In contrast, deep narrow-field surveys can reach more distant UCD populations, enabling measurement of disk structure and a greater proportion of halo and thick disk sources. The majority of deep surveys for UCDs (Table 1) have been undertaken with the Hubble Space Telescope (HST), as these objects often comprise a foreground to extragalactic surveys. Early work in this area includes measurement of M dwarf number counts in the HST Deep Field and Large Area Multi-Color Survey Groth Strip (Gould et al. 1997; Kerins 1997; Chabrier & Mera 1997). Analysis of these samples determined M dwarf thin and thick disk vertical scaleheights of ∼325 pc and ∼650 pc, respectively, and ruled out very low-mass stars as being an appreciable component (1%) of Galactic halo dark matter. Ryan et al. (2005) performed one of the first deep photometric surveys of distant UCDs, identifying 28 candidate L and T dwarfs in 135 arcmin2 of deep imaging data obtained with the HST Advanced Camera for Surveys (ACS) instrument, selected by their i − z colors to a limiting magnitude of z  25. They determined a thin disk vertical scaleheight of ∼350 pc, similar to prior measurements of deep M dwarf star counts. (Ryan et al. 2011) subsequently identified 17 candidate late-M, L, and T dwarfs in 232 arcmin2 of HST/Wide Field Camera 3 (WFC3) imaging of the Great Observatories Origins Deep Survey (Giavalisco et al. 2004) using optical and near-infrared color selection, and determined a thin disk vertical scaleheight for these sources of 290 ± 40 pc. Deep ground-based surveys have also identified samples of distant UCDs. Kakazu et al. (2010) identified seven late-L and T dwarfs in 9.3 deg2 of optical and infrared imaging data from the Subaru Suprime-Cam Hawaii Quasar and T dwarf survey to a limiting magnitude of z  23.3, spectroscopically confirming several of the targets. From this small sample, Kakazu et al. (2010) inferred a thin disk vertical scaleheight of ∼400 pc for brown dwarfs. Sorahana et al. (2019) used the larger (130 deg2) and deeper (z  24) Hyper Suprime-Cam Subaru Strategic Program survey (Aihara et al. 2018) to photometrically identify 3,665 L dwarfs, and inferred an average thin disk vertical scaleheight of 340–420 pc. Carnero Rosell et al. (2019) used multi-band imaging data from the Dark Energy Survey (The Dark Energy Survey Collaboration 2005), combined with photometry from wide-field imaging surveys, to photometrically identify and classify 11,745 L0–T9 dwarfs to a limiting magnitude of z ≤ 22, and estimated a thin disk vertical scaleheight of ∼450 pc. Recently, Warren et al. (2021) compiled a sample of 34,000 M7-L3 UCDs by searching over a large area of 3,070 deg2 in the Sloan Digital Sky Survey (SDSS; York et al. 2000) and UKIRT Infrared Deep Sky Survey (UKIDSS) down to J = 17.5, and measured a scaleheight of ∼270 pc. These last three studies, which comprise the largest compilations of UCDs to date, use multiple colors to segregate UCDs from other background sources (Skrzypek et al. 2016).


As a prototypical Seyfert 2 galaxy with starburst at a distance of 14.4 Mpc (1″ = 72 pc, Bland-Hawthorn et al. 1997), NGC 1068 was observed at radio (Greenhill et al. 1996), millimeter (Schinnerer et al. 2000), infrared (Jaffe et al. 2004), optical (Antonucci & Miller 1985), UV (Antonucci et al. 1994), and X-ray (Kinkhabwala et al. 2002). High spatial resolution CO (1–0) observations show two molecular spiral arms with a diameter of ~40″ and a northern half-bar, while a CO (2–1) map reveals a nuclear ring with two bright knots in the CND region (Schinnerer et al. 2000). The dense gas fraction as traced by HCN (1–0) (Tacconi et al. 1994; Helfer & Blitz 1995) and CS (2–1) (Tacconi et al. 1997; Takano et al. 2014) in the nuclear region is higher than the two arms. Observations of CO (3–2) (Krips et al. 2011; Tsai et al. 2012; García-Burillo et al. 2014) showed that the difference of molecular gas temperatures between the nuclear region and the two arms was not as large as that of densities. Dozens of molecular lines at millimeter wavelength were detected at CND with single-dish observations (Usero et al. 2004; Nakajima et al. 2011, 2013; Aladro et al. 2013). Moreover, several molecules were detected and resolved toward NGC 1068 with interferometers in the past few years (Tosaki et al. 2017; Kelly et al. 2017; Furuya & Taniguchi 2016; Izumi et al. 2016; Imanishi et al. 2016; Nakajima et al. 2015; Viti et al. 2014; Takano et al. 2014; García-Burillo et al. 2014, 2016). The molecular gas in the CND region was denser and hotter than that in the starburst ring, while chemical properties in the two regions were also different (Viti et al. 2014). The highest molecular gas temperature was higher than 150 K, and the gas density was above 105 cm−3 in the CND region (Viti et al. 2014). The distribution of different species of molecules were also different: CO isotopic species, for instance, were enhanced in the starburst ring, while the shock/dust related molecules were enhanced in the CND region (Nakajima et al. 2015). The spatially resolved observations showed that the CND region was a complex dynamical system. For instance, the east and west dots were dominated by a fast shock and a slower shock (Kelly et al. 2017), while the dust torus also showed complex kinematics (García-Burillo et al. 2016). Gas inflow was driven by a past minor merger (Furuya & Taniguchi 2016), while the outflow was AGN driven (García-Burillo et al. 2014). We conducted adeeper survey of millimeter lines toward the CND region of NGC 1068 with the IRAM 30 m telescope, with the goal to quantify the gas properties in the CND. Compared to previous single-dish observations, our data probe weaker transition lines, which could place more constraints on the physical and chemistry properties of the CND.


It is still unclear whether this incompatibility is evidence against the spatially flat ΛCDM model or is caused by unidentified systematic errors in one of the established cosmological probes or by evolution of the parameters themselves with the redshift (Dainotti et al. 2021b, 2022). Newer, alternate cosmological probes could help alleviate this issue. Recent examples of such probes include reverberation-mapped quasar (QSO) measurements that reach to redshift z ∼ 1.9 (Czerny et al. 2021; Khadka et al. 2021a,b; Yu et al. 2021; Zajaček et al. 2021), H ii starburst galaxy measurements that reach to z ∼ 2.4 (Mania & Ratra 2012; Chávez et al. 2014; González-Morán et al. 2019, 2021; Cao, Ryan & Ratra 2020, 2022a; Cao et al. 2021a; Johnson, Sangwan & Shankaranarayanan 2022; Mehrabi et al. 2022), QSO angular size measurements that reach to z ∼ 2.7 (Cao et al. 2017, 2020, 2021a; Ryan, Chen & Ratra 2019; Lian et al. 2021; Zheng et al. 2021), QSO flux measurements that reach to z ∼ 7.5 (Risaliti & Lusso 2015, 2019; Khadka & Ratra 2020a,b, 2021, 2022; Lusso et al. 2020; Yang, Banerjee & Ó Colgáin 2020; Li et al. 2021; Lian et al. 2021; Luongo et al. 2021; Rezaei, Solà Peracaula & Malekjani 2021; Zhao & Xia 2021),1 and the main subject of this paper, gamma-ray burst (GRB) measurements that reach to z ∼ 8.2 (Amati et al. 2008, 2019; Cardone, Capozziello & Dainotti 2009; Cardone et al. 2010; Samushia & Ratra 2010; Dainotti et al. 2011, 2013a,b; Postnikov et al. 2014; Wang, Dai & Liang 2015; Wang et al. 2016, 2022; Fana Dirirsa et al. 2019; Khadka & Ratra 2020c; Hu, Wang & Dai 2021; Dai et al. 2021; Demianski et al. 2021; Khadka et al. 2021c; Luongo et al. 2021; Luongo & Muccino 2021; Cao et al. 2021a). Some of these probes might eventually allow for a reliable extension of the Hubble diagram to z ∼ 3–4, well beyond the reach of Type Ia supernovae. GRBs have been detected to z ∼ 9.4 (Cucchiara et al. 2011), and might be detectable to z = 20 (Lamb & Reichart 2000), so in principle GRBs could act as a cosmological probe to higher redshifts than 8.2.


The cumulative total absolute magnitude distribution of the comets obeys N(  HT) ∝ 10− αTHT. Since we have imposed that the total brightness of the comets scales as BT ∝ fD2, it is easy to show that the slope of the total absolute magnitude distribution, αT, is equal to the slope of the nuclear absolute magnitude distribution, α. The latter is related to the cumulative size-frequency distribution, N( >D) ∝ D− γ, where γ = 5α. Even though there is a lot of scatter in the D − HT diagram caused by variation in f from one comet to the next (Fernández et al. 1999), there is a clear correlation between D and HT in Fig. 1 which must be caused by the underlying size distribution. For JFCs with diameters between approximately 2 km and 10 km the slope γ ~ 2 (Meech et al. 2004; Snodgrass et al. 2011), corresponding to α = 0.4. The number of JFCs with q  2.5 AU and HT  10.8 is then \hbox{$N_{\rm vJFC}=294_{-235}^{+556}$}NvJFC=294-235+556, about three times higher than the number reported in Levison & Duncan (1997) and Di Sisto et al. (2009). This is likely to be a lower limit because of the aforementioned incompleteness. However, the fading alters the mean active lifetime, τvFJC, as well. From the output of our simulations and using the delayed power law we computed a weighted mean period of JFCs with q  2.5 AU of 7.94 yr and a corresponding active lifetime \hbox{$\tau_{\rm vJFC} =1969^{+7479}_{-1540}$}τvJFC=1969-1540+7479 yr, lower than previous estimates (Di Sisto et al. 2009; Duncan & Levison 1997; Fernández et al. 2002). Following Brasser & Morbidelli (2013) the corresponding number of objects in the scattered disc with this updated active lifetime, taking into account the uncertainties in all relevant quantities, is then \hbox{$N_{\rm SD}= 5.9^{+2.2}_{-5.1} \times 10^9$}NSD=5.9-5.1+2.2×109. That same work computed an Oort cloud population of NOC = (7.6 ± 3.3) × 1010 for objects with D> 2.3 km. From our new analysis the Oort cloud to scattered disc population ratio turns out to be 13\hbox{$_{-11}^{+77}$}+77-11, which is consistent with the ratio of 12 ± 1 from simulations (Brasser & Morbidelli 2013). Thus, it is likely that the Oort cloud and scattered disc formed at the same time from the same source, and thus is consistent with a formation during the giant planet instability.


Following the first detection by ROSAT (Komossa & Bade 1999; Bade, Komossa & Dahlem 2016), about 50 TDEs have been observed (Komossa 2015) in hard X-ray (Bloom et al. 2011; Burrows et al. 2011; Cenko et al. 2012; Pasham et al. 2015), soft X-ray (Komossa & Bade 1999; Donley et al. 2002; Esquej et al. 2008; Maksym et al. 2010; Saxton et al. 2012, 2017; Bade et al. 2016), UV (Stern et al. 2004; Gezari et al. 2006, 2008, 2009) and optical (van Velzen et al. 2011; Gezari et al. 2012; Arcavi et al. 2014; Chornock et al. 2014; Holoien et al. 2014; Vinko et al. 2015) wavelengths. Some of the observed TDEs exhibit unusual properties. In particular, one of the detected TDEs shows an excess of variability in its light curve (Saxton et al. 2012) which can be explained if the black hole is actually a binary with a mass of 106 M⊙, mass ratio of 0.1 and semimajor axis of 0.6 milliparsecs (Liu, Li & Komossa 2014). This candidate appears to have one of the most compact orbits among the known SMBH binaries and has overcome the ‘final parsec problem’ (Colpi 2014). Upon coalescence, it will be a strong source of gravitational wave emission in the sensitivity range of the evolved Laser Interferometer Space Antenna (eLISA). Three other TDEs appear to be very bright in X-rays with peak soft X-ray isotropic luminosity being highly super-Eddington (Burrows et al. 2011; Cenko et al. 2012; Brown et al. 2015), while follow-up observations showed that these events were also associated with bright, compact, variable radio synchrotron emission (Zauderer et al. 2011; Cenko et al. 2012). The observed high X-ray luminosity can be explained if the tidal disruption of stars in these cases powered a highly beamed relativistic jet pointed at the observer (Tchekhovskoy et al. 2014). Based on these three observations, Kawamuro et al. (2016) concluded that 0.0007 per cent–34 per cent of all TDEs source relativistic jets, while Bower et al. (2013) and van Velzen et al. (2013) estimated that ≲10 per cent of TDEs produce jetted emission at the observed level. Formation of jets in TDEs is a topic of active research, e.g. works by Metzger, Giannios & Mimica (2012), Mimica et al. (2015) and Generozov et al. (2017).


The other criteria that we can use to categorize the reconstruction methods is whether the reconstruction is performed using forward-modelling or uses a direct inversion from the data. Inverting non-linear problems from partial, noisy, observations is an ill-posed inverse problem, which makes forward-modelled Bayesian methods particularly suitable for the task of reconstruction of high-dimensional fields. Bayesian reconstruction methods have become increasingly popular in cosmology and have been applied in a range of different applications such as initial conditions reconstruction (Jasche & Wandelt 2013; Modi, Feng & Seljak 2018; Jasche & Lavaux 2019), weak lensing (Fiedorowicz et al. 2022; Porqueres et al. 2021, 2022; Boruah, Rozo & Fiedorowicz 2022), and CMB lensing (Millea et al. 2021; Millea, Anderes & Wandelt 2020). Such methods have also been used for the local velocity field reconstruction. The simplest of such methods uses a Wiener filtering technique (Zaroubi, Hoffman & Dekel 1999). This approach assumes that the density/velocity field is described as a Gaussian random field and the Wiener filtered reconstruction is the maximum-a-posteriori (MAP) solution for the problem. The Wiener filtering approach has been extended to account for uncertainties and biases in the reconstruction using a constrained realization approach (Hoffman & Ribak 1991; Hoffman, Courtois & Tully 2015; Hoffman et al. 2018; Lilow & Nusser 2021) An alternative way to account for the biases in the reconstruction in Wiener filtering is using the unbiased minimal variance approach (Zaroubi 2002). Another similar approach is the Bayesian hierarchical method, virbius (Lavaux 2016), which is based on the constrained realization approach but accounts for many different systematic effects in its analysis. This approach has been been applied to the Cosmicflows-3 (Tully, Courtois & Sorce 2016) data set by Graziani et al. (2019). A similar reconstruction code, hamlet, was introduced in Valade et al. (2022). However, these methods fail to account for the inhomogeneous Malmquist (IHM) bias which is an important source of systematic error in peculiar velocity analysis. The IHM bias arises from an incorrect assumption on the distribution of peculiar velocity tracers due to neglecting the line-of-sight inhomogeneities.


It has also become evident that the normalization of the MS rapidly increases with redshift: distant galaxies form stars at higher paces than in the local Universe, at fixed stellar mass (e.g., Daddi et al. 2007; Elbaz et al. 2007; Whitaker et al. 2012; Speagle et al. 2014; Schreiber et al. 2015). This trend could be explained by the availability of copious molecular gas at high redshift (Daddi et al. 2010a; Tacconi et al. 2010, 2018; Scoville et al. 2017a; Riechers et al. 2019; Decarli et al. 2019; Liu et al. 2019a), ultimately regulated by the larger accretion rates from the cosmic web (Kereš et al. 2005; Dekel et al. 2009a). Moreover, higher SFRs could be induced by an increased efficiency of star formation due to the enhanced fragmentation in gas-rich, turbulent, and gravitationally unstable high-redshift disks (Bournaud et al. 2007, 2010; Dekel et al. 2009b; Ceverino et al. 2010; Dekel & Burkert 2014), reflected on their clumpy morphologies (Elmegreen et al. 2007; Förster Schreiber et al. 2011; Genzel et al. 2011; Guo et al. 2012, 2015; Zanella et al. 2019). IR-bright galaxies with prodigious SFRs well above the level of the MS are observed also in the distant Universe, but their main physical driver is a matter of debate. While a star formation efficiency (SFE = SFR/Mgas) monotonically increasing with the distance from the main sequence (ΔMS = SFR/SFRMS, Genzel et al. 2010, 2015; Magdis et al. 2012; Tacconi et al. 2018, 2020) could naturally explain the existence of these outliers, recent works suggest the concomitant increase of gas masses as the main driver of the starbursting events (Scoville et al. 2016; Elbaz et al. 2018). In addition, if many bright starbursting (sub)millimeter galaxies (SMGs, Smail et al. 1997) are indeed merging systems as in the local Universe (Gómez-Guijarro et al. 2018, and references therein), there are several well documented cases of SMGs hosting orderly rotating disks at high redshift (e.g., Hodge et al. 2016, 2019; Drew et al. 2020), disputing the pure merger scenario. The same definition of starbursts as galaxies deviating from the main sequence has been recently questioned with the advent of high spatial resolution measurements of their dust and gas emission. Compact galaxies with short depletion timescales typical of SBs are now routinely found on the MS, being possibly on their way to leave the sequence (Barro et al. 2017a; Popping et al. 2017; Elbaz et al. 2018; Gómez-Guijarro et al. 2019; Puglisi et al. 2019; Jiménez-Andrade et al. 2019); or galaxies moving within the MS scatter, due to mergers unable to efficiently boost the star formation (Fensch et al. 2017) or owing to gravitational instabilities and gas radial redistribution (Tacchella et al. 2016).


There have been previous studies that utilized coronal extreme ultraviolet (EUV) images in combination with models to try to more accurately determine the magnetic field. Conlon and Gallagher (Conlon & Gallagher 2010) used Extreme Ultraviolet Imager (EUVI) images to choose the best value of the parameter α in an LFFF model of a coronal active region. Aschwanden and co-authors (Aschwanden & Sandman 2010; Aschwanden 2013; Aschwanden & Malanushenko 2013) created NLFFF models of active regions by forward-fitting the underlying magnetograms with sets of buried magnetic monopoles and selecting the corresponding α values for each monopole that produced the greatest agreement with coronal loops traced in EUVI images. Malanushenko and co-authors (Malanushenko et al. 2009, 2012) have presented a method for deriving an NLFFF model from sparsely distributed EUV loop observations. These studies have focused on modeling the field in active regions, where the high density results in bright EUV emission and the limited size of the region allows for a reasonable number of free parameters. Additionally, the complexity of these methods suggests that their primary application would be the detailed study of a specific region of interest, rather than casual production of models for programmatic use. In contrast, the purpose of our study has been to develop a method for the fast production of global coronal magnetic field models based on widely available synoptic magnetograms and coronal images. Global models are necessary for studies on a wide array of topics, including the connectivity of active regions (Tadesse et al. 2012; Schrijver et al. 2013), the topology of the corona through the solar cycle (Wang & Sheeley 2003; Platten et al. 2014), and as a larger context for studies of coronal activity in localized regions (Conlon & Gallagher 2010; Schrijver et al. 2013). They are also instrumental for global heliospheric simulation and interpreting in situ measurements by upcoming near-Sun missions, Solar Orbiter (SO) and Solar Probe Plus (SPP).


The data presented here comprise quasi-simultaneous observations during secondary eclipse of WASP-33 b around the V and Y bands. The predicted planet-star flux ratio in the V-band is 0.2 ppt, four times lower than the accuracy of our measurements. Therefore, we can neglect the planet imprint and use this band to measure the stellar pulsations, and most specifically to tune their current phases (see phase shifts in von Essen et al. 2014). Particularly, our model for the light contribution of the stellar pulsations consists of eight sinusoidal pulsation frequencies with corresponding amplitudes and phases. Hence, to reduce the number of 24 free parameters and the values they can take, we use prior knowledge about the pulsation spectrum of the star that was acquired during von Essen et al. (2014). As the frequency resolution is 1/ΔT (Kurtz 1983), 3.5 h of data are not sufficient to determine the pulsations frequencies. Therefore, during our fitting procedure we use the frequencies determined in von Essen et al. (2014) as starting values plus their derived errors as Gaussian priors. As pointed out in von Essen et al. (2014), we found clear evidences of pulsation phase variability with a maximum change of 2 × 10-3 c/d. In other words, as an example after one year time a phase-constant model would appear to have the correct shape with respect to the pulsation pattern of the star, but shifted several minutes in time. To account for this, the eight phases were considered as fitting parameters. The von Essen et al. (2014) photometric follow-up started in August, 2010, and ended in October, 2012, coinciding with these LBT data. We then used the phases determined in von Essen et al. (2014) during our last observing season as starting values, and we restricted them to the limiting cases derived in Sect. 3.5 of von Essen et al. (2014), rather than allowing them to take arbitrary values. The pulsation amplitudes in δ Scuti stars are expected to be wavelength-dependent (see e.g. Daszyńska-Daszkiewicz 2008). Our follow-up campaign and these data were acquired in the blue wavelength range. Therefore the amplitudes estimated in von Essen et al. (2014), listed in Table 1, are used in this work as fixed values. This approach would be incorrect if the pulsation amplitudes would be significantly variable (see e.g., Breger et al. 2005). Nonetheless, the short time span of LBT data, and the achieved photometric precision compared to the intrinsically low values of WASP-33’s amplitudes, make the detection of any amplitude variability impossible.


The spatial distribution of OB stars and associations, young long-period Cepheids and open clusters, star-forming regions, H ii regions, interstellar dust, and giant molecular and neutral gas clouds in the solar vicinity that have been in existence generally τ ≲ 108 yr is known to correlate with the location of the inner Sagittarius, the closest Orion, and outer Perseus spiral arm segments. (The distances for the vast majority of these spiral tracers have been determined in the literature with trigonometric or photometric methods.) The Sun is situated at the inner edge of the Orion arm (Levine et al. 2006; Hou & Han 2014; Nakanishi & Sofue 2016; Xu et al. 2018, 2021; Lallement et al. 2019; Reid et al. 2019; Skowron et al. 2019; Cantat-Gaudin et al. 2020; Fig. 2 above).3 These three spatial features nearby to the Sun appear to form part of the global spiral structure in the Galaxy. Contrary, the objects of older population with larger random velocities, for instance, main-sequence A–K stars or the oldest Cepheids and open clusters, do not currently follow the exact location of those arms (e.g. Cantat-Gaudin et al. 2020, fig. 8 therein; Griv et al. 2020, fig. 7 therein). The latter can be explained by the difference in rotation velocity between the spiral density waves and the objects. Investigating the velocity field of Xu et al.’s (2018) O and early B-type stars in the framework of the Lin–Shu density-wave proposal, we also found that the Sun lies within the Orion arm, at the inner edge of this spiral. The radial distance from the Sun to the centre of the Orion arm is ≈0.2 kpc in the direction of the Galactic anticentre, the centre of the Sagittarius arm is ≈1.8 kpc from the Sun in the direction of the GC, and the width of the arms is ≈0.5 kpc. The radial distance between the centres of the Orion and Sagittarius arms near the Sun is λrad ≈ 2 kpc (cf. Hou & Han 2014; Wu et al. 2014; Bovy et al. 2015). As for us, the nearest Orion spiral arm forms part of the dominant density-wave structure of the system.


By considering the UV emission at several wavelengths, we have been able to reconstruct the evolution of the EFR at different layers using radiance maps. The optically thin view provided by the O i λ1355.6 line (Lin & Carlsson 2015) images the AFS that formed above the EFR. AFSs are typically observed in absorption in the chromospheric layers during flux emergence and reflect the serpentine nature of the emerging fields (Bruzek 1980; Spadaro et al. 2004; Zuccarello et al. 2005; Murabito et al. 2017). They also can reconnect with the ambient field (e.g., Zuccarello et al. 2008; Tarr et al. 2014; Su et al. 2018). Here the AFS appears in emission when observed in the O i λ1355.6 line, being brighter than the background. Some brightness enhancements are found along the AFS, suggesting the occurrence of small-scale energy release events related to the reconnection of the emerging field lines with the ambient field (see, e.g., Huang et al. 2018). The view of optically thick Mg ii k and C ii λ1335 lines (Leenaarts et al. 2013; Rathore et al. 2015) offers the possibility to see the counterpart of the AFS in the upper chromosphere. Threads observed in absorption, departing from the AFS, cover the whole structure. It should be stressed that the reconstructed radiance maps image the EFR along the entire IRIS scan: this means that the individual threads at every single slit position along the x-direction were only transiently observed. From the comparison with IRIS SJIs in the 2796 Å passband, it can be deduced that threads correspond to the surges, being viewed as individual ejections in slice imaging. The westernmost part of the UV burst, being not covered by threads, is seen as a compact brightening in the Mg ii k and C ii λ1335 radiance maps, in the latter having a higher contrast with respect to the background. Conversely, the optically thin emission in the Si iv λλ1402 and 1394 lines clearly illustrates the UV burst and other bright knots in the EFR area. Apparently, threads have no counterpart at Si iv λλ1402 and 1394 formation heights, although fluffy elongated structures appear in the northern part of the UV burst. Finally, dark elongated absorption structures are distinctly visible in the SDO/AIA 193 filtergrams, which are highly reminiscent of the threads seen by IRIS. To their west, a compact brightening cospatial to the UV burst is also detected, being not obscured by such structures.


The second equation of our system is the conservation of mass, (12)\begin{equation} \dfrac{\partial \rho}{\partial t} + \boldsymbol{\nabla}. \left( \rho {\vec V} \right) = 0, \end{equation}∂ρ∂t+∇.ρV=0,which, in spherical coordinates, writes (13)\begin{equation} \dfrac{\partial \delta \rho}{\partial t } + \frac{1}{r^2} \dfrac{\partial }{\partial r} \left( r^2 \rho_0 V_r \right) + \frac{\rho_0}{r \sin \theta} \left[ \dfrac{\partial }{\partial \theta} \left( \sin \theta V_\theta \right) + \dfrac{\partial V_\varphi}{\partial \varphi} \right] = 0. \label{conservation_masse} \end{equation}∂δρ∂t+1r2∂∂r(r2ρ0Vr)+ρ0rsinθ∂∂θsinθVθ+∂Vϕ∂ϕ=0.The thermal forcing (J) appears on the right-hand side of the linearized heat transport equation (see CL70, Gerkema & Zimmerman 2008) given by (14)\begin{equation} \frac{1}{\Gamma_1 p_0} \dfrac{\partial \delta p}{\partial t} - \frac{1}{\rho_0} \dfrac{\partial \delta \rho}{\delta t} + \frac{N^2}{g} V_r = \kappa \frac{\rho_0}{p_0} \left[ J - J_{\rm rad} \right], \label{transport_chaleur_1} \end{equation}1Γ1p0∂δp∂t−1ρ0∂δρδt+N2gVr=κρ0p0J−Jrad,where \hbox{$ \kappa = \left( \Gamma_1 - 1 \right)/\Gamma_1 $}κ=Γ1(−1)/Γ1 and Jrad is the power per mass unit radiated by the atmosphere, supposed to behave as a grey body. We consider that Jrad∝δT. This hypothesis is known as “Newtonian cooling” and was used by Lindzen & McKenzie (1967) to introduce radiation analytically in the classical theory of atmospheric tides (see also Dickinson & Geller 1968). Physically, it corresponds to the case of an optically thin atmosphere in which the flux emitted by a layer propagates upwards or downwards without being absorbed by the other layers. In optically thick atmospheres, such as on Venus (Lacis 1975), this physical condition is not verified. Indeed, because of a stronger absorption, the power emitted by a layer is almost totally transmitted to the neighbourhood. Therefore, this significant thermal coupling within the atmospheric shell should ideally be taken into account in a rigorous way, which would lead to great mathematical difficulties (e.g. complex radiative transfers, Laplacian operators) in our analytical approach. However, recent numerical simulations of thermal tides in optically thick atmospheres by Leconte et al. (2015) show behaviour of the flow that is in good agreement with a model that uses radiative cooling. Therefore, in this work we assumeNewtonian cooling as a first model of the action of radiation on atmospheric tides. Newtonian cooling brings a new characteristic frequency, denoted σ0, which we call radiative frequency and which depends on the thermal capacity of the atmosphere. The radiative power per unit mass is thus written (15)\begin{equation} J_{\rm rad} = \frac{p_0 \sigma_0}{\kappa \rho_0 T_0} \delta T. \label{phirad} \end{equation}Jrad=p0σ0κρ0T0δT.Like the basic fields p0, ρ0, and T0, the radiative frequency varies with r and defines the transition between the dynamical regime, where the radiative losses can be ignored, and the radiative regime, where they predominate in the heat transport equation. Assuming that the radiative emission of the gas is proportional to the local molar concentration C0 = ρ0/M, it is possible to express Jrad and σ0 as functions of the physical parameters of the fluid (Appendix D), (16)\begin{equation} J_{\rm rad} = \frac{8 \epsilon_a}{M} \mathscr{S} T_0^3 \delta T \label{phirad2} \end{equation}Jrad=8ϵaMST03δTand (17)\begin{equation} \sigma_0 \left( r \right) = \frac{8 \kappa \epsilon_a \mathscr{S} }{\mathscr{R}_{\rm GP} } T_0^3, \label{sigma0} \end{equation}σ0(r)=8κϵaSRGPT03,the parameter ϵa being an effective molar emissivity coefficient of the gas and S= 5.670373 × 10-8 W m-2 K-4 the Stefan-Boltzmann constant (Mohr et al. 2012). The substitution of Eq. (15) in Eq. (14) yields (18)\begin{equation} \frac{1}{\Gamma_1 P_0} \dfrac{\partial \delta p}{\partial t} - \frac{1}{\rho_0} \dfrac{\partial \delta \rho}{\delta t} + \frac{N^2}{g} V_r = \kappa \frac{\rho_0}{p_0} J - \sigma_0 \frac{\delta T}{T_0}\cdot  \label{transport_chaleur_2} \end{equation}1Γ1P0∂δp∂t−1ρ0∂δρδt+N2gVr=κρ0p0J−σ0δTT0·Finally, the system is closed by the perfect gas law (19)\begin{equation} \frac{\delta p}{p_0} = \frac{\delta T}{T_0} + \frac{\delta \rho}{\rho_0}\cdot \label{GPlaw} \end{equation}δpp0=δTT0+δρρ0·Substituting Eq. (19) in Eq. (18), we eliminate the unknown δT, and obtain (20)\begin{equation} \frac{1}{\Gamma_1 p_0} \left( \dfrac{\partial \delta p}{\partial t} \! +\! \Gamma_1 \sigma_0 \delta p \right) + \frac{N^2}{g} \dfrac{\partial \xi_r}{\partial t} = \frac{ \kappa \rho_0}{p_0} J + \frac{1}{\rho_0} \left( \dfrac{\partial \delta \rho}{\partial t}\! +\! \sigma_0 \delta \rho \right). \label{transport_chaleur_3} \end{equation}1Γ1p0∂δp∂t+Γ1σ0δp+N2g∂ξr∂t=κρ0p0J+1ρ0∂δρ∂t+σ0δρ.Because of the rotating motion of the perturber in the equatorial frame (RE;T), a tidal perturbation is supposed to be periodic in time (t) and longitude (ϕ). So, any perturbed quantity f of our model can be expanded in Fourier series of t and ϕ(21)\begin{equation} f = \sum_{m,\sigma} f^{m,\sigma} \left( \theta , r \right) e^{i \left( \sigma t + m \varphi \right)}, \label{perturbation} \end{equation}f=∑m,σfm,σ(θ,r)eiσt+mϕ,the parameter σ being the tidal frequency of a Fourier component and m its longitudinal degree1. We also introduce the spin parameter (22)\begin{equation} \nu \left( \sigma \right) = \frac{2 \Omega}{\sigma}, \label{nu} \end{equation}ν(σ)=2Ωσ,which defines the possible regimes of tidal gravito-inertial waves:


Our knowledge of magnetic fields in molecular clouds is based mainly on light polarisation, the optical and near-infrared (NIR) observations of background stars (Goodman et al. 1995; Whittet et al. 2001; Pereyra & Magalhães 2004; Alves et al. 2008; Chapman et al. 2011; Cox et al. 2016; Neha et al. 2018; Kandori et al. 2018), and the polarised dust emission at far-infrared (FIR), sub-millimetre, and radio wavelengths (Ward-Thompson et al. 2000; Koch et al. 2014; Matthews et al. 2014; Fissel et al. 2016; Pattle et al. 2017). The Planck survey provides a large amount of data for polarisation studies at cloud scales (Planck Collaboration Int. XX 2015; Planck Collaboration Int. XIX 2015; Planck Collaboration Int. XXXIII 2016). The Planck data have been used especially to study the polarisation fraction and the correlations in the relative morphology of column density and magnetic field structures (Planck Collaboration Int. XX 2015; Planck Collaboration Int. XXXIII 2016; Malinen et al. 2016; Soler et al. 2016; Alina et al. 2019). Particularly, the drop of polarisation fraction p towards PGCC clumps has been observed with high significance in the Planck 353 GHz data (Alina et al. 2019; Ristorcelli et al, in prep.). The variations ofp are interesting because they are related to the configuration of the magnetic fields in clumps and cores during the star formation process. However, p is also affected by variations in the efficiency of the grain alignment, as predicted, for example, by the theory of radiative torque alignment (RAT; Lazarian et al. 1997; Cho & Lazarian 2005; Hoang & Lazarian 2014) and demonstrated by numerical simulations (Pelkonen et al. 2009; Brauer et al. 2016; Reissl et al. 2018). These suggest that high optical depths and more frequent gascollisions should significantly reduce the grain alignment and thus the polarised emission observable from within the clumps. ThePGCC provides a statistically significant sample to study these questions observationally, although the Planck resolution limits the investigations to structures that are typically much larger than an individual cloud core. However, polarisation of selected PGCCs has already been studied at higher resolution with the SCUBA-2 POL-2 instrument at JCMT (Liu et al. 2018b,c; Juvela et al. 2018c), and many more will be covered by ongoing surveys (Ward-Thompson et al. 2017).


A large effort has been invested in understanding the chemical patterns of galaxies using analytical and numerical chemical modelling (e.g. Brook et al. 2007; Calura et al. 2012; Mollá et al. 2015). In particular, hydrodynamical simulations provide the chemical enrichment of baryons as galaxies are assembled in a cosmological framework, opening the possibility of understanding the interplay of different physical processes in the non-linear regime of evolution (e.g. Mosconi et al. 2001; Lia et al. 2002; Wiersma et al. 2009). Pilkington et al. (2012) carried out a comparison of the metallicity gradients in the ISM (traced by young SPs) obtained by different numerical and analytical models. Gibson et al. (2013) analysed different models of SN feedback schemes reporting different evolution for the gas-phase metallicity gradients. No evolution was reported when an enhanced SN model was used. Tissera et al. (2016b) studied the gas-phase metallicity gradients in discs and the specific star formation of the galaxies. For gas-phase metallicities, the simulated galaxies showed a correlation with stellar mass, which was erased when the metallicity gradients were renormalised by the effective radius, reproducing observations by Ho et al. (2015, and references there in). They also found indications of a correlation between the abundance slopes and the specific star formation rate (sSFR) in agreement with observational findings (Stott et al. 2014). As a function of redshift, the metallicity gradients of the gas-phase disc components were found to be more negative at higher redshift, principally for lower stellar-mass galaxies. The fraction of galaxies with positive metallicity gradients increased with increasing redshift and were found to be associated to mergers and interactions. The trends found for the gas-phase metallicity gradients by Tissera et al. (2016b) are relevant to the discussion of this paper because we are using the same set of simulated galaxies.


Many theoretical models have been proposed to explain the generation of QPPs. The most elaborated model of QPPs considers MHD oscillations, which affect almost all aspects of the flare emission generation. Indeed, QPPs are involved in triggering the magnetic reconnection, modulating the reconnection rate, accelerating and transporting non-thermal electrons, and changing the physical conditions in emitters (Nakariakov & Melnikov 2009). Other models are based on a sandpile system with self-organized critical states (Lu & Hamilton 1991; Baiesi et al. 2008), the quasi-stabilized system of non-linear plasmas governed by an oscillatory phase of wave-wave or wave-particle interactions (Aschwanden 1987). Different MHD oscillation modes have been identified to be responsible for QPPs in a single flaring loop (Nakariakov et al. 2003; Melnikov et al. 2005; Warmuth et al. 2005; Inglis et al. 2008; Kupriyanova et al. 2010, 2013; Kim et al. 2012). Kolotkov et al. (2015) studied the QPPs of the microwave emission generated in a X3.2-class solar flare. They found three well-defined intrinsic modes with mean periods of 15, 45, and 100s. These authors proposed that the 100 s and 15s modes are likely to be associated with fundamental kink and sausage modes of the flaring loop, respectively. The 100 s oscillations could also be caused by the fundamental longitudinal mode. The 45 s mode, on the other hand, could be the second standing harmonic of the kink mode. Inglis & Nakariakov (2009) reported a multi-periodic oscillatory event with three distinct periods, namely 28s, 18s, and 12s. They argued that the cause of this multi-periodic event is likely to be a kink mode that periodically triggers magnetic reconnection. Similar QPPs could be generated by different mechanisms. To discover, understand, and distinguish these mechanisms correctly, detailed and multi-wavelength observations are required. Within the framework of the EU FP7-project SOLSPANET1, we are developing a solar and space-weather knowledge base that will allow such extensive and detailed studies.


Throughout the initial collapse the halo structure is well approximated by ellipsoidal collapse models. We therefore explore radial profiles of various physical quantities to extract information about the galactic environment. The density is illustrated in Fig. 2, which is reasonably approximated by a broken power law over the range r ∈ (10−3, 103) pc. The break radius is due to the choice of the density resolution threshold, or equivalently, the limited resolution implies the pre-formation profile corresponds to roughly a dynamical time, as evaluated at the maximum resolved density, of ∼10 kyr prior to the formation of the protostar. If the evolution proceeds under self-similar, isothermal collapse then the break in the profile will shift to smaller scales, eventually reaching the radius of the protostar (Abel, Bryan & Norman 2002; Becerra et al. 2015). We note that secondary infall and accretion results in a density distribution that is steeper than the ρ ∝ r−2 profile produced by violent relaxation. We find a power-law scaling of ρ ≈ r− 7/3 in good agreement with Bertschinger (1985) where ρ ∝ r−9/4 and Wise, Turk & Abel (2008) where ρ ∝ r−12/5, except in the core where the slope flattens off to ρ ∝ r−0.4 around r ≈ 0.3 pc. During the initial collapse and formation, the gas remains neutral with only a small abundance of free protons. Specifically, the ionization fraction, $x_{\rm {H \small {II}}} \equiv n_{\rm {H \small {II}}} / n_{\rm H}$, is typically of order 10−5 to 10−3 depending on the density, such that $n_{\rm {H \small {II}}} \sim 0.1\,{\rm cm}^{-3}\,(r/10\,{\rm pc})^{-5/3}$. As expected for direct collapse, the central region has access to at least 105 M⊙ of gas within a radius of ≈1.3 pc. More broadly, the enclosed baryonic mass is $M_{<r} \approx 4 \pi \int _0^r \rho (r) r^2 {\rm d}r$ (for 1D profiles), calculated explicitly as Mr ≡ ∑rρiVi where the sum is over all Voronoi cells within a radius r, and the subscript denotes cell quantities for density ρi and volume Vi. For convenience and completeness, in Table 1 we provide radial scaling relations for several relevant quantities, calculated as mass-weighted averages within shell volumes, i.e.
(1)
\begin{eqnarray}
\langle q \rangle _{\rm shell} \equiv \frac{\int q \rho \, {\rm d}V}{\int \rho \, {\rm d}V} \approx \frac{\sum q_i \rho _i V_i}{\sum \rho _i V_i} \,,
\end{eqnarray}
where the discretized version sums over all cells within each shell. Similarly, we obtain mass-weighted line of sight averages with
(2)
\begin{eqnarray}
\langle q \rangle _{\rm LOS} \equiv \frac{\int q \rho \, {\rm d}\ell }{\int \rho \, {\rm d}\ell } \approx \frac{\sum q_i \rho _i \Delta \ell _i}{\sum \rho _i \Delta \ell _i} \,,
\end{eqnarray}
where the integral is along radial rays within each shell and the summation is the discretized version calculated by ray tracing.


Many of these objects have been confirmed as DNe through an identification spectrum or a measurement of the superhump period, but we find that 27 sources were not confirmed through any method. Quiescent multiband photometry of these remaining candidates can provide insights into the distance and ultimately constrain the luminosity of the transient. In the Galactic plane, a candidate that is relatively blue is likely close by and therefore will have a lower luminosity at peak brightness, suggesting a DN outburst. Conversely, a candidate that is brighter in redder filters is likely reddened by dust, implying a higher luminosity and a CN outburst. This strategy—identifying highly reddened quiescent counterparts—is only possible for candidates within a few degrees of the Galactic plane and that can be securely matched to multiband optical catalogs. As described in Section 2.4, we find quiescent counterparts in Pan-STARRS and also add in coverage of southerly declinations by using the DeCAPS catalog (Schlafly et al. 2018; cross-matching for both catalogs is as explained in Appendix A.3). We use the griz photometry to estimate reddening by fitting the observed spectral energy distributions of the CVs in question to dereddened SDSS CV colors from Kato et al. (2012) by varying the amount of reddening according to extinction laws (Cardelli et al. 1989; Mathis 1990). For each of our candidates, this results in a distribution of extinction values that are plugged into the three-dimensional all-sky extinction map stitched together in Bovy et al. (2016) to find a range of plausible distances. This strategy only worked for 19 of the candidates: those that we were able to cross-match and in fields close to the plane, where a large amount of dust can constrain the distance. We find that all 19 are consistent with the peak luminosity of a dwarf nova, and none are consistent with the peak luminosity of a classical nova. This analysis will also be useful to shed light on the nature of CV candidates that are discovered in the future, so it is made publicly available as an iPython notebook at https://github.com/amkawash/CV_colors_luminosity.


Scaling relations for the core radii rc, core densities δc, and core masses Mc as functions of the total halo mass M200 were fitted to the simulated halo populations, which largely agree with hydrostatic considerations of the halo cores where rc is nearly constant, as well as velocity dispersion tracing in the halo envelope,

v
c
2

≈
v

200
2

$ v^2_{\rm c} \approx v^2_{200} $

. However, these trends do not agree with those obtained by fitting the Burkert profile to nearby galaxies in the SPARC dataset and the classical Milky Way dSphs. This poses an issue for SIBEC-DM with Rc ≳ 1 kpc and a largely CDM-like matter power spectrum at late times (Harko 2011; Harko & Mocanu 2012; Velten & Wamba 2012; Freitas & Gonçalves 2013; Bettoni et al. 2014; de Freitas & Velten 2015; Hartman et al. 2022), as was used in our simulations, although these scenarios are not well-motivated. For SIBEC-DM given by the field Lagrangian in Eq. (1), the self-interaction is constrained to Rc  1 kpc, otherwise an early radiation-like period and a large comoving Jeans’ length washes out too much structure to be consistent with observations (Shapiro et al. 2021; Hartman et al. 2022). In fact, Shapiro et al. (2021) found by using constraints on FDM as a proxy for SIBEC-DM, and matching their transfer function cut-offs and HMFs, that the SIBEC-DM self-interaction should be as low as Rc ∼ 10 pc to not be in conflict with observations. We were unable to probe SIBEC-DM with initial conditions and parameters consistent with the Lagrangian in Eq. (1), since the large gap between the halo cores and the cut-off scale requires both a large simulation box and very high spatial resolution. It should be noted that our SIBEC-DM-only simulations do provide a better agreement with the slopes in observed scaling relations than FDM. In particular, FDM simulations generally find

M
c

∼

M

200

γ

$ M_{\mathrm{c}}\sim M_{200}^{\gamma} $

 with 1/3  γ  0.6, while we find γ ≈ 0.75, which is closer to the observed γ ≈ 1.1. Additionally, FDM halos have core radii that generally decrease with the halo mass, while we find a slightly increasing trend due to larger halos experiencing more thermal heating, although not as steep as in the SPARC dataset and the Milky Way dSphs.


Resonant dynamical friction may have applications beyond the relaxation of IMBHs examined in this paper. It may affect all objects in stellar clusters much more massive than the individual constituents of the disk, if present, including massive stars, stellar mass black holes (BHs), or the center of mass of massive binaries. Furthermore, it is also expected to operate in any type of disk with a high number of particles, including active galactic nucleus (AGN) accretion disks. Previously, it has been argued that stars and BHs crossing the disk on low-inclination orbits get captured by Chandrasekhar dynamical friction into the disk (Bartos et al. 2017; Panamarev et al. 2018; Tagawa et al. 2020). An interesting implication is that, if BHs settle into the disk, they interact dynamically and form BH–BH binaries efficiently, and frequent dynamical interactions and gas effects drive the BHs to merger, producing gravitational waves (GWs) detectable by LIGO, VIRGO, and KAGRA (McKernan et al. 2014, 2018; Bartos et al. 2017; Leigh et al. 2018; Yang et al. 2019; Tagawa et al. 2020, 2021; Samsing et al. 2020). Mergers are also facilitated by Lidov–Kozai oscillations in anisotropic systems (Heisler & Tremaine 1986; Petrovich & Antonini 2017; Hamilton & Rafikov 2019). The results in this paper show that resonant dynamical friction may accelerate the capture of objects in the accretion disks by a factor proportional to the SMBH mass over the local disk mass for large orbital inclinations. Pressure and viscosity in a gaseous disk do not inhibit the orbit-averaged torque from the IMBH, which leads to realignment and the warping of the disk (Bregman & Alexander 2012). Thus, RDF may efficiently catalyze the alignment of the orbital planes of BHs even in low-luminosity AGN or Seyfert galaxies with relatively small disk masses, which may not be possible for Chandrasekhar dynamical friction. In fact, this mechanism extends the scope of the “AGN merger channel” for GW source populations even beyond low-luminosity AGN and Seyfert galaxies, as it may organize BHs into disks also in nonactive galaxies with nuclear stellar disks.


Bond & Ciardullo (2018) identify a periodicity of 2.06 d in their data, with a similar period clearly evident in the newly acquired data. However, no single period and time of first minima could be found that fits all the data (perhaps not unexpected given that the variability is clearly not constant, see Section 2.3 for further discussion). In order to better constrain the period, as well as the changes between observing epochs, we focus on the periodicitiy of all the data taken between 2011 and 2015 (shown in the lower left panel of Fig. 1). Given the nature of the variability, we measure the period via the reduced χ2 of a sinusoidal fit as a function of frequency (ideally suited to sinusoidal variability, e.g. Horne, Wade & Szkody 1986; Munday et al. 2020). The resulting periodogram is shown in Fig. 2. Two strong minima in the reduced χ2 are found, the strongest at 2.061 ± 0.005 d (consistent with the period of Bond & Ciardullo 2018) and a second slightly shallower at 1.938 ± 0.005 d. The data from 2010, combining that of Bond & Ciardullo (2018) and our own from SAAO, phases well on the first period but not the second, lower period, likely indicating that this is an alias. As such, we conclude that the rotation period is indeed ≈2.06 d and that there is no strong evidence for a change in period before and after the phase of negligible variability in early 2011. There is, however, a clear shift in phase between the 2010 data and the later data used to derive the period (see Fig. 2). There is no statistically significant evidence for a shift between the 2011–2015 data and the later data from 2022, although the lack of data in the intervening seven years as well as the uncertainty on the period mean that we cannot exclude a phase shift between these two data sets. The 2022 data does, however, appear to have a larger photometric amplitude, more consistent with the 2010 data. None the less, if the variability did remain constant throughout this time, we can refine the period to P = 2.060561 ± 0.000002 d.


We use the final version of the MaNGA data (Abdurro’uf et al. 2022). MaNGA is the survey project in SDSS-IV (Sloan Digital Sky Survey) using IFU observations of galaxies to produce spatially resolved spectroscopic data (Gunn et al. 2006; Bundy et al. 2015; Drory et al. 2015; Blanton et al. 2017; Aguado et al. 2019; Abdurro’uf et al. 2022). MaNGA observed approximately 10 000 galaxies, selected as an unbiased sample in terms of stellar mass (${\it M}_{\star } \gt 10^{9}\, {\rm M}_{\odot }$) and environments (Law et al. 2015; Yan et al. 2016a; Wake et al. 2017). The MaNGA targets were selected as two main subgroups and two minor subgroups. Among the main subgroups, the primary sample of about 5000 galaxies was selected to observe the central part out to $\rm 1.5{\it R}_{eff}$. The secondary sample of the main subgroups includes about 3300 galaxies, observed by the IFU bundle out to $\rm 2.5{\it R}_{eff}$. These samples were selected without bias and covers a wide range in galaxy masses. The first of the two minor subgroups is a ‘colour-enhanced sample’ of about 1700 galaxies. It is selected to include blue massive galaxies and green valley galaxies that are important to study the quenching process. These targets are observed with an IFU coverage of $\rm 1.5{\it R}_{eff}$. A second minor sample includes about 1000 ancillary targets, selected for various observations using the unique capability of the MaNGA instrument (Yan et al. 2016a). The IFU bundles of the MaNGA consist of 19–127 fibres with hexagonal shape covering 12–$\rm 32~arcsec$ in diameter on sky. The spatial resolution of MaNGA is $\rm 2.5~arcsec$, which corresponds to 1.3–$\rm 4.5~kpc$ for the primary sample and 2.2–$\rm 5.1~kpc$ for the secondary sample. The BOSS spectrographs used by MaNGA provide spectra from 3600 to 10 300 Å  with a spectral resolution of about 2100–6000 Å  (Smee et al. 2013; Yan et al. 2016b). The observations were conducted to reach an signal-to-noise ratio (S/N) in the stellar continuum at $\rm 1{\it R}_{eff}$ of $\rm 14$–$\rm 35$ per spatial sample, which required about 3 h net integration for each target.


A lognormal mass function:
(7)$$\begin{eqnarray}
\psi (M;\mu ,\sigma)=\frac{1}{M\sqrt{2\pi \sigma ^2}}\exp {\left(- \frac{\ln ^2(M/\mu)}{2\sigma ^2}\right)},
\end{eqnarray}$$where μ > 0 and σ > 0. The mean PBH mass in the assumption of a lognormal mass function is $\bar{M}=\mu \exp \left(-\sigma ^2/2\right)$. Such mass function is a good approximation for a large class of PBH formation scenarios, e.g. axion-curvaton, running-mass, and single field double inflation (Green 2016; Kannike et al. 2017). The (μ, σ) pairs allowed in the window relevant for the operational gravitational wave detectors [$\mathcal {O}(1\operatorname{-}100)\, {\rm M}_\odot {}$; Abbott et al. 2019] are mainly constrained by (i) the results from searches for microlensing events on stars in our Galactic neighbourhood and (ii) the effect PBH gas accretion would have on the CMB temperature and ionization history (Carr et al. 2017; Sasaki et al. 2018). Together, the allowed points roughly constitute a sub-plane described as (see fig. 3 in Carr et al. 2017):
(8)$$\begin{eqnarray}
(\mu ,\sigma)\in [25\, {\rm M}_\odot ,100\, {\rm M}_\odot ]\times [0.0,1.0].
\end{eqnarray}$$It is worth mentioning that these points are ruled out completely if one further takes the following constraints into account (Carr et al. 2017): (iii) the survival of the stellar cluster in Eridanus II and of the entire stellar populations in UFDGs (Brandt 2016; Green 2016; Koushiappas & Loeb 2017; Zhu et al. 2018) and (iv) the survival of wide binaries in the Milky Way (Monroy-Rodríguez & Allen 2014). These constraints are somewhat less restrictive, as they rely on further astrophysical assumptions (Carr et al. 2017). For instance, the stellar cluster in Eridanus II could have only recently spiralled down into the centre of the galaxy, where dynamical heating by PBHs becomes effective (Brandt 2016). Additionally, wide binaries are in principle hard to detect, yielding some uncertainty in identifying them and consequently in drawing any conclusion on the PBH abundance (Sasaki et al. 2018). Moreover, we emphasize that, most recently, even previous microlensing constraints were called into question as spatial PBH clustering (García-Bellido & Clesse 2018) and updated galactic rotation curves (Hawkins 2015) tend to relax them.


Cosmological hydro dynamical N-body simulations offer another possibility to investigate the origin of the bimodality in the ([Fe/H], [α/Fe]) plane. Earlier simulations, e.g. full N-body simulations by Loebman et al. (2011), Brook et al. (2012) or hybrid simulations in which a semi-analytic chemical evolution was added on top of a cosmological simulation (Minchev, Chiappini & Martig 2013, 2014), were able to show that the thin and thick discs lie along different tracks in the ([Fe/H], [α/Fe]) plane, with the thick disc being old metal poor and rich in [α/Fe] and the thin disc being young, metal-rich and poor in [α/Fe]. They also showed that migration was important to generate the two discs. However, a clear bimodality in the ([Fe/H], [α/Fe]) plane was not seen. In the past few years good progress has been made to improve the spatial resolution as well as the chemical enrichment prescriptions. The bimodality has now been observed in some simulations (Grand et al. 2018; Mackereth et al. 2018; Clarke et al. 2019), and some of the simulations, in addition to the bimodality, also reproduce the basic trends of the ([Fe/H], [α/Fe]) distribution with radius R (Buck 2020; Vincenzo & Kobayashi 2020). Unlike analytical models, such simulations cannot be fine tuned to reproduce the Milky Way data, hence, the focus of these simulations is to qualitatively reproduce the abundance trends seen in the Milky Way, to understand how frequently do we get the bimodality and what is the mechanism for it. However, there is a lack of consensus between the different studies. Clarke et al. (2019) and Buck (2020) suggest that bimodality should be common in disc galaxies, whereas Mackereth et al. (2018) suggest that it is rare. Each simulation suggests slightly different mechanisms for the existence of the bimodality. Clarke et al. (2019) attribute bimodality to vigorous star formation in clumps at high redshift. Grand et al. (2018) suggest two distinct pathways, a centralized starbust pathway induced by mergers and a shrinking gas disc pathway. Buck (2020) suggest that after the formation of the high-[α/Fe] sequence a gas-rich merger dilutes the metallicity of the ISM leading to the formation of the low-[α/Fe] sequence. Mackereth et al. (2018) attribute the bimodality to unusually rapid gas accretion at earlier times, which is also characterized by a short time-scale to convert gas to stars. While some simulations clearly identify migration as key process to shape the sequences, others do not. In spite of the differences, it seems that some of the simulations (e.g. Mackereth et al. 2018; Buck 2020; Vincenzo & Kobayashi 2020) are not inconsistent with the Schönrich & Binney (2009a) paradigm.


The transport of angular momentum (AM) and chemical elements in stars strongly affects their evolution, from pre-main sequence (PMS) to evolved stages. These processes are particularly crucial in the stellar radiative zones, but their modelling remains an open question. In standard evolution models, these stably stratified zones are assumed to be motionless despite early works pointing out the lack of a static solution in uniformly rotating stars (Von Zeipel 1924) and a related large-scale meridional circulation driven by the centrifugal acceleration (Eddington 1925; Sweet 1950). A more complete formalism was then introduced by Zahn (1992) including a self-consistent meridional flow and models of the turbulent transport driven by hydrodynamical instabilities. The importance of additional processes such as internal waves (e.g., Talon & Charbonnel 2005) and magnetic fields (Spruit 2002) has also been investigated. Zahn’s formalism successfully explained a number of observed stellar properties, such as the nitrogen abundances at the surface of red supergiants or the observed blue-to-red supergiant ratio in the Small Magellanic Cloud (Maeder & Meynet 2001). The dynamics of internal gravity waves could possibly explain the flat rotation profile of the solar radiative zone (Talon et al. 2002 and Charbonnel & Talon 2005) inferred through helioseismology (Schou et al. 1998), as well as the lithium dip in solar-like stars (Charbonnel & Talon 2005). Despite these early encouraging results many stellar observations remain unexplained, especially the internal rotation rates revealed by asteroseismology in evolved stars and in intermediate-mass main sequence stars (see Aerts et al. 2019 for a review). The current theoretical understanding of the structure of the differential rotation in stellar radiative zones, crucial for the development of instabilities and thus for the related turbulent transport, is still largely incomplete. In particular, the assumption that the differential rotation is mostly radial, rather than radial and latitudinal, is at the base of Zahn’s formalism, but the validity of this assumption has never been thoroughly tested. In this paper we are particularly interested in the differential rotation and the large-scale meridional flows generated in periods of the stellar life when contraction, expansion, or both processes occur. This is the case for example for PMS stars which are gravitationally contracting before starting their core nuclear reactions, or for subgiant and giant stars which undergo contraction of their core and expansion of their envelope. Within these stars a strong redistribution of AM is expected to happen, producing differential rotation and thus potentially unstable shear flows.


Additionally, wide binaries are in principle hard to detect, yielding some uncertainty in identifying them and consequently in drawing any conclusion on the PBH abundance


In this study, the 272 eV suprathermal electron pitch-angle distributions (PADs) measured by ACE are used. The electron PADs are obtained from the Solar Wind Electron Proton Alpha Monitor (SWEPAM) with angular and time resolutions of 9° and 64 s respectively (McComas et al. 1998). Here we examined 16 s average magnetic field, 64 s average plasma, 1 h average O7+/O6+ ratio, and mean Fe charge state ⟨Fe⟩ data from 1998 to 2008 measured by ACE and identified 272 ICMEs in total. The ICMEs were identified by the following process: (1) We take the events in previous ICME lists of Jian et al. (2006), Chi et al. (2016), and Richardson & Cane (2004)1 as candidate ICMEs. (2) Some lists also report short-duration ( 10 h) structures as ICMEs. As the origin of these smaller-scale ICMEs and flux ropes are still debated (Feng et al. 2007; Rouillard et al. 2011; Janvier et al. 2014; Feng & Wang 2015; Wang et al. 2019), we excluded them from this study. (3) The high Fe charge states (⟨Fe⟩ ≥ 12) and abnormally high O7+/O6+ ratio (≥1) are the result of flare-related heating in the corona (Lepri & Zurbuchen 2004; Reinard 2005), and therefore they are independently reliable ICME indicators (Feng & Wang 2015). If the candidate ICMEs have high Fe charge states and/or abnormally high O7+/O6+ ratio, they are identified as ICMEs. (4) If the candidate ICMEs have no high Fe charge states and abnormally high O7+/O6+ ratio, we look for the following five characteristics: declining speed (apparent expansion), increasing total magnetic magnitude and helium abundance (He/P > 0.06) (Richardson & Cane 2004), and decreasing proton temperatures and proton densities. If the candidate ICMEs have three or more of the above characteristics they are identified as ICMEs. Given that magnetic flux ropes are special field topologies characterized by bundles of helical magnetic-field lines collectively spiraling around a common axis, the essential observational properties of magnetic flux ropes should be enhanced magnetic field strength and smooth rotations (Feng et al. 2008, 2010), namely, measured enhanced magnetic field strength, the center-enhanced magnetic components, and bipolar curve magnetic components. Therefore, if an ICME was found to have enhanced magnetic field strength, both center-enhanced and bipolar field components, it was identified as MC. Among the 272 ICMEs, 101 (37.1%) events were identified as MCs. All 272 ICMEs are listed in Table A.1. The second and third columns show the start and end times, the fourth column gives the duration of the ICMEs, and the fifth column provides the types of ICMEs (MC or nonMC).


Complementary to studies using the integrated emission and angular power spectrum of DM annihilation from a population of Galactic subhalos, in this paper we present a novel strategy using one-point photon statistics to search for the annihilation signature. Our technique takes advantage of the information in the entire population of sources, including both those that are resolved and those that are faint and unresolved. The concept of leveraging the one-point photon-count distribution to search for DM has previously been studied in Dodelson et al. (2009) and Feyereisen et al. (2015) in the context of emission from extragalactic sources and in Lee et al. (2009) and Koushiappas et al. (2010) with application to Galactic subhalos. We introduce a method to search for signatures of DM annihilation from a Galactic subhalo population using the non-Poissonian template fitting (NPTF) framework (Malyshev & Hogg 2011; Lee et al. 2015, 2016; Mishra-Sharma et al. 2017), which has previously been applied to characterize unresolved point sources in the inner Galaxy (Lee et al. 2016; Linden et al. 2016; Leane & Slatyer 2019, 2020a, 2020b; Chang et al. 2020; Buschmann et al. 2020) and at high latitudes (Zechlin et al. 2016; Lisanti et al. 2016; Zechlin et al. 2018). Using simulations, we show that the NPTF can constrain DM annihilation from a population of subhalos in the face of astrophysical background emission. We find that using photon statistics to look for collective emission from a subhalo population can be especially promising when a large number of individual subhalo candidates are identified in point-source catalogs. This establishes a method complementary to the established ones based on characterizing individual resolved point sources as subhalo candidates, as well as those based on using the measured 0-point (overall flux) and two-point (angular power spectrum) statistics to characterize a subhalo population. Moreover, note that our methodology is completely independent of assumptions about, e.g., the location of stellar overdensities, so we are less sensitive to certain uncertainties which can bias dwarf galaxy constraints such as those in modeling tracer populations. Thus, this framework provides an important comparison for the dwarf galaxy analyses as well.


By radio continuum surveys of interstellar space and direct in situ measurements in the solar system, it is well established that for many scenarios the background magnetic fields are spatially varying. However, the above research about parallel and perpendicular diffusion only explored the uniform mean magnetic field. One can show that the spatially varying background magnetic fields lead to the adiabatic focusing effect of charged energetic particle transport and introduces correction to the particle diffusion coefficients (see, e.g., Roelof 1969; Earl 1976; Kunstmann 1979; Beeck & Wibberenz 1986; Bieber & Burger 1990; Kóta 2000; Schlickeiser & Shalchi 2008; Shalchi 2009b, 2011; Litvinenko 2012a, 2012b; Shalchi & Danos 2013; Wang & Qin 2016; Wang et al. 2017b). To explore the influence of adiabatic focusing on particle transport, the perturbation method is frequently used (see, e.g., Beeck & Wibberenz 1986; Bieber & Burger 1990; Schlickeiser & Shalchi 2008; Schlickeiser & Jenko 2010; Litvinenko & Schlickeiser 2013; He & Schlickeiser 2014). To use the perturbation method, since the anisotropic distribution function is an implicit function, by using the iteration method, one can find that the anisotropic distribution function becomes an infinite series of the spatial and temporal derivatives of the isotropic distribution function. Therefore, the governing equation of the isotropic distribution function derived from the Fokker–Planck equation contains infinite terms because of the infinite series of the anisotropic distribution function. By using the truncating method to neglect the higher-order derivative terms, the approximate correction formulas of parallel or perpendicular diffusion coefficients were obtained (see, e.g., Schlickeiser & Shalchi 2008; Schlickeiser & Jenko 2010; He & Schlickeiser 2014). However, the higher-order derivative terms probably also make the correction to the parallel and perpendicular diffusion much like the lower-order derivative ones do. The magnitude of the correction from higher-order derivative term might not necessarily be a higher-order small quantity than the magnitude of the lower-order derivative terms. Therefore, the correction obtained by the previous authors is likely to contain significant errors. In this paper, by considering the higher-order derivative terms, we derive the parallel and perpendicular diffusion coefficients and obtain the correction formulas coming from all order derivative terms by using the improved perturbation method (He & Schlickeiser 2014) and the iteration operation. And for the weak adiabatic focusing limit we evaluate the correction to the parallel diffusion coefficient and compare it with the correction obtained in the previous papers.


Solar wind velocity distribution moments are described in Behar et al. (2017). The ion density nsw is the moment of order 0, and the ion bulk velocity usw (a vector) appears in the moment of order 1, the flux density

$n_{\mathrm{sw}} \ \underline{\mathbf{u}_{\mathrm{sw}}}$

n

sw

u

sw

_

. The bulk speed can be defined as the norm of the bulk velocity, that is,

$u_{\mathrm{sw}} = |\underline{\vec{u}_{\mathrm{sw}}}$

u

sw

=|

u

sw

_

|. However, this bulk speed is representative of single-particle speeds as long as the velocity distribution function is compact (e.g., a Maxwellian distribution). Complex velocity distribution functions were observed by RPC-ICA within the atmosphere of 67P. For instance, partial ring distributions were frequently observed for solar wind protons at intermediate heliocentric distances, when the spacecraft approached the SWIC (Behar et al. 2017). To illustrate the effect of such distorted distributions, a perfect ring (or shell) distribution centered on the origin of the plasma reference frame can be imagined, in which all particles have the same speed of 400 km s−1. The norm of the bulk velocity in this case would be 0 km s−1, whereas the mean speed of the particles is 400 km s−1, which is the relevant speed for SWCX processes. This mean speed, noted Usw, of the particles is calculated by first summing the differential number flux over all angles, and then taking the statistical average (Behar 2018). Over the entire mission, the deceleration of the solar wind using the mean speed of the particles is much more limited than the deceleration shown by the norm of the bulk velocity (Behar et al. 2017): there is more kinetic energy in the solar wind than the bulk velocity vector would let us think. This is the main difference with the paradigm used at previously studied (and more active) comets (Behar et al. 2018b). These complex, nonthermal velocity distribution functions also prevent us from reducing the second-order moment (the stress tensor) to a single scalar value, which, for a Maxwellian distribution, could be identified with a plasma temperature. In the context of 67P and for an important part of the cometary orbit around the Sun, the temperature of the solar wind proton has no formal definition.


The shock is then revived by adding an energy injection following the parameterized method of Fryer et al. (2018). In this model, roughly

 was deposited into the inner

 in the first

. Some of this energy is lost through neutrino emission and the total explosion energy at late times for this model is

. This explosion is then mapped into our three-dimensional calculations, using one million SPH particles. The mapping took place when the supernova shock had moved out of the iron core and propagated into the Si–S rich shell at

. We note that our 1D methods employed for modeling the collapse, core bounce, and initial explosion do not capture the full physics of the central engine (for a discussion, see Fryer et al. 2018), and this is a source of uncertainty in our yield calculations. The details of the engine change the shock trajectories, and neutrino chemistry can change Ye values (Saez et al. 2018; Fujimoto & Nagakura 2019). The nature of the shock affects mostly the yields after the shock falls below NSE (before it falls out of NSE, the yields are set by the equilibrium values, not the time-dependent evolution). Our model captures one instance of the range of asymmetric trajectories, and it should be noted that no model at this time is sufficiently accurate to dictate exactly the properties of the asymmetries (Janka et al. 2016). In addition, any model that does not include convection-driven asymmetries from the progenitor star cannot properly capture the asymmetries (Arnett et al. 2015). The 3D explosion model used here also displays stochastic asymmetries, implying that any manner of convective asymmetry could generate similar results. If this behavior is universal, it could have important implications. These points taken together indicate that nucleosynthetic patterns arising from convection-like behavior are robust, regardless of the driver. As discussed below, this increases the utility of NSE nucleosynthesis, particularly of

 and

, as diagnostics of the conditions in the progenitor star.


Gravitational-wave astronomy has recently become a reality with the first detection of gravitational waves (GW hereafter) by the Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo ground-based interferemeters. To date, eleven events have been reported by the LIGO and Virgo detectors (Abbott 2018), and this number will quickly increase to tens of events in the coming years. Some of these events may correspond to gravitationally lensed events with magnification factors ranging from a few tens to a few hundreds (Dai et al. 2017; Ng et al. 2018; Li et al. 2018a; Smith et al. 2018a,b; Broadhurst et al. 2019). Recent works have studied lensing effects in the existing LIGO/Virgo O1 and O2 events (Hannuksela et al. 2019; Broadhurst et al. 2019), while Smith et al. (2018c) searched for candidate galaxy cluster lenses for the GW170814 event. The most likely lenses for such events would be massive galaxies or galaxy clusters (Ng et al. 2018; Dai et al. 2017; Smith et al. 2018b; Broadhurst et al. 2019). On the other extreme of the lens mass regime, compact objects with masses of a few hundreds to a few tens M⊙ can also act as lenses (Lai et al. 2018). In this case, the geometric optics limit is not valid since the Schwarszchild radius of the lens is comparable to the wavelength of the wave. For these relatively low masses, the lensing effect has a modest impact on the average magnification, but it can introduce a frequency dependence on the magnification (see for instance, Jung & Shin 2019; Lai et al. 2018). An even smaller mass regime was considered in Christian et al. (2018) where the authors find that lenses with a mass as low as 30 M⊙ could be detected with current experiments. They also consider future, higher-sensitivity experiments and show how they can push the limit to even smaller masses of order 1 M⊙. These conclusions are, however, obtained assuming isolated microlenses and without accounting for the effect of the macromodel, or other nearby microlenses. In the small mass regime, microlenses such as neutron stars have been also considered as scattering sources of GWs, and it is found that a GW can be focussed at a focal point near the neutron star surface (Halder et al. 2019; Stratton & Dolan 2019).


Secondly, we focus on galaxies to discuss some remaining solutions. The miscentring (e.g. A1986, A1961) decreases the X-ray luminosity/SZ signal, as some flux moves outside of the aperture. Sehgal et al. (2013) demonstrated the effect of miscentring on decreasing SZ signal. They also proposed that the miscentring effect causes their lower measured SZ signal compared to Planck due to the finer resolution of ACT. However, as they point out, the miscentring distribution from their sample alone can only explain part of the discrepancy between optical and SZ, unless an unrealistic larger offset exists. Moreover, most miscentred clusters are merging or disturbed clusters with lower X-ray or SZ surface brightness, which makes them more difficult to be detected. The discrepancy of SZ signal is at a level of 10 per cent in our richness range (Biesiadzinski et al. 2012). The projection (e.g. A750, A1319) will increase the optical richness. As the cluster mass-richness relation is close to a linear relation, projection causes the projected clusters to simply slide up and down the mass-richness relation, without deviating from it (Simet et al. 2017). However, the LX−M or YSZ−M relation is a power-law relation with an index greater than one (∼1.6; Rozo et al. 2014a). For example, if we have two clusters with N200 = 80 ($M_{500|N=80}=5\times 10^{14} \, \mathrm{M}_{\odot}$, bolometric X-ray luminosity LX|N = 80 = 11 × 1044 erg s−1) projected together, they will be detected as a N = 160 cluster, the corresponding expected mass and X-ray luminosity are $M_{500|N=160}=10\times 10^{14} \, \mathrm{M}_{\odot}$ and LX|N = 160 = 43 × 1044 erg s−1, respectively. Though the mass is equal to the sum of two subclusters, the total X-ray luminosity is overestimated by a factor of ∼2 than the linear combination of 2LX|N = 80 = 22 × 1044 erg s−1. Thus, projection causes the expected X-ray luminosity or the SZ signal from the summed optical richness to be higher than the actual summed values. The projection fraction of samples extending to much lower richness is around 10 per cent (Simet et al. 2017), even higher for these richest maxBCG clusters (Fig. 2). The above two effects can act together, especially in super clusters and large-scale filaments (Fig. D1). The contamination of low-mass haloes, whose true halo mass is far below the value suggested by the optical richness, would also dilute and reduce the mean mass of the sample. We note that there is contamination of such low-mass systems based on Fig. A2. These low-mass haloes are mostly blended systems with boosted richness affected by nearby large-scale structure. Thus there is a mixture of halo masses at very high N200, the clean and the blended, and the PDF of M given N200 (or λ) will be asymmetric with a low-mass tail. A skew-normal or Hermite polynomial expansion (Shaw, Holder & Dudley 2010) are good alternatives to mixture modelling. Next, we roughly estimate the contamination fraction. There are four low LX systems beyond the 2σ line of LX−N relation from Rozo et al. (2014b) in Fig. A2 (and seven beyond the 1.5σ line towards lower LX versus 1 beyond the 1.5σ line towards higher LX). Taking these numbers at face value, the contamination is 10–15 per cent.


‘Blind’ searches through H i surveys performed by large aperture single-dish telescopes provide chances to uncover more H i absorption systems. Although such surveys usually utilize the non-tracking, drift scan observing strategy, with integration time for each individual source is limited, the collecting areas of the participating telescopes can still achieve considerable sensitivities. Allison, Sadler & Meekin (2014) identified four H i absorbers, including one previously unknown source, with the archival data of the H i Parkes All-Sky Survey (H i PASS; see Barnes et al. 2001), while Darling et al. (2011), Wu et al. (2015), as well as Song et al. (in preparation) have made attempts to perform ‘blind’ searches for absorption features using part of Arecibo Legacy Fast Arecibo L-Band Feed Array (ALFA) Survey (ALFALFA; see Giovanelli et al. 2005; Haynes et al. 2018) data, respectively, with 10 sources identified in total, including 3 samples remained undetected by other instruments so far, i.e., UGC 00613, CGCG 049-033, and PGC 070403, thus proving the feasibility of searching for new H i absorbers with massive blind sky surveys. Compared with radio interferometers, large single-dish telescopes such as Arecibo can provide better sensitivities and usually higher spectral resolution, which are all crucial to reveal the characteristics of extragalactic H i lines. And although the spatial resolution for such instruments are quite limited compared with interferometers, the chance of having two or more H i absorbing systems lying within the beamwidth with similar redshift is quite low, thus making confusions in source identification unlikely to happen. However, it should be noted that due to temporal variations in spectral baseline commonly seen during drift scans, follow-up observations are needed for reliable characterization of the newly identified absorbers, especially for the weak ones. Also, interferometric mappings are usually required to discern possible fine structures within each absorbing system.


Observation of amino acids and their most essential isomers and potential precursors in the interstellar medium (ISM) should be crucial for revealing the chemistry that may have led to life's origin (Ehrenfreund et al. 2001). In particular, the central question of whether glycine (CH2(NH2)C(O)OH) exists or not in the ISM is one of the most pursued targets in astrochemistry. Although several attempts to observe glycine have been reported (Hollis et al. 2003; Cunningham et al. 2007; Jones et al. 2007; Jiménez-Serra et al. 2016, 2020), its detection has never been confirmed (Snyder et al. 2005). Nevertheless, it has been found in the coma of comets 67P/Churyumov–Gerasimenko through in situ mass spectrometry (Altwegg et al. 2016). The presence of glycine in the volatile cometary material thus strongly suggests the existence of a process capable of generating amino acids in cold environments (Bizzocchi et al. 2020). Hence, as a prerequisite step for its astronomical identification, the rotational spectra of glycinamide (CH2 (NH2)C(O)NH2; Alonso et al. 2018; Kisiel et al. 2022) and aminoacetonitrile (CH2(NH2)CN; Kolesniková et al. 2017), which are relevant intermediates in the Strecker synthesis of glycine; hydantoin (CH2C(O)NHC(O)NH; Alonso et al. 2017) and hydantoic acid (C(O)OHCH2NHC(O)NH2; Kolesniková et al. 2019), potential glycine precursors through a different hydrolytic pathway (Ozeki et al. 2017), and the glycine isomer glycolamide (CH2(OH)C(O)NH2); Sanz-Novo et al. 2020) have been recently reported. In addition, Sanz-Novo et al. (2019) very recently carried out a computational study of the potential energy surfaces (PES) corresponding to the formation reactions of several protonated glycine isomers. Surprisingly, the only exothermic process with no net activation barrier led to protonated acetohydroxamic acid [CH3C(O)NH2OH]+. Its formation could therefore be feasible under interstellar conditions. Consequently, the corresponding neutral counterpart, CH3C(O)NHOH, might be a candidate molecule to be searched for in the ISM. Our previous simulations (Sanz-Novo et al. 2019) suggest that this glycine isomer should be searched for in the ISM, eventually, but there is no experimental rotational data available for this molecular system.


On the other hand, meteoroid rates on the Moon can be related to rates on Earth by taking into account the different gravitational focusing effect between both bodies. The gravitational focusing factor Φ is given by (6)\begin{equation} \Phi=1+\frac{V^{2}_{\rm esc}}{V^{2}}, \end{equation}Φ=1+Vesc2V2,where Vesc is the escape velocity of the central body and V the meteoroid velocity. The different gravitational focusing effect for the Moon and the Earth is given by the quotient γ between the gravitational focusing factors for both bodies. For sporadic meteoroids, with an average velocity of 20 km s-1 (Brown et al. 2002), this velocity-dependent focusing effect is higher for the Earth by a factor of 1.3 (Ortiz et al. 2006), and so γSPO = 0.77. According to this we have \begin{eqnarray} &&{\rm HR}^{\rm SPO}_{\rm Moon} =\gamma^{\rm SPO}{\rm HR}^{\rm SPO}_{\rm Earth}, \\[3mm] &&{\rm ZHR}^{\rm ST}_{\rm Moon} =\sigma\gamma^{\rm ST}{\rm ZHR}^{\rm ST}_{\rm Earth}. \end{eqnarray}HRMoonSPO=γSPOHREarthSPO,ZHRMoonST=σγSTZHREarthST.For the average hourly rate of sporadic events we have HR\hbox{$^{\rm SPO} _{\rm Earth} =10$}SPOEarth=10 meteors h-1 (Dubietis & Artl 2010). In Eq. (8) an additional factor σ is included to take into account that the distances from the Earth and the Moon to the meteoric filament will in general be different, and this would give rise to a different density of stream meteoroids for both bodies. If we assume a simple situation where this filament can be approximated as a tube where the meteoroid density decreases linearly from its central axis, the following definition can be adopted for σ, (9)\begin{equation} \sigma=\frac{d_{\rm Earth}}{d_{\rm Moon}}, \end{equation}σ=dEarthdMoon,where dEarth and dMoon are the distance from the center of the meteoric tube to the Earth and the Moon, respectively. On the other hand, the ZHR on Earth at solar longitude λ (which corresponds to the time of detection of the impact flash) can be related to the peak ZHR by means of (Jenniskens 1994) (10)\begin{equation} {\rm ZHR}^{\rm ST}_{\rm Earth}={\rm ZHR}^{\rm ST}_{\rm Earth}({\rm max})10^{-b|\lambda-\lambda_{\rm max}|}, \end{equation}ZHREarthST=ZHREarthST(max)10−b|λ−λmax|,where ZHR\hbox{$^{\rm ST} _{\rm Earth}$}STEarth(max) is the peak ZHR on Earth (corresponding to the date given by the solar longitude λmax). The values for the peak ZHR for different meteoroid streams and the corresponding solar longitudes for these maxima can be obtained, for instance, from (Jenniskens 2006). For streams with non-symmetrical ascending and descending activity profiles or with several maxima, Eq. (10) should be modified according to the expressions given in Jenniskens (1994). By putting all these pieces together in Eq. (2), we can write the following expression for the probability parameter: (11)\begin{equation} p^{\rm ST}=\frac{\gamma^{\rm ST}\cos(\phi)\sigma {\rm ZHR}^{\rm ST}_{\rm Earth}({\rm max})10^{-b|\lambda-\lambda_{\rm max}|}}{\gamma^{\rm SPO}{\rm HR}^{\rm SPO}_{\rm Earth}+\gamma^{\rm ST}\cos(\phi)\sigma {\rm ZHR}^{\rm ST}_{\rm Earth}({\rm max})10^{-b|\lambda-\lambda_{{\rm max}}|}}\cdot \end{equation}pST=γSTcos(φ)σZHREarthST(max)10−b|λ−λmax|γSPOHREarthSPO+γSTcos(φ)σZHREarthST(max)10−b|λ−λmax|·However, this formula does not take into account the fundamental fact that only those meteoroids capable of producing impact flashes detectable from Earth should be included in the computations. In fact, by employing only the hourly rates measured on Earth in Eq. (11), which measures the flux of meteor brighter than mag. +6.5, it is implicitly assumed that meteoroids producing meteor events on Earth can also produce detectable impact flashes on the Moon. However, this assumption is incorrect. Thus, for a given meteoroid stream (i.e., for a given meteoroid geocentric velocity), the mass mo of meteoroids giving rise to mag. +6.5 meteors on Earth can be obtained from Eqs. (1) and (2) in Hughes (1987). For instance, this mass yields 5.0 × 10-8 kg for Perseid meteoroids (Vg = 59 km s-1), 2.4 × 10-8 kg for Leonids (Vg = 70 km s-1), and 5.0 × 10-6 kg for sporadic meteoroids with an average velocity of 20 km s-1 (Brown et al. 2002). However, the masses corresponding to impact flashes recorded on the Moon are several orders of magnitudes larger than mo (see, e.g., Ortiz et al. 2006; Yanagisawa et al. 2006; Swift et al. 2011). This means that the minimum kinetic energy Emin to produce a detectable impact flash on the Moon is much higher than the kinetic energy of a portion of the meteoroids included in the computation of hourly rates on Earth. This means that the velocity and mass distribution of meteoroids must be somehow included in Eq. (11) to take into consideration for the computation of the probability parameter p only those meteoroids with a kinetic energy above the threshold kinetic energy given by Emin (the method for the computation of Emin will be explained below). According to Eq. (2) in Bellot Rubio et al. (2000a,b), this can be accomplished by including in Eqs. (2) and (11) the factor (12)\begin{equation} \nu=\left(\frac{m_{\rm o}V^{2}}{2}\right)^{s-1}E^{1-s}_{\rm min}, \end{equation}ν=moV22s−1Emin1−s,where V is the impact velocity, mo is the mass of a shower meteoroid producing on Earth a meteor of magnitude +6.5, and s is the mass index, which is related to the population index r (the ratio of the number of meteors with magnitude m + 1 or less to the number of meteors with magnitude m or less) by means of the relationship (13)\begin{equation} s=1+2.5\log(r). \end{equation}s=1+2.5log(r).According to the definition of ν, this parameter is different for each meteoroid stream (and for sporadic meteoroids, of course). By taking this into account Eq. (11) should be modified as follows: (14)\begin{equation} p^{\rm ST}=\frac{\nu^{\rm ST}\gamma^{\rm ST}\cos(\phi)\sigma {\rm ZHR}^{\rm ST}_{\rm Earth}({\rm max})10^{-b|\lambda-\lambda_{\rm max}|}}{{\nu^{\rm SPO}\gamma^{\rm SPO}{\rm HR}^{\rm SPO}_{\rm Earth}}{+\nu^{\rm ST}\gamma^{\rm ST}\cos(\phi)\sigma {\rm ZHR}^{\rm ST}_{\rm Earth}({\rm max})10^{-b|\lambda-\lambda_{\rm max}|}}}\cdot \end{equation}pST=νSTγSTcos(φ)σZHREarthST(max)10−b|λ−λmax|νSPOγSPOHREarthSPO+νSTγSTcos(φ)σZHREarthST(max)10−b|λ−λmax|·If by the time of detection of the impact flash n additional meteoroid streams with significant contributions to the impact rate (and with compatible impact geometry) must be considered, the denominator in Eq. (14) must be modified in the following way, (15)\begin{equation} p^{\rm ST}=\frac{\nu^{\rm ST}\gamma^{\rm ST}\cos(\phi)\sigma {\rm ZHR}^{\rm ST}_{\rm Earth}({\rm max})10^{-b|\lambda-\lambda_{\rm max}|}}{{\nu^{\rm SPO}\gamma^{\rm SPO}{\rm HR}^{\rm SPO}_{\rm Earth}}{+\nu^{\rm ST}\gamma^{\rm ST}\cos(\phi)\sigma {\rm ZHR}^{\rm ST}_{\rm Earth}({\rm max})10^{-b|\lambda-\lambda_{\rm max}|}+\kappa}} , \end{equation}pST=νSTγSTcos(φ)σZHREarthST(max)10−b|λ−λmax|νSPOγSPOHREarthSPO+νSTγSTcos(φ)σZHREarthST(max)10−b|λ−λmax|+κ,where (16)\begin{equation} \kappa=\sum_{i\,=\,1}^{n}\nu^{\rm ST}_i\gamma^{\rm ST}_i \cos(\phi_i)\sigma {\rm ZHR}^{\rm ST}_{i,{\rm Earth}}({\rm max})10^{-b_i|\lambda_i-\lambda_{i,{\rm max}}|} \end{equation}κ=∑i = 1nνiSTγiSTcos(φi)σZHRi,EarthST(max)10−bi|λi−λi,max|accounts for these n additional streams. The minimum kinetic energy Emin defined above corresponds to the minimum radiated energy Er_min on the Moon detectable from observations on Earth, which in turn is related to the maximum visual magnitude for detectable impacts (mmax). And these values depend on, among other factors, the experimental setup employed. The kinetic energy of the impactor and the radiated energy are linked by the luminous efficiency: (17)\begin{equation} E_{r\_{\rm min}}=\eta E_{\rm min}. \end{equation}Er_min=ηEmin.With our experimental setup, the maximum visual magnitude for detectable impact is mmax ~ 10. The radiated energy can be obtained by integrating the radiated power P defined by the equation (18)\begin{equation} P=1.36949\times 10^{-16}10^{(-m+21.1)/2.5}f \pi \Delta \lambda R^2, \end{equation}P=1.36949×10-1610(−m+21.1)/2.5fπΔλR2,where P is given in Joules, m is the magnitude of the flash, 1.36949 × 10-16 is the flux density in W m-2 μm-1 for a magnitude 21.1 source according to the values given in Bessel (1979), Δλ is the width of the filter passband (about 6000 Å for our devices), and R is the Earth-Moon distance at the instant of the meteoroid impact. The factor f is related to the degree of anisotropy of light emission. Thus, for those impacts where light is isotropically emitted from the surface of the Moon f = 2, while f = 4 if light is emitted from a very high altitude above the lunar surface. As expected, according to Eq. (18) the minimum radiated power for flash detectability (and hence the minimum radiated energy and the minimum meteoroid kinetic energy), which is obtained by using m = mmax, is higher when the distance between Earth and Moon is greater. So, the detectability limit is time-dependent.


Diffusive shock acceleration (DSA), a process entering the category of first-order Fermi acceleration, is the process by which astrophysical shocks accelerate charged particles to relativistic speeds. DSA requires the magnetic field near the shock front to reflect the particle, leading to repeated shock-crossings with the particle gaining energy at each crossing (e.g., Bell 1978; Blandford & Ostriker 1978; Drury 1983). DSA is a self-sustaining process because the presence of high-energy particles triggers instabilities in the magnetic field, which in turn allow the magnetic field to reflect the particles more efficiently (e.g., Bell 1978, 2004). DSA has been explored numerically using the particle-in-cell (PIC) method, as well as the PIC-hybrid method, whereby the ions are treated as particles and the electrons as a fluid. Simulations of this type seem to indicate that although this process is effective in the case of (quasi-)parallel shocks where the magnetic field is aligned with the direction of motion, it becomes ineffective once the angle between the magnetic field and the shock exceeds approximately 50° (Caprioli & Spitkovsky 2014a,2014b, 2014c).
4

4
Notice that most of the studies on DSA including the present one assume shocks are propagating into a homogeneous medium; effects of a nonmonotonous shock are discussed in Hanusch et al. (2019). Most simulations also assume that the pre-shock medium is fully ionized. Simulations for a partially ionized medium (Ohira 2013, 2016) show an increased injection rate, allowing for DSA even in oblique shocks. Also, studies by Kumar & Reville (2021) demonstrate that DSA can be triggered by the shock emitted waves at highly oblique shocks. However, different results were obtained by van Marle et al. (2018), using a combined PIC-MHD approach. This method, which treats the thermal gas as a fluid but nonthermal ions as individual particles, showed that, given a sufficient injection rate, even for magnetic obliquity up to 70°, shocks can accelerate particles through the DSA process. Several factors were believed to contribute to this discrepancy between PIC-MHD and PIC or PIC-hybrid methods:1.Time-period covered by the simulation. The DSA occurring in PIC-MHD simulations is only effective after more than 200 ion-gyrotimes (

ωci−1

) and it takes more than 500 ion-gyrotimes to fully develop whereas published hybrid simulations where limited to scales of the order of 200 ion-gyrotimes. Notice that at the time ∼200

ωci−1

 both PIC-hybrid and PIC-MHD simulations find similar results, namely that particles are accelerated by the shock-drift acceleration (SDA).2.Effective number of particles per cell. DSA requires an upstream current of CRs in order to develop. Because only a small fraction of the particles that cross the shock is reflected, a large particle population is required to produce sufficient nonthermal particles in the upstream medium.3.Simulation box size. van Marle et al. (2018) showed that the relevant upstream instabilities operate on long wavelengths, larger than the box size of hybrid simulations.


Galactic fountains or infall are the possible origins for the ECs in this sample. Both scenarios present possible explanations and restrictions. The accretion of low metallicity gas from the intergalactic medium may occur through filamentary structures with the gas cooling into clouds (Fernández et al. 2012). Subsequently HVCs may be destroyed or fragmented into smaller clouds by drag forces from the halo and phenomena such as Rayleigh-Taylor and Kelvin-Helmholtz instabilities. Star formation can be triggered by these interactions, within clouds that reach sufficient density (Figs. 9 and 10). However, there is evidence that star formation is possible only within dark-matter encapsulated HVCs such as the Smith Cloud (Smith 1963; Heitsch & Putman 2009; Nichols & Bland-Hawthorn 2009; Joung et al. 2012). Christodoulou et al. (1997) argue that without dark matter, HVCs are unable to reach the mass required to collapse. On the other hand, C 932, C 934, and C 939 are located right above the Local spiral arm (Fig. 11), which would be consistent with the chimney scenario. Schlafly et al. (2015) mapped various bubble-like structures vertically along the range 0.3 to 2.8 kpc, which form the Orion superbubble. The expansion of these substructures powered by massive stellar winds and supernovae triggers star formation in various shells and rings, inputting energy to the superbubble (Lee & Chen 2009). The star formation engine in the Galactic fountain may work in a similar way to the infall scenario, through the interaction of a cloud with the surrounding halo environment. However, high-latitude clusters in this study are located at distances from the disc larger than has been expected for a chimney-like event in recent studies (Melioli et al. 2009). Regardless of the scenario, a possible cloud-cloud interaction may be leading the clouds analysed in Fig. 9 to collapse and triggering not only star formation, but also cluster formation. However, the timescale for cloud-cloud collision in a cloud complex appears to be larger than 1 Gyr (Christodoulou et al. 1997). Therefore, additional studies are required to check the presence of dark-matter in HVCs, estimate the cloud-cloud interaction timescales, and provide more insight into the effect of the halo environment on the HVCs and chimney-like events. That is beyond the purpose of this study.


As Advanced LIGO and Virgo will upgrade while additional interferometers (KAGRA and LIGO-India) come online in the future, the detection horizon would be several hundred megaparsecs for BNS and BH–NS mergers with the localization accuracy reaching ∼10 deg2 for a network of these 2nd generation GW detectors (Abbott et al. 2018). In contrast, higher localization accuracy would be obtained by networking of 3rd generation GW detectors (Zhao & Wen 2018; Chan et al.2018; Hall & Evans 2019; Maggiore et al. 2020). In these regimes, present and future wide-field-of-view survey projects will be able to cover the sky localization given by GW detections in a few pointings and achieve deep detection depths with relatively short exposure integration times. The detection of GW170817/AT 2017gfo was made in an i-band filter and subsequently confirmed by larger telescopes (Coulter et al. 2017). Similar to this case, we assume that one can use only one filter to make follow-up searches after GW triggers. With quick response times of follow-up observations after GW events, we also assume that the survey telescopes would not miss the peaks of kilonovae in each band. Therefore, by assuming that all GW detectors in each era can operate normally (i.e., the most optimal situation for detector networks of different generations), the detection rates for target-of-opportunity observations for a given X-band limiting magnitude mX,limit can be expressed as
15

N

X

=

∫

0

z

max

ρ

m

X
,
limit

(
z
)

1
+
z

dV
(
z
)

dz

dz
,

where

z

max

 is the maximum detectable distance and

ρ

m

X
,
limit

(
z
)

 represents the cosmological event rate densities of the BH–NS mergers that can be triggered by GW detectors and be detected by telescopes in band X. Here, the astronomical magnitude system we adopted is the AB magnitude system, i.e.,

m

ν

=
−
2.5
log
(

F

ν

/

3631

Jy
)

.