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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

for mass loss may be necessary to obtain observed results, as done by Neilson et al. ( 2012a ). This is because the rate of period change is directly related to the mass-loss rate from taking the derivative of the period–mean density relation, typically . The greater the mass-loss rate the greater and more positive the rate of period change and if the average mass-loss rate is high enough it could cause more Cepheids to have positive rates of period change even while evolving on the second crossing of the instability strip where the rate of period change is expected to be less than zero. 4. Results For each initial rotation rate and convective core overshooting value we compute the relative fraction of models with positive and negative rates of period change. We find that regardless of the initial rotation rate or convective core overshooting parameter, the fraction of Cepheids with positive period change is about 90% and the fraction with negative period change is about 10%, as can be seen in Table 1 . This suggests that period change, at least statistically, is insensitive to the physics of core overshooting and rotational mixing. Table 1 Predicted Fractions of Cepheids with Positive and Negative Period Changes This insensitivity has been noted before for overshooting. Neilson et al. ( 2012b ) and Neilson ( 2014 ) found similar results in that overshooting acts to change the mass–luminosity relation for Cepheids. That is, in terms of period change, Cepheids with different masses have the same rates of period change for different values of core overshooting. This is because each Cepheid crossing of the instability strip depends on the physics driving stellar evolution. During the first crossing the evolutionary timescale is related to the Kelvin–Helmholtz timescale, hence it is proportional to the mass of the star. Evolution along the second crossing of the instability strip occurs as the star generates energy through mostly hydrogen shell-burning and is beginning helium core-burning. The timescale for blueward evolution is driven by the timescale for the star to have shell-burning, but not have ignited significant helium core fusion. The third crossing is determined by helium core-burning, hence its timescale is also a function of helium core mass. Over the mass range we consider in this paper, overshooting will not change the timescales, and thus the fraction of Cepheids on the first crossing, while the impact on the second and third crossings also remains unchanged. The same argument is also true for rotation. Rotational mixing impacts the mass of the helium core and rotation can change the shape of the Cepheid blue loop. However, neither appears to impact the relative timescales of evolution significantly. The fraction of Cepheids with positive period change decreases to about 77% for models with zero convective core overshooting. The fraction is smaller, but not enough to be consistent with the observed fraction of 67%. This


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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 O O 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 B-Formula I-Formula I-Formula I-Formula 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 O O O O O O O O O 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 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

gas and solids in discs (e.g. Öberg et al. 2011 ; Madhusudhan et al. 2014 ). We first explore the evolution of the C/O ratio in models without radial drift (Fig. 6 ). In these models, the total abundance (gas and ice phase) of carbon and oxygen bearing species does not change, only the partitioning of these species between the gas and ice phases. Figure 6. Evolution of the C/O ratio for models with viscous transport, but without radial drift or diffusion. For comparison the left-hand panel shows the evolution without transport. The solid lines denote the gas-phase abundances, while the dotted lines show the ice abundances. The changes in composition driven by chemical processes are best seen in the model without transport (and α = 10 −3 ). Inside the water ice line (0.5 au), all of the major carbon and oxygen are in the gas phase and thus chemical processing does not change the gas-phase carbon or oxygen abundance. Between the water and CO 2 ice lines (1.5 au) the gas-phase carbon and oxygen abundance is dominated by CO and CO 2 , with a small contribution from hydrocarbons (CH 4 and C 2 H 2 – a proxy for C 2 H 6 ; see Section 3.1 ). Here, the C/O ratio increases as CO 2 is destroyed, producing CO and O, with O eventually forming H 2 O, which freezes out. Between the CO 2 and CH 4 ice lines (10 au), CO and CH 4 are initially the main gas-phase carbon and oxygen carriers. CH 4 gets converted to larger hydrocarbons (C 2 H 2 ), which freeze out causing the C/O ratio to reduce to 1. The spike in C/O ratio near the CO 2 ice line is due to the slightly lower binding energy of C 2 H 2 than CO 2 (note that C 2 H 6 also has a lower binding energy than CO 2 , so Eistrup et al. ( 2018 ) see a similar spike in C/O). Beyond the CH 4 ice line CO is always the dominant the gas phase carbon and oxygen carrier, so the C/O ratio does not evolve. The nitrogen abundance evolution can be derived from Fig. 5 and is slow, thus the C/N of N/O ratio evolution will be driven primarily by the evolution of carbon and oxygen, respectively. As the speed of the viscous transport increases, the changes in composition driven by chemical reactions become restricted to regions of the disc at larger and larger radii. Already at α = 10 −3 , the effect of transport is first noticeable between the H 2 O and CO 2 ice lines, since CO 2 no longer depletes (see also Bosman et al. 2018a ), while at α = 10 −2 the carbon and oxygen abundance hardly evolve. At α = 10 −2 , the inward movement of the ice lines as the disc cools generates the only significant changes in abundance ratio. The influence of radial drift on the bulk abundances is sensitive to whether radial drift or viscous evolution is faster. When radial drift is included we see spikes in the gas-phase C/H ratio at α = 10 −3 (Fig. 7 ), as reported by Booth et al. ( 2017 ). These spikes are driven by volatile species being left at their snow lines when grains drift past them. We also see a peak in the C/O ratio inside of 10 au,


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conclusion that for positive (negative) helicity the apex of a filament rotates clockwise (counterclockwise). But the filament is believed to be associated with a flux rope taking on an S shape that is opposite to the corresponding sigmoid, the latter of which represents a current layer wrapping around the flux rope (Titov Démoulin 1999 ; Kliem et al. 2004 ). Green et al. ( 2007 ) hence rejected those models implying identical orientation for the sigmoid and the flux rope (e.g., Rust Kumar 1996 ; Kusano 2005 ). But in our sample and in the literature (e.g., Pevtsov 2002 ; Cheng et al. 2014 ; Zhou et al. 2017 ) often the cold filament and the hot sigmoid are co-spatial and have the similar S shape, suggesting that the filament is associated with a low-lying magnetic flux rope with its axis dipped in the middle (e.g., Zhou et al. 2017 ). Not all of these filament eruptions that are initiated make it to a full eruption; some of these cases expelled material flows back down to the Sun. Specifically, cases #4,#7,#9, and #11 expel material flows back down the legs of an erupting prominence and have no corresponding CME in the coronagraph observations, this subset of events are known as failed eruptions or confined eruptions, likely because of interactions with external magnetic field structures that may arrest the eruption or facilitate additional draining (McCauley et al. 2015 ; Zhou et al. 2019 ). This interaction may induce alternative rotation mechanism concerning the mutual orientation of the overlying arcade field and the erupting filament body (Isenberg Forbes 2007 ). For a given chirality of the erupting field, this mechanism yields the same rotation direction as the kink instability (e.g., Kliem et al. 2012 ). To summarize, by applying the method proposed by Chen et al. ( 2014 ) to determine filament chirality and using multiviewpoint observations to investigate the filament rotation, we established a strong relationship that during eruption sinistral/dextral filaments, which are located in the southern/northern hemisphere rotate clockwise/counterclockwise, when viewed from above, and corroborated a weak hemispheric preference that both the filament and related sigmoid exhibit a forward (reverse) S shape in the southern (northern) hemisphere. The one-to-one relationship between filament chirality and rotation direction may help understand the transformation of CMEs to interplanetary ejecta, and help predict statistically the latter’s characteristics, such as the axial orientation, the chirality of helical fields, and the strength and duration of southward magnetic field. As illustrated in Figure 4 , for both odd and even cycles, the rotation of eruptive active-region filaments makes their axes tilt toward the east–west direction. Such a statistical trend is already known for interplanetary magnetic clouds (Crooker 2000 ; Yurchyshyn et al. 2009 ), yet its connection with filament rotation has not been noticed. On the other hand, Figure 4


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Acknowledgements Based on observations obtained in the framework of the ESO Prgs. 097.D-0233(A) and 098.D-0185(A). LS acknowledges financial contribution from the grant from PRIN-INAF 2014 ‘Towards a unified picture of accretion in High Mass X-Ray Binaries’. AK acknowledges financial support from RFBR grant 16-02-00604A. We thank the referee Jerzy Madej for his useful comments.


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ACKNOWLEDGEMENTS The authors thank the referee, Dr. Leonardo J. Pellizza, for the constructive feedback provided on the manuscript. MB thanks Hai Fu for insightful discussions which helped to improve the quality of the paper. STSDAS is a product of the Space Telescope Science Institute, which is operated by AURA for NASA. We acknowlege the usage of the HyperLeda database ( http://leda.univ-lyon1.fr ). The scientific results reported in this article are based on joint observations made by the Chandra X-ray Observatory and the NASA/ESA Hubble Space Telescope . Support for this work was provided by the National Aeronautics and Space Administration through Chandra Award No. AR7-18005X issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics and Space Administration under contract NAS8-03060.


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

with data from observations taken from Pfuhl et al. ( 2015 ). Figure 7. The integrated Br γ luminosity as a function of time. The solid blue line results from our simulations while the points are the observed data taken from Pfuhl et al. ( 2015 ) with a 1σ error bar. As the cloud travels towards the SMBH, its volume decreases due to tides and hence its recombination rate and total emission increase. During pericentre passage, gas that passes through pericentre has its density greatly increased due to the vertical collapse. While the recombination rate for a fully ionized gas greatly increases during pericentre passage, the fact that the cloud is UV starved and that its total ionization rate is regulated by the background UV flux limit the increase in the Br γ emission to a mere doubling. This translates to roughly a doubling of the emission that is now limited by the UV flux. After pericentre passage, the emission decreases as the surface area of the cloud decreases due to the evolution of the cloud under tides. Our simulations also allow us to create mock PV diagrams that can be compared with observations. We create mock data cubes in the same manner as in Schartmann et al. ( 2015 ) using pixels of size 12.5 mas and 70 km s −1 . Fig. 8 shows the PV diagram for several different epochs before, during and after pericentre passage. There is good agreement between the observations before pericentre passage and our simulations. Figure 8. PV diagrams of the G2 cloud. The left-hand column is the observational data taken from Plewa et al. ( 2017 ) while the right-hand column are mock observations created from the simulations. The plots represent the epochs 2012.2, 2013.4, 2014.4, 2015.3 and 2016.4. 8 DISCUSSION We have presented a detailed model combining analytical arguments along with numerical simulations that successfully reproduce the observed Br γ emission. By utilizing the reduced diffusion of the moving mesh scheme along with high resolution and actively cooling the gas, we were able to simulate previously unnoticed physical phenomena. The tidal force combined with the efficient cooling collapses the vertical axis of the cloud during pericentre passage. Although the collapse produces a significant amount of ionizing radiation, due to the thinness of the cloud, most of the ionizing photons escape and only a small fraction of them end up ionizing neutral gas. The Br γ emission is regulated by the external UV flux from nearby massive stars. We find that the emission is UV starved, most of the gas is neutral during pericentre passage. This is true even for our enhanced ionizing background, which is 3.6 times larger than the Martins et al. ( 2006 ) rate. Motivated by the observed duration of simultaneous blueshifted and redshifted Br γ emission at pericentre passage, we chose to start our orbital plane simulation with a cloud that has an aspect ratio of 4, which is consistent with the observations due to viewing angles. If the elongated cloud is


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

K and log g = 3.55 model atmosphere calculated with different treatments of the hydrogen-line opacity, using the codes DETAIL (solid curve), SynthV_NLTE (dotted curve), and SYNTHMAG (dash-dotted curve). The position of the Ca ii IR triplet lines is marked with triangles. The vertical lines indicate the wavelength range covered by the Gaia spectra. Table 5 summarises the results of calcium abundance determination from different groups of reliable lines, i. e. lines of Ca i , lines of Ca ii in the visible spectrum range, and lines of Ca ii in the IR spectrum range 8912−27, 9890 Å. We also show in Fig. 9 the NLTE and LTE abundance differences between these groups of lines. For each star, NLTE leads to average abundances from lines of Ca ii in the visible and the IR spectrum range consistent within 0.1 dex, while the abundance discrepancy between these groups of lines varies from 0.6 dex down to −0.5 dex in LTE (Fig. 9 , top panel). The exception is 21 Peg, where NLTE leads to better agreement between these two groups of lines compared to LTE, however, a discrepancy of 0.2 dex remains. For HD 160762, the LTE abundance difference is not shown in Fig. 9 , because Ca ii 8912−27, 9890 Å lines are observed in emission and cannot be fitted in LTE. Figure 9. NLTE (filled circles) and LTE (open circles) abundance differences between Ca ii lines in the visible and IR spectral range (top panel) and between Ca i lines and Ca ii lines in the visible spectral range (bottom panel) in the investigated stars. Fig. 9 , bottom panel, shows the NLTE and LTE abundance differences between lines of Ca i and Ca ii in the visible spectrum range. For the majority of the investigated stars, an abundance difference = log A(Ca i )–log A(Ca ii , vis) does not exceed 0.1 dex in absolute value, independent of NLTE or LTE. However, for A-type stars, the absolute abundances from Ca i and Ca ii lines are higher in NLTE compared with LTE. 4.3 Calcium NLTE abundance determination with SME code As it was written in Section 3.1 , we calculated departure coefficients of Ca i and Ca ii levels for a grid of LLmodels atmospheres (Shulyak et al. 2004 ). Earlier, the same calculations were performed for grids of MARCS plane-parallel models (Gustafsson et al. 2008 ). These NLTE data are implemented in the current version of the SME (Spectroscopy Made Easy) package of automatic parameters and abundance determination based on high-resolution stellar spectra (Piskunov Valenti 2017 ). Atmospheric parameters and element abundances in SME are derived by the interpolation inside the grid models. For cool stars (MARCS model grids), the accuracy of authomatic NLTE Ca abundance determinations was tested in the paper by Piskunov et al. ( 2017 , see Figs 1 and 3 of this paper). Here, we tested the automatic method for hotter stars with HD 32115 and HD 72660. For HD 32115, the SME abundances are −5.68±0.07 (Ca i ) and −5.60±0.14 (Ca ii ). For HD 72660, the corresponding values are −5.44±0.13 (Ca i ) and


O O O O O B-Organization O B-Organization I-Organization I-Organization I-Organization O O B-Location I-Location O O O O B-Person I-Person O O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O O O O O B-Observatory O B-Identifier I-Identifier B-Observatory O O O O B-Observatory O O O O B-Organization B-Location 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

The authors acknowledge support by Allegro, the European ALMA Regional Center node in The Netherlands, and expert advice from Luke Maud in particular. This work was partially supported by grants from the Netherlands Organization for Scientific Research (NWO) and The Netherlands Research School for Astronomy (NOVA). This paper makes use of the following ALMA data: ADS/JAO.ALMA# 2013.1.01268.S. ALMA is a partnership of ESO (representing its member states), NSF (USA), and NINS (Japan), together with NRC (Canada), NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO, and NAOJ.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 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 B-Formula I-Formula I-Formula I-Formula I-Formula O B-Telescope O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Telescope O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-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 O O O O B-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 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 B-Telescope 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 B-Telescope B-Observatory O O O O O O O O O B-Telescope I-Telescope O O B-Telescope B-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Telescope O B-Telescope O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula 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 B-Telescope O O O B-Software O O O O O O O O O O O B-Software O O B-Telescope O B-Citation I-Citation 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 B-Software O O O O

of the potential field energy E p ( t ) (thick curve with diamonds) and the free energy E f ( t ) (thin curve with crosses), both normalized to their maximum, the loop elimination ratio q e , and cross-correlation coefficient CCC. Note that the potential field energy and the free energy are uncorrelated. 5. Interpretation and Discussion 5.1. Instrumental Oscillatory Effects As these observations report for the first time oscillations in the free (magnetic) energy of solar flares, we discuss first possible effects of instrumental origin. The range of observed oscillations (in 11 flare events) cover the range of P ≈ 10–22 minutes and have a mean and standard deviation of As the SDO spacecraft is positioned in the Lagrangian point L1, there are no eclipsing time intervals of the spacecraft orbit that could modulate the observed flux. Because the Sun is rotating, any tracking of a particular heliographic position of a solar flare or an active region needs to be interpolated between two pixels, which could possibly introduce a pixel-step modulation. We estimate the timescale of a pixel shift based on the synodic solar rotation rate,which amounts for a synodic rotation time of P syn = 27.27 days, an HMI pixel size of Δ x pix = 05, and an average solar radius of R ⊙ ≈ 960′′, to a time interval of Δ t pix = 3.2 minutes for HMI, or Δ t pix = 3.9 minutes for AIA pixels. The beat frequency between the two instruments amounts to a timescale ofAlthough the beat frequency is close to the frequency of the observed mean oscillation period (Equation ( 17 )), subpixel variations of the sensitivity (or modulation transfer function) of AIA are unlikely to explain the observed oscillations, as the width of the point-spread function (PSF) is substantially wider (15) than the pixel size (06) (Boerner et al. 2012 ; Grigis et al. 2012 ; Lemen et al. 2012 ). The PSF may also imply a slight subpixel variation of the sensitivity of CCD pixels (between the pixel center and pixel edge). We calculated this variation by pixel-wise superposition of PSFs, and found an interpixel variation of ≲3%. Moreover, the rms variation in the AIA flat field is found to be of order 2% (Boerner et al. 2012 ). The PSF was also measured during a lunar transit, finding that the PSF of AIA/ SDO is better by a factor of two than the EUV telescope on board TRACE (Poduval et al. 2013 ). In summary, no instrumental effect is known from AIA or HMI that could modulate the observed free energy evolution E f ( t ) with periods of P ≈ 10–20 minutes (J. Lemen et al. 2020, private communication). Incidentally, we did choose a cadence of 3 minutes for the AIA images with the VCA4-NLFFF code, while a cadence of 12 minutes is available from the W-NLFFF code using HMI data (Aschwanden 2019c ). The cadence of 12 minutes is close to the mean observed period of P obs = 15.1 ± 3.9 minutes, and thus the observed oscillations are fully resolved with the 3-minute cadence of the VCA4-NLFFF code only, while they


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O B-Model 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 B-Model 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 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 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 B-Model O O O O O O O O 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 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 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 B-Model 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

region. The distribution under the hypothesis that HMXBs are displaced from their parent star-forming region (the grey histogram) is extended compared with the distribution under the null hypothesis (the yellow histogram). We next quantify the observed displacement of HMXBs, which is attributed to kicks after an asymmetric SN explosion during the formation of the compact object (Fryer Kalogera 1997 ). The contribution of natal kicks is treated as a Gaussian smearing function of standard deviation σ that broadens the spatial distribution of HMXBs compared with their birth distribution. We simulate the vertical distribution of HMXBs from the mid-plane as the convolution P ( z |σ, z sfr ) between this Gaussian and the exponential distribution of SFR (equation 2 ) with a scale height of z sfr = 330 pc .: We apply the maximum likelihood method for finding the best estimate of the Gaussian smearing parameter σ. The likelihood function L ( z |σ, z sfr ) derived from the convolution P is where N = 41 is the number of HMXBs and z i is the vertical distance of the i th HMXB from the mid-plane of NGC 55. We perform 100 000 iterations and in order to account for the estimated AGN contamination, in each iteration our HMXB sample consists of all ‘verified HMXBs’ (Table 3 ) as well as randomly selected combinations of 22 out of 37 ‘candidate HMXBs’ (Table 3 ). In Fig. 10 we show the likelihood of the dispersion of the Gaussian smearing function (normalized to the maximum likelihood). The maximum at σ = 0.57 ± 0.07 kpc is the difference between the scale height of the vertical distribution of HMXBs and the vertical distribution of star-forming activity. In Fig. 11 we show the simulated vertical distribution of HMXBs (black dashed line) as the convolution between a Gaussian smearing function of standard deviation σ = 0.57 kpc (green line) that represents the contribution of natal kicks, on top of their birth distribution of 0.33 kpc (red line). Figure 10. The likelihood of the dispersion of the Gaussian smearing function (normalized to the maximum likelihood σ), described in Section 3.2 . The maximum at σ = 0.57 kpc is the scale height corresponding to the displacement between HMXBs and star-forming regions. Figure 11. Simulated vertical distribution of HMXBs (black dashed) as the convolution between a Gaussian smearing function of standard deviation σ = 0.57 kpc (green) that represents the contribution of kicks, on top of the their birth distribution of 0.33 kpc (red). The grey and yellow histograms show the observed vertical distribution of candidate and verified HMXBs, respectively. 3.3 Constraining the displacement of HMXBs The result of the previous section mainly provides an upper limit on the scale height of HMXBs. There are other factors such as contamination, incompleteness and in situ formation of HMXBs that would bias the result of this analysis toward larger scale heights. We investigate these factors in an effort to constrain the lower limit on


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This work was supported by the U.S. National Science Foundation (NSF) through award AST-1109257. D.C.J. is supported by an NSF Astronomy and Astrophysics Postdoctoral Fellowship under award AST-1401708. J.C.P. is supported by an NSF Astronomy and Astrophysics Fellowship under award AST-1302774. This work makes use of the Murchison Radio-astronomy Observatory, operated by CSIRO. We acknowledge the Wajarri Yamatji people as the traditional owners of the Observatory site. Support for the MWA comes from the NSF (awards: AST-0457585, PHY-0835713, CAREER-0847753, and AST-0908884), the Australian Research Council (LIEF grants LE0775621 and LE0882938), the U.S. Air Force Office of Scientific Research (grant FA9550-0510247), and the Centre for All-sky Astrophysics (an Australian Research Council Centre of Excellence funded by grant CE110001020). Support is also provided by the Smithsonian Astrophysical Observatory, the MIT School of Science, the Raman Research Institute, the Australian National University, and the Victoria University of Wellington (via grant MED-E1799 from the New Zealand Ministry of Economic Development and an IBM Shared University Research Grant). The Australian Federal government provides additional support via the Commonwealth Scientific and Industrial Research Organisation (CSIRO), National Collaborative Research Infrastructure Strategy, Education Investment Fund, and the Australia India Strategic Research Fund, and Astronomy Australia Limited, under contract to Curtin University. We acknowledge the iVEC Petabyte Data Store, the Initiative in Innovative Computing and the CUDA Center for Excellence sponsored by NVIDIA at Harvard University, and the International Centre for Radio Astronomy Research (ICRAR), a Joint Venture of Curtin University and The University of Western Australia, funded by the Western Australian State government.


O O O B-Person I-Person O O O O O O O O O O B-Instrument 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-Instrument I-Instrument I-Instrument B-Instrument O O O O O B-Survey I-Survey I-Survey B-Survey O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Collaboration I-Collaboration B-Organization I-Organization I-Organization B-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization B-Organization I-Organization I-Organization B-Observatory I-Observatory I-Observatory I-Observatory B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O O B-Survey O B-Instrument O O O O O B-Location B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization B-Location B-Organization I-Organization I-Organization I-Organization I-Organization B-Location B-Organization I-Organization I-Organization I-Organization B-Location B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Location O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Survey O O

The authors thank Dara Norman for her efforts in performing all observations made during the DECam science verification phase, including those of Abell 3128 used in this study. The authors also thank the anonymous referee for suggesting many useful improvements to the analysis. This project used data obtained with the Dark Energy Camera (DECam), which was constructed by the Dark Energy Survey (DES) collaborating institutions: Argonne National Lab, University of California Santa Cruz, University of Cambridge, Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas-Madrid, University of Chicago, University College London, DES-Brazil consortium, University of Edinburgh, ETH-Zurich, Fermi National Accelerator Laboratory, University of Illinois at Urbana-Champaign, Institut de Ciencies de l’Espai, Institut de Fisica d’Altes Energies, Lawrence Berkeley National Lab, Ludwig-Maximilians Universitat, University of Michigan, National Optical Astronomy Observatory, University of Nottingham, Ohio State University, University of Pennsylvania, University of Portsmouth, SLAC National Lab, Stanford University, University of Sussex, and Texas AM University. Funding for DES, including DECam, has been provided by the U.S. Department of Energy, National Science Foundation, Ministry of Education and Science (Spain), Science and Technology Facilities Council (UK), Higher Education Funding Council (England), National Center for Supercomputing Applications, Kavli Institute for Cosmological Physics, Financiadora de Estudos e Projetos, Fundao Carlos Chagas Filho de Amparo a Pesquisa, Conselho Nacional de Desenvolvimento Cientfico e Tecnolgico and the Ministrio da Cincia e Tecnologia (Brazil), the German Research Foundation-sponsored cluster of excellence “Origin and Structure of the universe,” and the DES collaborating institutions.


O O O O O O O O O O O O O O O O B-Observatory I-Observatory I-Observatory I-Observatory O O O O O B-Organization I-Organization I-Organization O O O O O B-Organization I-Organization I-Organization O O O O O O O B-Observatory O B-Identifier I-Identifier B-Observatory O O O O B-Observatory O O O O B-Organization B-Location O B-Organization B-Location O O B-Organization B-Location O B-Organization O B-Organization B-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 B-Wavelength I-Wavelength I-Wavelength I-Wavelength B-Wavelength O O O O B-Software I-Software I-Software O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O B-Database O O O B-Organization B-Location I-Location B-Citation I-Citation I-Citation I-Citation O O B-Telescope O O O O O O B-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Location I-Location O B-Organization I-Organization I-Organization O B-Location O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O B-Instrument O O O O B-Organization I-Organization I-Organization I-Organization O O O O O O O O O B-Instrument O O O O O O B-Identifier O B-Observatory O B-Telescope O B-Telescope O B-Telescope O O B-Software

The authors thank the referee for their careful and constructive comments which improved our paper. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. This paper makes use of the following ALMA data: ADS/JAO.ALMA# 2013.1.00187.S. ALMA is a partnership of ESO (representing its member states), NSF (USA), and NINS (Japan), together with NRC (Canada) and NSC and ASIAA (Taiwan), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO, and NAOJ. This research also made use of NASA’s Astrophysics Data System (ADS) Abstract Service and the IDL Astronomy Library hosted by the NASA Goddard Space Flight Center. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France (Wenger et al. 2000 ). The JCMT has historically been operated by the Joint Astronomy Center on behalf of the Science and Technology Facilities Council of the United Kingdom, the National Research Council of Canada and the Netherlands Organisation for Scientific Research. Additional funds for the construction of SCUBA-2 were provided by the Canada Foundation for Innovation. The identification number for the programme under which the SCUBA-2 data used in this paper is MJLSG32. Facilities: ALMA , Spitzer , JCMT , Herschel . Software: CASA.


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 B-CelestialObject O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 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 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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

Earth-Sun distance by changing the pixel scale accordingly. After the telemetric problems which occurred in January 2008, the images of the synoptic program were binned by a factor of two. Fortunately, this is not a problem in this work, since the images taken before this date were binned by a factor of two for analysis. So the size of all the analyzed images is 2048 × 1024 pixels. The program ended in February 2016, when both cameras broke down. All images were calibrated with the standard solar reduction software distributed under SSWIDL, which corrects for bad pixels, readout errors, dark current and flat field. A 1024 × 512 pixel subfield of a calibrated image is shown in Fig. 1 . In each image, the left and the right square subfields are analyzed separately; this helps us, by comparing the results in each of them, to disentangle solar variations from instrumental effects, which is crucial for our investigation (see the next section and Muller et al. 2011 ). Fig. 1. A 1024 × 512 (114′′ × 57′′) subfield of a 2048 × 1024 (228′′ × 114′′) blue continuum HINODE/SOT image from the synoptic program. 3. Granulation images analysis As mentioned in Sect. 2 , a significant number of images from the synoptic program appear to be blurred to a varying degree. In order to get a reliable variation, the sharpest images must be selected, and only these ones used for further analysis. About 25% of the images have been actually removed because of blurring. The method of selection is described in detail in Muller et al. (2011) and only a summary is presented here. In a first step, the images containing dark columns, sunspots pores, abnormal granulation 1 were removed visually; the images which clearly appear out of focus were also removed visually. In the second step the granulation contrast and scale of the selected images were derived from the power spectrum ( Muller et al. 2007 , 2011 ), separately in the left and right half fields of view of size 114′′ × 114′′. The root mean square of the intensity fluctuations, Irms, which, for simplicity, we refer to as contrast, is the square root of the integral, above the noise level, of the power spectrum in the granulation range, between 0′′̣3 (in order to remove the high frequency noise) and 4′′ (in order to remove non-granular larger scale fluctuations, like the 5-min oscillations and the mesogranulation). The scale is defined as the inverse of the mean wavenumber of the power spectrum in the granulation range, converted in arcseconds. The contrast and the scale derived in this way are about 12% and about 1′′̣6 (1160 km) respectively. When the contrast of the left field-of-view (FOV) of the selected images is plotted versus the contrast of the right FOV, they appear correlated: when the contrast is large (small) in one FOV it is also large (small) in the other FOV (see Fig. 5 in Muller et al. 2011 , which shows the correlation for the images selected in January 2007). But as the granulation evolves independently


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The authors wish to thank the anonymous referee for his insightful suggestions. NH thanks Evgeni Grishin for pointing out the matched filter technique to him. AC acknowledges support from CIDMA strategic project UID/MAT/04106/2013.


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

The Kepler Space Telescope was launched in 2009 March and its main scientific goal was to search for the terrestrial planets using the transit method (Borucki et al. 2010 ). The asteroseismology program is an extremely important byproduct of the Kepler mission (Gilliland et al. 2010 ). Due to the unprecedented photometric precision on the order of a few μ mag with a high duty-cycle, and continuous collection of data over about 4 years, Kepler data allows one to study the internal structure and physical process of stars with an ultra-high precision than that obtained with any telescope on earth (Koch et al. 2010 ). The Kepler telescope is in a 372.5 day Earth-trailing orbit and its field of view covers 105 deg 2 in the constellations of Cygnus and Lyra. Kepler provides two observation strategies for its targets, i.e., short cadence (SC) and long cadence (LC) with sampling times of 58.85 s and 29.424 minutes, respectively. The SC observations are adopted for the primary mission as they are able to obtain more data points during a candidate object passing in front of its host star. However, most of the targets are observed with LC in order to maximize the target’s number through long exposure time. Consequently, more than 170,000 targets are available in LC observations (Jenkins et al. 2010 ). More than 2000 δ Sct stars have been detected through the Kepler mission (Balona Dziembowski 2011 ; Balona 2014 ; Bowman et al. 2016 ). One of them, KIC 5950759, has been classified as a double-mode high-amplitude δ Sct (HADS) star by analyzing the LC data (Bowman et al. 2016 ). The δ Sct stars are typical A- and F-type variable stars with period from 0.02 to 0.25 days. They are usually on or above the main sequence on the H-R diagram, and are situated in the lower classical instability strip (Breger 2000 ). Their oscillations are mainly driven by the κ mechanism that occurs in the partial ionization zone of He ii (Gautschy Saio 1995 ; Breger 2000 ). The δ Sct stars can oscillate in both pressure and gravity modes (Breger 1995 , 2000 ; Balona 2016 ). As a subclass of δ Sct stars, the HADS stars usually pulsate with a light amplitude larger than 0.3 mag and generally rotate slowly with v sin i ≤ 30 km s −1 (Breger 2000 ). Compared with the low-amplitude δ Sct stars, the HADS stars possess a more restrictive instability strip with a width in temperature of about 300 K and tend to shift to a lower temperature with evolution (McNamara 2000 ). Lee et al. ( 2008 ) reveal that only about 0.24 percent of the stars suited in the δ Sct region belong to HADS stars. The majority of HADS stars are typically young and metal-rich Population I stars; some have been confirmed to be SX Phe variables, and are Population II metal-deficient stars (Breger 2000 ; Balona Nemec 2012 ). In general, the HADS stars pulsate with only one or two modes (e.g., AE UMa, Niu et al. 2017 ; YZ Boo, Yang et al. 2018 ; etc.), and most of their pulsations belong to radial modes. AI Vel (Walraven


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

to the lepton number transport; indeed, the neutrino contribution is just a few percent. This is simply because the number density of electron/positron is much larger than that for the neutrinos. The neutrino diffusion in the fluid rest frame is even subtler, although it does exist (see the blue line in Figure 7 ). It should be noted, however, that the momentum feedback from neutrinos is still comparable to the momentum imparted by the matter-pressure gradient, as discussed above. This occurs because the lateral matter-pressure gradient is partially compensated by the temperature asymmetry: the temperature in the northern hemisphere is ∼1% higher than in the southern hemisphere. Although the temperature asymmetry is much smaller than that of Y e , it still reduces the total asymmetry in the matter pressure substantially, because the baryon and photon pressure are dominant in the total pressure. Figure 7. Radial distributions of angle-average lateral number flux of measured in the laboratory frame (red) and fluid rest frame (blue). The counter part of electron/positron gas corresponds to the black line in the panel. It is also important to note that Y e decreases via deleptonization as the matter moves toward the north pole. The Y e -depleted matter then submerges in the PNS envelope near the north pole. When it hits the PNS core, it is deflected and flows southward along the surface of the PNS core, increasing Y e this time by ν e absorptions. The matter emerges again to the PNS surface by the local PNS convection near the south pole. Although the strong downflow induced by the dislocation of PNS tends to suppress the convection around the north pole, the convection activity continues to occur in the vicinity of the south pole and supplies the Y e -rich material to the PNS envelope there. This closes the cycle and creates the coherent lateral circular motion, with the Y e asymmetry sustained. Then the circulation will continue until the PNS convection shuts off or the neutrinos in PNS have dried up, both of which may take more than a few seconds. If this is in fact the case, the PNS may be accelerated to more than a hundred km s −1 , which is the typical proper motion velocity of pulsars. Finally, we give some comments on other works on the asymmetric Y e distributions. Glas et al. ( 2018 ) found a circular motion in the envelope of PNS in their 3D simulations, which produced the LESA phenomenon. They speculated that the thermal instability of spherical shells discussed by Chandrasekhar ( 1961 ) may be responsible for the sustained asymmetric Y e distribution. It seems, however, that the circular motion found in their study was not as coherent as what we observed in our study; indeed, they look more like a superposition of some smaller eddies instead (see Figure 6 in Glas et al. 2018 ). Powell Müller ( 2018 ) also observed LESA in their simulations and suggested that LESA is in effect a manifestation of PNS convections under a different


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Formula I-Formula I-Formula I-Formula 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 O O O O O O O O O O O O O O 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 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 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 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 O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O

between the curves of Figure 6 (a) are due to this anisotropic and coherent velocity strength. The Fourier transform as a function of k y (not shown) is almost the same as Figure 6 (a). Figure 6 (c) shows the kinetic energy power spectrum as a function of ; the differences between the energy contribution of the modes in the cases with and without shear are more pronounced, but still rather small. We speculate that the action of the stress tensor (when the shear is applied) leads to an increase of mode contributions at all scales, but in particular near the diffusion region, increasing the reconnection rate; this is in agreement with Nakamura et al. ( 2008 ), who reported an enhancement of island production when shear was present. Figure 6. (a) Power spectra of the velocity as a function of k . (b) Velocity as a function of k x . (c) Kinetic energy as a function of k . For all cases the red line represents the fan stage at t = 303.0 s just before the shear is applied, and the blue one just after it, at t = 304.0 s. If we consider a magnetic configuration scheme (see Figure 1 of Paper I ), the setup described by Table 1 , and whose results are shown in Figure 4 , will represent the face-on view. To also consider the edge-on view, we perform another simulation where the initial magnetic field, instead of being homogeneous, is the CS given bywith B 0 = 3.0 G. The preparation of the fan is performed with the two stages as in the previous case, but in this case the shear (Equation ( 12 )) coincides with the CS location. The instantaneous pressure pulses are again applied at time t = 305.9 s. Figure 7 shows the temperature (i) and the density with overlapped magnetic field lines (ii) at an early time t = 312 s. The resulting pulse patterns are labeled ( E ), ( F ), ( G ), and ( H ). Figures 7 (c)–(d) show the same evolved patterns 1 minute later, at t = 372 s, for the temperature with magnetic field lines superimposed (iii) and the EM with temperature contours (iv). Same as before, the EM contrast of the SAD candidates will fade away fast and before the desired time if during their evolution they are not sufficiently isolated by the magnetic field. In fact, the feature ( F ) triggered in a location where the magnetic field lines are almost straight is not appreciated even at an early time (Figures 7 (a)–(b)). The cavities that survive and can be identified as SADs are located mainly in the neighborhood of the CS, 7 7 This is noted more clearly when the turbulence stage is carried out using larger wavenumbers compared with those chosen here. See also Paper I . where the magnetic field is rolled up, forming closed vortices and islands. Figure 7. (a) Temperature at t = 312 s; ( E ), ( F ), ( G ), and ( H ) labeled cavities triggered at t = 305.9 s. (b) Density at t = 312 s. Same as before, but with magnetic field lines superimposed. (c) Same as (i), but 1 minute later, at t = 372 s. (d) EM, also at t = 372 s. Cavities ( G ) and ( H ) have an EM


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We thank Neal Katz for useful discussion and Phil Hopkins for comments on the manuscript. We thank the anonymous referee for a constructive report that helped improve the manuscript. CCH is grateful to the Gordon and Betty Moore Foundation for financial support and acknowledges the hospitality of the Aspen Center for Physics, which is supported by the National Science Foundation Grant No. PHY-1066293. PSB was supported by a Giacconi Fellowship provided through the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy under NASA contract NAS5-26555.


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H 0 has been proposed previously (Zibin et al. 2007 ). We take the additional step of propagating the uncertainties on T CMB to H 0 and present example noise curves to produce such a measurement, including a detailed treatment of foregrounds. Studies of the time evolution of the CMB angular power spectrum and forecasts for observations have also been conducted (Lange et al. 2007 ; Zibin et al. 2007 ; Moss et al. 2008 ). In particular, Lange Page ( 2007 ) found that the change in the power spectrum could in principle be detected over the course of a century. 2. Method 2.1. Hubble Cooling of <italic>T</italic>CMB The monopole temperature of the CMB, hereafter denoted , decreases in time with the scale factor asThe time derivative of T is then . This can be evaluated to first order, taking as an example and T 0 = 2.725 K, 6 6 The forecast for depends on the true value of the current CMB temperature T 0 but the change in is small given the current sub-mK constraints on T 0 from COBE/FIRAS (Fixsen et al. 1996 , 2011 ). Therefore the temperature of the CMB decreases by 2 nK over a 10 yr period. One could thus in principle measure the real-time cooling of the CMB due to the expansion of space and from this infer the value of the Hubble constant. 2.2. Requirements to Measure <italic>H</italic>0 The simplest method to measure the Hubble constant from the monopole temperature would amount to fitting for the slope of T as it decreases in time. The model is linear in time with a slope of ,We have in mind a future version of the COBE/FIRAS experiment, where the data can be reduced in discrete time intervals to evaluate the monopole temperature of the CMB repeatedly over the mission duration. For example, the mission could take data continuously for 10 yr, potentially mapping out large portions of the sky, and the monopole CMB temperature would be inferred from these data every year. Given the expected level of cooling, we can then propagate uncertainties from T ( t ) to H 0 and determine what sensitivity to T ( t ) is required to measure H 0 with a given precision. We make some simplifying assumptions that will allow us to analytically calculate the uncertainty on H 0 using an ordinary least-squares estimator. First, we assume that T ( t ) is measured with (foreground-marginalized) uncertainty σ T in discrete uniform time intervals with spacing Δ t , such that t = k Δ t , where k = 1,2..., N . The mission duration is thus t total = N Δ t with N data points. Second, the uncertainties on T ( t ) are time-independent, parameter-independent, and Gaussian uncorrelated. 7 7 This is not entirely true as the CMB photon noise is one of the dominant noise sources and therefore the noise depends on T CMB . However, the change in the CMB photon noise over these timescales is negligible. The foreground-marginalized uncertainty σ T can then be written in terms of an effective sensitivity s T of the experiment such that,where s T is understood as


O B-Collaboration I-Collaboration I-Collaboration 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 B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O O B-Location I-Location O B-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Location O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Location O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O B-Organization I-Organization I-Organization I-Organization B-Organization O B-Location O O B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization O B-Location O O O O O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization O B-Location O O B-Organization I-Organization I-Organization I-Organization O B-Location O B-Observatory B-Telescope

The Fermi -LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT as well as scientific data analysis. These include the National Aeronautics and Space Administration and the Department of Energy in the United States, the Commissariat à l’Energie Atomique and the Centre National de la Recherche Scientifique/Institut National de Physique Nucléaire et de Physique des Particules in France, the Agenzia Spaziale Italiana and the Istituto Nazionale di Fisica Nucleare in Italy, the Ministry of Education, Culture, Sports, Science and Technology (MEXT), High Energy Accelerator Research Organization (KEK), and Japan Aerospace Exploration Agency (JAXA) in Japan, and the K. A. Wallenberg Foundation, the Swedish Research Council, and the Swedish National Space Board in Sweden. Additional support for science analysis during the operations phase is gratefully acknowledged from the Istituto Nazionale di Astrofisica in Italy and the Centre National d’Études Spatiales in France. Facility: Fermi -(LAT).


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has an outer radius of 38 kpc and Bruce Rout found a value of 55 kpc (Bruce 2009 ). Figure 1. Rotation curve of NGC 3198. Figure 1 shows the observed rotation curve of NGC 3198 with two fitting lines: the line “ab” for the radius r r t and the line “bc” for the radius r > r t . The quantities α (the slope of the line ab), β (the slope of the line bc), r t (the turn-off radius), and γ (the intersection point between the line bc and the velocity axis) were taken from the rotation curve and their values are shown below,The flatness characteristic of spiral galaxies is bound with the eccentricity ( k ) calculated from the relation (Binney Tremaine 1987 ). Calculations of the mass and density at different radii of the galaxy NGC 3198 using the above values taken from rotation curve ( α , β , γ , and r t ) and using Equations ( 8 )–( 11 ) were carried out using a computer program constructed for this purpose. The central inner density (at r r t ) calculated for NGC 3198 is found to be constant ( ρ 1 = 0.387 M o pc −3 ), where M o is one solar mass. The density of the outer regions ( r > r t ) of the spiral galaxy NGC 3198 is much less than that of the inner regions. The value of ρ 2 (r) changes from 0.0187 M o kpc −3 at r = 4 kpc to reach 0.00278 M o pc −3 at r = 30 kpc, so the outer density decreases with increasing the distance from the center of the galaxy (Figure 2 ). Figure 2. Outer density as a function of radius. The behavior of the calculated densities of the spiral galaxy NGC 3198 (constant inner density and declining outer density) is consistent with other works (Rubin et al. 1977 ; Binney Tremaine 1987 ; Daod et al. 2014 ). The inner mass (at r r t ) of spiral galaxy NGC 3198 grows up very quickly, as in Figure 3 . The inner mass grows from 1.334 × 10 9 M O at r = 0.1 kpc to a mass of 8.5391 × 10 9 M O at a distance of 4 kpc from the galactic center. Therefore, the mass at the turn-off radius (4 kpc) is more than 10 4 times the mass near the center of the galaxy. Figure 3. Inner mass distribution. The calculated outer mass of NGC 3198 changes from 8.539 × 10 9 M O at the turn-off radius to 5.262 × 10 10 M O at the outer radius ( r g = 30 kpc) of the galaxy. In other words, the mass at the edge of the galaxy is only five times more than that at the turn-off radius. Therefore, the outer mass ( r > r t ) of the galaxy NGC 3198 grows slowly compared to the inner mass, as in Figure 4 . Since outer borders of spiral galaxies extend to a large distance from the visible region. The outer halo mass is significant and it is four times more than the mass of the inner (more dense) regions, which confirm the existence of a massive halo and giving evidence as to the existence of dark matter (Begeman 1989 ). Figure 4. Mass distribution of NGC 3198. The galaxy is usually divided into four regions, the nucleus, the bulge, the disk, and the halo. The mass of these four regions can be calculated if the radius (distance from the center of the galaxy to the


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ACKNOWLEDGEMENTS This work has been supported financially by Research Institute for Astronomy Astrophysics of Maragha (RIAAM) under research project No. 1/6025-33.


O B-CelestialObject O O O O O O B-CelestialObject O O O O O B-CelestialObject O B-CelestialObject O O B-CelestialObject O O O O O O O O B-Telescope I-Telescope I-Telescope 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Software I-Software I-Software I-Software I-Software 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 B-Citation I-Citation I-Citation O O O O O B-Database I-Database 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 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-Citation I-Citation I-Citation O O O O B-Survey 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 B-Model I-Model I-Model 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 B-Model 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

and B1 shock regions along the outflow of L1157 are marked here with circles (B0), triangles (B1), and squares (B2). The dashed circles represent the HPBW of the IRAM 30 m spectra at 86 GHz (29′′), 210 GHz (12′′), and 350 GHz(7.5′′). The green contours in the channel maps show the 10, 60, and 120 σ levels of the integrated intensity map of 28 SiO, shown in Fig. 1 . 4 LVG analysis In this section we analyse the single-dish spectra of the SiO and its isotopologues 29 SiO and 30 SiO from the 2−1 up to the 8−7 transition ( E up from 6 to 163 K), shown in Fig. 2 . The 12–11 spectrum was excluded from the analysis because it is too noisy: we note, however, that the fluxes reported in Table 1 are consistent with the solutions provided below. The line properties are summarised in Table 1 . This table also reports the integrated intensity in three velocity ranges: EHV: –23 to –13 km s −1 , HV: –13 to –3 km s −1 , and LV: –3 to +5 km s −1 . In order to derive the average physical properties of the gas that emits SiO, we carried out a non-LTE analysis using the large velocity gradient (LVG) code described in Ceccarelli et al. (2003) . We used the collisional coefficients of SiO with H 2 computed between 10 and 300 K for the first 20 levels by Dayou Balança (2006) that are provided by the BASECOL database ( Dubernet et al. 2013 ). We ran a large grid of models (≥7000) covering a SiO column density N SiO from 1.5 × 10 13 to 8 × 10 15 cm −2 , a H 2 density n H2 from 1 × 10 3 to 2 × 10 7 cm −3 , and a temperature T from 30 to 300 K. We then determined the solution by simultaneously fitting the 28 SiO, 29 SiO, and 30 SiO lines and left as free parameters N SiO , n H2 , and T , while the emitting sizes and line widths were those measured. We assumed 28 Si/ 29 Si = 19.7 and 28 Si/ 30 Si = 29.8, as obtained by Anders Grevesse (1989) and confirmed by our SOLIS observations for L1157-B1 (see Sect. 3.3 ), and we added the 20% calibration uncertainty in the observed intensity error bars. We sampled the parameter space unevenly (with steps of 10 K until 100 and 20 K for higher temperatures, steps of a factor of 2 for densities lower than 6 × 10 6 cm −3 and 1.3 at higher ones, steps of a factor of 1.5 in column densities until 1 × 10 14 cm −2 and 1.1–1.2 at higher ones to ensure better cover close to the minimum χ 2 . The beam dilution was taken into account, assuming that the emitting gas has a circular Gaussian shape and using the standard equation for beam dilution. We carried out the non-LTE analysis for the HV and EHV components. The results are described in the two following subsections and are summarised in Table 2 . Table 2 Result of the non-LTE LVG analysis. Notes. The HV and EHV emissions are composed of two physical components each: the first is associated with the B1a clump, and the second is more extended (see text). ( a ) SiO abundance with respect to molecularhydrogen. The H 2 column density used to calculate the SiO abundance is derived from the CO


O O O B-Observatory O O O O O O O B-Observatory I-Observatory O O O O O O O O O O O O O O B-Instrument O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization 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 O O O O O B-Survey I-Survey O O O O O O O O O O O O O O O O O O O O B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person O B-Person I-Person B-Person O B-Person O O O O O B-Organization I-Organization O B-Grant I-Grant I-Grant O O O O O O O O O O O

We thank the ESO staff, and in particular the staff at Paranal Observatory, for their helpful and enthusiastic support during the many observing runs over which the KMOS GTO were carried out. We thank the entire KMOS instrument and Commissioning team for their hard work, which allowed our observational program to be carried out so successfully. We also thank the software development team of SPARKfor all their work with us to get the most out of the data. This paper and the KMOS 3D survey have benefitted from many constructive, insightful, and enthusiastic discussions with many colleagues whom we are very grateful to, especially M. Franx, A. Renzini, K. Whitaker, K. Glazebrook, and R. Bassett. D.J.W. and M.F. acknowledge the support of the Deutsche Forschungsgemeinschaft via Project ID 387/1-1. We thank the referee for a thorough reading and valuable comments.


O O O 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 O O O B-ComputingFacility I-ComputingFacility O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility B-Observatory I-Observatory I-Observatory I-Observatory I-Observatory B-Person O O O O B-Fellowship I-Fellowship O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Observatory I-Observatory I-Observatory I-Observatory I-Observatory O B-Observatory I-Observatory I-Observatory I-Observatory I-Observatory O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization

The authors thank a referee, H. J. Melosh, for useful comments that substantially improve the quality of this work. Numerical computations were in part carried out on the GRAPE system at Center for Computational Astrophysics, National Astronomical Observatory of Japan. Y.H. is supported by an EACOA Fellowship that is supported by East Asia Core Observatories Association, which consists of the Academia Sinica Institute of Astronomy and Astrophysics, the National Astronomical Observatory of Japan, the National Astronomical Observatory of China, and the Korea Astronomy and Space Science Institute.


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 B-Formula I-Formula I-Formula O O O O O O O O O O O O B-Model I-Model O O B-CelestialObject I-CelestialObject 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 B-EntityOfFutureInterest I-EntityOfFutureInterest 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 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 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 B-Formula I-Formula I-Formula O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest 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 B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O B-Wavelength 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-Citation I-Citation I-Citation I-Citation I-Citation I-Citation 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 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 B-CelestialObject O O B-CelestialObjectRegion I-CelestialObjectRegion O 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 B-Model I-Model 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 B-Telescope I-Telescope I-Telescope B-Telescope O O O O O O O O O O O O O O O B-Model O B-Model I-Model 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-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 O B-Model I-Model O O O O O B-Telescope O O O O O O O O O O O O O O O O O B-Model I-Model 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

The fall-off dependence of the dark-energy density as a function of r is given by the parameter n (c.f. eq. 1 in paper II). For a value of n = 3 the dark-energy density versus radius dependence does not contradict the tests of standard GR in the Solar system. Nielsen Birnholz ( 2018 ) have pointed out that a larger value of n is required to account for the results obtained from gravitational wave observations (c.f. their eq. 4). Paper II shows that for larger values of n , the predicted intensity and velocity structures will be almost identical within pc-GR, with only slight changes in the absolute values. For instance, increasing n from 3 to 4 results in a shift in the maximum orbital frequency from 1.72 to 1.89 m and a shift in the maximum orbital frequency from 0.21 to 0.22 (c.f. eq. 4 of paper II and Fig. 2 in this paper). Therefore the appearance of a dark and a bright ring in the intensity profiles discussed in Section 2 are robust and will not change for steeper values of n . In this paper we assume a value of n = 4 for the tests on the timing properties to account for the detection of gravitational waves. We assume a value of n = 3 for the ray-tracing simulations, as the structures in the intensity behaviour will not change. The Galactic Centre has been studied in great detail with near-infrared observations. Based on the orbital motions of stars in the vicinity of the Galactic Centre, the mass of the central black hole has been constrained to [Gillessen et al. ( 2009 ), see also Genzel et al. ( 1996 ) and Eckart Genzel ( 1997 )]. Gravity Collaboration et al. ( 2018a ) have, for the first time, measured the gravitational redshift of the star S2 near the Galactic Centre. In addition, Gravity Collaboration et al. ( 2018b ) have detected bright flares at distances of approximately 150 μas from the central black hole. In this paper we summarize our imaging and timing predictions based on the pc-GR theory for the Galactic Centre. In Section 2.1 the ray-tracing simulations are summarized. In Section 2.2 we predict the orbital velocities of particles which can be compared to Event Horizon Telescope (EHT) observations at different epochs. Finally in Section 2.3 we compare the emission profiles predicted by pc-GR and standard GR, which show remarkable differences. The theory of pc-GR in general, along with a specific focus on the tests discussed in this work, is presented in Hess et al. ( 2019 ) (hereafter Paper II : Theory and robust predictions). 2 OBSERVATIONAL TESTS In this section we describe the observational tests we have developed to date to verify the predictions of the pc-GR theory in preparation for the upcoming EHT observations. These tests include ray-tracing simulations of the flow of accreting matter around black holes using both standard GR and pc-GR. In addition, we have produced diagnostic plots comparing both theories with regard to emissivity profiles and the timing properties of orbiting matter. The main results are


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

to resolving the Ba puzzle. To examine this possibility, we have selected a set of nine iron lines from the table in Gurtovenko Sheminova ( 2015 ) whose formation depth is far from the continuum forming layers in the range of log ( τ 5000 ) = −2.0 to −4.0. We show in Figure 12 the differential iron abundances of these lines (Table 4 ) covering the EWs range 60 to 160 mÅ in the spectra of HD 96116 and HD 222582 as a function average depth of line formation. All these abundances are measured using the stellar parameters listed in Table 1 whose values are based on the analysis of weak and moderate strength iron lines of EW 70 mÅ (Nissen 2015 ). It is evident from Figure 12 that HD 96116 with relatively high stellar activity has a systematically higher iron abundances for the strong lines formed in the upper layers of the photosphere (log ( τ 5000 ) −2.0) than the mean abundance of +0.01 dex derived for lines formed deep in the photosphere. Such a trend of iron abundance with depth of line formation strongly suggest a height-dependent microturbulence with velocity increasing toward the top of the photosphere and the transition to the chromosphere. From the very similar iron abundances for the strong Fe lines in HD 222582 suggest that the photospheric structure of the inactive star HD 222582 of age 7 Gyr is very similar to that of the Sun. Figure 12. Differential iron abundance derived from the adopted stellar parameters in Table 1 as a function of the average depth of line formation. Table 4 Iron Abundances for a Set of Nine Saturated Iron Lines along with the Average Depth of Formation in the Stellar Photosphere These results strongly suggest that the microturbulence increases steeply with height in the photospheres of active stars relative to dwarfs of age less than the Sun. As a result, the application of the microturbulence value derived from the weak and moderate strength iron lines to strong lines such as the Ba ii lines result in a serious overestimation of the Ba ii abundances in stars younger than the Sun. For the star HD 96116, an increase of microturbulence by about 0.3 km s −1 will drop [Ba/Fe] from the Ba ii 5853 Å line close to the abundance measured for the other heavy elements La−Sm. It is well understood from the analysis of the Sun that the chromospherically active phase of the Sun is associated with active upper photospheric layers (Schrijver et al. 1989 ) and thus chromospherically active young stars in the field, OCs, and associations have active photospheric layers from where the Ba ii lines emerge. As a result all those active stars, as found here and in previous studies, have Ba ii abundances overestimated by the standard LTE abundance analyses where the microturbulence is assumed depth-independent and derived from the weak/moderate strength Fe lines whose formation depth in the photosphere is very deep and differ greatly from the Ba ii line forming depths. Accordingly, we argue that the Ba abundances determined from the