K are six orders of magnitude lower than the bimolecular rate constants calculated here for CH + OH (compare Corchado et al. 2009 ; Espinosa-García et al. 2009 ; and Li et al. 2013 with values mentioned in Appendix A ). The next question is whether or not the isotope-substituted reaction R5, CD + OH CD + HDO, leads to D-abstraction by OH radicals. In this case, the mass of the atom that is transferred is twice as high, the activation energy is also higher due to a ZPE effect, and if tunneling is important, the reaction rate should drop significantly. In Fig. 3 , and especially from the zoomed-in spectra in Fig. 4 , it is clear that no detectable amounts of CDH are produced during experiment 5. Since OH radicals are present, HO is formed and can be seen at its respective peak positions, around 3315, 2835, and 1385 cm ( Oba et al. 2014 ). Furthermore, the OH radicals that are produced are not being used for reactions with CD and therefore are available for other reactions, leading to the formation and detection of the HO bending mode at 1630 cm, while the stretching mode overlaps with that of HO. HO can also be formed via H + HO HO +

O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength B-Wavelength O B-Wavelength I-Wavelength O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O


), and it has a mass accretion rate of about 10 −9 M ⊙ yr −1 (Hartmann et al. 1998 ). The outer edge of the dust disk inferred from continuum emission is at ∼150 au (Piétu et al. 2007 ; Isella et al. 2012 ). The dust mass estimated from 1.3 mm continuum observation is about 5 × 10 −4 M ⊙ (Isella et al. 2012 ). Recent images of scattered light suggest a warped inner disk component inside the inner gap, providing clear picture details of the inner gap region of the LkCa 15 disk (Thalmann et al. 2015 , 2016 ; Oh et al. 2016 ). As a young star, LkCa 15 is a luminous source of X-ray and extreme ultraviolet (EUV) emission (Skinner Güdel 2013 ), indicating that the LkCa 15 disk could still be undergoing the active evolution phase of disk physics and chemistry. Consequently, the protoplanetary disk of LkCa 15 has been found to be especially chemically rich and has been detected in several molecular transitions (Thi et al. 2004 ; Piétu et al. 2007 ; Chapillon et al. 2008 ; Öberg et al. 2010 ; Punzi et al. 2015 ). Molecular line emission shows that the gas disk around LkCa 15 is the size of ∼900 au (Piétu et al. 2007 ; Isella et al. 2012 ). It is highly optically thick in the emission of 12 CO but is optically thin in 13 CO emission (Punzi et al. 2015 ; van der Marel et al. 2015 ). The discrepancy between the outer disk radii shown in the dust continuum and molecular line emissions (∼150 au versus 900 au) suggests that the mm-size dust is depleted in the outer part of the LkCa 15 disk, which is consistent with dust drifting and trapping models (Birnstiel et al. 2010 ; Pinilla et al. 2012 ). Being a protoplanetary disk that may have a young planet candidate, the LkCa 15 system serves as a unique laboratory to study the dust evolution models under planet–disk interaction (Zhu et al. 2011 ; Pinilla et al. 2012 ). The distribution of dust and gas in the LkCa 15 disk provides an important constraint on theoretic models. Here, we fit the gas and dust surface density profiles based on the high-resolution dust continuum image and CO 3–2 line maps obtained from the ALMA. We study how the goodness-of-fit changes along with different key parameters used in the disk density profile, which is related with different physics. Our disk model and the parameter grid is described in Section 3 . In Section 4 , we show the best-fit model with respect to the observed 12 CO image. We discuss the dependence of the parameters in Section 5 . 2. Observation The LkCa 15 was observed on 2014 August 17 and 29 with ALMA Band 7 (345 GHz, 880 μ m) in ALMA program 2012.1.00870.S (PI Pérez, L. M.). The 12 CO, 13 CO, and C 18 O 3–2 line maps and 0.87 mm dust continuum image were taken with two different tunings. The 12 CO 3–2 data were obtained with a spectral window centered on 345.796 GHz with 1885 channels of 122.06 kHz (0.106 km s −1 ) channel width. The angular resolution of the 12 CO image is 036 × 023 (50 au × 32 au). The 13 CO 3–2 data were centered on 330.588 GHz, with 1967

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Si iv . Solid contours represent and 1.04. The dotted contour represents T b = 6500 K. An animation of the observations is available. The animation runs from 14:19 to 14:54 UT on 2017 April 29. (An animation of this figure is available.) Panel (b) shows the distribution of the relative brightness in the ALMA 100 GHz data defined aswhereis a temporally averaged brightness over the entire observed period (Δ t ≈ 1 hr). The ALMA 100 GHz relative brightness and its corresponding animation (panel b) show a dynamic thorn-like structure coming from the saw-tooth patterns on the limb. Because these structures show dynamic motion with elongation and shortening, hereafter we call them ALMA jets. Their length reaches at least 8′′, suggesting jet-like activity in the ALMA microwave range. Unfortunately owing to the insufficient signal-to-noise ratio in the data beyond the limb particularly in the area more than 10′′ beyond the limb (see Section 4 ), we can not recognize the maximum height of the elongated jets. The speed of the elongation is 30–40 km s −1 . The width of each jet is less than the spatial resolution of the observation, i.e., less than ≈2′′. The IRIS /SJI Mg ii images (panel d) clearly show the appearance of spicules on the limb. Some of the spicular jets reach more than 20′′ beyond the Mg ii limb. It is noteworthy that the spicular jets show clustered structures, i.e., multiple needle-like features display a collective up-and-down motion. Each needle-like structure has a width less than 1′′ and each cluster has a few to several needle-like structures. In comparison with the ALMA data (contours in panel d), the ALMA jets are in good agreement with the IRIS jet clusters. The IRIS Mg ii limb (panel d) is ≈5′′ below the ALMA limb. Again, this confirms the distribution of cool chromospheric plasmas between the IRIS Mg ii and ALMA limbs (For an IRIS limb analysis, see Alissandrakis et al. 2018 ). In the IRIS /SJI Si data (panel f), one can observe the activities on the solar surface inside the limb. Some of them correspond to the footpoints of the Mg ii spicules. The AIA 304 Å data (panel e) has a low signal-to-noise ratio and is difficult to extract information on jet activities. In one of the tall jets in IRIS Mg ii , an ALMA blob ejection was found. From Figure 2 , one can find the trajectory of the blob co-located with the Mg ii jet. The brightness enhancement in the ALMA images is by 135 K beyond the background (Figure 3 ). The blob shows a systematic proper motion at a speed of 40 km s −1 (panel c), which is similar to the IRIS jet speed (panel e). There are no significant features in the IRIS Si or the AIA data sets co-located with this blob event. However, by the careful inspection of the IRIS Si data, we found short (≈a few arcseconds) elongated structures at the base of this event. They show shifting from east to west changing its inclination angle. Figure 2. ALMA blob-ejection event associated with a tall IRIS Mg ii jet. (a) Brightness

O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Observatory B-Wavelength I-Wavelength O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O B-Observatory B-Telescope I-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Observatory O O O O O O O O O O O O B-Observatory B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Observatory O O O O O O B-Observatory O O O O O O O B-Telescope O O O B-Telescope O O O O O O O O O B-Observatory O O O O O O O O O O O O B-Telescope O O O B-Observatory O O O B-Telescope O O O B-Citation I-Citation I-Citation I-Citation O O O B-Telescope B-Instrument O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O B-Telescope B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O B-Observatory O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Observatory O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O B-Telescope B-Instrument O O B-Telescope O O O O O O O O O O O O O O B-Telescope B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Observatory O O O O O O B-Telescope O O O O O


, and references therein) also been explained as a possible delayed effect (not perfectly stable thermohaline circulation) of the deglaciation in the carbon cycle (e.g., Muscheler et al. 2004 ). However, as we show here, this explanation is unlikely for two reasons. More details of the long-term relation between the series are shown in Fig. 9 , where we plot the pairwise wavelet coherence between the modulation potential (shown in Fig. 12 ) from the three long series. Panel a shows that the EDML series is coherent with the 14 C series at all timescales shorter than ≈2000 yr and again (but insignificantly) longer than 4000 yr, while no coherence exists between 2000 and 4000 yr. The GRIP-based series (panel b) is well coherent with the 14 C one on timescales longer than 100–200 yr, and the coherence disappears at timescales longer than 2000–3000 yr. The two 10 Be are hardly coherent with each other on timescales longer than 1000 yr (panel c), with a small insignificant isle of coherence beyond the cone of influence. It is noteworthy that each of the 10 Be series exhibits a higher coherence with the 14 C one than with each other. A similar conclusion was made by Usoskin et al. (2009) using different 10 Be data series. A reason for this discrepancy is yet to be discovered. Since the reason for this discrepancy is unknown, we did not correct for it. In the following we apply fixed coefficients for 10 Be series, thus keeping the long-term variability as it exists in the original data. It is interesting that while the coherence between EDML- and 14 C-based reconstructions has been improved compared to the coherence between the raw data series ( Fig. 4 ), the coherence is degraded for the GRIP series (panels b) in timescales longer than 2000 yr. This suggests that beryllium may be better mixed for Greenland than was derived through the applied beryllium transport parametrization based on Heikkilä et al. (2009) . The reconstruction based on the 14 C series has no residual correlation with VADM ( R 2 0.01). A new full-size model of the atmospheric transport and deposition of 10 Be in polar regions, particularly in Greenland, is needed to resolve the issue. 4.4 Reconstructions from individual series Two beryllium series, GRIP and EDML, were used here for a preliminary assessment of this method for their overlap. The mean modulation potential for the period 6800 BC–700 AD based on radiocarbon is ⟨ φ 14C ⟩ = 0.468 GV. First, we scaled each 10 Be series individually with a free scaling factor κ 0 and reconstructed the series of φ . The values of κ 0 were defined such that the mean value ⟨ φ 10Be ⟩ is equal to that for 14 C for the same period. The scaling factor we found for the GRIP data is close to unity, κ 0 = 1.1. This implies that 14 C and 10 Be data are fully consistent in the framework of the model, and that our modeling of the cosmogenic isotope production and transport or deposition is appropriate. The best-fit scaling factor for EDML is κ 0 = 0.8,

O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset I-Dataset O O O O B-Dataset I-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset I-Dataset O O O O O O O B-Dataset I-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O B-Dataset I-Dataset I-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O B-Dataset I-Dataset O O O O O O O O O O O O O O O O O B-Location O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O B-Dataset I-Dataset I-Dataset O O O O O B-Model O B-Model I-Model I-Model O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O B-Location O O O O O O O O O O O O O O B-Dataset O B-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset I-Dataset O O O O B-Formula I-Formula I-Formula I-Formula O O O B-Dataset I-Dataset I-Dataset I-Dataset I-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset O B-Formula I-Formula I-Formula I-Formula


may have a significant impact on dynamical processes that remain poorly known, such as star formation in molecular clouds, dissolution of open clusters in galactic tidal fields, tidal heating of thin discs, etc. Crucially, our results open up the possibility to test the existence of planet-sized microhaloes via experiments that are sensitive to tidal force fluctuations induced by dark matter substructures, e.g. by measuring the heating rate of weakly bound gravitational systems in different regions of the stellar halo, as well as in the dwarf spheroidal galaxies of the Milky Way (see also Peñarrubia et al. 2010 ). This type of experiments may also constrain a wide range of cosmological theories where dark matter is made of ‘warm’ particles or ULAs (see Section 4.2 ). The mathematical technique explored in this paper provides a computationally efficient tool to model the gravitational perturbations induced by an arbitrarily large number of CDM microhaloes. In follow-up contributions, we plan to run numerical experiments that follow the trajectories of tracer particles in smooth galactic potentials that incorporate the force and tidal distributions derived in Sections 2 and 3 as external stochastic fields. Such codes may provide a useful tool to model observational data (e.g. the separation function of wide binaries, see Section 4.3 ) at a low computational cost. Finally, it is worth stressing that our statistical method can also be used to describe stochastic fluctuations in the force and tidal fields generated by baryonic substructures covering a wide range of mass and sizes, such as GMCs, MACHOs, black holes, stellar clusters, individual stars, planetoids, etc., which may have several applications in areas other than cosmology. APPENDIX A: THE LOCAL APPROXIMATION In Sections 2 and 3 , we derive the distributions and , respectively, under the assumption that the number density of substructures remains constant across the entire system, and that corresponds to the value measured at the galactocentric location of the tracer particle, . Although the local approximation greatly simplifies analytical derivations 1 of the Fourier transform , in general it fails on scales r ≳ d , where d = |∇ n / n | −1 is the distance associated with the spatial variation of the number density profile ( 61 ) The fact that γ 1 in cosmological simulation of structure formation implies that the scalelength d decreases towards the centre of the potential, suggesting that the local approximation may not be valid at small galactocentric radii. The second scale of relevance corresponds to the average separation between substructures, D ( R ). In Section 2 , we found that the large-force fluctuations generated by non-overlapping subhalo populations are dominated by the nearest substructure, which is typically located at a distance D ( R ) ≈ [2π n ( R )] − 1/3 . Hence, the local approximation is justified for d ≫ D , that is when the number density profile varies on

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O


steps; we therefore estimate the above convergence to be sufficient. Convergence is however not fully reached in the line wings within the allocated computing time. Development of efficient acceleration methods would be desirable for future work. Fig. 2. Convergence of the linear polarization rate Q / I , for the D 2 line ( left ) and for the D 1 line ( right ) at line center ( upper row ) and in the line far wing ( lower row ). Fig. 3. Convergence of the emerging linear polarization Q / I : evolution of the step increment Δ( Q / I ) as a function of the step number N . The aim is to show that the step increment decreases more rapidly than the inverse of the step number 1/ N (as for a Riemann series). In this respect, their ratio is the upper plot and the logarithm of their ratio is the lower plot, which also includes linear fits and their equations. The two terms of the Q / I ratio, namely the Stokes parameters Q and I , each nevertheless converge much less quickly, in such a way that they are not at all converged within the 166 iteration steps. However, the behavior of the ratio Q / I appears to be different, because some simplifications certainly occur when forming the ratio. 4. Concluding discussion Although the calculation seems reasonably converged in the line wings, the agreement between the observed and computed profiles remains only qualitative. As described below, we investigated the different possible causes of this difference. We questioned the accuracy of collision rate calculations, in particular those with hydrogen neutral atoms that determine the coherent scattering weight in PRD, and therefore in the far wings. We artificially varied these rates, but the Na I D 2 wing profile was not improved with respect to observations. We questioned the model electron density, whose determination is very indirect from observations, and in light of the recent investigation by Bommier (2020) , who suggests that the electron density at the solar surface would be much higher than in present models, and similar to the neutral hydrogen atom density. We artificially varied the model electron density, but again the Na I D 2 wing profile was not improved with respect to observations. We questioned the accuracy of our model of Rayleigh scattering on neutral hydrogen atoms, which is responsible for the continuum below spectral lines, which is of more relative importance in their wings. Our model is taken from the MALIP code for computing the Stokes parameter profiles of magnetoactive Fraunhofer lines by Landi Degl’Innocenti (1976) , and we did not try to modify it. We questioned the very rough HOLMUL approximation ( Holweger Mueller 1974 ) we applied to our atmosphere model. This approximation consists in not considering atmosphere higher than the temperature minimum. The temperature reversal there may be responsible for a central bump in the line profile, following a well-known result for a two-level atom in LTE. As our model considers only the

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-Model I-Model O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O


agreement with the numbers published by Hassan et al. ( 2017 ) (∼50 sources in 5 h and in 10 000 deg 2 ), while it is intermediate (but broadly consistent, considering the large uncertainties) between the expectations discussed by Padovani Giommi ( 2015 ) (100–160 BL Lacs expected) and the values estimated by De Franco et al. ( 2017 ) (24 detections). The predictions by Hassan et al. ( 2017 ) are extrapolated by the Fermi -LAT (3FHL) catalogue and, therefore, they consider only the blazars currently detected by Fermi -LAT. In our work, we are considering also Fermi -LAT undetected objects but, as discussed above, the expected detections in 5 h exposure times (3 objects) are all present in current Fermi -LAT catalogue (FL8Y). This means that current predictions for a (shallow) CTA extragalactic survey based on Fermi -LAT catalogue should be reliable while, for deeper pointing, the current Fermi -LAT catalogues could miss up to 50 per cent of objects. In the very close future e-ROSITA (extended ROentgen Survey with an Imaging Telescope Array, Merloni et al. 2012 ) will survey the entire sky, reaching in the soft X-ray band (0.5–2 keV) a flux 100 times fainter than the ROSAT All Sky SURVEY (RASS) data and with an on-axis spatial resolution of ∼15 arcsec. A cross-match of the point sources detected by e-ROSITA with radio catalogues as the NVSS or the Sydney University Molonglo Sky Survey (SUMSS) will provide virtually all the expected ∼800 HBL that could be detected by CTA. 8 SUMMARY AND CONCLUSIONS We have presented a well-defined and representative sample of HBL selected from the REX survey that was obtained by cross-matching radio (NVSS) and X-ray data ( ROSAT -PSPC pointed data). In particular, we selected all the REX with an X-ray-to-radio flux ratio typical of an HBL and falling in a well-defined area of sky covering about 560 deg 2 . We then completed the spectroscopic follow-up of all these sources and we focused on the 46 sources showing no emission lines in the optical spectrum. We called these source Te-REX, standing for TeV-emitting REX candidates, since HBL are the most promising sources to be detected at TeV energies. Out of these 46 sources, 25 have a clear non-thermal nucleus detected in the optical spectrum as a significant reduction of the Ca ii break (40 per cent). In the remaining 21 Te-REX sources, instead, we measured a Ca ii break value above 40 per cent, i.e. the non-thermal nucleus is swamped by the stellar light. We called these 21 sources PEGs (for ‘PEGs’). We expect that most PEGs should be faint HBL nuclei dominated by the host galaxy light. We then evaluated the intensity of the VHE emission of all the 46 Te-REX. To this end, we compare the predicted SEDs with the sensitivity curves of current and future Cherenkov telescopes. Considering deep, pointed observations of 50 h, we found 14 Te-REX (2.5 objects per 100 deg 2 , corresponding to ∼800 objects on the entire extragalactic sky above ∣ b ∣ ≥ 10°) that could be

O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O B-Observatory B-Telescope B-Dataset O O O O O O O O O O O B-Observatory B-Telescope O O O O O O O B-Observatory B-Telescope O O O O O O O O O O O O O O O O O O O O O B-Observatory B-Telescope O B-Dataset O O O O O O O O B-Survey I-Survey I-Survey O O B-Dataset I-Dataset I-Dataset O O O O O O O O O B-Dataset I-Dataset I-Dataset O O O O O O O O O O O O O O B-Survey B-Survey I-Survey I-Survey I-Survey I-Survey I-Survey I-Survey I-Survey B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Wavelength O B-Wavelength I-Wavelength O O O O O O O B-Survey I-Survey I-Survey I-Survey B-Survey O O O O O O O O O O O O O O O O O O B-Survey O B-Wavelength O O O B-Survey O O B-Survey I-Survey I-Survey I-Survey I-Survey B-Survey O O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O B-Survey I-Survey O O O O O B-Instrument B-Survey O B-Wavelength O O B-Telescope B-Instrument O O O O O O O O B-Survey O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O B-Wavelength B-Survey O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O B-Telescope I-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion O O O


of the largest angular scale being exceeded can be seen around zero velocity. It is important to be prudent when dealing with such data, as the potential for misinterpretation is significant. For instance, erroneously assuming a spherically symmetrical outflow for a source which is intrinsically EDE-like, or has both a radial outflow and an EDE-like component, may result in serious deviations on the estimations of the physical properties of the system. This has been shown by e.g. Homan et al. (2015) . The authors outline and quantify the uncertainties related to a misinterpretation of embedded spiral shapes in stellar winds. Their conclusions on the uncertainties, related to falsely interpreting the emission from a narrow spiral (which is effectively a kind of equatorial density enhancement) as originating from a simple spherically outflowing stellar wind, are also applicable here. 6.2. ALMA Using CASA we have simulated ALMA observations of the Keplerian disk model with a bipolar outflow. Since the considered radiative transfer model has no substructure, there is no reason to explore the effect of angular resolution. Its effect will only be of importance if the aim is to properly resolve the inner EDE, the edges of the EDE or the EDE-wind boundary. We have opted to show the effect of exceeding the chosen configuration’s largest angular scale (LAS), determined by the shortest baseline of the interferometer, on the emission distribution in the PV diagrams of the Keplerian disk model with a bipolar outflow. Table 5 The ALMA observation simulation specifications. A synthetic observation is shown in Fig. 23 , for which the main simobserve parameters are presented in Table 5 . To obtain the results in Fig. 23 we have simulated an observation with the most compact of the extended configurations, C36-1. This configuration has an angular resolution of 1.5 and a largest angular scale of 11. To properly show the effect of a decent observation, we have rescaled the pixel size to artificially place the object at the minimal distance for no EDE flux to be lost. Morphologically, the intrinsic emission and the emission in Fig. 23 are very similar, as expected. The sheer number of antennae available for cycle3 ensures even for modest integration times a decent filling of the UV-plane. The high inclination models show that even though the signature of the EDE is barely unaltered, the bipolar wind emission has exceeded the LAS of the antenna configuration around zero velocity. Some of the flux of the wind is thus lost. Because our models are confined to a numerical region, and bipolar outflows are not expected to exhibit such abrupt edges, this effect is expected to be more pronounced in real physical objects. Fig. 25 Synthetic ALMA observation simulation of the Keplerian disk model (with a bipolar outflow) with the C36-1 antenna configuration (, ), for which the original model has been rescaled to a size 18 times greater than it was in Fig. 23 . The effect

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Observatory O B-Software O O O B-Observatory O O O B-Model I-Model I-Model O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O B-Observatory O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Observatory O O O O B-Model I-Model I-Model O O O O O O O O O B-TextGarbage I-TextGarbage O O O O O O O O O O O O O O O O O O O O O O O


of the 9 year period observed, we find reductions in the GDF, consistent with an average decline in the ram pressure when correcting for solar wind propagation times. The conditions reflected by GDF maps from 2009 through 2016 are consistent with an expanding heliosheath, provided that plasma cooling overcomes any increase in the LOS from expanding heliospheric boundaries. The conditions appear to change abruptly in the 2015–2017 GDF map. In fact, as reported by McComas et al. ( 2018 ), the conditions change so quickly that there appears to be a longitudinal discontinuity near the nose. The brightening observed within this 2015–2017 GDF map reflects a strongly time-dependent change manifesting most prominently in 2017. The heliosheath responds to time-dependent changes in the solar wind ram pressure. Over most of the 9 year period analyzed we have observed drops in the LOS-integrated pressure due to expansion of the heliosheath driven by reductions in the solar wind ram pressure. In the 2015–2017 period, we have observed some recovery in the LOS-integrated pressure due to a significant increase in the ram pressure observed at 1 au beginning in 2015. Despite the large changes near the nose, the LOS-integrated pressure near the tail shown in Figure 6 remain relatively stable. Accounting for the stability of the tail will require understanding how time variations propagate downtail along the LOS. Presumably this stability requires that the LOS in the tail is significantly longer than the LOS near the nose. This reinforces the conclusion that the structure of the heliosphere is not round, and has a long comet-like tail (Schwadron Bzowski 2018 ). 3.3. Time-dependent Changes in the IBEX Ribbon We approach the time-dependent changes in the IBEX ribbon by considering the secondary neutral solar wind as the source. In this model, the solar wind conditions at 1 au are reflected in the ENA flux from the IBEX ribbon after a time delay consisting of a travel time from 1 au to the source region, the charge-exchange lifetime of a newly ionized proton in the ribbon, and the time necessary to return from the source region to IBEX located at 1 au. We use the parallax distance of au based on the study of Swaczyna et al. ( 2016a ). We find that a 1 keV neutral atom moves from 1 au to the source region in years. The charge-exchange lifetime of a newly ionized proton in the ribbon at 1 keV is ∼2.5 years. The transit time of the neutral atom back to 1 au is also years. Adding up these terms, we find a time delay of years between the observation of solar wind at 1 au and the ENA observations of manifestations of this solar wind within the ribbon at 1 keV. At 4 keV, the propagation time from 1 au to the ribbon distance (and vice versa, for propagation from the ribbon to 1 au) is years. The charge-exchange lifetime of this 4 keV ENA is ∼2 years, yielding a time delay of . The estimations of these time delays are rough, largely due to uncertainties in our

O O O O O O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O B-CelestialObjectRegion O O O O O O O O O O O O B-CelestialObjectRegion O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O B-Mission O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


2 sequences, respectively. This results in all periodicities being identified with spacings similar to other Kepler -observed g-mode pulsators (Reed et al. 2011 ). Figure 4. Period spacing sequences indicated by the KS test. The solid blue (green) line indicates the l = 1 (2) period spacing sequence with the dashed line the overtone alias. Figure 5. Period transform of PG 1142 showing evenly spaced periods. Short blue (green) lines indicate the asymptotic l = 1 (2) sequence with full-length lines indicating those which match detected periodicities. The horizontal line indicates 4.35σ for reference. 3.2 Binary analysis PG 1142 has proven to be a very exciting target. The detection of fA and fB prompted follow-up spectroscopic observations (described in Section 2.1 ) to search for velocity variations, which were subsequently detected. Fitting the 24 RVs (in Table 1 ), and assuming a circular orbit, gives an orbital solution period of 0.541089 ± 0.000020 d (21.39 μHz), amplitude of 85 ± 2 km s −1 , and phase of BJD = 2457099.74105 ± 0.00204 (top panel of Fig. 6 ). The eccentricity was subsequently fitted at 0.079 ± 0.028, showing it is negligible for our calculations. Using the values of K = 85 ± 2 km s −1 and P = 0.541 d from spectroscopy, the sdB canonical mass M1=0.47 and assuming i = 90 o , we get the minimum values for M 2 of 0.26 M ⊙ and for the orbital separation a = a 1 + a 2 = 2.52 R ⊙ . Of course we know this is not the inclination as no eclipses are evident in the light curve. Figure 6. Velocity and photometric data folded over the orbital period. The K2 data have been phase-binned into 72 bins with 1σ error bars shown. We attempted several phase-folding and binning combinations of the photometry to improve the period and phase, however the thruster firings, at roughly every six hours, and pulsations decrease the accuracy, and so the RV data are better for constraining the period. Still, the photometry show evidence of two-component variations, occurring at similar levels, in agreement with the FT. From the phasing of the variations, we can deduce the sources. A reflection-effect companion in the binary would produce a reflection-effect maximum, which would occur during a Doppler boosting zero-point (halfway between maximum and minimum) or an ellipsoidal-effect minimum. A Doppler boosting maximum would occur during an ellipsoidal-variable maximum. Figs 7 and 8 show the results of two-component fits to the folded light curve (described below). The phasing indicates that the components are Doppler boosting and ellipsoidal variations. These two components indicate that PG 1142 is most likely an sdB+WD binary. Figure 7. Orbital elements removed from the light curve. Top panel shows original folded and binned light curve. Orbital fits are indicated by lines with green being the combined fit, blue the ellipsoidal deformation, and red the Doppler boosting. Middle panel shows the Doppler-corrected light curve (with ellipsoidal deformation

O O O O O O O O O O O O O O O B-Telescope O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula O O O O O O B-Formula O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Mission O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


gives a power spectrum with the desired shape. We then inverse Fourier transform back to get the pink or red time stream. We then take samples with a positive value to contain a pulse and samples with a negative value to contain none. In the stationary Poisson case, the rate of bursts in the immediate follow-up is the same as the multiyear follow-up since all times are statistically equivalent. However, with flicker noise, the variance is strongly time dependent. If we imagine an object that repeated on average once per two hours, then if those pulses were Poisson-distributed, the probability of seeing zero bursts in 11.4 h or longer is ∼0.007. With pink noise, one expects this roughly 20 per cent of the time, since the system prefers either to be in ‘on’ or ‘off’ mode. If the average repeat period were more like 5–20 h, then we would often see nothing in a multiday follow-up observation that took place weeks or years after the initial event. This is consistent with what Petroff et al. ( 2015b ) saw, though the conclusions differ depending on the assumed statistics. In Fig. 1 , we show a sample from this simulation for three repeat distributions. The right-hand panel shows how, if an FRB's burst rate has long-term correlations (1/ f γ ), the likelihood of a repeat is greatly increased if the follow-up observation is immediately after the initial event, rather than months or years after. Figure 1. Realization of our mock follow-up Monte Carlo. Left-hand panel: power spectrum for pulse arrival times of a single FRB. Grey shows a flat spectrum, corresponding to the often assumed Poissonian repetition rate. The red and blue spectra show flicker noise, with pink (1/ f ) noise and Brownian (1/ f 2 ) noise, respectively. Right-hand panel: we found the first ‘event’ in our Monte Carlo (represented by a star) for the three different spectra and plotted their behaviour in the subsequent 48 h of follow-up. Though the average probability over the whole simulation is 0.5 for each distribution, when we zoom in on this short period, the strong time-like correlations in the 1/ f γ cases means there are many repetitions, they are in an ‘on’ state at this time. 2.2 FRBs 110220 and 140514 Using the event rate of roughly 10 4 sky −1 d −1 from Thornton ( 2013 ), it was originally reported that the probability of seeing a new FRB in the field of 110220 during the 85 h of follow-up was 0.32 (Petroff et al. 2015a ). It was then pointed out by Maoz et al. ( 2015 ) that this underestimated the coincidence by an order of magnitude, since they estimated the rate in any one of the 13 beams, while the new event occurred in the identical beam. The probability also dropped due to the updated daily event rate, given the Thornton ( 2013 ) estimate is now thought likely to be too high. In general, we expect the true rate of FRBs to be lower than what is reported due to non-publication bias. If archival data are searched and nothing is found, it is less likely to be published

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O B-CelestialObject O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


of any other considerations. The best-fitting central masses associated with smaller spins were systematically lower, but always with M > 9 × 10 8 M ⊙ . In general, smaller black hole spins produced poorer fits to the observed light curves. A Schwarzschild black hole (best-fitting mass M = 9 × 10 8 M ⊙ ) produced the worst fit,, and would require a 28.3 M ⊙ solar-type star for disruption (fig. 2, Kesden 2012 ). This makes a low spin value very unlikely. For larger spins, the quality of fit is similar to the near-maximal a / r g = 0.99 case. When a / r g = 0.9, the best-fitting light curve has , with a very similar best-fitting black hole mass M = 1.35 × 10 9 M ⊙ . However, even this slight reduction from maximal spin now requires an 8.3 M ⊙ star for a disruption, compared to M ⋆ = 2.6 M ⊙ for a / r g = 0.99. From the light curves alone, we cannot rule out the possibility of an extremely massive star being disrupted by a more moderately rotating black hole. The strong dependence of TDE rate on stellar mass ( as noted above) clearly favours a near-maximal spin. The light curves of Section 3 were produced assuming a face-on inclination. The best-fitting parameters are, in fact, only weakly sensitive to the disc–observer inclination, with only minor changes to the fitted parameters for θ 20 o . For higher inclination angles, larger black hole masses were required. Taking the uppermost black hole mass allowed from the galactic bulge range as a hard upper limit, we may constrain the inclination to θ 60 o . Given that a relatively massive (∼2 M ⊙ ) star has been disrupted, it is somewhat surprising that the disc component of the evolving light curves is powered by only a relatively small accreted mass M acc ≃ 0.07 M ⊙ . It is important to note that this accreted mass value does not include the matter required to power the (extremely bright) early-time emission (observed in all bands), or the late-time UV emission. Rather, the disc mass represents only a lower bound on the debris mass. Given the likely highly relativistic orbit of the disrupted star, it may well be that a significant portion of the stellar mass was directly accreted in the earliest stages. It has also been argued (Guillochon Ramirez Ruiz 2015 ) that relativistic orbital precession of the tidal disruption streams (induced by a large black hole spin) can lead to inefficient disc formation. 3.2 Radio and X-ray observations No radio emission has been detected from ASASSN-15lh, with upper limits of order ν L ν ≲ 10 38 erg s −1 ( L16 ; Kool et al. 2015 ). Given the likely near-maximal spin of its central black hole, it is perhaps surprising that a jet is not observed. [The observed radio emission is at least two to three orders of magnitude lower than the bright, jetted TDE Swift J1644+57 (Levan et al. 2011 ).] Moreover, unlike other jetted TDEs, ASASSN-15lh is X-ray dim. Initially undetected at X-ray energies ( L16 ), X-ray emission has been more recently detected by Margutti et

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