Fig. 1 were obtained with the 1.6-m telescope of the National Laboratory for Astrophysics (Brazil) on 2011 May 31 (Ivanova et al. 2018 ). The instrumental setup and data processing are presented in detail in Cavichia, Costa Maciel ( 2010 ) and Ivanova et al. ( 2016 ). Table 1 summarizes the characteristics of our observations: the date of observation (the mid-cycle time, UT date), the geocentric ( ∆ ) and heliocentric ( r ) distances, the phase angle of the comet ( α ), the position angle of the extended Sun–comet radius vector ( φ ), the filter (photometry) and grid (spectroscopy), the total exposure time during the night ( T exp ), and the mode of the observation. Table 1. Log of the observations of comet 29P/Schwassman–Wachmann 1. 3 MORPHOLOGY OF THE COMA As can be seen in Fig. 1 , the λ4277/39 Å filter transmits the radiation of CO + ions and the continuum, whereas the transmitted radiation flux through the λ5309/169 Å filter may truly be considered as the continuum, without CO + ions. Thus, to derive the pure ion image, we subtracted the composite image of the continuum that was obtained in the SED537 filter from the combined CO + image, controlling the particular light transmission of each filter and various continuum levels. We used values of reddening obtained from the spectral observations of comet 29P presented by Korsun et al. ( 2008 ) and Ivanova et al. ( 2016 , 2018 ). The images of the comet in the two filters were centred using the central isophotes, which was closest to the maximum brightness of the comet. The panels on the left of Fig. 2 present the intensity maps of the isolated CO + coma after subtraction of the continuum intensity from the observed intensity in the CO + band, and the panels on the right present the images of the dust coma of comet 29P. Figure 2. Isolated CO + (a, c, e, g) and dust (b, d, f, h) coma of comet 29P derived from observations on November 8, 2007, December 4, 2008, March 29, 2009 and December 26, 2009. All images are scaled to erg cm −2 s −1 Å −1 . The values near the white contours, corresponding to the column density at a cometocentric distance about 20 000 km, are presented in Table 2 . The sunward (⊙), north (N) and east (E) directions, and the cometary motion vector (V) are shown. The isolated CO + coma is clearly observed on all the dates of observation presented here (see Fig. 2 ): it is compact, asymmetric relative to the optocentre, and always elongated in the sunward direction, although this elongation does not coincide exactly with the direction to the Sun. The CO + coma observed on 2007 November 8 was only slightly elongated in the sunward direction, while on 2008 December 4 the comet had a very compact and strongly elongated CO + coma in the solar hemisphere to at least 60 000 km. On 2009 March 29, the comet had a small asymmetric coma with strong sunward elongation. In contrast to the CO + coma, the dust coma, formed by sunlight scattered from dust particles, was more extended and

O O O O O O B-Telescope I-Telescope O O B-Observatory I-Observatory I-Observatory I-Observatory B-Location 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-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-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 B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O B-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-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 B-CelestialObject I-CelestialObject 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 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 B-CelestialObject I-CelestialObject 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 B-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion 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-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O


the positions on the SED of the observational wavelengths for various instruments of interest here: 250, 350, and 500 μ m for the SPIRE instrument on board Herschel ; 450 and 850 μ m for the SCUBA-2 instrument at the James Clerk Maxwell telescope; ∼1100 μ m for AzTEC at the LMT; 1400 μ m for SPT ; and 850, 1400, and 3000 μ m for ALMA . We have also highlighted the 5 σ detection limits for such instruments (attained in the deepest large-scale surveys undertaken so far or in the near future): S 250 ≈ 35 mJy, S 350 ≈ 40 mJy, and S 500 ≈ 50 mJy for SPIRE; S 450 ≈ 8 mJy and S 850 ≈ 2 mJy for SCUBA-2 ; S 1100 ≈ 1 mJy for AzTEC ; S 1400 ≈ 20 mJy for SPT ; and S 850 ≈ 0.42, S 1400 ≈ 0.11, and S 3000 ≈ 0.02 mJy for ALMA (500 hr on 100 arcmin 2 ). The accurate determination of the spectroscopic redshift for a large sample of dusty galaxies is a major problem. In order to probe the bright end of the SFR function at z ≳ 3, a strategy could be to preselect high-redshift sources using flux/color criteria from surveys conducted with Herschel or SCUBA-2 , and then perform a more accurate photometric (or even spectroscopic) redshift determination with observations on source by, e.g., AzTEC and ALMA . Commonly used preselection criteria (e.g., Dowell et al. 2014 ; Asboth et al. 2016 ) for high-redshift sources based on Herschel photometry involve looking for “350-peakers,” which are defined as sources with S 350 / S 250 ≳ 1 and S 500 / S 350 ≲ 1, or “500-risers,” which are defined as sources with S 350 / S 250 ≳ 1 and S 500 / S 350 ≳ 1. Actually, the uncertainties in the flux measurements make the distinction between peakers and risers quite loose; moreover, at z ≳ 4, the channel at 250 μ m refers to rest-frame wavelengths λ ≲ 50 μ m, where details of the SED due to different dust properties and a possible contribution from an AGN component can be relevant. Thus, here, we mainly focus on the color S 500 / S 350 . In Figure 9 (bottom panel), we plot its evolution with redshift and compare it with the measurements from ALMA /ALESS by Swinbank et al. ( 2014 ), finding reasonable agreement within the large uncertainties. Sources with S 500 / S 350 ≳ 0.8 are high-redshift z ≳ 3 candidates. However, the rather high limiting fluxes of Herschel cannot probe the SFR function much above z ∼ 5, since even sources with SFR ψ ≳ 10 3 M ⊙ yr −1 are too faint to be detected. To go much beyond z ≳ 4, the preselection based on the color S 850 / S 450 from SCUBA-2 photometry is much more efficient. In Figure 9 (bottom panel), we plot its evolution with redshift and compare it with the measurements from SCUBA-2 by Koprowski et al. ( 2016 ), again finding reasonable agreement. It can be seen that the color condition S 850 / S 450 ≳ 0.6 can be exploited to preselect candidate galaxies at z ≳ 4. In Figure 10 , we show our predictions for the differential counts at 500 and 850 μ m for the red sources preselected according to the color criteria discussed above. At 500 μ m, the

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


in steps of 1′′ (a total field of view 15 × 119). The roll angle of the slits is –45° to the N–S direction on the Sun. Here, we focus on FUV spectra from both channels containing ∼1333–1337 Å (C ii lines), ∼1342–1344 Å (continuum), ∼1348–1351 Å (Fe xii line), ∼1353–1356 Å (Fe xxi and O i lines), and ∼1399–1406 Å (Si iv line), and on the NUV channel containing four spectral regions: 2791–2806 Å (Mg ii h and k lines), 2813–2816 Å, 2825–2828 Å, and 2831–2834 Å. IRIS also recorded SJIs for four passbands with a step of 2′′ and a total field of view 120 × 119: 1330 Å (C ii transition-region filter), 1400 Å (Si iv transition-region filter), 2796 Å (Mg ii k chromospheric filter), and 2832 Å (Mg ii wing photospheric imaging). 2.2. Solar Flare on 2014 March 29 An X1 flare observed on 2014 March 29 occurred in the active region NOAA 12017 with the GOES 1–8 Å flux starting to rise impulsively at 17:45 UT and peaking at 17:48 UT. IRIS started to observe the active region three hours before the flare, and the observations lasted a few minutes after the flare peak with the NUV exposure time of 8.00 s before 17:46:04.78 UT and 2.44 s after 17:46:13.98 UT, and a 75 s raster cadence (see e.g., Heinzel Kleint 2014 and Kleint et al. 2015 , 2016 ; Liu et al. 2015 ; Young et al. 2015 for detailed descriptions of IRIS observations of this flare). In contrast to the previous flare, the gradual phase was detected only at its beginning, and the flare loops are barely visible. Moreover, the slit rasters cover only the less pronounced parts of the loop system. We add this X-type flare because it was widely studied in the literature; however, our detailed analysis is focused mainly on IRIS spectra from the flare of 2015 June 22. To show the time lag between the flare ribbons and loops, light curves from a small part of the flare ribbons (red) and their corresponding loop tops (blue) in 1400 and 2796 Å are plotted in Figure 2 . It is seen that the loop tops peak about 3 minutes later than the ribbons in both 1400 and 2796 Å channels. Figure 2. Time lag between the flare ribbons and loops for 2014 March 29. Light curves from a small part of the flare ribbons (red lines) and their corresponding loop tops (blue lines) in 1400 and 2796 Å. Black lines represent the integral emission from the whole flare. Note that the sharp blue peak between 17:45 and 17:46 is due to leakage of saturated emission from the ribbon. 2.3. The Radiometric Calibration In our analysis, we used IRIS -calibrated data (Level 2 data), which are corrected for dark current, flat field, and geometry effects, and are wavelength calibrated. The radiometric calibration was performed in the following way. Intensities in the IRIS data are given in Data Number (DN) or counts (DN s −1 ). We perform radiometric calibration of the observed intensities to absolute units [erg s −1 cm −2 sr −1 Å −1 ]. To convert intensities to absolute units, we used the following calibration procedure:where I abs is the absolute

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


in Section 5 . To facilitate discussion, we define as a reference value. In order for MI to be disfavoured by less than 3σ, must be lowered by with fixed degrees of freedom. Hence, it would likely require a combination of (1) a different definition of r bar , (2) different values for the mass-to-light ratios, possibly including radial dependence, (3) removal of statistical outliers, and (4) other effects. Regarding point (1): There is an unaccounted bias in that the bins are defined by r bar , a point that is affected by uncertainty. The impact of this bias can be roughly estimated by moving r bar one point towards smaller (larger) radii. Doing so yields a reduction in χ 2 relative to , however with the accompanying degrees of freedom . The reduction in degrees of freedom (galaxies) are due to the criterion of at least two points at small radii. Considering the reduced chi square changes from to after the shift to smaller radii, it can be concluded that although the shift in r bar greatly affects the χ 2 it only slightly reduces the statistical disfavouring of MI. Regarding point (2): The dependence on the mass-to-light ratios may significantly affect g bar and consequently both the expected value of MI and the specification of r bar . The fixed mass-to-light ratios used here ( and ) are not optimal for all galaxies. This is clear from the rotation curve plots in Appendix C , where for some galaxies v bar > v obs for limited radial range (e.g. as is the case for CAMB and NGC 4217). To roughly gauge the effect of radically different mass-to-light ratios, we take (corresponding to galaxies dominated by DM at all radii, Lelli et al. 2017 ), yielding an increase in the χ 2 relative to (the result become slightly more significant). This is, however, just an example and one can imagine changing individual mass-to-light ratios and uncertainties potentially having a great impact on the result. Regarding point (3): Fig. 5 shows the distribution of residuals. Of the galaxies with | R i | > 4 UGC11455, NGC 4217, NGC 3109, ESO563-G021, and D631-7 have quality flag 1 whereas CAMB have quality flag 2 (listed in the SPARC data base). This indicates that the disfavouring of MI is not rooted in bad data (Fig. B1 in Appendix B shows residuals after discarding all galaxies with quality flag larger than 1). That being said, as mentioned in point (2), the fixed mass-to-light ratios used are too large in case of NGC 4217 and CAMB and possibly also affect the innermost radii of UGC11455 and ESO563-G021. It can also be argued that the high residual value in case of ESO563-G021 is at least partially rooted in a peculiar selection of points (e.g. see Fig. C1 in Appendix C ). Hence, although data are of good quality, for several of the significant outliers, there are valid arguments that could at least partially explain the high residuals. To be conservative and test the dependence on the outliers, we proceed to discard all galaxies with | R i | > 4. Doing so yield a

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


The x -axis in the line profiles gives the lambda channels and the y -axis is the intensity in arbitrary units. Both [S ii ] lines at 6717 Å and 6731 Å are detected. The decomposition of each profile is indicated by the thin lines. The resulting profile is shown as hollow circles and with numbers. The dotted line represents the sum of all fitted components. We assume the brightest component of the line to be the main velocity component of the SNR. It is marked with a 0 in Fig. 6 . For each emission line, we can also identify two extreme velocity components. We shall refer to these as V min and V max . These are marked with a 2 and a 4, respectively. Table 3 reports the velocity components of the [S ii ] λ6717 Å line. Column 1 is the region ID. Columns 2, 3 and 4 indicate the main and extreme velocity components ( V min and V max ) corrected for the local standard of rest (LSR). Column 5 gives the difference in velocity between the extreme velocity components. Column 6 lists the distance of each region in arcmin to the geometrical centre of the SNR. Column 7 lists the [S ii ]/H α line ratio and finally column 8 indicates the associated filament to which each region belongs. As one can see from Fig. 6 and Table 3 , the radial velocity profiles are, in general, composite, implying large motions as expected in a SNR. They show at least three velocity components. The brightest one corresponds to the systemic motion of the SNR, while two faint velocity components are seen at extreme velocities. The several velocity components found in the velocity profiles of the filaments are probably due to the SNR shock expansion, as well as to contamination due to the interaction of the SNR gas with dense interstellar clouds that could be associated with the H ii regions located to the north and south-west of the remnant. Note the existence in the SNR velocity profiles of a velocity component also identified with those of regions located in the Perseus arm, as we will discuss below. The velocities of the main component vary from −34 to −89 km s −1 . Taking the average of all the velocities of the main components in Table 3 , we obtain a LSR velocity of −59 ± 17 km s −1 as a first estimate of the systemic velocity of the SNR. The averages for the extreme velocity components, in all the boxes where velocity profiles were extracted, are V min ∼ −122 km s −1 and V max ∼ +152 km s −1 . Another way of obtaining the systemic velocity is to average the extreme velocity components ( V min and V max ). Doing this, we obtained a systemic velocity V LSR = −50 ± 6 km s −1 . For some regions, we find an additional velocity component averaging 1 km s −1 . This latter velocity component agrees with the component found by Roberts ( 1972 ) in the theoretical H i profile of the TASS model at 12° pitch angle ( V LSR = 0 km s −1 ) in the direction of SNR CTB 109. Roberts ( 1972 ) attributed this component to gas located very close to the Sun in the Orion spur. Fig. 7 shows a

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


flux ratio . The sum of the model primary and rescaled secondary spectra was then rectified to a unit continuum. We then repeated the CCF and tomography analysis of this model set of spectra in the same way as was done with the observed spectra to derive a relationship between reconstructed secondary CCF peak height and the assumed flux ratio at 1525 Å. Interpolating the observed CCF peak height in this relation led to a monochromatic flux ratio estimate of at 1525 Å. This flux ratio is related to the ratio of stellar radii bywhere is the monochromatic surface flux ratio of the stars and is equal to in the continuum at 1525 Å for the adopted temperatures of the two stars in the TLUSTY models. Using the above relation, the resulting radius ratio is , where the uncertainty includes the range of associated with the error in . Koubský et al. ( 2000 ) estimate that the Be star mass and mean radius of 60 Cyg are and , respectively. If we adopt these values, then the mass, radius, and gravity of the subdwarf are , and , respectively. This estimate of the companion mass places it above the Chandrasekhar limit of , so it is possible that the subdwarf may become a neutron star in the future. If so, then 60 Cyg may be a progenitor of a Be X-ray binary system. The estimated gravity of the subdwarf is higher than the limit in the TLUSTY grid that we used in deriving the best-fit . The relative strengths of the spectral features in the model spectra depend on the ionization balance in the model, so if we had used a higher model, we would probably arrive at a slightly higher estimate of and a somewhat lower value of R 2 . It is remarkable that among the now five known Be+subdwarf systems that 60 Cyg and 59 Cyg are separated by about one degree on the sky. The stars are not known as cluster members, but they may be affiliated with other early-type stars in their vicinity. We formed a list of stars with B spectral classifications from the catalog of Skiff ( 2014 ) that are situated within 2 deg of the midpoint between 59 Cyg and 60 Cyg, and then collected proper motions from the Gaia Collaboration et al. ( 2016 ) and parallaxes from Leeuwen ( 2007 ) for these stars. Table 3 shows those selected with proper motions and parallaxes within of those of 59 Cyg (HD 200120) and 60 Cyg (HD 200310). This collection of six objects may form part of a hitherto unknown co-moving group of equal age stars. If so, then 59 Cyg and 60 Cyg may be at a similar stage of binary evolution because of their common origin and age. Table 3 Co-moving Stars in the Vicinity of 59 Cyg and 60 Cyg Note. The spectral classifications are from the collection by Skiff ( 2014 ), proper motions and are from the Gaia Collaboration et al. ( 2016 ), and parallaxes are from van Leeuwen ( 2007 ). The V magnitude and radial velocity data are from SIMBAD, with the exception of the systemic velocities for 59 Cyg (Peters et al. 2013 ) and 60 Cyg (Koubský et al. 2000 ). We found no evidence of the

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


to the analytical Newtonian, adiabatic and steady-state wind model, referred to in the following as NASS, derived by Takahashi Janka ( 1997 ). It provides a simple, fully analytical description of the dynamics of the wind outflow at relatively late times or sufficiently far away from the PNS surface. The NASS wind model relies on the general assumptions listed above, in particular, those of a Newtonian PNS gravitational potential and of an adiabatic expansion. In addition, all the elementary and e − /e + weak interaction processes are assumed to be frozen out, nuclear β-decays not to affect Y e or s , and possible deviations from nuclear equilibrium with regard to strong and electromagnetic interactions to have no influence on the thermodynamical properties of the wind. Under such simplifying assumptions, the NASS model cannot predict any time variations of the entropy s , electron fraction Y e , or of the wind mass-loss rate , which are thus treated as constant input parameters. The basic NASS wind dynamics in the regime under consideration, and in particular for high enough entropies, is well approximated (Takahashi Janka 1997 ; Arnould et al. 2007 ) by where M * is the PNS mass, r the radius, v the velocity, T the temperature. The total energy per unit mass E may be obtained by setting a boundary condition and is usually expressed as a function of the wind energy: E = f w × E wind , where and v s equals the local adiabatic sound speed (Arnould et al. 2007 ). For f w = 1, the solutions correspond to a sonic wind, whereas for f w > 1, they are of sub-sonic wind type and usually referred to as breeze solutions. More details about the wind model can be found in Arnould et al. ( 2007 ). The entropy is dominated by photons, electrons and positrons in the wind so that the so-called radiation entropy is given by where f e = 1 in the high- T limit when electrons and positrons are highly relativistic, and decreases with T for high -values. In this study, it is approximated by , where T 9 is the temperature expressed in 10 9 K (Witti et al. 1994 ). Since the nucleosynthesis in the wind is followed by starting at a temperature of T 9 = 9, the total entropy is essentially equal to the radiation entropy (within a few per cent). Note that the ‘radiation entropy’ is measured here per baryon in units of the Boltzmann constant k B and includes both the photon and lepton contributions, but not the baryonic ones. For the initial conditions adopted here, the latter amounts to typically 9 k B /baryon. In the wind model of Takahashi Janka ( 1997 ), the radial evolution of the velocity, v ( r ), and density, ρ( r ), for specified total energy ( E ) per unit mass of outflow material (or, equivalent, for given f w ), given entropy and given mass-loss rate () is determined by the energy equation (based on Bernoulli's equation, see equation 1 ) and the continuity equation . The temperature then follows from the assumption of constant entropy, which couples

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


indicating a harder γ-ray spectrum. The curvature parameter β gives a measure of the presence of cut-off in the spectrum at high energies with a large value of β indicating a sharper cut-off. Therefore, investigation of any changes in the values of α and β parameters during the five epochs can point to changes in the γ-ray spectral shape. A change in the γ-ray spectral parameters during a flaring state could point to a change in the position of the γ-ray-emitting region. The variation of the α and β against flux during the five epochs studied here is shown in Fig. 14 . No trend on the variation of α with flux was seen during the five epochs considered here. However, a plot of β with flux (Fig. 14 ) shows a clear trend of a decrease in the curvature parameter with increasing flux. Linear least-squares fit to the data gives β = (−0.005 ± 0.009) F V + (0.168 ± 0.029) with a correlation coefficient of −0.77. Clearly the value of β is high and low at the lowest and the highest flux levels among the five epochs analysed here. Such a trend is also seen by Ackermann et al. ( 2015 ) on analysis of the FSRQs in the third catalogue of AGNs detected by Fermi (3LAC). The changes in the γ-ray spectral shape during different brightness states of 3C 454.3 could point to the emission site located at different regions during different brightness states; however, other explanations could not be ruled out. Studies on the flares of 3C 454.3 in December 2009 and November 2010 that fall in the epochs A and B studied here concluded that the γ-ray emission regions were located close to the central black hole (Jorstad et al. 2012 ; Isler et al. 2013 ). Figure 14. Variations of the parameters α and β with flux. 4.2 Connection between optical and GeV flux variations In a majority of the multiwavelength monitoring observations of blazars, close correlations between the flux variations in different bands were noticed (Bonning et al. 2009 ). This was explained on the co-spatiality of the emission regions emitting in different bands and the correlated optical and GeV flux variations can be understood in the standard leptonic emission processes according to which the same relativistic electrons produce optical and γ-ray emission via synchrotron and IC processes. However, there are a handful of blazars where the emission in the optical and GeV γ-ray bands are found not to be correlated (Chatterjee et al. 2013a ; Dutka et al. 2013 ; Cohen et al. 2014 ; MacDonald et al. 2015 ). During the 9 yr of monitoring data analysed here we found four flaring epochs in the optical, namely A,B, D, and E. During epochs A and B, the optical flare is accompanied by a γ-flare, while at the other two epochs D and E, though the optical flares have amplitudes similar to those of epochs A and B, the γ-rays during epochs D and E were either weak or undetected. This is clearly seen in Fig. 15 , where the logarithm of γ-ray flux is plotted against the logarithm of optical flux. The results of the linear

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


a radius of 3 arcmin. The Galactic north/south line runs through azimuthal angles 35°/215°. Of the profiles in Fig. 8 , the maximum from ring 2 appears to align the closest with the Galactic north direction, as might be expected if the column density were increasing towards the Galactic plane. Further discussion is deferred to Section 4.1 . VP15 also noted the presence of azimuthal structure in the XRT halo data; however, they did not separate out the behaviour of rings 1 + 2 or 3 + 4, or proceed to discuss the findings in any depth. 2.3 Halo spectral analysis Spectra from the rings were extracted from the longest PC mode snapshots, or adjacent snapshots, using annular extraction regions tuned specifically for each case. Given their relative separations, spectra from rings 1 and 2 were extracted as one, which increased the statistical quality of the data. The same was done for rings 3 and 4. PC event grades 0–12 were selected for the spectra. As the rings dominate the field of view and leave limited space on the detector from which to extract a good quality background spectrum, the PC mode observations from 2012 (total exposure 132 ks) were used to obtain an accurate non-halo background spectrum, which was extracted using an annulus of size 2.95–7.66 arcmin centred on the source, after five faint background point sources were removed. (Note, the background sources were too faint to have any effect on the radial profiles in Section 2.1 .) Also, as the central source was often observed offset from the centre of the CCD, a given ring samples different parts of the telescope vignetting. To correct for this in the ancillary response files (ARFs), we followed the procedure outlined by Moretti et al. ( 2011 ). This involved using a vignetting map, created by dividing exposure maps made with and without the vignetting correction (calculated at 1.5 keV) applied, to work out the mean vignetting correction in each extraction annulus. Then, using the analytical description of the vignetting given by Tagliaferri et al. ( 2004 ), these were converted to mean off-axis angle estimates that were used as an input to the XRT software task xrtmkarf to apply the energy-dependent mean vignetting correction to the on-axis ARF. The non-vignetted exposure map was also used to estimate the mean exposure in the annulus and the spectral file exposure time was updated accordingly. The spectra were fit in xspec (version 12.8.2; Dorman Arnaud 2001 ), using its implementation of the Cash ( 1979 ) statistic (C-stat), which, when a background spectrum is supplied, is a profile likelihood statistic. The spectra for a given ring at different epochs were modelled using an absorbed power law, with the photon indices and column densities tied between spectra. The absorption was provided by the tbnew model, 3 using the abundances of Wilms, Allen McCray ( 2000 ) and cross-sections of Verner et al. ( 1996 ). The fitting was performed over the energy range 1–5 keV, where the low

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of Fig. 5 , since the contact between the QS and HS surfaces does not occur yet, QS and HS surfaces coexist independently and we use ‘QSHS’ to denote this stage. When = −1.502164, the contact between the QS and HS surfaces begins to occur, and we define this critical value as the upper boundary of of the TS motion, . In the blue region of Fig. 5 , the compound isosurface is made up of QS, TS, and HS portions, and we use ‘QS + TS + HS’ to denote this stage. Figure 5. Evolution of isosurfaces with i m = 15°, where blue points denote values used in the following figures. Fig. 6 displays phase structures with (a) i m = 45° and (b) i m = 75° in the torus space, where the colours denote different values of . Compared with the result in Fig. 2(b) , we can observe that i m has a significant influence on the phase structure. The evolution of isosurfaces of i m = 45° and 75° with the decrease of are shown in Fig. 7 . Different the result in Fig. 5 , we can observe that when i m = 45°, is larger than . Numerical computation indicates that when i m = 29.65°, is equal to ; if i m > 29.65°, is larger than . QS and TP surfaces coexist independently in the yellow region of Fig. 7(a) , and when the contact between the QS and TP surfaces begins to emerge, the isosurface is made up of QS, TS, and TP portions (see the blue region in Fig. 7a ). If further deceases, the TP portion on the compound surface will be replaced by the HS portion. Numerical computation also shows that with the increase of i m , gradually decreases and approach , so the yellow region in Fig. 7(a) shrinks with the increase of i m . When i m ≥ 61°, is equal to and independent TP isosurfaces totally disappear. Hence, as we can see from the result of i m = 75° in Fig. 7(b) , the compound isosurface in the blue region is made up of QS and TS portions. Figure 6. isosurface with (a) i m = 45° and (b) i m = 75° in the torus space, where the colours denote different values of . Figure 7. Evolution of isosurfaces with (a) i m = 45° and (b) i m = 75°, where blue points denote values used in the following figures. Fig. 8 displays collision curves of i m = 15°, 45°, and 75° in (a) torus space and (b) ω − e projection. From Fig. 8(a) , we find that the φ range of collision curves starting from the point P = ( e 0 , 0, 0) expands with the increase of i m . In the ω − e projection, we can observe that with the increase of i m , the angle between the branches of collision curves increases. In the following section, we will demonstrate that collision curves play an important role in the co-orbital motion and the above findings can explain some co-orbital phenomena. Figure 8. Collision curves of i m = 15°, 45°, and 75° in (a) torus space and (b) ω − e projection. 4 LOCI IN THE TORUS SPACE In this section, we implement numerical integration in the Sun–Jupiter CRTBP to demonstrate the validity of the semi-analytical analysis in the last section and the detail of the co-orbital motion. Numerical integration is

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


et al. 2016a ) in the standard canonical inflationary scenario ( c s = 1), as has been explicitly shown in Rezazadeh et al. ( 2015 , 2016 , 2017a ). In the present paper, we aim to refine the power-law, intermediate, and logamediate inflationary models in light of the current observational results by considering them in the DBI scalar field setting. Motivated by Spaliński ( 2008 ) and Tsujikawa et al. ( 2013 ), we assume in our work that the sound speed is constant during inflation. We examine the viability of each scale factor in light of the Planck 2015 results (Ade et al. 2016a ) and also present some observational constraints on them. The outline of this paper is as follows. In Section 2 , we review briefly the basic equations governing the background cosmology in the DBI inflation. In addition, we also represent the power spectra of the primordial scalar and tensor perturbations. Then, in Sections 3 – 5 , we respectively investigate the power-law, intermediate, and logamediate DBI inflationary models with constant sound speed. Finally, in Section 6 , we summarize our conclusions. 2. DBI Inflation Within the framework of Einstein’s gravity, the action of non-canonical scalar field models is given by (Armendáriz-Picón et al. 1999 ; Garriga Mukhanov 1999 )where g and R are the determinant of the background metric and the Ricci scalar, respectively. Throughout this paper, we work in units where the Planck reduced mass is taken equal to unity, = 1, for the sake of simplicity. In the present work, we concentrate on the DBI non-canonical scalar field with the Lagrangian density (Alishahiha et al. 2004 ; Silverstein Tong 2004 )where is the warp factor, while , and are the canonical kinetic term and potential of the DBI scalar field φ , respectively. For the DBI Lagrangian ( 2 ), the energy density and pressure of the non-canonical scalar field φ are given by where the subscript, “,” indicates the partial derivative with respect to X . Moreover,is the parameter determining the relativistic limit of brane motion in a warped background. Note that the parameter γ is defined in analogy of the Lorentz factor appearing in relativistic particle dynamics. The sound speed is generally defined bywhich specifies the propagation speed of the inflaton fluctuations relative to the homogeneous background. In order for the sound speed to be physical, it should be real and subluminal, (Franche et al. 2010 ). Applying Equations ( 3 )–( 5 ), the sound speed in DBI inflation takes the form For the homogeneous and isotropic background spacetime, we consider the spatially flat Friedmann–Robertson–Walker (FRW) metric. Therefore, varying the action ( 1 ) with respect to the metric yields the Friedmann equations in the DBI inflation as follows: Here, is the Hubble parameter, and a is the scale factor a of the universe. The dot denotes the derivative with respect to the cosmic time t . Considering the FRW metric, the canonical kinetic term is simplified to . Taking the

B-Citation I-Citation I-Citation I-Citation O O B-Model I-Model I-Model I-Model 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 O B-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 B-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 B-Dataset I-Dataset I-Dataset 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-Model B-Model O B-Model I-Model I-Model I-Model O O O O O O O O O O O O O O B-Model I-Model O O O O B-Model I-Model O O O B-Model I-Model I-Model I-Model 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 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 B-Model I-Model I-Model I-Model 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 B-Model I-Model I-Model O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation 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 B-Model B-Model B-Model 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-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O


photons via the inverse Compton process makes it necessary to simultaneously compute the photon distribution . It becomes time dependent and is integrated according toSince all radiation processes are calculated in the isotropic approximation, i.e., from , and no external photon fields are considered, the gradient of the photon distribution is very small. Hence, in this case photon propagation can be neglected. The synchrotron power spectrumis computed in the Melrose approximation (Brown et al. 1983 ): Employing the same approximation, the synchrotron self-absorption coefficientis calculated (Ginzburg Syrovatskii 1965 ). As pointed out earlier, the inverse Compton process takes place in the Klein–Nishina regime. The resulting losses and gains are obtained fromThe catastrophic loss is parameterized by the escape timescale and depends on the radius of the cell. The total flux emerging from all spatial cells is calculated similar to the model of Blandford Konigl ( 1979 ). The integrated flux per cell can be calculated viaThe observed frequency depends on the Doppler factor and the redshift . The flux from one cell is proportional to the photon density and the surface of the cylindrical cell , where is the cell size along z . The speed of light c reflects the escape timescale given above. In the time domain, light-travel times have to be accounted for. The total flux from the source is then the sum over the fluxes F i from all zn cells at the time when they were causally connected to the reference point. This point is chosen to be the end point at , i.e., closest to the observer:The time delay t i can be calculated from the additional distance along the line of sight:where is the angle between the z -axis and the line of sight. For time-dependent simulations any time interval in the observer’s frame is boosted from the shock frame according to . 3. RESULTS In this section we will first present a classical SSC fit to the high-energy data of the observational campaign by Abdo et al. ( 2011a ). Based on the resulting fit, we argue that the artificial spatial boundary condition should and can be replaced by a specific morphology of the radial confinement behind the shock. 3.1. High-energy SSC Fit Similar to our previous work RS13 , the starting point is a classical SSC fit, meaning that the size of the emission region is a free parameter, shown as sim1 in Figure 2 . In addition to the parameters in Table 2 , the parameters r = 2.5, , an injection energy , and an isotropization timescale were used. These values were used for all simulations, except log2c. The fit was done “by eye,” as is common for complex radiation codes. Figure 2. Overall SEDs for various simulations and a detailed view of the radio band. sim1 was obtained with a variable box size z max , altering the resulting SED. Simulations log[1–3] were obtained with a fixed but large z max and show the effect of an increase in expansion speed. The peak in the optical is due to the host

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


range 4.7 M ⊙ –7.8 M ⊙ . In Fig. 1 (a)– (c), variations of TCAF model fitted shock location (in r s ), normalization and mass values with time (day in MJD) are shown, when all model parameters were assumed to be free. Fig. 1 (d) shows the variation of model fitted masses when the normalization was frozen at an average value of 139.07. Figure 1. Variations of TCAF model fitted parameters: (a) shock location (in r s ), (b) normalization ( N ) and (c) mass of the black hole ( M BH in M ⊙ ) over the entire period of the 2010 outburst of MAXI J1659−152, when all model parameters are kept as free. In (d), TCAF fitted M BH is shown when the model normalization was kept frozen at 139.07, which we obtained from taking an average of the normalization values of panel (a). Table 1. TCAF model fitted mass and normalization values. Here, X=95358-01, Y=95108-01, and Z=95118-01 are the initial parts of the observation IDs. In columns 4 and 5, the TCAF fitted model normalization and BH mass values are shown when all TCAF-related parameters are free while fitting the spectra and in column 6, model fitted mass values are shown when normalization is frozen at 139.07. 1σ errors for N and masses are shown in superscripts. We can also cross-check the range of the predicted mass by the above method when we vary M BH versus the reduced χ 2 of the best-fitted spectra. The best fit using the current version (v0.3) of the TCAF model was obtained based on the model fitted reduced χ 2 values when found nearly equal to unity. In Paper I and in Table 1 , model parameters are given when best fits are obtained. After achieving satisfactory model fits, we kept all model parameters, such as sub-Keplerian rate , Keplerian rate , location of the shock X s , compression ratio R and normalization N , frozen, except the mass of the black hole, and found how the reduced χ 2 changed with the mass of the black hole. In Fig. 3 (a)–(c), the variation of reduced χ 2 with mass of the BH is shown for three different spectra (obs. IDs: 95118-01-06-01, 95118-01-16-01, 95118-01-21-00) selected from three different spectral states (SIMS, HIMS and HS, respectively). As in the earlier cases, if we consider to be the upper limit for acceptable fits, we obtain a mass in the range 4.4 M ⊙ –7.3 M ⊙ . 3.2 QPO frequency(νQPO) – time (day) evolution: fitted with POS model Low-frequency QPOs are very commonly seen in PDSs of X-ray intensity variations (light curves) emitted from discs surrounding stellar massive black holes. Sometimes the dominating frequencies of these QPOs (generally type ‘C’) are found to evolve with time, mostly in HS and HIMS from both rising and declining phases of an outburst. The monotonic evolution of these QPO frequencies could be fitted very well by a propagating oscillatory shock (POS) model (see Chakrabarti et al. 2005 , 2008 ; Chakrabarti, Dutta Pal 2009 ; Debnath et al. 2010 , 2013 ; Nandi et al. 2012 ). According to the POS model, the frequency is inversely

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are compatible with there being no correlation of κ 500 with any of the parameters considered. Similarly, for each relationship, Spearman rank correlation tests do not allow us to reject the null hypothesis (of there being no correlation) to a likelihood of 0.01. We note, however, that the size of our sample is small compared to the scale of the uncertainties on κ 500 ; hence we in no way rule out that such correlations could exist, but not be detectable in our data. 7 COMPARISON TO PREVIOUS ESTIMATES As can be seen in Fig. 1 , our determined value of κ d is low compared to existing literature values (although the very commonly used values of Draine 2003 and Draine Li 2007 are within our bootstrapped uncertainty). Converting the James et al. value to a wavelength of 500 μm for comparison with our own, as per equation ( 1 ), translates it to κ 500 = 0.20 ± 0.06 m 2 kg −1 ; a factor of 3.92 larger than our value, despite the fact we employ the same fundamental technique; it is important to address the reasons for this. As discussed in Section 2 , our consideration of systematic effects, using ξ (i.e. the contribution of helium and metals to a galaxy's gas mass) and δ O (i.e. oxygen depletion in H ii regions) will account for a factor of 1.86 reduction in κ d relative to James et al. We also employ a slightly larger value of ε d (0.5 versus 0.456), leading to a further factor of 1.10 reduction in κ d . However, our use of a more modern, smaller value of (0.0134 versus 0.019) works in the opposite direction, diminishing the reduction in κ d by a factor of 0.71. In combination, these global effects correspond to a factor of 1.42 reduction in κ d relative to James et al.; additional effects must be at work to explain the full difference between our values. Fortunately, M 61 (NGC 4303) is present in both the James et al. sample and our own, allowing for a direct comparison of the reasons for the difference in values for a specific case. For M 61, we find that our result of κ 500 = 0.039 m 2 kg −1 (see Table 1 ) is a factor of 5.13 less than the κ 500 = 0.20 m 2 kg −1 value that James et al. found for their sample as a whole. James et al. did not work out values of κ d for individual sources, but do say that there is scatter of a factor of 2 around their sample-wide relation, hence we need to account for a factor of difference between our κ d for M 61, and the James et al. sample-wide value. In Appendix A , we work through each of the sources of difference in our values of κ d in the case of M 61, and find that a factor of 6.31 is to be expected, well within the predicted range – highlighting the dramatic influence of considering systematic effects and utilizing superior observations. During the Herschel science demonstration phase, Eales et al. ( 2010 ) applied a resolved variant of the James et al. method (where they pegged the dust mass surface density to the gas mass surface density, assuming a fixed Schmidt–Kennicutt law and a Milky Way

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


corresponding to the position of the hydrogen-burning shell that is slowly moving outwards in mass as the helium core continues to grow. The surface chemical composition is the same as obtained at 7 R ⊙ since, in the absence of any additional mixing process, there is no change in the surface composition after the RGB-bump (see Table C.2 ). Age differences remain at the same level as they were at 7 R ⊙ (cf., Fig. 2 ) and are sustained in the subsequent evolution towards the RGB tip. 5.2. Evolution of 1.5 M⊙, 2.0 M⊙, and 2.5 M⊙ models Using the same initial composition as in the 1 M ⊙ case, we calculated and compared tracks and stellar structures at higher masses: 1.5 M ⊙ , 2.0 M ⊙ , and 2.5 M ⊙ . The first and most evident difference with respect to the lower-mass case is the existence of a convective core during the main-sequence evolution, whose extent as a function of age is depicted in Fig. 6 . Although all codes rely on the Schwarzschild criterion for defining the core convective boundary there are differences in the predicted core size of the order of 10% across codes. Fig. 6. Evolution of the convective-core size during the main-sequence phase as a function of age for the 1.5 M ⊙ ( left ), 2.0 M ⊙ ( centre ), and 2.5 M ⊙ ( right ) solar-radius calibrated models. In many cases a saw-tooth profile is visible at the edge of the core as a consequence of changes in its chemical composition throughout the evolution. Nuclear burning produces changes across the chemically homogeneous central region of the model. In the case of growing convective cores (1.5 M ⊙ ), the sharp increase in density at the edge of the core increases the opacity, which consequently increases the radiative temperature gradient in that position. As evolution proceeds and the discontinuity becomes larger, the radiative gradient outside the core surpasses the value of the adiabatic gradient turning that additional layer convectively unstable. The core suddenly increases in size as is revealed by the sharp spikes in the core profiles (see left panel in Fig. 6 ), and the subsequent fast decrease in the core extent occurs once the composition of the layer is homogenised to the core value. The radiative temperature gradient then decreases as a result of the opacity decrease and the layer becomes convectively stable again (see e.g. Silva Aguirre et al. 2011 ; Gabriel et al. 2014 ). The existence of these “peaks” in the core size as a function of time are the result of the numerical implementation of the Schwarzschild criterion in evolutionary codes, and the behaviour of the core boundary is expected to be smooth as a function of time in real stars. For the higher-mass cases (2 M ⊙ and 2.5 M ⊙ ) the evolution of the convective-core size is indeed smoother as it reaches it maximum extension at the beginning of the main sequence and contracts throughout the core hydrogen-burning phase. One of the expected consequences of the 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 B-Tag O B-Tag O O B-Tag O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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


show that the dependence of the mass loss rates on the EUV SED is mild. Thus, using an arbitrary EUV SED profile provides a reasonable estimation for the mass loss rate. Figure 13. The variations of the total mass loss rate with the variation of spectral index F 50–400 / F 50–900 . The mass loss rates are determined by the amount of effective absorption of stellar EUV radiation. Thus, the heating is related to the product of number densities of species and the absorption cross-sections ( H heat ∼ nσ ν ). High-energy photons can penetrate deeper into the atmosphere due to the smaller cross-sections. In the dense regions of the atmosphere, more species can absorb the stellar irradiation. On the other hand, the regions where low-energy photons are absorbed are at a higher altitude than those where high-energy photons are absorbed. Due to the decrease in the number density of species with increasing altitude, the number of particles absorbing the stellar irradiation also decreases. However, the effective heating by high- and low-energy photons is comparable because the heating of the atmosphere is proportional to the number density of particles and the cross-section of photoionization. For atomic hydrogen, the cross-section of photoionization is inversely proportional to the cube of the frequency (Spitzer 1978 ). This also explains why the total mass loss rates predicted for different EUV spectra are comparable. 4. SENSITIVITY OF ATMOSPHERIC PROPERTIES TO EUV SEDS: DISCUSSION 4.1. The Effect of Hydrodynamic Escape Parameters on the Temperature In Table 2 , we have shown that the hydrodynamic escape parameter (where R p and M p are the radius and mass of the planet, and μ and T 0 are the mean mass per particle and temperature at the lower boundary of the atmosphere) is smaller for Kepler-11b than for other planets. The hydrodynamic escape parameter is defined as the ratio of the potential energy to the kinetic energy of the gas. The gas can be bound to the planet if the temperature of the gas is very low or the radius of the planet is small (the mass of the planet is assumed to be constant). In such a case, the value of λ is large. For higher temperatures and/or larger R p values, however, the kinetic energy of the gas can be greater than the potential energy. Thus, the atmosphere can escape the bounds of the planet. The latter case corresponds to a smaller λ . In an atmosphere heated by XUV radiation of the host star, the temperature of the gas can reach a few thousand kelvin at the bottom of the atmosphere (Yelle 2004 ; Murray-Clay et al. 2009 ; Guo 2011 , 2013 ). Thus, the value of λ can decrease with increasing altitude as a result of high temperatures and a large radius. This means that the gas can escape the planet at some altitudes. The critical value of λ to produce a hydrodynamic wind is about 10–15 (Stone Proga 2009 ). Thus, a thermally driven hydrodynamic wind can be produced easily in the atmosphere with a smaller λ because weak XUV

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


observers (black dot, Vaquero et al. 2016 ) and additional sunspot observations by Fisher (gray triangle, Denig McVaugh 2017 ) and Hallaschka (green triangle, Carrasco et al. 2018 ). In Figure 5 , we have incorporated the sunspot group number in Derfflinger’s summary manuscript and logbooks as they are and contextualized them upon the existing sunspot group number by contemporary observers. The summary manuscript and logbooks occasionally provide observations with different group number and observations on different days. As observed in Figure 6 , based on our revised sunspot group number series, we have revised Derfflinger’s yearly sunspot group number during 1802–1824 in comparison with the number before our revision in the existing data sets (Hoyt Schatten 1998a , 1998b ; Vaquero et al. 2016 ). Our revision shows a significantly different trend of yearly Derfflinger’s sunspot group number (Figure 6 ) in comparison with that before our revision (Figure 7 ). We observed that Derfflinger’s trend is much more consistent with the sunspot number (v. 2; Clette et al. 2014 ; Clette Lefevre 2016 ) than the group sunspot number series (Svalgaard Schatten 2016 ; Usoskin et al. 2016 ) in Cycle 5. However, Derfflinger’s data are more consistent with the group sunspot number series than the sunspot number (v. 2; Clette et al. 2014 ; Clette Lefevre 2016 ) in Cycle 6. The cycle amplitude seems slightly larger in Cycle 5 than in Cycle 6. Figure 6. Derfflinger’s revised yearly sunspot group number in the summary manuscript (red diamond) and logbook (blue square) with standard errors from averaging, in comparison with the yearly number before our revision (black circle, Hoyt Schatten 1998a , 1998b ; Vaquero et al. 2016 ). Figure 7. Comparison of the yearly international sunspot number (Clette Lefevre 2016 ) divided by 20 (Muñoz-Jaramillo Vaquero 2019 ) and existing yearly sunspot group number series with backbone method (green curve, Svalgaard Schatten 2016 ; purple curve, Chatzistergos et al. 2017 ) and active day fraction method (blue curve, Usoskin et al. 2016 ). 6. Measurements of the Sunspot Positions It is difficult to determine the heliographic coordinates of the sunspots from Derfflinger’s drawings as he had not recorded an explicit time for each drawing. There are horizontal and vertical lines in the drawings, which are supposed to be parallel to the horizon and pointing to the zenith, respectively, as the manuscripts mention that the observations are made with an azimuthal quadrant. The manuscript also states that the images are upside down, i.e., the lower end of the vertical line points to the zenith. An indication of the observing time comes from the logbooks in which the sunspot drawings are inserted above, below, or within the solar elevation timings. Hence, we are using two ways of fixing the position angle of the solar disk to obtain the heliographic coordinates. The first method uses the nearest time of the solar elevation measurements to

O O O B-Citation I-Citation I-Citation I-Citation O O O O O O B-Person O O B-Citation I-Citation I-Citation O O B-Person O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O B-Person O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-Person 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 O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Person O O O O O O O O O O O O O O O O O O O B-Person O O O O O O O O O B-Identifier I-Identifier B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation 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 B-Person O O O O O O O O O O O O O O B-Identifier I-Identifier 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 B-Person O O O O O O O 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 O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Citation I-Citation I-Citation O O O O B-Citation I-Citation I-Citation 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 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 B-Person O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-CelestialObjectRegion I-CelestialObjectRegion 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 B-Instrument 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 O O O O O O O O O O O O O O O O O O O O O O O O O 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-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 B-Citation O O O O B-Dataset I-Dataset I-Dataset B-Citation I-Citation I-Citation I-Citation O O O O O B-URL O O O O O O O O B-Database I-Database I-Database I-Database I-Database I-Database I-Database I-Database I-Database I-Database O O B-URL O O O B-Database I-Database I-Database I-Database I-Database O O B-URL O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Database O O O O O O O O O O O O B-Database O O O O O O O O O O O O O O O B-Wavelength O O O O O O O B-ObservationalTechniques I-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O 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-ObservationalTechniques I-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O O O B-Database I-Database O O O O O O O O O O O O O B-ObservationalTechniques I-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O O O B-ObservationalTechniques I-ObservationalTechniques I-ObservationalTechniques O O O O B-Dataset I-Dataset I-Dataset I-Dataset O B-Citation I-Citation I-Citation I-Citation I-Citation O O O B-Model I-Model I-Model O B-Citation O O O O O O O O O O B-Dataset I-Dataset I-Dataset B-Citation I-Citation I-Citation I-Citation O O O B-CelestialObject O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O B-Citation I-Citation I-Citation O O O


of these frequencies as the result of nonlinear mode coupling. Note that we focus on the significant frequencies (S/N > 4) that appear both in the spectra of single-quarter data and all-quarter data. Other tidally induced pulsations with low amplitudes could also exist. For example, the peaks at 0.7095 day −1 and 4.3990 day −1 are 5 and 31 times the orbital frequency, respectively. Figure 5. Fourier spectrum of light curve residuals with eclipses masked. The upper panel was calculated from the quarter 1 long cadence data. The lower panel presents a similar plot but using all quarters (0–17) of long cadence data. The 10 dominant frequencies listed in Table 2 are labeled. Filled and open circles mark the harmonic and nonharmonic orbital frequencies, respectively. The spectral window is shown in the inset. Table 3 Main Oscillation Frequencies of KIC 3230227 Many frequency triplets can be seen in the spectrum, with equal spacing of orbital frequency. Close examination reveals that all these triplets have frequencies that are equal to times orbital frequency. Thus they can be explained as a combination of one real oscillation peak and two side-lobes due to the spectral window (Figure 5 ). The nonharmonic peaks generate side-lobes at and . We find that after pre-whitening , and f 4 , these triplets essentially disappear, and only peaks remain, supporting the above argument. Low amplitude m = 0 modes can also exist. At high inclination, these modes are expected to have low amplitudes. As discussed below, the Ledoux constant C nl (Ledoux 1951 ) is about 0.16 for the g -modes in the observed frequency range. This means the splitting is about for modes with frequencies much higher than f rot . If we adopt pseudo-synchronous rotation day −1 , are then 0.49 and 0.98 day −1 for m = 1 and m = 2, respectively. Thus the splittings will be located several orbital harmonics away from their central m = 0 peak. This also suggests that the splittings are not due to rotation. The amplitude variations of these oscillations are shown in Figure 6 and listed in Table 4 . Most of the frequencies have relatively stable amplitudes over 16 quarters, with variations less than 0.05 milli-mag. The exception seems to be f 3 , which decreased from 0.174 milli-mag in quarter 1 to 0.078 milli-mag in quarter 16. Figure 6. Amplitude variations of 10 dominant oscillation frequencies (Tables 3 and 4 ). Filled and open circles indicate the harmonic and nonharmonic orbital frequencies, respectively. Table 4 Amplitude Variations of the Main Frequencies ( mag) 3.2. Mode Identification from Phases For tidally induced oscillations in KIC 3230227, it is sufficient to consider only the dominant l = 2 term since higher order terms are at most times (an order of magnitude) smaller than the l = 2 term (Equation (8) in Burkart et al. 2012 ). Additionally, the observed amplitudes of higher order modes () are reduced by geometrical cancelation upon integration over the stellar surface, so

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


linear relation and the deviation is about 4%. Furthermore, Hansen et al. ( 2014 ) and Niu et al. ( 2015 ) found that the abundance patterns and the decreasing trends of the weak r-process abundances versus atomic number are robust. In this work, using the decreasing relation, we estimate the abundances of the weak r- and main r-process for the elements As and Se, which are listed in Table 1 . For comparison, the corresponding r-process abundances in the solar system (Sneden et al. 2008 ) are also listed. Table 1 Main r-process and Weak r-process Abundances of As and Se Adopted in this Work Note. a Sneden et al. ( 2008 ). The five superposition coefficients in Equation ( 1 ) can be derived by comparing the calculated abundance N i, cal with the observed abundance N i, obs and seeking the smallest χ 2 which is calculated aswhere is the observed uncertainty. Thirty-eight elements are used in the calculations, thus K = 38. The value of K free is five, which means five superposition coefficients. All observed abundances of the star HD 94028 are taken from Roederer et al. ( 2016 ). The abundances derived from neutral lines are adopted for the light neutron-capture elements Mo and Cd. For the best-fitting results, the value of χ 2 is 0.887 for case A and 0.938 for case B. The calculated superposition coefficients for case A are C r , m = 1.50, C pri = 3.90, C s , m = 1.84, , and C Ia = 0. For case B, these coefficients are C r , m =1.49, C pri = 4.10, C s , m = 1.82, , and C Ia = 0. The coefficients C r,m , C pri , and C s,m are larger than 1.0, which means that the fractions contributed by the main r-, primary, and main s-process for HD 94028 are larger than those of the solar system. On the other hand, C sec is smaller than 1.0, which implies that the fraction contributed by the secondary process for this star is smaller than that of the solar system. The coefficient C Ia is 0, which is consistent with the prediction of Kobayashi et al. ( 1998 ) that SNe Ia did not occur for the progenitors with [Fe/H] ≤ −1.0. Direct comparisons of calculated and observed abundances for case A and case B are plotted in Figures 1 (a) and (b), respectively. In the upper panels, the solid lines are the calculated abundances and the filled circles are the observed abundances of HD 94028. The lower panels show the related offsets () and the corresponding observed uncertainties. From Figures 1 (a) and (b), we can see that, for most elements, the calculations are consistent with the observations within the uncertainties. Comparisons between the individual component abundances and the observed abundances in HD 94028 are shown in Figures 2 (a) and (b). Figure 1. Upper: comparisons of calculated results (solid lines) with the observed abundances (filled circles). The observed upper limits are represented by circles with downward arrows. The data are taken from Roederer et al. ( 2016 ). Lower: the relative offsets ( ) and the observed uncertainties. Figure 2. Abundance

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shift for all sources in each track, the task uti _ doppler _ fix is then called. Applying this calibration technique is straightforward and is described in the MIR cookbook. We applied this new correction to every calibrated data set for the MASSES program, including the previously published data described in Paper I . The effect of the correction is significant for Perseus protostars given the relatively narrow lines (on order of 1 km s −1 ). We found that over the course of a track for Perseus, the Doppler velocity correction for each integration could amount to differences of up to ∼1 km s −1 . In comparison of pre- and post-correction data at locations where the spectral lines are bright, flux differences in each channel of up to 50% were not uncommon. The correction, by removing the effects of the smearing, significantly improved the sharpness of all narrow spectral line features, allowing for easier identification of weak narrow lines and higher signal-to-noise ratio for stronger ones. In Figure 1 , the products before and after applying the Doppler correction fix are shown for C 18 O(2–1) spectra at a single pixel for Per-emb-2 and Per-emb-40. It is apparent that without the fix, the velocity has a significant shift, and the spectral features are smoothed. Because the real-time error was not identified until after the publication of Paper I , the results presented there were adversely affected; we stress that the data presented in this paper improves on and supersedes that presented in Paper I . After the Doppler shift correction was applied, all data were converted to MIRIAD format (Sault et al. 1995 ). Figure 1. Primary-beam-corrected C 18 O(2–1) spectra, taken at the 1.3 mm continuum peak pixel for Per-emb-2 (top panel) and Per-emb-40 (bottom panel). The blue spectra show what the spectra looked before the fix, while the red spectra show after the fix. 3.2. Data Imaging All imaging was done using MIRIAD and is also described in detail in Paper I . We repeat most of the details here, as there are a couple of minor differences which will be specified below. For spectral lines, the continuum is first subtracted using task uvlin , where a range of line-free channels (visually identified) is specified by the user. The task fits a DC offset to these channels and subtracts the offset from the window. For both continuum and spectral lines, an inverse Fourier transform was used on all visibilities (i.e., specifying all tracks for each target as specified in Table 1 ) to create a dirty image using the MIRIAD task invert and specifying options “systemp” and “double.” During the invert task, we create two data products of different resolutions by specifying Brigg’s robust parameters of both −1 and 1. This differs from the subcompact release (Paper I ), where we only delivered products that use robust = 1. A robust parameter of 2 is similar to natural weighting, which minimizes the noise in the image, while a robust parameter of −2 is

O O O O O O O O O B-Software I-Software I-Software I-Software I-Software 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-Survey I-Survey O O O O O O O B-Citation I-Citation 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 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 B-Wavelength I-Wavelength I-Wavelength O O O O O O B-CelestialObject 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 B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O B-Software I-Software B-Citation I-Citation I-Citation I-Citation O O O O B-Wavelength I-Wavelength I-Wavelength O O O O B-Wavelength I-Wavelength O O O O B-CelestialObject 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 B-Software 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 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 O O O O O O O O O O O B-Software O B-Software 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 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