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

model when adding the centimeter data emission with = 2.60 and with parameters of m ⋆ = 16 M ⊙ , a core of mass M c = 480 M ⊙ , and a Σ cl = 0.1 g cm −2 clump. The source detected at the Inner scale (or source 8a in Beltrán et al. 2016 ) is slightly extended at 6 cm, and it is blended with other components; however, it is a point source at 1.3 cm and 0.7 cm. Thus, it is possible that we are missing part of the flux at 6 cm, and this may explain why the models seem to overestimate the expected free–free emission at 6 cm. Our resulting protostellar mass of 16 M ⊙ is consistent with the value of of 18 M ⊙ estimated by Sánchez-Monge et al. ( 2013 ) when fitting the velocity field of the core with a rotating Keplerian disk, although they argue that this value corresponds to the total mass of a binary system in core B. Our results disfavor the models with protostellar mass and with relatively low core masses and high Σ cl clumps, because the expected free–free emission for these models is many orders of magnitude lower than the observed one. G45.47+00.05: The observed centimeter continuum emission from G45.47+00.05S (which is the dominant source in the region) is significantly higher (by a few orders of magnitude) than the predicted free–free emission from any of our IR-derived ZT models. This is despite the fact that the best two models from the ZT results already predict a rather high-mass protostar in the range of 30–50 M ⊙ embedded in a massive core, a relatively high Σ clump, and low accretion rates in the range of ∼10 −5 M ⊙ yr −1 . Among the eight sources presented in this study, this is the only case where none of the free–free models can describe the centimeter emission observed in the source. This region is also the most luminous and likely the most evolved one in this sample, which leads us to think that the radio emission from this source may be boosted by the process of photoevaporation. Photoevaporation is not yet accounted for in the TTZ model, which only considered photoionization of the magnetocentrifugally driven wind. However, as the protostar increases its mass above ∼20 M ⊙ , the ionizing radiation becomes dramatically stronger, creating a photoevaporation flow from the disk and infall envelope that is exposed by the outflow cavity wall, i.e., a wind driven by ionized gas-pressure. By enhancing the mass of ionized gas, the centimeter continuum emission is expected to be much higher than that predicted by the TTZ model without such a photoevaporation flow. IRAS 20126+4104: Including the centimeter continuum fluxes to better sample the SED, we can see in Figure 3 that the best five models seem to be overestimating the expected free–free emission. Therefore, after exploring other resulting models from the DLT17 study and the ZT models, we found a matching model with = 3.38 and = 5.42, which yields protostellar parameters of , core mass M c = 240 M ⊙ , and Σ cl = 0.1 g cm −2 . This protostellar mass is consistent with the value of


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

HEMT receiver followed by an autocorrelation spectrometer configured to record 4096 channels over 4 MHz for each polarization, yielding a spectral resolution of 0.09 km s −1 after Hanning smoothing. The system temperature varied between approximately 30 and 50 K during the observations. The telescope has a half power beam-width of 5.8 arcmin and rms pointing errors of 25arcsec. The spectra were obtained in a frequency-switching mode as a series of 30 s integrations. Most sources had an on-source integration of approximately 30 min. The system was regularly calibrated by observing the continuum source 3C123 (Ott et al. 1994 ) and daily checked using the source G32.744−0.076. This methanol maser source was reported as non-variable within ∼5 per cent (Caswell et al. 1995b ). Indeed, high-cadence observations reveal that some spectral features of the source have not shown variability higher than 8 per cent on time-scales from weeks to a few years. Detailed analysis of the light curves of five main spectral features of the source was reported in Szymczak et al. ( 2014 ). The features at 30.3, 38.5 and 39.1 km s −1 were non-variable during the monitoring period and the standard deviation of the flux density of these features indicates that the resulting accuracy of the absolute flux density is better than 10 per cent (Szymczak et al. 2014 ). The system temperature for the observations was measured by a continuously switched noise diode. Standard procedures were used to reduce the spectra. The typical rms noise level in the final spectra was 0.20-0.35 Jy at 0.09 km s −1 velocity resolution after averaging over polarization and time. There was no detectable interference on the spectra of our targets with the exception of G27.286+0.151. 2.3 Effect of offset observation and confusion For several sites in the sample (Table 1 ), accurate positions have recently been published (e.g. Bartkiewicz et al. 2014 , 2016 ; Breen et al. 2015 ), which show that for a majority of the targets the observed positions deviate from the interferometric positions by less than 0.4 arcmin. These differences (the fourth column of Table 1 ) are much less or comparable to the telescope pointing errors and have no significant effect on the flux density measurements. The measured profile of the telescope beam (Fig. 2 ) implies that our observations at an offset higher than 1.3 arcmin systematically underestimate the flux density by 9 per cent and its uncertainty increases by more than 10 per cent due to the pointing errors. There are 10 sites (11 distinct sources) in the sample for which the flux density measurements are significantly influenced by these effects and all of them are discarded in the following statistical analysis. Furthermore, the spectra of 18 sources (12 star-forming sites) are contaminated by confusion introduced by other sources in the telescope beam or side-lobe response from nearby bright sources and these sources are also excluded from the statistical


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This work was supported by grant HST-AR-12123.001-A from the Space Telescope Science Institute. W.A.F. participated in the Research Experiences for Undergraduates (REU) Program of the National Science Foundation under award number 1262810. A. M. R. acknowledges support from the Kenilworth Fund of the New York Community Trust. The HST observations presented here were obtained from the Mikulski Archive for Space Telescopes (MAST). STSci is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.


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 B-Instrument 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 B-Instrument O B-Instrument O O O O O B-Instrument I-Instrument O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O 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 B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

i and inclination do not affect the derived ephemeris in this paper. 4. PROSPECTS FOR GWS DETECTABILITY 4.1. Precision Estimates Throughout Advanced LIGO (aLIGO)/VIRGO (AdV) Observations Observing runs for GW searches are planned to commence in 2015, and will run through to 2022+. Estimated run duration for 2015, 2016–17 and 2017–18, are 3, 6, and 9 months, respectively. Starting from 2019, more extended runs are expected take place with aLIGO and AdV per every year. In addition, LIGO India is also expected be included in the observing schedule from 2022 onwards (LIGO Scientific Collaboration et al. 2013 ). The inferior conjunction value for the future GW searches ( T n ) will depend on the uncertainties on both T 0 and P orb when aLIGO/VIRGO observations commence. We consider here how the error on T 0 may be projected in time to any given epoch. Given the epoch for inferior conjunction, T n = nP orb + T 0 , following Galloway et al. ( 2014 ), we derive the projected uncertainty for T n aswhere and are the uncertainties in the P orb and T 0 , respectively, and is the cross-term of the covariance matrix. Substituting the values from Table 2 , we express the error on T n as follows: Here, is the uncertainty in the epoch of inferior conjunction at the time of t in days since T 0 . The evolution of is shown as a function of time in Figure 3 . In the absence of additional epochs of observations, term will grow linearly due to the factor, 4.1× day. The effective uncertainty will grow approximately as a function of time, 2× in 2018 and 3× or greater in/after 2022 compared the current error level. Figure 3. Projected uncertainty throughout the aLIGO observing period (shaded regions) is plotted as a function of time. The solid line denotes the approximately linear growth of the effective error throughout the aLIGO observing period (from 2015 onwards) in the absence of the additional epochs of optical data. The open squares describe the approximate effect on the additional observing epochs and the T 0 uncertainty is represented by the dotted curves. The estimated orbital period uncertainty ( σP orb ) is denoted by a dashed line. The above estimated values show that additional epochs of RV measurements will be needed to further refine the system parameters in order to improve the future GW searches. Based on the following assumptions, we also carried out simulations to estimate the effect of additional epochs of RV measurements. First, that the uncertainty on T 0 decreases as the total number of observations increases. Second, that the uncertainty on P orb decreases as the total span of the observations increases. We generated 6 epochs of 100 simulated radial velocity measurements in total. We considered each observing epoch to consist of 15 random observations of LT between 2015 and 2025. We have estimated the parameter uncertainties by combining all existing data with the simulated 100 RV measurements. Simulations allow us to improve the uncertainty


O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-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-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O B-ObservationalTechniques 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 B-Survey O B-Survey O O O O O O O O O B-Survey O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey B-ObservationalTechniques I-ObservationalTechniques O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O B-Survey I-Survey I-Survey I-Survey B-ObservationalTechniques I-ObservationalTechniques O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Dataset I-Dataset 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 B-Survey O B-CelestialObject B-CelestialObject O B-CelestialObject 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-CelestialObject O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation 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

dispersion by scaling the dynamical mass to the Einstein radius: A key ingredient in all measurements concerning strong lensing systems is the observed velocity dispersion, which is a projected, luminosity-weighted average of the radially dependent velocity dispersion profile of the lensing galaxy. In order to predict this value based on a set of galaxy parameters, we start with equation ( 6 ). Note that this equation is valid when the relationship between stellar number density and stellar luminosity density is spatially constant, an assumption unlikely to be violated appreciably within the effective radius of the early-type lens galaxies under consideration. Furthermore, the actual observed velocity dispersion is measured over the spectrometer aperture θ ap blurred with atmospheric seeing. In our analysis, we will apply the aperture weighting function provided by Schwab, Bolton Rappaport ( 2010 ) where χ = θ ap /σ atm and σ atm is the seeing recorded by the spectroscopic guide cameras during survey observations. Considering the effects of aperture with atmospheric blurring and luminosity-weighted averaging (see Schwab et al. 2010 for details), the observed velocity dispersion can be expressed as The observed stellar velocity dispersion is a luminosity-weighted average dispersion inside the fibre aperture. Spectroscopic data obtained in different surveys comprise luminosity-averaged line-of-sight velocity dispersions σ ap measured inside different apertures. According to Cao et al. ( 2015 ), whose compilation of lenses is used in this paper, SLACS and BELLS source papers reported effective circular apertures, while for the SL2S and LSD surveys they have been assessed from the sizes of the slit reported in source papers. In our analysis, we take for σ atm the median value recorded by the spectroscopic guide cameras during survey observations. More specifically, we have added 1.4 arcsec seeing for the SLACS spectroscopic observations according to Bolton et al. ( 2008 ) and 1.8 arcsec seeing for the Baryon Oscillation Spectroscopic Survey spectroscopic observations according to Bolton et al. ( 2012 ) and Shu et al. ( 2015 ). For the SL2S sample, the seeing for each individual lens was taken after Sonnenfeld et al. ( 2013b ). In the case of LSD systems: CFRS03-1077, HST14176 and HST15433, the seeing data were taken from Treu Koopmans ( 2004 ). Since they reported two seeing values per lens, we have taken the median. For Q0047−281, we took the seeing value after Koopmans Treu ( 2003 ), but for MG2016+112 we assumed 0.8 arcsec seeing because there was no seeing reported in the source paper. From the above equation, one can immediately observe that there are degeneracies among α, β and δ. More importantly, if we accurately knew the distance ratio D s / D ls , we could get more stringent constraints on the parameters α and δ describing the mass distribution of lensing galaxies. In our analysis, the angular diameter distance D 12 ( z ) between


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

Bildsten 2010 ), we obtain ejecta mass , kinetic energy erg, magnetic flux density , rotation period ms. Here we have assumed an expansion velocity at peak of 5600 km s from the Fe ii velocity, and opacity . This simple model cannot reproduce the early peak, and therefore we fit only the later epochs; however, including all the epochs provides almost identical parameters. To reproduce the early peak in the magnetar scenario as well, we consider the early light curve as possibly produced by a magnetar-induced shock breakout (SBO), as described by Kasen et al. (2016) . Using the above derived parameters from the fit of the main peak with the magnetar model, we can derive the time of the SBO peak and its luminosity ( Kasen et al. 2016 , their Eqs. (26) and (27)). Both these values are off from what we actually observe in PTF11mnb; we obtained a peak epoch for the SBO of 83 days, with luminosity erg. Therefore, we do not favor a magnetar as the energy source for the early peak. Since a magnetar-induced SBO model does not fit the early light curve of PTF11mnb, whereas the early peak was nicely fit by a Ni decay model (see Sect. 6.2 ), here we also consider a hybrid model in which the first peak is due to a regular SN explosion powered by radioactivity, while the main peak is powered by a magnetar. It is indeed possible to fit the bolometric light curve with a simple Arnett model ( Arnett 1982 ) representing the radioactive component, plus a magnetar model ( Kasen Bildsten 2010 ) that injects energy in the ejecta starting a few days after explosion. This is illustrated in Fig. 11 , where the Arnett model is plotted as a dotted blue line and the magnetar model by a dashed black line. The sum of the two models, shown as a dashed red line, fit the bolometric light curve well. The magnetar injection of energy would have to start after 18 days from the SN explosion, otherwise it is not possible to reproduce both peaks simultaneously. In such a scenario, the SN explosion is characterized by , erg, , and the magnetar by and ms. The magnetar parameters in the hybrid model are different from those of the magnetar-only model previously described. Despite the nice fit of this hybrid model to the bolometric light curve, we still favor a progenitor scenario with the explosion of a massive star and a double-peaked Ni distribution because such a scenario requires a single source of energy and fewer parameters and, in particular, it naturally fits the post main-peak light curve. 6.4. Early light-curve modeling The early -band light curve of PTF11mnb appears rather flat in the first three epochs, which occur merely 4 d after the last non-detection. To reproduce this early emission, we adopted the model by Piro Nakar (2013) for the shock breakout cooling tail, assuming and kinetic energy and ejecta mass from the hydrodynamical fit to the bolometric light curve. We solved for the explosion epoch and for the progenitor radius, obtaining a radius of 90–105 and an


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 I-Instrument I-Instrument B-Instrument B-Citation I-Citation I-Citation I-Citation O O O B-Observatory O O O O O O O B-Dataset I-Dataset I-Dataset I-Dataset O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Instrument I-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Identifier I-Identifier I-Identifier O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Identifier I-Identifier O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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

outlines the global expansion of the FR. Later on, this prominence eruption was accompanied by a CME observed by the Large Angle and Spectrometric Coronagraph (LASCO, Brueckner et al. 1995 ) onboard the SOHO satellite and it is given in the SOHO/LASCO CME catalog 1 ( Yashiro et al. 2004 ). The CME first appears in the LASCO C2 field-of-view at ≈15:45 UT. The speed of the CME leading edge is 452 km s −1 so it is less than twice its velocity in the low corona (Fig. 3 b). At the distances observed by C2, the CME was already decelerating with a mean value of deceleration of 12 m s −2 . 2.2. Photospheric magnetic field We analyze the AR magnetic configuration with the HMI magnetic field data. Since the studied eruption was at the limb on 02 March 2015, the photospheric magnetic field is not available. Therefore, we follow its associated AR evolution when it was on the solar disk. AR NOAA 12290 was on the eastern limb on 18 February 2015. One day later, it started to show on the solar disk as a small bipolar AR with a negative leading and a positive following polarity. During its disk crossing, it progressively grew in size as its magnetic field got dispersed by convective motions. Then, AR 12290 was well in its decay phase when it reached the western limb. Figure 4 shows four magnetograms of the longitudinal field component with a time cadence of one day. The AR was located at ≈15° of longitude after the central meridian on 25 February 2015 in panel a, and at ≈55° of longitude on 28 February 2015 in panel d. The magnetograms are spatially de-rotated to the central meridian so that the spatial extension of the polarities could be compared between the different panels. However, we kept the longitudinal component so projection effects appeared as the AR approached the limb (mostly on the limb side of the leading polarity where fake positive polarities appear). The magnetic field mostly disperses with time in each polarity so that the polarities become more extended. Then, the global bipolar magnetic configuration is progressively larger in size, which is expected to induce a global expansion of the coronal loops. This dispersion also implies that the polarities of opposite signs become into contact at the PIL. This induces cancellations of the magnetic flux, for example, at the locations surrounded by a green ellipse in Figs. 4 a and c. These cancellations of flux are best seen in the movie associated with Fig. 4 . Such cancellations imply a progressive buildup of an FR above the PIL ( van Ballegooijen Martens 1989 ; Amari et al. 2003 ; Green et al. 2018 ). Finally, the FR becomes unstable leading to an eruption (Sect. 2.1 ). Fig. 4. Evolution of the AR magnetic field from 25 to 28 February 2015. The locations of the flux cancellation are shown by green ellipses. The location of the H α filament on 28 February 2015 is displayed in panel d with a red contour. A movie of magnetic field during 25−28 is available online . The above analysis shows that


O O O O O O 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 I-Organization B-Organization I-Organization O O O B-Grant O O O O O B-Person I-Person O O O O O O O O O O B-Person I-Person O O O O O O O B-Software I-Software I-Software I-Software I-Software I-Software I-Software I-Software I-Software B-Software B-Identifier 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 B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship B-Person O O O O B-Grant I-Grant I-Grant I-Grant I-Grant B-Grant O O B-Organization I-Organization I-Organization O O O O O O O B-Grant I-Grant B-Grant O O B-Organization I-Organization O O O B-Organization I-Organization I-Organization B-Organization O O O O O O O O O O B-Observatory I-Observatory I-Observatory I-Observatory O B-Proposal B-Proposal O B-Proposal O O O O O O O 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 I-Organization O O O O O O O O O O O O B-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 B-Location O O O O O O B-Location O O O O O O O O O O O O O O O

ACKNOWLEDGEMENTS This research was conducted by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013. The authors wish to thank E. Zackrisson for useful discussion in the early stages of this work, D. Nicholls for assistance in constructing photoionization models using Modeling And Prediction in PhotoIonized Nebulae and Gasdynamical Shocks (MAPPINGS) V, and the anonymous referee for their comments that have helped to improve the focus, clarity, and relevance of this work. JC acknowledges research support from Australian Research Council Future Fellowship grant FT130101219. TG is grateful to the LABEX Lyon Institute of Origins (ANR-10-LABX-0066) of the Université de Lyon for its financial support within the programme ‘Investissements d’Avenir’ (ANR-11-IDEX-0007) of the French government operated by the National Research Agency (ANR). (Some of) The data presented herein were obtained at the W. M. Keck Observatory (programs 2015A_W012LA, 2015A_W033M, and 2016A_W034LA), which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain.


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

We thank Zara Scoville for proof reading the manuscript and Sue Madden for suggesting use of the SPIRE fluxes for calibration. This paper makes use of the following ALMA data: ADS/JAO.ALMA# 2013.1.00034.S. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2013.1.00111.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. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. R.J.I. acknowledges support from ERC in the form of the Advanced Investigator Programme, 321302, COSMICISM.


O O O O O O B-Grant I-Grant I-Grant O O B-Organization I-Organization O O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Grant I-Grant O O O B-Organization I-Organization O O B-Grant I-Grant I-Grant B-Grant I-Grant O O O O O O B-Collaboration B-Collaboration B-Collaboration O B-Collaboration I-Collaboration O O O O O O O O O O O O B-Software O B-Citation I-Citation I-Citation O O B-Software O B-Citation I-Citation I-Citation I-Citation O O O O O O B-Person I-Person O B-Person I-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

This work was supported by the Young Investigators Program of the Helmholtz Association, by the Deutsche Forschungsgemeinschaft (DFG) within the Collaborative Research Center SFB 876 “Providing Information by Resource-Constrained Analysis”, project C3 and by the European Commision through the ASTERICS Horizon2020 project (id 653477). We would like to thank the H.E.S.S., MAGIC, VERITAS, and FACT collaborations for releasing the data that were used. This work made use of astropy ( Astropy Collaboration 2013 ) and sherpa ( Freeman et al. 2001 ). The authors are indebted to Abelardo Moralejo and Hans Dembinski for their useful suggestions on the statistical and systematic uncertainty estimation. We are grateful to the anonymous referee for improving the paper with helpful comments.


O B-Telescope I-Telescope O O O O O O B-Observatory I-Observatory I-Observatory O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O O B-Organization I-Organization O O B-Organization I-Organization O O O O O O O B-Observatory O B-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 B-Person O O O O O B-Grant I-Grant 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 O O O O O B-Telescope O B-Observatory O

The Submillimeter Array is a joint project between the Smithsonian Astrophysical Observatory and the Academia Sinica Institute of Astronomy and Astrophysics and is funded by the Smithsonian Institution and the Academia Sinica. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2011.0.00172.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. K.S. was supported by the grant NSC 102-2119-M-001-001-MY3. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities Inc. We thank the anonymous referee for thorough and constructive comments. Facilities : SMA , ALMA .


O O O B-Person I-Person B-Person I-Person O B-Person I-Person O O O O O O O O O O O O O B-Person I-Person O O O O O O O O O O O O O B-Grant O O B-Organization I-Organization I-Organization I-Organization B-Person O B-Person O O O O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Grant I-Grant O O B-Organization I-Organization I-Organization B-Organization B-Person O B-Person O O O O B-Organization I-Organization I-Organization I-Organization O O O O O B-Location

Acknowledgements We thank G. Ambrazevičiūtė, V. Dobrovolskas, and D. Prakapavičius for their input during the various stages of this project. We also thank V. Vansevičius for the useful comments and discussions. This research was funded by a grant (MIP-089/2015) from the Research Council of Lithuania. HGL and AK acknowledge financial support by the Sonderforschungsbereich SFB 881 “The Milky Way System” (subproject A4) of the German Research Foundation (DFG). HGL and MS acknowledge funding from the Research Council of Lithuania for the research visits to Vilnius.


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at +1542d (Stritzinger et al. 2012 ), and SN 2010jl at +461 day and +573 day (Fransson et al. 2014 ). Other coronal lines detected in SN 2017ens are similar to those seen in SN 2010jl (Figure 3 , bottom panel): [Fe x ] λ 6374.5 is strong, as are [Fe xi ] λ 7891.8, [Ne v ] λλ 3345.8, 3425.9, [Ca v ] λ 6086.8, and [Ar x ] λ 5533.2. The presence of these lines is indicative of a highly ionized and dense CSM, although we do not detect the highest-ionization coronal lines such as [Fe xiv ] λ 5302.9 and [Ar xiv ] λ 4412.3, which were seen in SN 2005ip. The flux ratio of the [O iii ] λ 4363 to λ 5007 lines is a function of the CSM density and temperature. Following Fransson et al. ( 2014 , their Figure 26), we use our measured flux ratio, log( λ 4363/ λ 5007) = −0.22, to constrain the CSM electron density to lie between 10 6 and 10 8 cm −3 for T e = 50,000 to 10,000 K. This density range is consistent with that observed for SN 2010jl. From our mid-resolution X-Shooter data, we resolve narrow P-Cygni profiles on top of the ∼2000 km s −1 wide Balmer and Paschen lines. We measure the blueshifted wavelength from the absorption component of the H γ , H β , and H α P-Cygni profiles, which suggests that the unshocked CSM has a low velocity of ∼50 km s −1 . A similar velocity of ∼60 km s −1 is obtained from the P-Cygni profile of the He i λ 10,830 line. Moreover, we measure the FWHM intensity of the wide components, such as H α (2500 ± 700 km s −1 ), H β (2300 ± 400 km s −1 ), Pa γ (2000 ± 200 km s −1 ), and He i λ 10,830 (2200 ± 200 km s −1 ). We also detect narrow absorption lines from the Balmer series (no clear emission), spanning H to H33 (3659 Å). In addition, we see emission from the H ii region close to the host-galaxy center (see Figure 4 , marked B1), as part of a faint galaxy (SDSS J120409.47–015552.4) with g = 21.92 ± 0.24 mag ( M g ≈ −16.5 mag). These lines have a slightly different redshift ( z = 0.1084) than SN 2017ens. In particular, the (noisy) detection of the weak auroral [O iii ] λ 4363 line indicates a low host-galaxy metallicity of ∼0.04–0.4 Z ⊙ using the direct T e -based method. If we instead use the empirical N2 metallicity diagnostic (Pettini Pagel 2004 ), we measure Z = 0.3 ± 0.2 Z ⊙ 4. Bolometric Light Curve and Model Fitting Using all of our available UV-through-NIR photometry, we built a pseudobolometric light curve for SN 2017ens using the prescription from Inserra et al. ( 2018b ). The results are very similar to those derived when using a blackbody fit, as expected as our photometry covers a large wavelength range. From a polynomial fit to the bolometric data we obtain L bol = (5.86 ± 0.20) × 10 43 erg s −1 at peak and an integrated energy of (3.53 ± 1.42) × 10 50 erg. To fit our bolometric light curve, we used a two-component model consisting of a central heating and an interaction component. First, the centrally heated component uses the standard Arnett method (Arnett 1982 ; Inserra et al. 2013 ). We tested three possible


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but relatively insensitive to temperature. From fig. 1 of Keenan et al. ( 1995 ), the observed λ1483.3/λ1486.5 ratio corresponds to an electron density of (2.0–3.6) × 10 5 cm −3 in the temperature range (1–2) × 10 4 K. We conclude that the CSM density should be safely lower than the critical densities of the semiforbidden lines. 3.2.4 Line profiles Fig. 7 compares the velocity profile of several UV and optical lines at ∼3100 d. The Hα line extends to ∼2600 km s −1 on the blue side and only ∼1000 km s −1 on the red. Hβ, He i λ5876, and Mg ii λλ2796, 2803 have similar line profiles. While the blue side can be well fitted with an electron-scattering wing, the line centroid is shifted to the blue, with a ‘shoulder’ at ∼−800 km s −1 . As shown by Taddia et al. ( 2020 ) and Dessart et al. ( 2015 ), this type of profile can be explained by a combination of emission from the shock wave and emission from the pre-shock CSM. The emission from the shock is responsible for the blueshifted shoulder, while the central component is coming from pre-ionized gas in the CSM. Both components are affected by electron scattering in the low-velocity CSM. This gives rise to the smooth, blue wing shortward of the ‘shoulder.’ Because of the smoothing by the electron scattering, the velocity of the ‘shoulder’ is lower than the shock velocity. Figure 7. Line profiles of Hα (black), Hβ (green), He i λ5876 (red), Lyα (magenta), and N iv ] λλ1483.3, 1486.5 (blue). Note the narrower line profile of the N iv ] lines, as well as the contribution of the semiforbidden λ1483.3 component on the blue side. Both Hβ and He i λ5876 have line profiles similar to that of Hα, as expected if these arise from similar regions (Fig. 7 ). The Lyα line has a profile broadly consistent with Hα, although strongly distorted by a central absorption feature from both the Galactic and host-galaxy ISM. The C iii ], N iii ], N iv ], and N v UV lines are considerably narrower than Hα, and consistent with being unresolved at the ∼300 km s −1 instrumental resolution of STIS. These lines do not show the velocity shift of the Balmer and He i lines, and most likely come from the same optically thin, highly ionized region of the CSM as the high-ionization optical lines. 3.2.5 Spectral evolution The optical spectra in this paper span one of the longest periods of any SN. Fig. 8 highlights only a very slow evolution of the spectrum over three epochs: 736, 3099, and 5105 d. Unlike most other SNe, there is no obvious transition to a nebular spectrum even at this extremely late stage. However, the line ratios do exhibit some interesting quantitative changes that are consistent with the shock wave propagating into a medium of decreasing density. Figure 8. Evolution of the optical spectrum from day 736 to 5105 with identification of the high-ionization lines at the top and colour coding and identification of the low-ionization lines for the day 3099 spectrum. We start with a look at some with the most


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The centres of the two groups projected on the sky are not very different. Given the low density and extended nature of the foreground population, it is possible that it extends beyond our field of view. The statistical parameters obtained for each group distribution ( d N and σ N of Model 2, see Table 1 ) suggest that the two groups are spatially separate. We consider the larger population to be the main Cygnus OB2 association (Group 2) and consider the foreground population to be a separate group approximately ∼400 pc in the foreground (Group 1). The distance of the foreground group of ∼1350 pc puts it at a similar distance to Cygnus-X as a whole (see Rygl et al. 2012 ) suggesting that the main part of Cygnus OB2 is actually behind Cygnus-X by several hundred parsecs (though the line-of-sight depth of Cygnus-X is not well constrained). Consequently, the main group is more distant than previously thought, and therefore its stellar content will both be more luminous (approximately 1.5 times more luminous compared to the estimates in Wright et al. 2015 ) and more massive. Interestingly, this puts the distance to the main part of Cygnus OB2 closer to that originally derived by Massey Thompson ( 1991 ). 5.2 The foreground group We have identified 19 stars in the foreground group ( of the sample), seven of them classified as O-type stars. The bright BD + 40 4212 double system ( G = 9.39 mag) is included in this group, as well as the star HD 195213 ( G = 8.38 mag). This group includes approximately 10 of the total population of O-type stars in Cygnus OB2, and thus its total mass can be estimated as a similar fraction of the total mass of 16 500 M ⊙ estimated by Wright et al. ( 2015 ), i.e. 1650 M ⊙ , similar to that of the Orion Nebula Cluster (although according to our results, the estimation by Wright et al. 2015 will have to be corrected upwards). We note that the foreground group is appreciably more dispersed on the sky than the main group. The proper motions also suggest it to be more diffuse and less likely to be a bound group. This could suggest that it is a part of older foreground population that extends further outside our field of view. However, a detailed study of the physical properties of its stellar content is needed to establish the most probable scenario. 5.3 Potential contaminants Here, we discuss the sources identified as probable foreground or background contaminants (Group 3) and not part of either the main Cyg OB2 population or the foreground group. Foreground contaminants : HD 196305 is a very luminous star and has a parallax that places it at a distance of pc, in agreement with previous studies that suggest it to be a foreground contaminant (Chentsov et al. 2013 ). CCDMJ20323 + 4152AB has been reported as a visual double star by Gili Bonneau ( 2001 ) and therefore its binary nature could be affecting the parallax. MT91-426 and MT-170 also appear as foreground sources, despite the fact that Wright et al. ( 2015 ) proposed them


O O O O O O O O O O O O O B-Telescope B-Dataset I-Dataset B-Citation I-Citation I-Citation O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O O B-Instrument I-Instrument 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 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 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 O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model 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 B-Survey O O B-CelestialObject O B-CelestialObject O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength 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-Software O O O B-Survey O O B-Software 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 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

and a global alignment to an absolute reference frame, here defined by the Gaia DR2 catalogue (Gaia Collaboration 2018 ). As there are no telescope offsets between the paired F 814 W direct and G800L grism exposures, the alignment of the former is applied directly to the latter. Finally, we combine the F 814 W direct exposures into a rectified mosaic with astrodrizzle at a final sampling of arcsec pix −1 and generate a source catalogue and segmentation map from this mosaic using the sep software package. 9 The global contamination model for a given field is constructed in two passes. In the first, we assume that each object has a spectrum flat in units of f λ flux density with a normalization set by its observed flux in the F 814 W direct image (integrated over the object’s segmentation polygon). In the second pass, we step through objects in the catalogue sorted by increasing magnitude and compute a third-order polynomial fit to each spectrum after subtracting the contamination model from any neighbours (i.e. either the flat spectra of fainter sources or the polynomial models of brighter sources). This refinement is iterated three times. In both passes, the spatial template of the dispersed 2D model spectra is taken from the observed F 814 W cut-out within an object’s segmentation polygon. Note that this approach neglects morphological variation across the G800L bandpass; e.g. the PSF, continuum colour gradients, and morphological differences between line- and continuum-emitting regions. However, it provides a spatial model with much higher fidelity than any simple parametrized representation (e.g. Gaussian or Sérsic approximations). The above process automatically yields a source and contamination model for each galaxy detected in the reference image. These can be used to ‘decontaminate’ source spectra – i.e. remove overlapping light from neighbouring sources – to provide more accurate line and continuum characterizations. This was critical in GLASS’ crowded cluster G102 and G141 pointings, but the ACS parallels are sparse enough that source contamination is often negligible (Section 3 ). Note that no spectra are modelled or extracted for objects not detected in the reference frame. As such, the catalogue presented here is truncated at a F 814 W flux of m 814 = 26 with various subsamples defined by brighter flux limits (Section 3 ). There are two main differences between grizli and the previous GLASS pipeline. First, grizli automatically handles HST grism spectra taken at one or more telescope roll angles that translate into different spectral dispersion PAs. This is implemented in that the 2D spectral models are computed in the pixel space of each separate grism exposure. This is the space in which the field-dependent grism dispersion configuration is measured and defined (e.g. Kümmel et al. 2009 ). This approach allows for evaluating model fits in the space of the original detector pixels with a well-calibrated noise model. Recent works


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

) assigned both peaks to transpolyacetylene at grain boundaries and surfaces of nanodiamonds. The weak peak at ∼1020 cm −1 along with the broad feature centered at ∼1270 cm −1 are also associated with nanodiamonds (Veres et al. 2007 ; May et al. 2008 ), and the broad doublet at ∼1800 and 1900 cm −1 may be due to overtones and/or combinations. In the 2000–4000 cm −1 region (not shown), the Raman spectra show broad CH-stretching peaks centered at ∼2900 cm −1 in addition to the second-order peaks of nanodiamonds and graphitic/amorphous carbon. Figure 2. Reflected-light image from the KBr pellet of the Kapoeta carbonaceous-chondrite material showing a cluster of diamond particles. Figure 3. Raman spectra of the Kapoeta nanodiamonds (see the text for details). Thus, in the cluster of particles shown in Figure 2 , each particle may be considered as an aggregate of nanodiamonds. To estimate the sizes of these nanodiamonds from their Raman spectra, we consider the particle-size dependence of the position and FWHM of the 1333 cm −1 diamond peak (Yoshikawa et al. 1993 ). Based on the analyses of 26 Raman spectra, the average diamond peak position and FWHM are 1332.6 cm −1 ( σ = 0.3 cm −1 ) and 4.0 cm −1 ( σ = 0.6 cm −1 ), respectively, suggesting a particle size of ≥50 nm for the Kapoeta diamonds that show the Raman diamond peak in their spectra. However, some spectra do not show the Raman diamond peak at 1333 cm −1 , but they display all the other peaks shown in Figure 3 (a), including the peaks and features associated with nanodiamonds at ∼1020, 1150, 1450 cm −1 , and ∼1270 cm −1 (Figure 3 (b)). The spectrum shown in Figure 3 (b) is very similar to the Raman spectra of ultrananocrystalline diamonds having an average particle size of ∼3–5 nm, i.e., single-digit nanodiamonds, where the 1333 cm −1 diamond peak is absent and they show the D- and G-bands along with the 1150 and 1450 cm −1 peaks (Popov et al. 2004 ). One difference is that the G-band in their spectra occur at a lower wavenumber (1560 cm −1 ), possibly due to differences in sp 2 /sp 3 ratios in the amorphous carbon phase. Thus, our Raman spectroscopic data suggest the existence of two populations of nanodiamonds in the Kapoeta CC material: nanodiamonds that are ≥50 nm and single-digit nanodiamonds. 3.3. Micro-FTIR Spectroscopy Figure 4 (a) shows a typical micro-FTIR spectrum taken from the diamond-enriched region (spot size is ∼70 μ m). It is dramatically different from the KBr-pellet spectrum (Figure 1 ) both in the high- and low-frequency sides. The position of the absorption bands and their possible assignments are listed in Table 1 . Figure 4. (a) Micro-FTIR spectrum collected from the diamond-enriched region in the KBr pellet of the Kapoeta carbonaceous-chondrite material (see the text for details). (b) Expanded view of the C–H stretch region. Table 1 Assignment of IR Bands in FTIR Spectrum of the Diamond-enriched Region of the Kapoeta CC Material 3.3.1. C–H Stretching Bands The C–H


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We thank the anonymous referee for a critical reading of the paper and valuable suggestions that helped improve the quality and clarity of this work. We also thank Charles Dermer, Tyce DeYoung, Markus Bötcher, and Bin Zhang for useful discussions.


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

f.u., is obtained from the 16th and 84th percentiles. The lognormal parameters, μ and σ , can be calculated from the recommended (median) rate ( x med = e μ ) and the factor uncertainty ( f.u . = e σ ; for a coverage probability of 68%). The rate factor uncertainty is 1.1% for both reactions at most temperatures. Figure 6. Reaction rate probability density of d(d, n) 3 He at different temperatures. The rate samples (red histograms) are computed using the S -factor samples obtained from the Bayesian analysis. Blue curves represent lognormal approximations, where the lognormal parameters μ (“mu”) and σ (“sig”) are directly calculated from the expectation value and variance of all rate samples, ln(), at a given temperature. T9 is the temperature in GK. Figure 7. Reaction rate probability density of d(d, p) 3 H at different temperatures. The rate samples (red histograms) are computed using the S -factor samples obtained from the Bayesian analysis. Blue curves represent lognormal approximations, where the lognormal parameters μ (“mu”) and σ (“sig”) are directly calculated from the expectation value and variance of all rate samples, ln(), at a given temperature. T9 is the temperature in GK. Table 3 Present Recommended Reaction Rates a Note. a Reaction rates in units of cm 3 mol −1 s −1 , corresponding to the 50th percentile of the rate probability density function. The rate factor uncertainty, f.u., is obtained from the 16th and 84th percentiles (see the text). The parameters μ and σ of the lognormal approximation to the reaction rate are given by x med = e μ and f.u . = e σ , respectively, where x med denotes the median rate. Values for T > 2 GK, shown in italics, are adopted from Coc et al. ( 2015 ). The present rates for d(d, n) 3 He and d(d, p) 3 H agree with the results of Coc et al. ( 2015 ) within 1% at most temperatures. However, our rates are more than 15% larger than those of Coc et al. ( 2015 ) at very low temperatures (near 1 MK). This is caused by a low-energy cutoff that is too high for the numerical integration of the rates in the previous analysis. The theoretical model of Arai et al. ( 2011 ) only applies to low energies, thus we can derive Bayesian reaction rates only up to a temperature of 2 GK. The results in Table 3 for higher temperatures, shown in italics, are adopted from Coc et al. ( 2015 ). The most important temperatures for BBN are near 1 GK, corresponding to an effective kinetic energy range of 250 keV for the d+d reactions. The last step is to calculate the effect of the new reaction rates on the predicted primordial D/H ratio. The Bayesian mean value for the scale factor is larger by 0.21% for d(d, n) 3 He and larger by 0.12% for d(d, p) 3 H compared to Coc et al. ( 2015 ). The discrepancies of both reaction rates (0.21% and 0.12%, respectively), weighted by the sensitivity of the D/H abundance ratio to each reaction rate variation (−0.54 and −0.46, respectively; Coc Vangioni 2010 ), result in a 0.113% and


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-Telescope O B-CelestialObject O O B-Citation I-Citation I-Citation I-Citation I-Citation 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 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 B-Dataset I-Dataset O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O B-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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation 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 B-Telescope 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 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-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Collaboration I-Collaboration I-Collaboration B-Collaboration O B-Collaboration I-Collaboration B-Citation I-Citation I-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

with the SPT cluster cosmology analysis of Bocquet et al. ( 2015 ), when it is combined with the first release of the Planck primary CMB cosmology results (Planck Collaboration et al. 2014 ). The combination of the velocity-dispersion-based MOR normalization constraints of Bocquet et al. ( 2015 ) with CMB data leads to a shift in Ω m – σ 8 orthogonal to the cluster SPT cosmology constraints on these parameters. As a result the normalization of the mass–SZE MOR shifts accordingly, to account for the implied different cluster mass scale, leading to the difference seen in Fig. 9 . For a quantitative comparison, we follow Bocquet et al. ( 2015 ) to compute the significance of the difference of two distributions. We randomly draw points from two distributions and compute the difference δ between pairs of points. We use this to estimate the probability distribution P δ of these differences and compute the likelihood that zero is within this distribution. Assuming a normal distribution, this likelihood is then converted to a significance. The lower normalization parameter A SZ , corresponding to higher cluster masses, inferred from a joint cosmological analysis of the SPT cluster sample and Planck CMB data sets (Bocquet et al. 2015 ) disagrees with our result at the 2.6 σ level. We emphasize that the change in normalization in Bocquet et al. ( 2015 , yellow to cyan line in Fig. 9 ) when the underlying cosmology shifts is caused by the self-calibration of the scaling relations from cluster number counts. In this work, we adopt a cosmology with Ω m , σ 8 and H 0 close to the results of Bocquet et al. ( 2015 ) without the Planck data added. Because we use the cluster mass function only for Eddington bias correction and not for self-calibration of the MOR, small changes in the cosmological parameters do not have any big impact on our recovered normalization A SZ . In particular, changing the cosmological parameters to the ones obtained from SPT clusters with Planck data (Bocquet et al. 2015 ) changes our normalization by less than 1 per cent and does not bring it into better agreement with their lower A SZ value. Also used in the SPT–SZ cosmology analysis is the mass– Y X scaling relation. As for the mass– ζ relation, our marginalized posterior for the normalization is in very good agreement with the prior utilized in the cosmology analysis (de Haan et al. 2016 ). This is an important result, as the prior was based on an external calibration of the normalization of the mass– Y X scaling relation, namely the Vikhlinin et al. ( 2009 ) scaling relation updated with the weak lensing mass calibration of the Weighing the Giants (WtG) and CCCP projects (von der Linden et al. 2014 ; Applegate et al. 2014 ; Hoekstra et al. 2015 ). We are now able to confirm that these priors were appropriate for cosmology analysis based on an internal calibration . Fig. 10 shows a comparison of the marginalized and joint posterior probability distributions for the normalizations A


O O B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person O B-Collaboration I-Collaboration O B-Person I-Person O O O O O O O O B-Person I-Person O O O O O O O O O O O O O O O O B-Person I-Person I-Person O O O O O B-Telescope O O O O O O B-Grant I-Grant I-Grant I-Grant B-Grant B-Grant B-Grant B-Grant O O B-Organization I-Organization I-Organization I-Organization O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization O B-Grant B-Person O O B-Organization I-Organization I-Organization O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Person 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-Grant I-Grant O O O O O B-Organization I-Organization O O O B-Person I-Person B-Person O O B-Organization I-Organization O O O O O O O B-Grant I-Grant I-Grant O B-Organization I-Organization B-Person O B-Person I-Person O O B-Organization I-Organization I-Organization I-Organization B-Person O O O B-Grant I-Grant I-Grant O O B-Observatory I-Observatory I-Observatory B-Person O O O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship O O O B-Fellowship B-Person O O O O O B-Organization I-Organization I-Organization I-Organization 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 O O O O B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization O O O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization O O O B-Observatory O O O O O

We thank Alessandro Manzotti, Ariel Goobar, Mike Hudson, WeiKang Zheng, Bill Januszewski, Robert Kirshner, Licia Verde, Liz Humphreys, Dan Shafer, the PHAT collaboration, and Peter Stetson for valuable discussions and contributions, as well as Doug Welch for providing the optimal temporal spacings used in the optical Cepheid searches. We are grateful to Melissa L. Graham for her assistance with the Keck observations. This research was supported by NASA/ HST grants GO-12879, 12880, 13334, 13335 13344 from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. L.M.M.'s group at Texas AM University acknowledges additional support from the Mitchell Institute for Fundamental Physics Astronomy. D.S. acknowledges support from the Kavli Institute for Cosmological Physics at the University of Chicago through grant NSF PHY-1125897 and an endowment from the Kavli Foundation and its founder, Fred Kavli. A.V.F.'s group at UC Berkeley is also grateful for financial assistance from NSF grant AST-1211916, the TABASGO Foundation, Gary and Cynthia Bengier, and the Christopher R. Redlich Fund. P.C. is supported by NSF grant AST1516854 to the Harvard College Observatory. J.M.S. is supported by an NSF Astronomy and Astrophysics Postdoctoral Fellowship under under award AST-1302771. R.J.F. gratefully acknowledges support from the Alfred P. Sloan Foundation. Some of the results presented here are based on data obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and NASA; the observatory was made possible by the generous financial support of the W. M. Keck Foundation. We thank the Keck staff for their expert help.


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 B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-CelestialObject I-CelestialObject O O O B-CelestialObject I-CelestialObject B-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O B-Wavelength O O O B-Wavelength 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-Citation I-Citation I-Citation I-Citation O O O O O B-Citation I-Citation O B-CelestialObject I-CelestialObject O O O O O O O B-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O B-CelestialObject I-CelestialObject O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O B-CelestialObject I-CelestialObject O O O O O O O O O O B-CelestialObject I-CelestialObject 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 B-Survey O O B-Wavelength I-Wavelength O O B-CelestialObject I-CelestialObject 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 B-Citation I-Citation I-Citation I-Citation I-Citation O O O O B-CelestialObject I-CelestialObject O O O B-CelestialObject I-CelestialObject O O O O O B-Mission I-Mission O O O O O O O O B-CelestialObject I-CelestialObject O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject 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 B-CelestialObject I-CelestialObject 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 B-CelestialObject I-CelestialObject O B-Telescope B-Wavelength 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 B-Telescope B-Dataset 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 B-Citation I-Citation I-Citation O O O O O O O O O O O O O O

a list of new associations in the Galaxy. Clustering depends on the choice of length-scale and groups begin to merge for larger length-scales. In this scenario, although the presence of different groups and associations is ascertained from the results of their cluster analysis using an independent method, their boundaries are not well defined. This, consequently, affects the membership assignment and identification of parent associations for those stars located at the association boundaries. Here, we investigate the properties of the well-known association Cyg OB3. We primarily focus on the distances, proper motions, and three-dimensional velocity components of the members. We study a particular case of a confirmed black hole X-ray binary Cyg X-1 (otherwise known as HD 226868; Bolton 1972 ; Webster Murdin 1972 ) located at the association boundary (Fig. 1 ). Cyg X-1 is one of the brightest X-ray binaries in the X-ray sky and is composed of a black hole of 14.8 ± 1.0 M ⊙ (Orosz et al. 2011 ) and a companion of 19.2 ± 1.9 M ⊙ (Orosz et al. 2011 ) of spectral type O9.7Iab (Walborn 1973 ). Cyg X-1 has been included in the catalogues of Humphreys ( 1978 ), Garmany Stencel ( 1992 ), Ruprecht et al. ( 1981 ), and Blaha Humphreys ( 1989 ) as a member of Cyg OB3. The cluster analysis algorithm implemented by Mel’Nik Efremov ( 1995 ) divided the association Cyg OB3 into two subgroups for a length-scale of 15 pc viz. Cyg 3A and Cyg 3B; however, Cyg X-1 was not included in either of the subgroups and remained as a field star. Figure 1. Image obtained with DSS2 in the R band shows the Cyg OB3 region. The positions of the O- and B-type stars studied in this work are encircled. Cyg X-1 is encircled in red. There are a total of 41 stars shown in the image and given in Table 1 . Mirabel Rodrigues ( 2003 ) studied the connection between Cyg X-1 and the association Cyg OB3 using the astrometry from the Hipparcos mission. The authors suggested that the parent association of Cyg X-1 is indeed Cyg OB3, and showed that the binary is located at the same distance as the other stars in Cyg OB3 and exhibits a proper motion similar to that of the association. The authors also showed that the peculiar velocity of Cyg X-1 is very small (9 ± 2 km s −1 ) with respect to the association, and is consistent with the expected random velocities of stars in expanding associations. These results indicate that Cyg X-1 is most likely a member of Cyg OB3. This was later confirmed with precise measurement of the trigonometric parallax and the proper motion of Cyg X-1 using VLBI radio observations (Reid et al. 2011 ). In this paper, we revisit the proposed connection between Cyg X-1 and Cyg OB3 using the astrometric data from Gaia DR2, which provides trigonometric parallaxes and proper motions for over 1 billion stars in the Galaxy with the best accuracy and precision available to date (Gaia Collaboration 2018 ). We define the sample of stars and their filtering criteria in the next


O O O B-Instrument O O O O B-Organization I-Organization I-Organization O B-Grant I-Grant I-Grant I-Grant O O O B-Organization I-Organization I-Organization I-Organization O O B-Grant I-Grant I-Grant I-Grant B-Person O O O O B-Fellowship I-Fellowship I-Fellowship O O O O O O O O O B-Observatory I-Observatory I-Observatory O O O O O O O B-Instrument O O B-Telescope O O O O O O O O O O O O O O O B-Person I-Person I-Person O O O O O O

The development of HIPPI was funded by the Australian Research Council through Discovery Projects grant DP140100121 and by the UNSW Faculty of Science through its Faculty Research Grants program. JPM is supported by a UNSW Vice-Chancellor's Fellowship. The authors thank the Director and staff of the Australian Astronomical Observatory for their advice and support with interfacing HIPPI to the AAT and during the three observing runs on the telescope. The authors wish to thank referee Hans Martin Schmid for constructive criticism of the Letter.


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

we find κ = 2 − 835.6440/582.143 23 = 0.564 5388. With these values of κ for both stars and a representative range for the neutron star radius (see Section 2.1 ), we can solve for M in equation ( 1 ), including the κ corr term from equation ( 3 ), the rotational correction κ 2 as given by Fig. 2 and a differential rotation term κ 3 consistent with a realistic differential rotation with Δ f ≳ 1 Hz inside the star. In Fig. 3 , we present our results for uniformly and differentially rotating models, and compare with the fit given by equation ( 5 ) of Andersson et al. ( 2014 ). Our results for uniformly rotating stars are ≈ 15 per cent lower than the estimate given by Andersson et al. ( 2014 ), where the fully relativistic r-mode frequency for slowly rotating uniform density stars from Lockitch et al. ( 2003 ) was combined with the second-order rotational corrections for Newtonian polytropes from Lindblom et al. ( 1999 ). As we mentioned in Section 3.3 , the main factor for this difference is our improved calculation of the rotational correction κ 2 (see Fig. 2 ). Differential rotation increases our mass estimate, but the effect is rather small: Δ f = 10 Hz increases the total mass by only ≈0.02 M ⊙ . In the range 11–13 km for the stellar radius, we find from our results 1.41–1.71 M ⊙ for XTE J1751−305 and 1.53–1.87 M ⊙ for 4U 1636−536. We can use the transversal curves in Fig. 3 , which indicate M ( R ) for a choice of three realistic tabulated equations of state (APR4 Akmal, Pandharipande Ravenhall 1998 , SLy Douchin Haensel 2001 and H4 Lackey, Nayyar Owen 2006 ) to gain more insight. Each equation of state crosses our M ( r ) line only once, providing a unique prediction for M and R . However, we can see that H 4 requires R > 13 km for both stars and is therefore less favoured according to current expectations for the neutron star radius. Combining the constraints from both the r-mode frequencies and the APR4 and SLy equations of state, we find a more restricted range of values for M and R : R ≈ 11.5–12 km and M ≈ 1.48–1.56 M ⊙ for XTE J1751−305 and R ≈ 11.4–11.9 km and M ≈ 1.60–1.68 M ⊙ for 4U 1636−536. However, it must be stressed here that these tight constraints are only valid if the frequencies reported in Strohmayer Mahmoodifar ( 2014a , b ) are indeed core r-mode frequencies (see the discussion in Section 1 ). 5 CONCLUSIONS Here, we have explored the consequences for the mass and radius estimates of these two stars if the frequencies detected by Mahmoodifar and Strohmayer really correspond to their r-modes. We used a careful calculation of the r-mode frequency, taking into account relativistic, rotational, and differential rotation corrections, as well as an estimate for the error due to the Cowling approximation, to find improved constraints on the compactness M / R of XTE J1751−305 and 4U 1636−536. Our results yield, for a representative radius of 12 km, masses of 1.55 M ⊙ and 1.70 M ⊙ , respectively. For XTE J1751−305, our value is


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We thank the referee for a careful reading of the manuscript and for suggesting the inclusion of Table 2 . I.D. is supported by the Harvard College Observatory Menzel Fellowship and the Natural Sciences and Engineering Research Council of Canada Postdoctoral Fellowship (NSERC PDF-421224-2012). The Smithsonian Institution supports the research of M.J.G. H.J.Z. gratefully acknowledges the generous support of the Clay Fellowship.


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We thank an anonymous referee for helpful comments that improve the presentation of this paper. This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education (2017R1D1A1B03035359). We thank Attila Juhasz for help with radmc3dPy and J.-Y. Seok for discussion. One of the authors (Q.L.N.) was supported by the U.S. Department of Energy under Nuclear Theory grant DE-FG02-95-ER40934 and in part by the National Science Foundation under grant no. PHY-1430152 (JINA Center for the Evolution of the Elements).


O O O O O O B-Person I-Person I-Person B-Organization O B-Person I-Person B-Organization O O O O O B-Person O O O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship B-Person O O O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship O O O O O O O O O B-Telescope I-Telescope I-Telescope I-Telescope 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 B-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Telescope I-Telescope I-Telescope

The first author is grateful to Prof. Lynne Hillenbrand (Caltech) and Ben Zuckerman (UCLA) for their advice and comments. T.J.D is supported by the National Science Foundation Graduate Research Fellowship under grant No. DGE1144469. M.B. is supported by a NASA Space Technology Research fellowship, grant No. NNX13AN42H. This publication makes use of data products from the Wide-field Infrared Survey Explorer , which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration. Facility: Very Large Telescope.


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5 per cent lower). This can be attributed to the same reason EPICal underperformed with the full sky model: EPICal only used a single pixel in the sky to form its solutions. When using the full sky model, it was under utilizing the information in the rest of the sky. But when the sky model only contains the bright point source, the single pixel used in EPICal is the location where this model is most accurate, effectively downweighting the pixels with incomplete sky model. In contrast, the visibility-based calibration method does not have any preference to a certain direction, and weights the sky equally (beyond the inherent response of the instrument). This results in a more harsh penalty for missing sources in the model. In the regime typical of HERA discussed above, EPICal's error floor was 10 per cent lower than that of visibility-based solutions. Any realistic sky model will lie somewhere between the two extremes explored here. In the case where the sky is modelled by a single source, as is often the case for an initial calibration, EPICal actually achieves smaller gain errors compared to the traditional visibility-based calibration. As the sky model improves, both visibility-based and EPICal gains improve, though the former quicker than the latter. In the limit of a perfect model, both calibration methods produce noise-like errors in their gains which scale down with more integration time. Comparing the two regimes of receiver noise levels (red versus black lines in Fig. 8 ), we see that the gains errors behave as one might expect given our above interpretations. In the case of a perfect sky model, the higher receiver noise results in larger gain errors for a given integration time, but follows the same t −1/2 noise trend. The imperfect model lines begin exhibit the same offset at low integration time because the errors are dominated by the thermal noise. But as integration time increases, they approach the same floor due to the same level of power from unmodelled sources. 5 APPLICATION TO LWA DATA We next demonstrate our calibration algorithm using an observation from the LWA station in New Mexico (Ellingson et al. 2013 ). The data are from the LWA narrow-band transient buffer, with time-domain voltage data from the 255 core antennas within a 110 m × 100 m ellipse. The central frequency is 74.03 MHz, with a total observing bandwidth of 100 kHz, analysed by a filter bank into 512 channels of bandwidth 195.3125 Hz each and with a post-channelization sampling period of 5.12 ms. For this demonstration, we limit ourselves to a single polarization. For the gridding step, we adopt a grid with extent 120 m to encompass the footprint of the array, and a grid spacing of half-wavelength (≈2 m). The result is a 64 × 64 pixel grid, making the MOFF computational complexity of N g log 2 N g on the same order as the N a 2 computations for a cross-correlator. Our gridding kernel is a square tophat function with sides of 3 m, corresponding to the size of


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The authors thank K. Bowen, P.-M. Hillenbrand, J. Liévin, D. C. Lis, O. Novotný, I. R. Sims, and A. Viggiano for stimulating discussions. D.W.S. and R.G.B. were supported in part by the NASA Astrophysics Research and Analysis (APRA) program and the NSF Division of Astronomical Sciences Astronomy and Astrophysics Grants (AAG) program. S.V. was supported in part by a Barry Goldwater Scholarship and the USRA James B. Willett Educational Memorial Scholarship Award. X.U. is a Senior Research Associate of the Fonds de la Recherche Scientifique-FNRS.


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ACKNOWLEDGEMENTS We thank Frank van den Bosch and the anonymous referee for constructive comments on the paper. The simulations analysed in this paper were run on the Harvard Odyssey and CfA/ITC clusters, the Ranger and Stampede supercomputers at the Texas Advanced Computing Center as part of XSEDE, the Kraken supercomputer at Oak Ridge National Laboratory as part of XSEDE, the CURIE supercomputer at CEA/France as part of PRACE project RA0844, and the SuperMUC computer at the Leibniz Computing Centre, Germany, as part of project pr85je. KTEC acknowledges support from the Singapore National Science Scholarship.