O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O B-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 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 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 O O O O

that gas outside halos, not necessarily following any given profile, also contributes to the signal. Furthermore, we would like to conduct an analysis that is as model independent as possible, and thus blind to any specific model for the gas spatial distribution. The correction by a redshift-averaged quantity introduced in the last equation above was justified by Hand et al. (2012) through the need to correct for possible redshift evolution of the tSZ signal in the sources. In practice, this correction allows us to measure relative changes in temperature anisotropies between nearby galaxy pairs after minimizing other noise sources, such as CMB residuals. Fig. 1 Absolute value of versus distance to the observer after obtaining AP kSZ temperature estimates on the real positions of CGs (black line) and on a rotated CG configuration (red line). The green line provides the theoretical expectation for the rms of , and the blue histogram displays the radial distribution of the CGs (see text for further details). We next conduct an analysis into the motivation behind this -dependent monopole correction. In Fig. 1 we display the amplitude of for versus the comoving distance to the observer . The value of the aperture chosen in this exercise is 8 arcmin. The black line refers to the real position of the CGs, while the red line refers to a rotated-on-the-sky configuration of the CGs. Since we are plotting absolute values of , the solid (dashed) parts of these lines refer to positive (negative) values of . The amplitude of these curves is close to the solid green line, which corresponds to the theoretical prediction for the rms of under the assumption that the AP temperature estimates are dominated by CMB residuals. That is, the amplitude of the green curve equals , where K is the rms of the 8 arcmin AP kSZ estimates and is the number of CGs effectively falling under the redshift Gaussian window given in Eq. ( 5 ). While K is computed from real data, its amplitude is very close to the theoretical predictions of Fig. 6 in Hernández-Monteagudo et al. (2006b) , for an angular aperture of 8 arcmin after considering the CMB exclusively. We can see that the amplitude of is lowest for those distances where the number density of CGs is highest (as displayed, in arbitrary units, by the blue histogram in Fig. 1 ). Therefore Fig. 1 shows not only that AP kSZ estimates are dominated by CMB residuals, but also that the difference in for CG pair members lying 50–100 Mpc away in radial distance typically amounts to few times K. We shall show below that this amplitude is not completely negligible when compared to the typical kSZ pairwise momentum amplitude between CGs at large distances, and thus subtracting becomes necessary. However, this should not be the case when cross-correlating AP kSZ measurements with estimates of radial peculiar velocities (see Sect. 3.2 below), since in this case the residual will not be correlated with those velocities and should not


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

that all star formation within Upper Sco has ceased. According to de Geus ( 1992 ) and Preibisch Zinnecker ( 1999 ), star formation in Upper Sco may have been triggered by a supernova-driven shock wave from a massive star in the parent Sco-Cen OB Association (see also Preibisch Zinnecker 2007 ; Slesnick et al. 2008 ). In this context, smooth star formation could occur over a long interval, followed by a supernova that triggers a burst, and subsequent quenching of star formation. 4.1. Comparing Synthetic Populations to the Known Upper Sco Members Our simulations of the star formation history of a cluster correspond to smooth star formation with no trigger (the Smooth-Quench model) and smooth star formation followed by a supernova trigger (Smooth-Burst model). Figure 11 compares the results of these simulations to the stellar population in Upper Sco for the Smooth-Burst model with parameters , , and A = 60, and for the Smooth-Quench model with and . Figure 11. The inferred age vs. temperature of stars in Upper Sco (black, standard deviation in gray dotted lines), compared to results from the Smooth-Quench (top) model, with and , and the Smooth-Burst model (bottom) with A = 60, , and . The shaded regions are the standard deviation from 1000 simulations. The dashed line shows the same results, but when all binaries are resolved. The Smooth-Quench model exhibits a temperature-dependent age measurement up to ∼6 Myr between KM stars and F stars, thereby accounting for half of the ∼12 Myr discrepancy (see Table 2 ). This simplest model demonstrates that an age spread of more than a few Myr in a young ( Myr) population will lead to a significant temperature dependence in age estimates. This qualitative result is required by the evolution of intermediate-mass stars from the Hayashi track to the Henyey track. Cool stars are young and have a median age that changes slowly. For stars with , the median age increases rapidly. At temperatures higher than , stars tend to be older and have median ages that change slowly. These simulation results are consistent with the age spreads of 4–5 Myr over a relatively large temperature range of cool stars (e.g., Herczeg Hillenbrand 2015 ), and with the ∼3 Myr age spread for G type and F type stars (Pecaut et al. 2012 ). Figure 11 shows that the Smooth-Burst model may explain entirely the empirical temperature-age relationship of Upper Sco. The burst increases the population of cool stars at the end of the star formation process, thereby maximizing the possible differences in ages between cool and hot stars. Some of the age difference between K-M type and F type stars may be attributed to the incomplete physics in the calculations of pre-main sequence evolution of low-mass stars (e.g., Feiden 2016 ), although these explanations may introduce problems into other clusters. However, the age difference between G type stars (9 ± 3 Myr) and F type stars (13 ± 1 Myr), as calculated by Pecaut et al. ( 2012 ), are not easily


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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 O O O O O O O O O O O O O O O O O B-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 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 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 B-Citation I-Citation I-Citation I-Citation I-Citation 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 O O O 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 O O O O O O O O O O O O O

the PCs would contain the changes. Materials that are detached from the surface, such as the surface-independent clouds in the case of the Earth, would also appear in one of the PCs if they have a large influence on the light curve. If these materials can be constrained by the reflection spectra, their fractions can be derived from the magnitude of the corresponding PC. Once the surface information is extracted from light curves, the surface map of the exoplanet can be recovered from the observational geometry without making any spectral assumptions. Aside from orbital elements, which can be determined from light curve observations, the only two geometry assumptions required for constructing the 2D surface map are the summer/winter solstice and the obliquity. The rotation period of a clear or partially cloudy exoplanet can be inferred from the power spectrum of PCs using a Fourier transform (Figure 3 (d)), which requires the observation frequency to be higher than that of the exoplanet’s rotation. Studies have been performed to identify a planet’s rotational period from light curves at different viewing geometries (e.g., Pallé et al. 2008 ). The summer/winter solstice would coincide with the maxima and minima of the PC time series as long as the asymmetry between the northern and southern hemispheres is noticeable, and the reflection changes monotonically with latitude when the sub-stellar point is near extremum. For the Earth, the peak of the time series of PC2 takes place on 2016 June 15 (Figure 3 (c)), which is within one week of the true value. The obliquity of an exoplanet could be derived through its influence on the light curves. A number of recent publications (e.g., Kawahara 2016 ; Schwartz et al. 2016 ) developed methods for deriving the obliquity using its influence on the amplitude and frequency of light curves. Although these inversion methods are mostly based on a cloudless Earth and known surface spectral features, our SVD analysis of separating clouds from the surface could fill the gap. Some issues exist in constructing and interpreting the retrieved Earth surface map. Degeneracy resulting from the convolution between pixel geometry and spectrum is the dominant factor affecting map construction quality. As discussed in Cowan Strait ( 2013 ) and Fujii et al. ( 2017 ), light curves only cover a small portion of the PC plane, which results in a trade-off between the spatial and spectral variation. Although only PC2 is used for constructing the surface map in this work, its time series covers only a small range of all valid values, whose corresponding land fractions are between 0 and 1. Therefore, we introduce a regularization parameter, λ , when constructing the map, to constrain the pixel values of PC2 within a reasonable range; the resulting effect is described in Appendix B . We select the value of λ based on the ground truth of Earth’s surface map. Glints, features that are small in area but contribute significantly to the


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 I-Citation O O O O O O O O B-CelestialObject O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O B-Wavelength O O O B-Telescope O O O O O O O B-Wavelength B-Wavelength O B-Wavelength O O O O O O B-CelestialObject O O B-CelestialObject 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 B-CelestialObject I-CelestialObject I-CelestialObject 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-CelestialObject I-CelestialObject O O O O B-Wavelength O O O B-Survey I-Survey I-Survey I-Survey I-Survey B-Survey B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Wavelength O O O O O O O O O B-Telescope I-Telescope I-Telescope I-Telescope O O O B-Telescope B-Instrument I-Instrument I-Instrument B-Instrument O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O B-Survey I-Survey I-Survey I-Survey I-Survey I-Survey B-Survey 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 B-Survey O O O O B-CelestialObject I-CelestialObject O O O O O B-Wavelength O O O O B-Telescope O B-Citation I-Citation I-Citation I-Citation O B-Survey O O B-Wavelength B-Wavelength B-Wavelength O B-Wavelength I-Wavelength O O O O O O B-Software I-Software I-Software B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Software I-Software B-Software I-Software I-Software O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Telescope O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O B-Wavelength I-Wavelength 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 B-CelestialObject I-CelestialObject O O O B-Telescope O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O B-Wavelength I-Wavelength O O O O B-Telescope B-Instrument O B-Wavelength B-Wavelength O B-Wavelength I-Wavelength O O O B-Telescope I-Telescope O O B-Wavelength B-Wavelength I-Wavelength O O O O O O O O O B-Observatory I-Observatory I-Observatory O O O 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 B-CelestialObject O B-CelestialObject I-CelestialObject O O O O O O O O O O B-CelestialObject I-CelestialObject O O B-CelestialObject O O O O O O O O O O O B-Wavelength O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O

arcmin away, in a low density environment (Cernicharo et al. 1998 ; Rosado et al. 1999 ; Yusef-Zadeh, Biretta Wardle 2005b ). Evidence of shocked gas associated with core TC1 has also been provided by Yusef-Zadeh, Biretta Geball ( 2005a ). Finally, Rho et al. ( 2004 ) reported the detection of 304 X-ray sources with the Chandra satellite, 70 per cent of which having near-infrared (near-IR) counterparts. X-ray emission was detected from within condensation TC1 and possibly TC4, two star-forming cores with bipolar wings and associated Class 0 candidates (Rho et al. 2004 ). A recent comprehensive review of the Trifid star-forming region has been presented by Rho et al. ( 2008 ). In order to study in detail the principal star-forming cores within M 20, we present here new far-IR images from the Herschel Infrared Galactic Plane Survey (HI-GAL; Molinari et al. 2010 ), combined with a new set of deep near-IR images obtained through broad- and narrow-band filters from the Calar Alto 3.5-m telescope. In addition, archival Spitzer Infrared Array Camera (IRAC) images (Fazio et al. 2004 ; Werner et al. 2004 ), part of its Galactic Legacy Infrared Midplane Survey Extraordinaire (GLIMPSE) survey (Benjamin et al. 2003 ), are used to supplement these observations. The observations are described in Section 2 , whereas in Section 3, we present the results and discussion. Finally, Section 4 lists our conclusions. 2 OBSERVATIONS AND DATA ANALYSIS 2.1 HI-GAL images and photometry The Trifid nebula has been observed in the far-IR as part of the Herschel satellite (Pilbratt et al. 2010 ) HI-GAL survey at 70,160, 250, 350, and 500 μm. The images were reduced using the HI-GAL standard pipeline (Traficante et al. 2011 ). From these, source extraction and photometry were performed using the CuTEx package (Curvature Threshold Extractor), independently at each band (Molinari et al. 2016 ). Fig. 1 (lower right-hand panel) illustrates the Herschel three-colour image of an area of 12 × 12 arcmin 2 around the Trifid nebula, composed from the 70 μm (blue), 160 μm (green), and 250 μm (red) single images. Figure 1. 12 × 12 arcmin 2 (7.0 × 7.0 pc) colour-coded images of the Trifid nebula. Lower right-hand panel: Herschel at 70 μm (blue), 160 μm (green), and 250 μm (red); lower left-hand panel: Spitzer /IRAC at 3.6, 4.5 and 5.8 μm; upper left-hand panel: CAHA 3.5m in the JHK s bands; upper right-hand panel: a visible public image from the European Southern Observatory. All images have the same scale and are centred at the same position. The white contours are from the Herschel 160 μm frame. The white labels indicate the TCs that were studied in this work. The yellow arrows indicate the location of the early-type trapezium system HD 164492, which ionizes the H ii region, and the Herbig–Haro jet HD 399 associated with TC2. The brightest dense cores have been associated with those found at millimetre wavelengths (Lefloch et al. 2008 ) as labelled in Fig. 1 . In addition, filamentary


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We are grateful to J. Chen, J. Delabrouille, Z. Huang, J. Liu, X. Tong, L. Xue, D.-G. Wang, Z. Wang, and S.-Y. Zhou for valuable discussions. We also thank the anonymous referee for constructive comments. Y.F.C. and J.J. are supported in part by the NSFC (grants No. 11653002, 11722327, 11421303, J1310021), by the National Youth Thousand Talents Program of China, by the CAST Young Elite Scientists Sponsorship Program (2016QNRC001), and by the Fundamental Research Funds for the Central Universities. Q.Y.L. is supported in part by the Department of Physics Astronomy at the University of Pennsylvania. Y.Z. is supported in part by the NSFC (Nos. 11675165, 11633001), the CAS Strategic Priority Research Program “The Emergence of Cosmological Structures” (No. XDB09000000) and SRFDP. All numerical computations are operated on the computer clusters “ Linda Judy ” in the particle cosmology group at USTC.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation 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 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 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-Citation I-Citation I-Citation O B-Citation I-Citation O B-Citation I-Citation 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 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 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 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 B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation 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 O O O O O O O O O O O O O O O O O O O O O O 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 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 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 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

to 1.99 × 10 −18 cm 3 s −1 for temperatures ranging from 300–14 000 K, respectively, and can be approximated (within 7 per cent) as for temperatures between 300 and 1000 K and for temperatures higher than 1000 K. Because we do not take into account the fine structure of the phosphorus atom (∼227 cm −1 ), our predicted rate coefficients are uncertain at temperatures lower than about 327 K. Moreover, the B 2 Σ + state has a barrier against dissociation into P( 4 S) + O( 3 P). This has already been seen in the theoretical works of Liu et al. ( 2013 ) and Izzaouihda et al. ( 2014 ). Due to the potential barrier, the rate coefficients decrease rapidly at low temperatures. However, the height of the barrier is about 2416.49 cm −1 at 4.8 a 0 , which is about 508.66 cm −1 lower than the value reported by Liu et al. ( 2013 ). Also, the barrier in our PO B 2 Σ + potential appears to be significantly lower than the one shown in fig. 1 of Izzaouihda et al. ( 2014 ). The uncertainty in the barrier height results in a significant uncertainty in the rate coefficients at low temperatures. Other sources of error at low temperatures are quantum mechanical effects such as tunnelling and shape resonance (Bain Bardsley 1972 ; Smith 1989 ; Gustafsson 2013 ). At 300 K, quantum mechanical calculations (Antipov et al. 2009 ; Franz, Gustafsson Nyman 2011 ) show that the classical calculations (Dalgarno, Du You 1990 ; Singh et al. 1999 ; Singh Andreazza 2000 ) underestimate the rate coefficients by about 25 per cent and one order of magnitude for CN (Singh Andreazza 2000 ) and CO (Dalgarno et al. 1990 ; Singh et al. 1999 ) formation, respectively. At temperatures higher than 1000 K, the quantum mechanical (Antipov et al. 2009 ; Gustafsson 2013 ) and semiclassical (Dalgarno et al. 1990 ; Singh et al. 1999 ; Singh Andreazza 2000 ) rate coefficients are in good agreement. In these studies, CN and CO formation was assumed to occur mainly through the A 2 Π and A 1 Π states, respectively. The former potential curve has no barrier, while the latter shows a potential hump. In semiclassical studies, Dalgarno et al. ( 1990 ) and Singh et al. ( 1999 ) used the same set of potentials for the A 1 Π and X 1 Σ + states of CO and different transition dipole moment functions. The rate coefficients obtained by these authors are in agreemnet with each other. However, in quantum mechanical calculations, Franz et al. ( 2011 ) used a different set of potentials with a low barrier height for the A 1 Π state of CO. For CO, the resonance contribution to the rate coefficients arises from quantum mechanical tunnelling through the barrier (Franz et al. 2011 ). At low temperatures, both quantum mechanical and semiclassical theories depend strongly on barrier height. As previously mentioned, the uncertainty in barrier height results in a significant uncertainty in the rate coefficients at low temperatures. Considering all these effects, mainly the uncertainty in barrier height, it is likely that


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 B-CelestialObject O O B-CelestialObject 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 O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O B-CelestialObject O O 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 O O O 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-CelestialObject O O O O O B-CelestialObject O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength

of orders of magnitude (Dong et al. 2018b ), thereby potentially attaining values as high as ∼0.1 mJy for weak magnetic fields. 3.2. Atmospheric Escape Next, we direct our attention to the central issue of atmospheric ion escape facilitated by the stellar wind in conjunction with the stellar radiation. Figure 2 depicts the pressure balance arising from the stellar wind–planet interactions. The first and second columns present the unmagnetized Venus-like and magnetized Earth-like cases, respectively. As a result of the supermagnetosonic nature of the stellar wind at TOI-700 d, bow shocks are formed ahead of this planet, regardless of the inclusion of the planetary magnetic field. Compared to the unmagnetized Venus analog, the presence of the global magnetic field results in a larger interaction cross-section with the stellar wind for the magnetized Earth-like case. An inspection of the bottom panels of Figure 2 reveals that the planetary magnetosphere (or induced magnetosphere for unmagnetized cases) is compressed, and the total pressure becomes intensified due to the stronger stellar wind pressure. Figure 2. Logarithmic scale contour plots of the total pressure ( P total , units of nPa)—the sum of the ion ( P ion ) and electron ( P electron ) pressure—in the meridional plane based on the stellar wind conditions at P min (first row) and P max (second row). The first column shows the unmagnetized Venus-like case, while the second column depicts the magnetized Earth-like case. The salient results concerning atmospheric escape are depicted in Figure 3 , which shows the calculated oxygen ion density with the associated magnetic field lines in the meridional plane for all six cases. This figure yields some general conclusions. To begin with, as seen from Table 1 , we note that O + constitutes the dominant ion species undergoing escape for all configurations considered here. The atmospheric oxygen escape rates vary from s −1 to s −1 , indicating that they are higher by a few orders of magnitude than the typical escape rates of ) s −1 for the terrestrial planets in our solar system (e.g., Dong et al. 2017b , 2018c ). Figure 3. Logarithmic scale contour plots of the O + ion density (units of cm −3 ) with magnetic field lines (in white) in the meridional plane based on the stellar wind conditions at P min (first row) and P max (second row). The first column shows the unmagnetized Venus-like cases, whereas the second and third columns depict the unmagnetized and magnetized Earth-like cases. Let us first compare the unmagnetized cases, namely, the first and second columns. We find that the Earth-like case exhibits a stronger and broader flux of escaping O + compared to the Venus-like case; this result is also consistent with the atmospheric ion escape rates shown in Table 1 . The reason chiefly stems from the fact that the upper atmosphere of a Venus analog is cooler than its Earth-like counterpart due to the efficient CO 2 cooling caused by 15 μ m


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

(some works on this topic are Uitenbroek 1989 ; Uitenbroek Bruls 1992 ; Belluzzi Trujillo Bueno 2014 ; del Pino Alemán, Casini Manso Sainz 2016 ). However, in the case of the K i lines it seems that this effect is very weak even at extremes heliocentric angles (see the results for the K i D 1 line presented in Uitenbroek Bruls 1992 ). Still, we study the PRD effects for both K i lines using the FALC model [in the previous work the VALC model (Vernazza, Avrett Loeser 1981 ) was used instead]. In this regard, we plot in Fig. 3 the results for the K i D 1 (left) and D 2 (right) lines. For the latter case, we also included the neighbouring photospheric Fe i line (see label 4 in Table 1 ) as it is relatively close. We can see that, for all the selected heliocentric angles, the differences between the computed PRD and CRD profiles are negligible (see the bottom part of each plot). This is in agreement with the results of Uitenbroek Bruls ( 1992 ) and indicates that PRD effects are very small for these lines, at least for the intensity spectrum. Figure 3. PRD (solid) and CRD (squares) profiles for the K i D 1 D 2 lines (we also included the neighbour Fe i line for the latter case). Colours indicate the selected heliocentric angle (larger μ corresponds to an LOS closer to the disc centre and to higher continuum intensity). In addition, we show the difference between PRD and CRD profiles in the bottom of each panel. 3.2 NLTE effects In previous works related to the alkali lines as in Bruls et al. ( 1992 ) it has been demonstrated that the K i D 1 line, in particular its line core, is sensitive to NLTE effects. In other words, the LTE assumption is unable to reproduce the observed line depth. In this section, following the steps of the previous one, we check if the same occurs for the K i D 2 line and also revisit the studies of the K i D 1 line with the FALC model. In addition, as the results of the previous section revealed that PRD effects are negligible for the K i lines, we also compute the differences between NLTE and LTE for the polarization spectrum. We show in Fig. 4 the comparison between an NLTE and an LTE computation for the K i lines (the Fe i is always computed in LTE) assuming a heliocentric angle μ = 1. If we look at the first column, we can see that the line core in case of the NLTE computation (pink) is much deeper than for the LTE case (black). This happens for both potassium lines; the K i D 2 line is very deep with a line core intensity (in NLTE) of almost 0.1 of I c . Moreover, if we examine the rest of the columns, we also find differences between the NLTE and LTE polarimetric signals, the latter always with less amplitude. This is an interesting result that points out the necessity of an NLTE treatment for both the intensity and the polarization spectrum. Finally, we can see that these differences also affect additional spectral features as the Stokes V asymmetries. We plot in Fig. 5 the Stokes V LTE and NLTE profiles for both K


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P.N. acknowledges the support of the Royal Society through the award of a University Research Fellowship, the European Research Council, through receipt of a Starting Grant (DEGAS-259586) and the support of the Science and Technology Facilities Council (ST/L00075X/1). N.B. acknowledges funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement No. 312725. L.D. and S.J.M. acknowledge support from the European Research Council Advanced Investigator grant, COSMICISM and Consolidator grant, cosmic dust. The H-ATLAS is a project with Herschel, which is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA. The H-ATLAS web site is http://www.h-atlas.org/ . Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the US Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/ . SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University.


O O O O O O B-CelestialObject I-CelestialObject 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 B-CelestialObject O O O O O O O O O O O B-Instrument O O O B-Observatory O O 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 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 O O O O O O O O O O B-CelestialObject 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O B-Citation I-Citation O B-Citation I-Citation O B-Citation I-Citation 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 B-ObservationalTechniques I-ObservationalTechniques 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 I-Citation I-Citation O O O O O O O O O O O O O O O O O O B-Model I-Model B-Model O B-Citation I-Citation O O O O B-Model B-Citation I-Citation I-Citation I-Citation O B-Citation 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 O O B-Tag 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 O O O O B-Citation I-Citation

uranium, in the very metal-poor star BPS CS31082-001. This star, also called Cayrel’s star, was found to be more metal deficient than the globular clusters, and was likely born in the Galaxy during very early times. This measurement, carried out with the high-resolution UVES spectrograph of the ESO/VLT telescope, gave rise to the determination of the age of formation of U and Th in the early Galaxy, using, for the first time, the U/Th ratio. The derived uranium abundance yielded an age 12.5 ± 3 Gyr, which led to the best estimate of the age of the Galaxy and consequently provided a lower limit to the age of the Universe. However, as mentioned by Cayrel et al. ( 2001b ), the accuracy of this uranium dating is still affected by uncertainties in the measured abundance ratio, and in the calculated U/Th production ratio. The improvement of this situation depends not only on a better estimation of the production ratio U/Th, on advances in nuclear astrophysics models and on the investigation of other stars in which U and Th can be detected, but also on a comprehensive knowledge of the radiative properties for the potentially observable spectral lines, notably for the strongest U ii electric dipole transitions. To our knowledge, there have been very few available calculations of radiative parameters for singly ionized uranium so far. The main reason is that the complexity of the strongly mixed states involved in the lowest configurations, with five electrons distributed on the 5f, 6d, 7s, and 7p subshells, and the fragmentary knowledge of the experimental spectrum of this ion made theoretical computations extremely difficult. Most of the available oscillator strengths were deduced from quite old line intensities measured on arc spectra (Meggers, Corliss Schribner 1961 , Corliss Bozman 1962 , Voigt 1975 , Corliss 1976 , Kurucz 1995 ) if we except the results published by Nilsson et al. ( 2002 ) who obtained accurate gf values by combining branching fraction measurements with laboratory lifetimes determined using laser spectroscopy (Lundberg et al. 2001 ). These latter data concern however only a small number of strong U ii lines. This lack of reliable radiative parameters in singly ionized uranium justifies the work reported in this paper. An additional motivation was also found in the new analysis of the experimental spectrum recently published for this ion by Meftah et al. ( 2017 ). More precisely, we carried out detailed calculations of oscillator strengths for the strongest U ii transitions using the pseudo-relativistic Hartree-Fock (HFR) method (Cowan 1981 ) with core-polarization corrections (HFR+CPOL; Quinet et al. 1999 , 2002 , Quinet 2017 ). This allowed us to draw up a list of 38 visible spectral lines that could be used in cosmochronology. 2 AVAILABLE ATOMIC DATA IN U <sc>ii</sc> In their critical compilation related to actinides, Blaise Wyart ( 1992 ) listed some preliminary U ii energy levels, using the emission lines listed by Steinhaus et


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 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 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 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 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 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 O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation 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 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 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 B-Citation I-Citation I-Citation I-Citation 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 B-Citation I-Citation I-Citation O O O O O O O O O O O O

brought by these results on asymmetric jet launching models. Lovelace et al. (2010) , Dyda et al. (2015) and Lii et al. (2014) have all studied the launching of asymmetric outflows from the magnetospheres of rapidly rotating stars in the propeller regime. They find that the presence of a small dipole component leads to the formation of one-sided accretion funnel flows accompanied by episodic outflows in the opposite hemisphere. The dominant direction of ejection changes stochastically on timescales of ≃30–50 inner disk orbital periods. The inclusion of a disk magnetic field does not significantly affect these results ( Dyda et al. 2015 ; Lii et al. 2014 ). On longer timescales, the jets will therefore look essentially symmetric. Such models therefore cannot account for the velocity asymmetry sustained over typically an order of magnitude longer timescales observed in the DO Tau bipolar jet. A more promising scenario is provided by recent numerical works studying the launching of outflows from magnetised disks. If originating from an MHD disk-wind, a difference of a factor 4 in launching radius would account for a difference of a factor 2 in terminal velocities. Alternatively, different lambda values could be achieved between the two surfaces of the disk. The pioneering studies of Fendt Sheikhnezami (2013) and Dyda et al. (2015) , using a simplified α prescription for the disk viscosity, have shown that indeed asymmetric high velocity jets can develop and endure over long lasting timescales, ≃ a few hundred orbital timescales at the inner disk radius, depending on the disk magnetic properties. Bipolar jet velocity asymmetries of up to a factor 2–2.5 are observed in such models. Recent global non-ideal MHD simulations of magnetised disks, including more comprehensive disk microphysics and evolving both hemispheres, have confirmed these early results and shown that pronounced asymmetries between the lower and upper disk halves of the disk can develop and launch asymmetric outflows which persist over timescales of at least 1000 times the orbital period at the inner disk radius ( Béthune et al. 2017 ; Bai 2017 ; Gressel et al. 2020 ; Riols et al. 2020 ). However, most of these recent simulations do not currently include the very central regions of the disk ( r ≤ 1 au) from which the high-velocity jets are launched. 4.3 The origin of jet axis wiggling As seen in Sect. 4.1 , the DO Tau bipolar jet shows a quasi-sinusoidal small amplitude wiggling of its axis. Similar wiggling has been recently revealed at the base of other T Tauri jets (e.g. Dougados et al. 2000 ; Anglada et al. 2007 ; Garufi et al. 2019 ). This wiggling is often interpreted as tracing the dynamical perturbation due to an unseen companion. A companion can induce wiggling of the jet axis in two different ways. The first one is orbital motion of the jet source ( Masciadri Raga 2002 ; hereafter ‘orbital scenario’). Alternatively, a mis-aligned companion can cause retrograde precession


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Dataset I-Dataset 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 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 O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

fact that we do not know the interstellar reddening for most of these stars, and that the assumed spectral types were only derived on the basis of their photometric indices (i.e. a kind of lower limit). However, the stars having early spectral types have mostly been studied during the last century, and it is only during the last decades with the use of large telescopes did the focus of stellar astronomers shift to the more late and fainter systems. We also have more systems with longer orbital periods (> 30 d) than appear in Bulut Demircan (2007) . Fig. 3. Distribution of omega angles with respect to the eccentricity. We can also address the issue of selection effects for our sample of stars. These “serendipitous” discoveries should be more likely detected as eccentric when the two minima are displaced from their positions 0.0 and 0.5 in phase diagram, but the binaries which have ω close to 90° or 270° should be only rarely detected. This can more easily be done when the photometry is sufficiently precise and also when the eccentricity is higher (i.e. the durations of both eclipses are significantly different). Hence, we tried to test this distribution of ω versus eccentricity in our Fig. 3 . One can see that the diagram is almost uniformly covered with data points, but the number of systems with higher eccentricity is still rather low (see Sect. 4 ). 4. Period eccentricity relation The diagram which should be discussed in more detail is the period-eccentricity distribution of our systems. We plotted our results together with those already published before by Bulut Demircan (2007) and also with the spectroscopic binaries from the SB9 catalogue by Pourbaix et al. (2004) in the Fig. 4 . As can be seen, orbital circularization plays a role in binaries with shorter periods ( Raghavan et al. 2010 , Duchêne Kraus 2013 ), while practically all systems that have periods below one day are already circular. Besides the plotted observed data we have also plotted several solid lines representing the limits of very close periastron approaches of both components (i.e. 1.5 × R ⋆ ) when these likely collide with each other. These periastron distances were computed for different spectral types (B to M) according to their typical radii and masses (see Zombeck 1990 ) with the assumption that both components are similar to each other (same masses and radii). As we can see, the sample of eclipsing apsidal motion systems has increased significantly with our new data set and should be very helpful in future when analysing the P-e diagram in detail. However, we still have to be very careful when interpreting these results with our new data. For some systems a significant change of eccentricity could appear for the case when the star still has poor data coverage of both light curve and the O–C diagram. The P-e diagram still lacks of such systems which have significant eccentricity close to its upper limit for a particular period. The system with the highest


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need of high angular resolution observations to robustly discriminate different flavours of magnetically regulated collapse models, since an hourglass at large scales can arise from different initial conditions, and outcomes of the protostellar accretion process. The B335 case could be more similar to the L1157 one if L1157 would be observed at similar physical scales (50 au), although our B335 ALMA map does not show a clear complete hourglass morphology at the envelope scale as the one observed in L1157. This is due to a combination of distance (L1157 is 2–3 times farther than B335), and filtering of the extended emission from the lower column density outer envelope, in our ALMA observations. L1527 in Taurus is another case of protostar seen almost perfectly edge-on, although it is probably more evolved than B335 (Chen et al. 1995 ; Ohashi et al. 1996 ). In L1527, the 1.3 mm polarized continuum at scales of 500–1000 au shows a magnetic field mostly aligned along the equatorial plane (Hull et al. 2014 ; Segura-Cox et al. 2015 ), while at larger scales it is roughly aligned with cavity walls (Davidson et al. 2014 ). This source has a larger disc radius, ≃60 au, and rotation is detected (Ohashi et al. 2014 ). Segura-Cox et al. ( 2015 ) use this example to suggest the topology of the B-field lines could be a method to help identify candidate Class 0 disc sources with R > 10 au because a transition from poloidal to radial field in the equatorial plane should be detected only in the sources where large rotational energy led to the formation of large discs: our observations of an equatorial component in B335, which harbours no disc at R > 10 au, challenge this simple view, and we suggest both strong pinching and strong coiling of the field lines can produce such a pattern. We also stress that inclination effects (B335 is an isolated edge-on source) and a simple environment might (i) help to enhance the detection of the strongly pinched magnetic field in the equatorial plane, and (ii) identify whether the magnetic field is regulating the evolution of the collapsing matter. For example, in more dynamic and/or clustered environments, polarization studies do not always reveal hourglass shapes, nor well-organized fields (Zhang et al. 2014 ). Among the few other cases where the magnetic field has been resolved well enough, the Serpens protostar SMM1 observed with ALMA (Hull et al. 2017 ) shows a complex magnetic field morphology, although mostly aligned with the outflow's cavity. 5 CONCLUSIONS Our ALMA 233 GHz polarized dust emission map shows a well-organized pattern at scales 50–500 au, mostly distributed along two structures: the pronounced east–west outflow cavity walls where the field is aligned with the outflow direction and reminiscent of the large-scale east–west native field, and the high-density equatorial plane where the field line segments appear to be mostly aligned with the equatorial plane. Because observations suggest there is only room for


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This research was supported by NASA/ HST Guest Observing grant #14277 (PI: JTS). B.D.O.’s contributions were supported by a NASA/ HST Archive/Theory grant #14308. Facilities : HST /COS, WIYN, APO 3.5m.


O O O O O O O B-Grant I-Grant O O B-Organization I-Organization O O O O O O B-Organization I-Organization B-Grant I-Grant I-Grant O O O B-Grant I-Grant I-Grant I-Grant O O O B-Organization I-Organization I-Organization I-Organization B-Grant I-Grant I-Grant O O O O O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility O O O B-Organization I-Organization O O B-Organization I-Organization I-Organization O O O O O B-Person I-Person B-Person I-Person O B-Person I-Person

The research has been sponsored by an Odysseus grant of the FWO Vlaanderen. The results were obtained in the KU Leuven GOA project GOA/2015-014 and by the Interuniversity Attraction Poles Programme initiated by the Belgian Science Policy Office (IAP P7/08 CHARM). Part of the simulations used the infrastructure of the VSC—Flemish Supercomputer Center, funded by the Hercules Foundation and the Flemish Government—Department EWI. We acknowledge fruitful discussion with Hugh Hudson, Yang Guo and Patrick Antolin.


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

the text. A close examination of Figure 1 discloses that all UVBs evolve with time and most UVBs last for several minutes. In particular, we note that UVB 8, when viewed in Figure 1 (e), appears to be one larger UVB, while when it is viewed in Figure 1 (d) 68 s earlier, it appears to be two closely related but seemingly separate UVBs. UVB 7 appear to last for the shortest time: slightly more than one minute. Figure 1. Panels (a)–(f): time series of IRIS SJI 1400 A logarithmic intensity (DN/s). All panels are normalized between 0.1 and 1000 DN/s, with black being the lowest intensity and white being the highest intensity. The preceding/next three slit positions for each plot are marked with dotted lines. The contours mark the identified UVBs where the intensity is a factor of 24 above the image median. We enumerate the UVBs that have been measured by the slit. Each UVB’s number is mark on top of itself. Table 1 UVBs with Spectrogram (SG) Measurements Notes. If more than one UVBs are observed at a time on the slit, we enumerate them from the top to the bottom along the slit. a We refer to Figure 1 SJI image panels (a)–(f) to denote slit position in this table. If there is no corresponding SJI image at a SG data time, the preceding/next SJI image is referred to. The slit position is subsequently noted as the ±(1–3) slit position of that SJI image. For example, “a+2” means that the corresponding slit position is along the second dotted line to the right of the slit position in Figure 1 (a), and “b−2” means that the corresponding slit position is along the second dotted line to the left of the slit in Figure 1 (b). Note that “a+2” and “b−2” mark the same slit position, likewise “b+1” and “c−3” also mark the same slit position. b Each UVB’s position along Solar-Y is taken from the center (highest intensity) of the UVB as measured by the slit. Figure 2 is an overview of UVB 1's optically thin Si iv 1393.78/1402.77 A lines. Note that the Si iv 1394 A/1402 A ratio can be used to test whether the ion is formed under optically thin or thick conditions. A ratio close to 2, which is the case for the UVBs studied in this paper, is compatible with the lines being optically thin (e.g., Peter et al. 2014 ; Yan et al. 2015 ). However, optically thick lines can still have a ratio of about 2, so one cannot use the line ratio to conclusively state that the lines are optically thin. Panels (a) and (b) show that the UVB has remarkably intensive brightening and broadening of the Si iv lines, being orders of magnitude brighter in spectral radiance and significantly wider in wavelengths than the background Si iv emissions. To form the Si iv line, one needs a temperature of at least ∼80,000 K (Peter et al. 2014 ) or higher. The strong brightening of this line indicate strong heating of the UVB region plasmas to ∼10 5 K. Note that there is a significant absorption line (Ni ii 1393.33 A) on the left wing of the 1393.78 A line, as seen before (e.g., Young et al. 2018 ).


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9 ) and ( 10 ), and then substituting into equations( 4 ) or ( 7 ) allows us to calculate the discrete terms. We now need to calculate the continuous terms. 2.2 Calculating the transition coefficients for the continuous terms The radial wavefunction of the hydrogen for the discrete R nl and the continuum state can be found in Landau Lifshitz ( 1981 ) and Bethe Salpeter ( 1957 ), where is the confluent hypergeometric function. Then, we can derive the transition coefficients required in equations( 4 ) and ( 7 ) from equations( 13 ) and ( 14 ) using with where m j 1 and j 3 in equations( 16 ) and ( 17 ), respectively, and denotes the m th derivative of the term in square brackets. The evaluation of equation( 18 ) for m 1 can be found in the textbook (Bethe Salpeter 1957 ). Evaluating the continuous term in equation( 7 ) evidently requires evaluating equations( 16 ) and ( 17 ). The latter involve summations over j up to ( n f l 1). Since in principle n f , practical computation forces us to assess the number of summation terms required in order to reach a sufficiently accurate convergence. The transition amplitudes are given by equations( 4 ) and ( 7 ) and the overall continuum term is the sum of the Rayleigh and Raman continuum states, and , which are obtained from where as shown in equations( 4 ) and ( 7 ). Fig. 3 illustrates the rapid cross-section convergence by the fourth term in and with f 2, 3, and 4 s i.e. the green dotted curve is the one adopted. Figure 3. Illustration of the KHT absorption cross-section KHT (relative to Thomson scattering) for the first five lines in the Lyman series. The relevant KHT cross-sections are equations ( 57 ) and ( 58 ) and the Thomson cross-section is given in equation( 5 ). The purposes are (i) to illustrate that the continuous terms are of decreasing importance as more continuous terms are added, and (ii) that the same is true down the Lyman series. Hence, we are justified in simplifying (i.e. truncating) the series calculation for continuous terms, as described in Section 2 . To more clearly distinguish between the various curves, the vertical scale cuts off the line centre (shown in later figures). Five curves are illustrated in each panel, in which all discrete terms are included, but the number of continuous terms is increased from zero to four: grey solid line: no continuous terms are included. ( ) is evaluated from equation( 8 ) with . Blue solid line: the most important continuous transition (Rayleigh scattering) is included (i.e. from initial state i 1 s to all continuous states and back to the final state, f 1 s ) such that ( ) is evaluated from equation( 8 ) with and keeping . Red dashed line: the first two continuous transitions are included (from initial state i 1 s to all continuous states, back to f 1 s and 2 s ) such that ( ) is evaluated with and , where is calculated from equation( 19 ) and the remaining for all possible states above 2 s . Yellow dotteddashed line: the first three


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ACKNOWLEDGEMENTS We thank Michael Zevin, Christopher Berry, and Moritz Hübner for helpful comments on the manuscript. This work is supported through Australian Research Council (ARC) Future Fellowships FT150100281, FT160100112, Centre of Excellence CE170100004, and Discovery Project DP180103155. This is LIGO Document P1900228.


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We thank the referee for a constructive report. BJS is supported by NASA through Hubble Fellowship grant HF-51348.001 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc. , for NASA, under contract NAS 5-26555 . TW-SH is supported by the DOE Computational Science Graduate Fellowship, grant number DE-FG02-97ER25308 . CSK is supported by NSF grants AST-1515876 and AST-1515927 . This paper used data obtained with the MODS spectrographs built with funding from NSF grant AST-9987045 and the NSF Telescope System Instrumentation Program (TSIP), with additional funds from the Ohio Board of Regents and the Ohio State University Office of Research. This paper is based on data acquired using the LBT. The LBT is an international collaboration among institutions in the United States, Italy, and Germany. LBT Corporation partners are: The University of Arizona on behalf of the Arizona university system; Istituto Nazionale di Astrofisica, Italy; LBT Beteiligungsgesellschaft, Germany, representing the Max-Planck Society, the Astrophysical Institute Potsdam, and Heidelberg University; The Ohio State University, and The Research Corporation, on behalf of The University of Notre Dame, University of Minnesota and University of Virginia.


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

rotational periods cannot be confidently measured because double-peaked and evolving light curves have been observed in many variable brown dwarfs to date (e.g. Apai et al. 2017 ; Vos et al. 2018 ). Longer duration follow-up observations are necessary to robustly measure the rotational periods of the variable objects detected in this survey. 5 SENSITIVITY TO VARIABILITY SIGNALS We construct a sensitivity plot for each observation to determine our sensitivity to variability signals of given amplitudes and periods. We inject simulated sinusoidal curves into random permutations of each target light curve. For targets found to be variable in the survey we divide the light curve by a polynomial fit to the light curve before injecting the simulated sinusoidal signals. The 1000 simulated sine curves have peak-to-peak amplitudes of and periods of 1.5−20 h, with randomly assigned phase shifts. Each simulated light curve is put through our periodogram analysis, which allows us to produce a sensitivity plot, showing thepercentage of recovered signals as a function of amplitude and period. Sensitivity plots for all light curves are shown in the bottom panel of Fig. 5 for variable objects and Fig. A3 (available online) for non-variables in the survey. Figure 5. Light curves, periodograms, and sensitivity plots for variable objects. Top panel: Relative photometry of target. Middle panel: Periodogram of target light curve (black) and periodograms of reference stars (grey). Blue dashed lines show the and significance thresholds. Bottom panel: Sensitivity plot showing the percentage of recovered signals for injected sinusoidal signals of various variability amplitude and periods. 6 SIGNIFICANT DETECTIONS OF VARIABILITY We detect significant variability in seven objects in the survey. Variable objects and their estimated variability amplitudes are presented in Table 2 . We present the light curves of these variable objects along with their reference stars in Fig. 4 . We show their periodograms and sensitivity plots in Fig. 5 . We discuss the first epoch variability detection of each object below. Table 2. Measured first epoch variability amplitudes for variability detections. 2MASS J00452143+1634446 – Gagné et al. ( 2014a ) classify the L2 object 2M0045+16 as a very low gravity brown dwarf, with H α emission and unusually red colours. It has been identified as a bona fide member of the Argus association (30−50 Myr), giving it an estimated mass of 14.7 ± 0.3 M Jup (Gagné et al. 2015a ), however recent work by Bell et al. ( 2015 ) has called into question the validity of the Argus association. We observed 2M0045+16 on 2014 November 11 using NTT SofI. We detect highly significant variability in this object at this epoch. The light curve of 2M0045+16 and the reference stars used for detrending are shown in Fig. 4 and the periodogram and sensitivity plots are shown in Fig. 5 . A lack of stars in the field resulted in only three references stars suitable for


O O O B-Telescope B-Survey O O B-Person I-Person I-Person O O O O O O O O O O O O O O O O O B-Person I-Person O B-Person I-Person O O O B-Person O B-Person O O O O O O B-Grant O B-Grant O O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Person O O O B-Organization O B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship O O O B-Organization I-Organization I-Organization I-Organization O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization O O O B-Grant I-Grant B-Person O O O O B-Location I-Location B-Grant I-Grant I-Grant I-Grant B-Organization O O O B-Grant I-Grant I-Grant O O B-Person I-Person I-Person B-Person O O O O B-Fellowship I-Fellowship O O O O O B-Organization I-Organization B-Organization B-Organization I-Organization I-Organization O B-Grant I-Grant I-Grant I-Grant B-Person O O O O O B-Collaboration I-Collaboration O O O B-Grant O O O B-Organization I-Organization I-Organization O B-Grant O O O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-Person B-Person O B-Person O O O O B-Organization O B-Location O O O B-Grant B-Grant B-Person O O O B-Organization B-Location O O O B-Organization B-Grant I-Grant B-Person O B-Person O O O O O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Person B-Person O B-Person O O O O O B-Location I-Location B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Grant B-Person O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Location O O B-Grant O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Grant B-Person O B-Person O O O O O B-Organization I-Organization I-Organization B-Organization O O B-Location I-Location B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Person O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship O O O O B-Organization B-Organization B-Grant I-Grant I-Grant O B-Organization I-Organization O O B-Organization I-Organization O O O O O O O O O O O O O O O O B-Observatory O B-Identifier B-Observatory O O O O B-Observatory O O O O O B-Location B-Organization I-Organization I-Organization B-Organization O B-Organization B-Location O O B-Organization B-Location B-Organization O B-Organization B-Location O B-Organization B-Location I-Location I-Location O O O O B-Location I-Location I-Location O B-Observatory I-Observatory I-Observatory O O O B-Observatory B-Organization O B-Observatory O O O O O O O O O B-Organization I-Organization I-Organization B-Organization O B-Telescope O B-URL O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-URL O O O O B-Organization O O O O O O O O O O O O O B-Collaboration I-Collaboration I-Collaboration O O O O B-Instrument I-Instrument I-Instrument I-Instrument B-Instrument O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O O O O B-Location B-Organization O O O B-Grant O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization O B-Organization O O O O O O B-Telescope I-Telescope I-Telescope O B-Observatory I-Observatory B-Observatory O O O O O O O O O O O O O O O O O B-Telescope O O O B-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Organization I-Organization O B-Software B-Citation I-Citation I-Citation I-Citation O B-Software B-Citation I-Citation I-Citation I-Citation O B-Software B-Identifier I-Identifier 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 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 B-Citation I-Citation I-Citation I-Citation O B-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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation I-Citation O O O O B-CelestialObject O O O O O O O O O O O O O

region (see panel a of Fig. 8 ). This chemical interface induces a bump in at (panel a of Fig. 9 ). This interface also affects the shape of the Lamb frequency. In the case of white dwarfs with carbon-oxygen cores, the internal chemical structure is substantially more complex than in the case of the helium-core white dwarf models (see panels b, c, and d in Fig. 8 ). This results in a much more complex form of the run , as can be seen in panels b, c, and d of Fig. 9 . Indeed, in these cases, the Brunt-Väisälä frequency is characterized by additional maxima induced by the presence of the C/O-He and C/O chemical interfaces. Fig. 9 Propagation diagrams, the spatial run of the logarithm of the squared Brunt-Väisälä and Lamb frequencies (Unno et al. 1989 ), corresponding to the white dwarfs models shown in Fig. 8 for . The number and shape of the chemical interfaces present in the interior of DA white dwarf models strongly affect the propagation properties of nonradial pulsation modes, in particular through mode trapping and confinement ( Brassard et al. 1992 ; Bradley 1996 ; Córsico et al. 2002 ). Mode trapping or confinement results in a strong departure from uniformity of the forward period separation, (), when plotted in terms of the pulsation period , where is the radial order of the mode. Thus, the period difference between an observed mode and adjacent modes can be considered as an observational diagnostic of mode trapping. For a helium-core white dwarf, which is characterized by a single chemical interface such as that of the model of mass considered here, local minima in usually correspond to modes trapped in the hydrogen envelope; this is in contrast to local maxima in , which are associated with modes trapped in the inner core. The forward period spacing for modes in terms of the periods corresponding to the helium-core model of mass is depicted in panel a of Fig. 10 . We also show the asymptotic period spacing, computed as in Tassoul et al. (1990) , with a dotted blue line. Mode-trapping signatures are clearly noticeable, particularly for periods shorter than 1500 s. Longer periods seem to fit the asymptotic predictions, although small departures from constant period spacing are still clearly seen. In the case of white dwarfs with carbon-oxygen cores, the presence of multiple chemical transition regions causes much more complex patterns of mode-trapping/confinement, as can be seen in panels b, c, and d of Fig. 10 . In particular, strong departures from uniform period separation are evident for the models with , , and . These features persist for the entire range of periods analyzed here. Also, we note some “beating” modulating the amplitudes of the departures of . This beating is due to the combined mode-trapping and confinement effects caused by the various steps in the C/O profile in the core; see Córsico Althaus (2006) for the case of PG1159 star models. Clearly, the mode trapping and confinement features of models with C/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 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-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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion 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 I-Citation O B-Citation O B-Citation I-Citation I-Citation I-Citation O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Model I-Model 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 O 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 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 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 B-Citation I-Citation I-Citation I-Citation O O O O O O O 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 O O O O O O O O O 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 O O O O O B-Wavelength O O O O O O O O O O O B-Wavelength O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O B-Formula I-Formula I-Formula I-Formula I-Formula 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-Wavelength 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O B-Wavelength 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 B-Model I-Model I-Model 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

Fig. 7 ). Figure 7. The surface density profile (top panel) and the K -band luminosity function (bottom panel) of early- and late-type stars in the Galactic Centre. The points mark the stellar number counts in distance and magnitude bins, as indicated by the horizontal error bars, and the vertical error bars indicate Poisson standard errors of the bin counts. For model fitting, the unbinned values are used (see Section 4.2 ). We can reproduce and confirm the results of Buchholz et al. ( 2009 ) and other studies of the spatial distribution of stars in the Galactic Centre (e.g. Paumard et al. 2006 ; Bartko et al. 2009 ; Do et al. 2009 , 2013 ; Lu et al. 2009 ). Following Do et al. ( 2013 , appendix E), we determine the respective surface density profiles by means of Bayesian inference, using a power-law profile as a model (Σ ∝ R α ). This approach does not require binning the star counts, and allows taking into account the estimated class membership probabilities as weights. For the late-type stars, we find a rather flat density profile (α = −0.33 ± 0.05), which appears essentially core-like towards the very centre. This still presents a puzzle, because these stars are old enough to be relaxed and would be expected to form a significantly steeper Bahcall Wolf ( 1976 ) cusp in that case (−0.75 α −0.5, but see Gallego-Cano et al. 2018 ; Schödel et al. 2018 ). For the early-type stars, we find a broken power-law profile with a turnover radius at about 10 arcsec, which we interpret as the outer edge of the young stellar disc (see Støstad et al. 2015 ). Within that radius, the surface density profile has a well-defined index of α = −0.83 ± 0.10, or α = −1.00 ± 0.15 if we exclude the central S-star cluster (at R 1 arcsec). Beyond that radius, the number of early-type stars drops rapidly. We can also reproduce the results of previous studies focused on the stellar K -band luminosity function (KLF). For the late-type stars with K 14.5, i.e. if we exclude red clump stars, we find a KLF well-described by a relation N ∝ 10 β K with an index of β = 0.36 ± 0.02, which is similar to that of the Galactic bulge (e.g. Genzel et al. 2003 ; Buchholz et al. 2009 ). The KLF of the early-type stars appears to be top-heavy in the disc region (1 arcsec ≲ R ≲ 10 arcsec), as also found by Paumard et al. ( 2006 ), Buchholz et al. ( 2009 ), and Bartko et al. ( 2010 ). The question of whether the KLF of these stars is indeed flat or somewhat steeper at the faint end, as found by Do et al. ( 2013 ), can likely be answered conclusively only on the basis of spectroscopic observations with a high completeness for B-stars over the entire region, which is currently only reached by deep imaging observations (e.g. ). 5 CONCLUSIONS For a proof of concept, we have constructed a machine-trained, random forest classifier to identify early- and late-type stars in the environment of the Galactic Centre black hole, based on intermediate-band photometry using seven filters in the


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We thank Tetsu Kitayama and Daichi Suto for providing us with simulated data points that are presented in Figure 8 . We thank the anonymous referee for providing constructive suggestions that lead to the improvement of this paper. K.U. acknowledges support from the Ministry of Science and Technology of Taiwan (grants MoST 103-2112-M-001-030-MY3 and MoST 106-2628-M-001-003-MY3) and from the Academia Sinica Investigator Award. M.S. acknowledges financial support from the contracts ASI-INAF I/009/10/0, NARO15 ASI-INAF I/037/12/0, ASI 2015-046-R.0, and ASI-INAF n.2017-14-H.0. J.S. was supported by NSF/AST-1617022. M.M., M.S., S.E., J.S. acknowledge support from the Italian Ministry of Foreign Affairs and International Cooperation, Directorate General for Country Promotion (Project “Crack the lens”). This work was made possible by the availability of high-quality lensing data produced by the CLASH survey. This paper made use of the code colossus (Diemer 2017 ) and the packages from Bocquet and Carter ( 2016 ) and Hinton ( 2016 ) for plotting. This work made use of the IPython package (Pérez Granger 2007 ), SciPy (Jones et al. 2001 ), TOPCAT, an interactive graphical viewer and editor for tabular data (Taylor 2005 ), matplotlib, a Python library for publication quality graphics (Hunter 2007 ), Astropy, a community-developed core Python package for Astronomy (Astropy Collaboration et al. 2013 ), NumPy (Van Der Walt et al. 2011 ).


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(host) galaxies are typically early-type (E/S0) galaxies, poor in gas (Whitmore, McElroy Schweizer 1987 ; Finkelman, Funes Brosch 2012 ; Reshetnikov Combes 2015 ). In contrast, the polar structures are generally younger, blue (e.g. Reshetnikov, Hagen-Thorn Yakovleva 1994 ; Iodice et al. 2002 ), with large amount (several times 10 9 M ⊙ ) of HI (e.g. van Gorkom, Schechter Kristian 1987 ; van Driel et al. 2000 ). Various scenarios have been proposed to explain the formation of the two kinematically and morphologically decoupled structures in PRGs: the capture of matter from an approached galaxy (Reshetnikov Sotnikova 1997 ; Bournaud Combes 2003 ), the merging of galaxies (Bekki 1997 , 1998 ; Bournaud Combes 2003 ), the misaligned accretion of matter from cosmic filaments (e.g. Maccio, Moore Stadel 2006 ; Brook et al. 2008 ), and some others. Observations show that several formation mechanisms can apparently be realized. Galaxies with polar structures are an important class of objects that allows us to study a wide range of problems, linked with the formation and evolution of galaxies under external accretion, and to study the properties of their dark haloes. Unfortunately, PRGs are very rare objects, with a fraction of ∼10 −3 of all galaxies in the local Universe (Whitmore et al. 1990 ; Reshetnikov, Faúndez-Abans de Oliveira-Abans 2011 ). Consequently, most recent studies of PRGs are concentrated mainly on a few relatively nearby and bright galaxies: NGC 4650A (e.g. Coccato, Iodice Arnaboldi 2014 , Iodice et al. 2015 ), A0136-0801 (Spavone, Iodice Arnaboldi 2015 ), NGC 660 (Smirnova, Wiebe Moiseev 2017 ), and some others. There were several attempts to collect large samples of such galaxies. Whitmore et al. ( 1990 ) have presented a photographic atlas of PRGs and related objects containing 157 galaxies but, according to further studies, only a small part of the atlas galaxies appeared to be true PRGs. The next important step was the catalogue SPRC by Moiseev et al. ( 2011 ) based on the results from the Galaxy Zoo project 1 (Lintott et al. 2008 ). The SPRC catalogue contains 275 objects split into four groups. The first two groups comprise ‘best candidates’ (70 objects) and ‘good candidates’ (115 objects) for PRGs. The remaining objects are related galaxies (mergers, strong warps) and possible face-on polar rings. A further study showed that an appreciable fraction of the SPRC objects are indeed PRGs (fig. 1 in Moiseev et al. 2015 gives several examples). In this work we present a new sample of ‘best’ and ‘good’ (in the sense of SPRC) candidates to PRGs. Our sample includes 31 galaxies compiled from Galaxy Zoo discussion boards. Throughout this article, we adopt a standard flat ΛCDM cosmology with Ω m = 0.3, Ω Λ = 0.7, H 0 = 70 km s −1 Mpc −1 . All magnitudes in the paper are given in the AB-system. 2 THE SAMPLE AND DATA REDUCTION 2.1 The sample To select new candidates to PRGs, we analysed discussion boards 2 of the Galaxy Zoo project. By