Alternatively, if a magnetar is the central engine powering GRBs, we might expect to see periodic features in the emission. Known magnetars have clear periodic signals in their emission caused by their rotation periods (e.g. Mazets et al. 1979; Kouveliotou et al. 1998). The X-ray pulsations typically contribute to 30 per cent of the signal, with a range of 10–80 per cent (Israel et al. 1999; Kargaltsev et al. 2012; Kaspi & Beloborodov 2017). There is an energy dependence on the pulsed fraction of the signal, where low energies tend to have smaller pulsed fractions (Vogel et al. 2014). Detection of a periodic signal during the plateau phase in the X-ray light curve would provide excellent supporting evidence for the magnetar central engine model. There have been searches for a periodic signal in the prompt emission of GRBs with a number of instruments with no success, for example: Burst And Transient Source Experiment (BATSE) GRBs ( Deng & Schaefer 1997), INTErnational Gamma-Ray Astrophysics Laboratory (INTEGRAL) GRBs (Ryde et al. 2003), GRB 051103 (an extragalactic Soft Gamma-ray Repeater giant flare candidate detected by the Inter Planetary Network; Hurley et al. 2010) and Burst Alert Telescope (BAT) GRBs (Cenko et al. 2010; de Luca et al. 2010; Guidorzi et al. 2012). Dichiara et al. (2013) searched the prompt emission of a number of short GRBs for evidence of a precessing jet (predicted by Stone, Loeb & Berger 2013). However, these searches typically target the prompt emission and have not probed the regime where we might expect periodic signals from a magnetar central engine (i.e. during the plateau phase). Only two GRBs have been searched for periodic emission during the X-ray observations when the magnetar central engine may dominate the emission, GRB 060218 (Mirabal & Gotthelf 2010) and GRB 090709A (Mirabal & Gotthelf 2009; de Luca et al. 2010). The prompt emission of GRB 090709A possibly showed evidence of a periodic signal (Golenetskii et al. 2009; Gotz et al. 2009; Markwardt et al. 2009; Ohno et al. 2009), however this was ruled out with a more careful analysis of the prompt data from BAT, X-ray Telescope (XRT) and X-ray Multi-mirror Mission (XMM) observations of the X-ray afterglow (Cenko et al. 2010; de Luca et al. 2010). However, in the majority of these studies, the authors have targeted a constant spin period whereas a magnetar central engine is expected to have a rapidly decelerating spin period which would be very difficult to detect in standard searches for periodic signals. Dichiara et al. (2013) did conduct a deceleration search, however they were targeting signals in the prompt emission where we do not expect the signal from a spinning down magnetar.


As stated earlier, during review of this manuscript Croviser et al. announced in a CBET a tentative water production rate approximately five times larger than our reported value. While the brief nature of the CBET precludes a detailed comparison, we discuss some possible reasons for this discrepancy. At the high airmass of these observations and the small dimensions of the ARCES slit, differential refraction can result in wavelength-dependent slit loss, which can skew flux measurements. However, this is not expected for [O i] 6300 Å emission because this feature is close to the guiding wavelength (∼5500 Å). We confirmed that this is indeed negligible for [O i] 6300 Å emission based on observations of comet C/2012 S1 (ISON) that were performed at a similarly high airmass with ARCES, and found that the production rates derived from the ISON [O i] 6300 Å measurements were consistent with values determined using other methods (McKay et al. 2018). Therefore, we do not consider this or other airmass-dependent phenomena as the reason for the discrepancy. At certain geocentric velocities the cometary [O i] 6300 Å emission sits on top of a strong telluric absorption, and at high airmass inaccurate removal of this feature can result in a decrease in the measured flux and therefore production rate. This was observed for C/2012 S1 (ISON) (McKay et al. 2018). However, the geocentric velocity of 2I/Borisov during our observations was ∼−35 km s−1, while the effect on observed [O i] 6300 Å line fluxes in comet ISON was only observed at geocentric velocities of ∼−50 km s−1. Therefore, this is also not a likely candidate to explain the discrepancy. It is also possible that the activity is highly variable, and we observed Borisov at a minimum in activity, while the Nançay observations, which were coadded over three weeks of observations, provide a long-term average production rate. However, no such variability is observed for CN, with the CN production rate being fairly constant over a several week period (Kareta et al. 2019; Opitom et al. 2019).


In the framework of the hierarchical formation of structures, clusters of galaxies are continuously accreting galaxies. It has been suggested that in this process of falling, galaxies could undergo different physical processes that could affect the star formation even before they reach the cluster. Consequently, to fully understand what the cluster environment produces in galaxies, it is of key importance to have a throughout characterisation of the population of galaxies in the outskirts of clusters. Several observations have shown that properties of galaxies such as star formation, gas content, and colour are affected by the cluster environment at large clustercentric distances (e.g. Lewis et al. 2002; Solanes et al. 2002; Gómez et al. 2003; Braglia et al. 2009; Hansen et al. 2009; Park & Hwang 2009; von der Linden et al. 2010; Haines et al. 2015; Rhee et al. 2017). In particular, spiral galaxies with low star formation rates were found in the outskirts of clusters in early studies such as Couch et al. (1998) or Dressler et al. (1999). In recent years, a deficit of star-forming galaxies in the infalling region of clusters has been reported (e.g. Wetzel et al. 2013; Haines et al. 2015; Bianconi et al. 2018). This has been reproduced in simulations by Bahé et al. (2013). These results can be explained by the presence of environmental effects accelerating the consumption of the gas reservoir before galaxies enter in a cluster, a process known as pre-processing (e.g. Fujita 2004; Mihos 2004). An important fraction of the cluster galaxies has spent time in groups or filaments before they fall into the cluster (e.g. McGee et al. 2009; De Lucia et al. 2012; Wetzel et al. 2013; Hou, Parker & Harris 2014). The population of galaxies in the outskirts of clusters includes not only galaxies that have not yet entered the cluster but also backsplash galaxies, i.e. galaxies that have passed close to the centre of the cluster since their infall and are now beyond the virial radius (e.g. Mamon et al. 2004; Gill, Knebe & Gibson 2005; Mahajan, Mamon & Raychaudhury 2011). For an adequate characterisation of the properties of galaxies that are falling into clusters, it is important to take into account the contamination by backsplash galaxies, which, having orbited through the inner regions of a cluster, could have been affected by the physical processes present in that extreme environment. The backsplash scenario in the evolution of galaxies has also been explored in Rines & Diaferio (2005), Pimbblet et al. (2006), Aguerri & Sánchez-Janssen (2010), and Muriel & Coenda (2014).


From observations it is known that the interstellar gas has a complex structure with different phases – a hot volume-filling phase and a dense cold gas phase – both of which should be represented in galaxy formation simulations (see Naab & Ostriker 2017; Tumlinson et al. 2017). To model this, we treat the gas as a multiphase medium with many co-existing phases (see Marri & White 2003). We let two SPH particles i and j decouple into separate phases, if the following two conditions apply (Aumer et al. 2013):
(1)$$\begin{eqnarray*}
\max \left(\frac{A_i}{A_j}, \frac{A_j}{A_i} \right) \gt 50 , \quad -\mu _{ij} \lt c_{ij} .
\end{eqnarray*}$$Here, Ai,j are the entropic functions of the particles (Springel & Hernquist 2002), $\mu _{ij} := (\boldsymbol{v}_i - \boldsymbol{v}_j) \cdot \frac{\boldsymbol{r}_i - \boldsymbol{r}_j}{|\boldsymbol{r}_i - \boldsymbol{r}_j|}$ is the relative velocity of the particles along their vector of separation, and cij is the pair-averaged sound speed. Two SPH particles decouple if their entropy (actually their entropic functions2) are very different unless they approach faster than with the local sound speed. The velocity restriction (equation 1) is required to capture shocks properly (Marri & White 2003). This multiphase treatment results in a continuum of phases from cold to hot and the results are not very sensitive to the exact ratio in equation (1). This model is aimed at preventing overcooling, i.e. artificially short cooling times (see e.g. Naab & Ostriker 2017, for a review) and allows for the simultaneous representation of, and energy injection into, a hot and a cold phase on the resolution scale (see Scannapieco et al. 2006, for a detailed discussion). Such multiphase ISM structure naturally arises in much higher resolution simulations of the supernova-driven multiphase ISM (see e.g. Walch et al. 2015). For further details on the multiphase model, see Marri & White (2003) and Aumer et al. (2013, 2014).


Another notable accretion-regulated halo property is gas temperature, with the CGM of haloes nominally having both a hot and cold-phase. The hot coronal gas phase (at ≈Tvir) originates from the virial shock-heating of gas accreting high-mass haloes ($M_{\rm halo}\gtrsim 10^{12}\, \mathrm{M}_{\odot }$; e.g. Rees & Ostriker 1977). A cold-phase of the CGM at ≈104 K has also been observed, but its origins are less clear (e.g. Adelberger et al. (e.g. Adelberger et al. 2003; Stocke et al. 2006; Lehner & Howk 2011; Prochaska, Hennawi & Simcoe 2013; Werk et al. 2014; Zhu et al. 2014; Heckman et al. 2017; Zahedy et al. 2019). Several origins of this cool CGM phase have been proposed, namely pristine IGM accretion (e.g. simulation-based findings in van de Voort & Schaye 2012; Afruni, Fraternali & Pezzulli 2019, 2021), the condensation of hot halo gas (e.g. the empirical arguments of Voit 2018 and illustris-TNG findings in Nelson et al. 2020), feedback-driven outflows (e.g. Bouché et al. 2013; Borthakur et al. 2015; Anglés-Alcázar et al. 2017; Oppenheimer et al. 2018; Hafen et al. 2019), and the stripping of satellite galaxies in larger systems (e.g. Hafen et al. 2019 using the fire-2 simulations). Afruni et al. (2019, 2021), using semi-analytic models and results from the COS-Halos and COS-GASS surveys, argue that star-formation-driven outflows cannot account for the amount of cool gas in the CGM of observed haloes, pointing towards IGM accretion as the origin of this gas. Additionally, the radial variation of CGM properties was explored in Fielding et al. (2020) using a number of hydrodynamical simulations (as part of the smaug project). They find that the properties of the outer-CGM (at ≳0.5R200,crit) are shaped by larger scale processes, such as cosmological accretion, rather than galactic feedback that dominates the inner regions, ≲0.5R200,crit. In any case, the wide range of observed metallicities and temperatures observed implies that the CGM is a diverse, multi-phase gas reservoir, making it an ideal laboratory to study the influence of cosmological inflows.


Located in the star-forming region ρ-Ophiuchi, inside the dark cloud L1689N and at a distance of 141 pc (Dzib et al. 2018), IRAS16293−2422 is a well-studied Young Stellar Object (YSO) classified as a Class 0 source with less than 104 yr (Andre, Ward-Thompson & Barsony 1993), and represents one of the very early stages of low-mass star formation. It was the first source identified as a hot corino (Blake et al. 1994; van Dishoeck et al. 1995) based on the detection of Complex Organic Molecules (COMs) in the source, which was later supported by follow-up studies (Ceccarelli et al. 1998, 2000; Schöier et al. 2002; Crimier et al. 2010; Jørgensen et al. 2011, 2016; Pineda et al. 2012; Oya et al. 2016; Jacobsen et al. 2018; van der Wiel et al. 2019). Higher resolution observations revealed that IRAS16293−2422 is in fact a triple system, composed of sources A1 and A2, separated by 54 au from each other (Maureira et al. 2020) and source B, 738 au (5 arcse; Wootten 1989) away from source A. Due to this larger separation, tidal truncation between the three protostars is discarded and therefore source B is considered to have evolved as an isolated source (Rodríguez et al. 2005). It was initially proposed to be either an evolved T Tauri star (Stark et al. 2004; Takakuwa et al. 2007) or a very young object (Chandler et al. 2005), however, Chandler et al. (2005) suggested that source B has large-scale infalls based on SO line emission. Pineda et al. (2012) confirmed the infall of an inner envelope, with mass accretion rates of 4.5 × 10−5 M⊙yr−1, based on ALMA detections of inverse P-Cygni profiles in CH3OCHO-E, CH3OCHO-E-A and H2CCO, ruling out the possibility of it being a T Tauri star. The interpretations of infall from these profiles was also suggested by Jørgensen et al. (2012) and Zapata et al. (2013). Unlike the A1 and A2 protostars, source B has not shown clear signs of outflow launching, explained by the lack of free–free emission at low frequencies (Chandler et al. 2005; Rodríguez et al. 2005; Loinard et al. 2007; Rao et al. 2009; Liu et al. 2018; Hernández-Gómez et al. 2019b) and also based on molecular lines (Loinard et al. 2002; van der Wiel et al. 2019).


Idealized simulations have the advantage of carefully controlled conditions but the disadvantages that the turbulence is driven in an artificially prescribed manner to maintain a fixed overall turbulent amplitude and the processes leading to cloud formation and destruction are not followed. In reality, GMCs form due to a combination of large-scale ISM flows (including turbulence, shear, and epicyclic motion) and gravity (both stellar gravity and self-gravity) that lead to collection of material from a large volume, as mediated by thermal and magnetic pressure, and a change from the atomic to the molecular phase as the gas cools (e.g., McKee & Ostriker 2007; Dobbs et al. 2014; Chevance et al. 2020). Turbulence on scales less than the scale height of the warm–cold ISM likely originates primarily due to the feedback from young stars (Elmegreen & Scalo 2004; Mac Low & Klessen 2004; McKee & Ostriker 2007),3

3
Gravitational instabilities in the combined gas–stellar system (e.g., Jog & Solomon 1984; Romeo 1992; Rafikov 2001; Kim & Ostriker 2007) can drive horizontal motions at very large scales, as seen in numerical simulations (e.g., Kim & Ostriker 2007; Shetty & Ostriker 2008; Agertz et al. 2009; Dobbs et al. 2011; Hopkins et al. 2012; Agertz & Kravtsov 2015, and citations within), but these motions generally do not reach supersonic amplitudes unless they are associated with gravitational collapse. In addition, turbulence at scales less than the disk scale height can be driven by spiral shocks and the magnetorotational instability, but numerical simulations show that the corresponding amplitudes are relatively modest in cold gas (e.g., Wada & Koda 2004; Piontek & Ostriker 2005, 2007; Kim et al. 2006, 2010; Dobbs & Bonnell 2007; Bonnell et al. 2013, and citations within).
 whether inherited from a GMC’s formation stage or produced internally. Considering that GMCs live for at most a few turbulent crossing or freefall times (Kawamura et al. 2009; Kruijssen et al. 2019), it is not clear that internal GMC conditions can control star formation in a way that is entirely divorced from their formation and destruction processes.


In this paper, we explore the conditions required for hyper-Eddington accretion on to a BH when both radiative and mechanical feedback operate simultaneously, performing two-dimensional (2D) hydrodynamical simulations with multifrequency radiation transfer. We conduct a comprehensive survey on the parameter dependence of outflow models, varying the outflow opening angle, mass loading degree into outflows, velocity of outflows, and density of gas surrounding the BH. To model mechanical feedback, we adopt a phenomenological model proposed by Ostriker et al. (2010), while radiative feedback is treated by adopting the standard and slim disc model (Shakura & Sunyaev 1973; Abramowicz et al. 1988; Watarai 2006) as in Takeo et al. (2019). We find that the flow structure consists of two distinct parts in the early sub-Eddington phase; the bipolar outflowing region heated up to T ∼ 106−7 K due to strong shock and the equatorial inflowing region where ionized gas is mildly heated to T ∼ 105 K due to photoionization. When the ambient gas density exceeds a critical threshold, as in the cases where only radiative feedback is included (Inayoshi et al. 2016; Takeo et al. 2018), the mass accretion rate on to the nuclear region rises to a hyper-Eddington value. Since mechanical power of outflows driven by the rapidly accreting BH is sufficiently strong, bipolar outflows completely evacuate the surrounding gas in the polar region and reduce the mass inflow (BH accretion) rate by a factor of ≈3–13 (≈6–26, respectively) from the case without mechanical feedback. Furthermore, we find that the critical gas density required for hyper-Eddington accretion is reduced by a factor of ∼3 and the transition occurs in a shorter dynamical time-scale when mechanical feedback is modelled in the simulations. In fact, the effects that alleviate the transition to rapid accretion tend to be more prominent as the outflow is stronger, i.e. a wider opening angle, higher mass loading factor, and higher outflow velocity. This is because suppression of BH accretion owing to outflows reduces the radiative output from the nuclear BH, leading to hyper-Eddington accretion.


The many unexpected surprises of comet 67P/Churyumov-Gerasimenko (hereafter 67P) revealed by the historic Rosetta mission highlight the importance of observing the evolution of comets throughout their orbits. One of the surprises was the drastic heterogeneity in both the major and minor volatile species in the coma that was observed early on in the mission (Hässig et al. 2015; Luspay-Kuti et al. 2015, hereafter ALK15). When Rosetta first arrived at comet 67P in August 2014, the Rosetta Orbiter Mass Spectrometer for Ion and Neutral Analysis/Double Focusing Mass Spectrometer (ROSINA/DFMS; Balsiger et al. 2007) detected large diurnal variations in the intensity profiles of various species in the coma from distances to the comet as far as 250 km. At this time, 67P was still at a distance of about 3 AU and inbound from the Sun. The intensity variations in the major and minor volatile species were found to be periodic, and were dependent on both the observing sub-spacecraft latitude and longitude (Hässig et al. 2015; Luspay-Kuti et al. (2015)). As reported in Hässig et al. (2015), the intensity of H2O in the coma dominated the overall signal, with maxima in the H2O signal every ~6 h, about twice during a rotation. Interestingly, however, CO2 and CO displayed a separate additional maximum when the H2O signal was near its minimum. This independent maximum in CO2 and CO only occurred at negative observing latitudes that are associated with a particular “view” of Rosetta at 67P, with the larger lobe blocking out the neck and head. At this time, 67P had not yet reached its first equinox (10 May 2015), and the poorly illuminated southern hemisphere was experiencing winter. In addition, the largest H2O activity was localized at the well-illuminated neck region, as also seen by the Microwave Instrument on the Rostta Orbiter (MIRO; Gulkis et al. 2015; Biver et al. 2015; Lee et al. 2015) and by the Visible InfraRed Thermal Imaging Spectrometer (VIRTIS; Bockelée-Morvan et al. 2015; Migliorini et al. 2016). VIRTIS also measured weak H2O production in regions with low solar illumination, while CO2 was outgassing from both illuminated and non-illuminated regions pre-inbound equinox (Bockelée-Morvan et al. 2015; Migliorini et al. 2016; Fink et al. 2016). The observed outgassing pattern of the major cometary species suggested that CO and CO2 may be sublimating from a depth below the diurnal skin depth.


X-ray reverberation in black hole X-ray binaries was first robustly detected in GX 339–4 by Uttley et al. (2011) when the source was in its hard state. Previous studies of GX 339–4 pointed to the approximate central mass being ≥6 M⊙ (e.g. Hynes et al. 2003) and a small disc inclination angle (De Marco et al. 2015). Miller et al. (2008) fitted the Suzaku spectra and found that the central black hole has a very high spin, a ∼ 0.998. The X-ray spectroscopic analysis of the hard state spectra from the RXTE archive carried out by García et al. (2015) suggested the black hole spin to be a ∼ 0.95. Spectral fitting of GX 339–4 during its very high flux state using NuSTAR and Swift also suggested a high spin of a ∼ 0.95 (Parker et al. 2016). According to the time-lag analysis, Uttley et al. (2011) found that the disc thermal emission (∼0.3–0.7 keV, soft band) leads the power-law variations (∼0.7–1.5 keV, hard band) on long timescales (> 1s). Mahmoud et al. (2019) assumed that the soft component that leads the power-law emission is a soft Comptontized component. Rapisarda et al. (2016) and Rapisarda et al. (2017) instead modelled it as a variable inner region of the thin disc. However, the disc black-body variations lag behind the power-law variations by a few milliseconds on short timescales ( 1s). This switch from low-frequency hard to high-frequency soft lags is thought to be produced by two distinct mechanisms. While the hard lags are likely due to inward propagating fluctuations (e.g. Kotov et al. 2001; Arévalo & Uttley 2006), the soft lags can be explained by thermal reverberation associated with the longer light-travel time the hard photons take from the central power-law X-ray source to the disc where they are reprocessed into relatively soft black-body emission. The thermal reverberation lags then provide clues to the geometry of the X-ray source and the inner accretion flow close to the event horizon of the central black hole.


Our parameter range reaches into the “propeller” regime, where the azimuthal velocity of the star’s outer magnetosphere exceeds the Keplerian velocity at disk truncation (Romanova et al. 2005), i.e., where the disk is truncated near and outside of the corotation radius. Observations of the propeller regime have been discussed in relation to various astrophysical systems, such as rapidly rotating neutron stars, white dwarfs in cataclysmic variables, and CTTS (see, e.g., Stella et al. 1986; Treves et al. 1993; Cui 1997; Alpar 2001; Ekşı & Alpar 2003; Mori & Ruderman 2003). The propeller regime has been investigated both analytically (Davies et al. 1979; Li & Wickramasinghe 1997; Lovelace et al. 1999; Ikhsanov 2002; Rappaport et al. 2004; Ekşi et al. 2005), and via MHD simulations (Wang & Robertson 1985; Romanova et al. 2003, 2004, 2005, 2009; Ustyugova et al. 2006). It has been shown that, for a rapidly rotating star with a strong magnetic field, a significant proportion of accreting material is in fact centrifugally expelled as it reaches the inner region of the disk and is redirected as a propeller-driven outflow, allowing the star to rapidly spin down (Davidson & Ostriker 1973; Illarionov & Sunyaev 1975; Lipunov 1992). For example, MHD simulations performed by Romanova et al. (2005) and Zanni & Ferreira (2013) demonstrate the following quasi-periodic behavior: (1) disk material accumulates at the inner region of the disk, which moves the truncation radius closer to the star; (2) some material can then accrete onto the star, reducing the mass of material at the disk inner edge; (3) remaining inner-disk material gains angular momentum and is ejected at the centrifugal barrier, which moves the truncation radius further away from the star, for the cycle to repeat. In this regime, accretion becomes intermittent, or can even be inhibited completely, and the net effect acts to remove angular momentum from the star. Therefore, it is possible that the propeller mechanism is responsible for the slow rotation rates observed in CTTS.


We use the N-body simulation package—MERCURY (Chambers 1999)—to numerically investigate the effects of photo-evaporation on the dynamical evolution of planet–satellite systems. We choose the Bulirsch–Stoer integration algorithm, which can handle close encounter accurately. It is important in the simulations, as we will see below, that many close encounters among moons and the planet are expected to happen. Collisions among moons, the planet, and the central star are also considered in simulations and treated simply as inelastic collisions without fragmentations. Each simulation consists of a central star, a planet, and some moons orbiting around the planet. The photo-evaporation is simply modeled as a slow (adiabatic) and isotropic mass-loss process of the planet. In reality, the photo-evaporation is a very slow process on a timescale of the order of 107–108 year (Owen & Wu 2013). However, it is impractical and unnecessary to perform a simulation on such a long timescale. Instead, we model the mass-loss process on a timescale of τevap, and each simulation typically lasts for several τevap. As long as the adiabatic requirement is met, i.e., the mass-loss timescale is much longer than the dynamical timescale of the system (τevap ≫ Pp, where Pp is the orbital period of the planet), one could study the dynamical effects of the mass-loss process equivalently. As we discussed in Section 3.3, the results converge if τevap > 102–103 Pp, indicating the adiabatic condition is met. Therefore, in all other simulations, we set τevap = 104 Pp. Other parameters are set to represent the typical values of Kepler planets. In particular, we consider a planet–satellite system orbiting a star of solar mass (M⋆ = M⊙) in a circular orbit (ep = 0.0) with semimajor axis of ap = 0.1 au. The orbit has a period of ∼10 days (typical value of Kepler planets), and it is sufficiently close to the central star to be subject to significant photo-evaporation effect (Owen & Wu 2013), which removes massive hydrogen envelopes of the planet. The planet has an initial mass of Mpi and a final mass of Mpf after photo-evaporation. In this paper, we adopt Mpi = 20 M⊕ and Mpf = 10 M⊕ nominally (close to the standard model adopted in Owen & Wu 2013). The mean density of the planet is set to the same as that of Neptune (1.66 g cm−3). The effect of changing the planetary density is discussed in Section 3.3. We performed a number of sets of simulations by considering different planet–satellite configurations. Similar to the definition in MERCURY, hereafter, we define “small moons” as test particles (TPs) whose mutual gravity and corresponding effects on the planet and the star are ignored, while “big moons” are gravitationally important enough that their gravitational effects are fully considered. Table 1 lists the initial setups and parameters of various simulations, whose results are presented in the following subsections.


Characterizing and understanding the distribution and transport of chemical elements inside galaxies is a critical aspect of galaxy evolution. Successive generations of star formation enrich the interstellar medium (ISM) with metals. Therefore, the spatial distribution of chemical abundances in galaxies is a powerful tracer of the history of gas flows, star formation, accretion, and mergers throughout their assembly (e.g. Edmunds & Greenhow 1995; Kewley et al. 2010; Torrey et al. 2012; Finlator 2017; Ma et al. 2017; Bresolin 2019; Hemler et al. 2020). Over the last few decades, our understanding of chemical inhomogeneities in galaxies has advanced dramatically, largely due to the advent of integral field unit (IFU) spectroscopy (see Maiolino & Mannucci 2019 for a review). Negative radial metallicity gradients have been widely observed in the low-redshift galaxy population (e.g. Searle 1971; Vila-Costas & Edmunds 1992; Berg et al. 2013, 2020; Ho et al. 2015; Belfiore et al. 2017; Poetrodjojo et al. 2018) with other studies additionally observing azimuthal variations from these radial metallicity trends (Li, Bresolin & Kennicutt 2013; Vogt et al. 2017; Ho et al. 2018, 2019; Kreckel et al. 2020). Observational limitations mean that metallicities are more challenging to measure at high redshift. In the absence of gravitational lensing, spatial resolution is reduced. Furthermore, fainter targets mean that metallicities are typically derived from fewer emission lines, limiting our ability to control for possible redshift evolution in the ISM conditions of galaxies when constructing an abundance scale (see Appendix A for a more comprehensive discussion). Existing determinations of radial gradients in high-redshift galaxies are generally limited to modest samples of lensed galaxies, or samples of the largest disc galaxies, and show substantial amounts of scatter from steep negative gradients to positive gradients (Yuan et al. 2011; Swinbank et al. 2012; Jones et al. 2013; Leethochawalit et al. 2016; Wuyts et al. 2016; Carton et al. 2018; Wang et al. 2019a,b; Curti et al. 2020b; Gillman et al. 2021). Extending observations to smaller, fainter galaxies remains a challenge.


The basic idea, summarized in Dekel et al. (2009), is that during VDI, the high surface density of gas and ‘cold’ young stars, Σ, drives the Toomre Q parameter below unity, Q ∼ σΩ/(πGΣ) ≲ 1, where σ is the 1D velocity dispersion and Ω is the angular frequency, a proxy to the epicyclic frequency κ, which is related to the potential well (Toomre 1964). It has been established that under such conditions, the disc will fragment and produce large star-forming clumps. This has been shown using idealized simulations of isolated galaxies (Noguchi 1999; Gammie 2001; Immeli et al. 2004a,b; Bournaud, Elmegreen & Elmegreen 2007; Elmegreen, Bournaud & Elmegreen 2008; Bournaud & Elmegreen 2009; Hopkins et al. 2012b), as well as cosmological simulations (Agertz, Teyssier & Moore 2009; Ceverino et al. 2010; Ceverino et al. 2012; Genel et al. 2012; Mandelker et al. 2014; Oklopcic et al. 2016). The ratio of clump mass to the mass of the cold disc scales as Mc/Md ∝ δ2, where δ = Md/Mtot is the ratio of the cold disc mass to the total mass within the disc radius, which includes the bulge and dark matter halo (e.g. Dekel et al. 2009). This leads to much larger clumps at z ∼ 2 than the low-redshift giant molecular clouds (GMCs). Gravitational interactions in the perturbed disc drive turbulence causing the disc to self-regulate in a marginally stable state with Q ≲ 1 (Dekel et al. 2009; Ceverino et al. 2010; Krumholz & Burkert 2010; Cacciato, Dekel & Genel 2012; Forbes, Krumholz & Burkert 2012; Forbes et al. 2014) that can last for more than a Gyr so long as the accretion is not interrupted. Some recent works have called into question the validity of linear Toomre analysis in the context of these highly non-linear galaxies (Behrendt, Burkert & Schartmann 2015; Tamburello et al. 2015; Inoue et al. 2016) and others have suggested alternate fragmentation mechanisms related to turbulence (e.g. Hopkins 2013). However, since clump formation is largely determined by the balance between self-gravity, turbulent pressure and the centrifugal force, the largest clumps are always roughly at the Toomre scale. Larger clumps would be disrupted due to the shear and/or tidal forces within the disc, or would not collapse in the first place due to the centrifugal force. Therefore, regardless of the full validity of linear Toomre analysis, it is plausible that the Toomre Q parameter can serve as a crude criterion for instability, possibly with a critical value that is larger than unity.


Since it is infeasible to observe the evolution of individual galaxies over time, theoretical approaches focusing on understanding the formation of ETGs have made use of numerical simulations to trace the evolution of individual galaxies. Through zoom-in and cosmological simulations, a consensus has emerged between these simulations that the formation of ETGs proceeds through two phases, where galaxies first go through dissipative gas-rich wet mergers followed by in situ star formation bursts at redshifts above z ≈ 2, and then evolve towards low redshift through non-dissipative gas-poor dry mergers (Naab et al. 2007; Guo & White 2008; Hopkins et al. 2009; Nipoti et al. 2009b; Nipoti, Treu & Bolton 2009a; Oser et al. 2010; Johansson, Naab & Ostriker 2012; Moster, Naab & White 2013; Remus et al. 2013; Furlong et al. 2015; Wellons et al. 2015, 2016; Rodriguez-Gomez et al. 2016). However, regarding the redshift evolution of ETGs’ total power-law density slopes, no consensus has been reached neither among different cosmological hydrodynamic simulations nor between simulations and observations, despite the many advances in cosmological simulations (Vogelsberger et al. 2019a). While the Magneticum pathfinder simulation (Remus et al. 2017) and the Illustris simulations (Xu et al. 2017) produce shallower total density profile with time, the Horizon-AGN simulations (Peirani et al. 2019) produce steeper total density profile with time, in better agreement with the redshift evolution trend found in observations. However, the latter simulation has smaller slope values compared to the former two, which are closer to the observed slope values due to different implementation of feedback models, etc. Apart from cosmological simulations, dedicated zoom-in simulations (Johansson, Naab & Burkert 2009; Johansson et al. 2012; Remus et al. 2013) have revealed that dry mergers that dominate the passive evolution of ETGs below z ≈ 2 could make the total density profile shallower than isothermal (Hilz et al. 2012; Hilz, Naab & Ostriker 2013; Remus et al. 2017). The inclusion of wet mergers is also crucial for reconciling the simulated redshift evolution trend of the slope with strong-lensing observations (Sonnenfeld, Nipoti & Treu 2014).


In order to investigate the signal-to-noise ratio (SNR), ρ of NS–WD binaries for LISA-type space GW detectors, we calculate the averaged square SNR $\overline{\rho ^{2}}$ over the sky location, inclination, and polarization as
(30)$$\begin{eqnarray*}
\overline{\rho ^{2}} = \int _{f_{1}}^{f_{2}}\frac{4\cdot \frac{4}{5}fA^{2}(f)}{(P_{\rm n}(f)/R(f))} \rm d (\ln \it f),
\end{eqnarray*}$$(Moore, Cole & Berry 2015; Robson, Cornish & Liu 2019), where f1 and f2 are the lower and upper limits of the integral, respectively. The factor 4 in the numerator of the integrand comes from the addition of strain noise in the detector arms and the two-way noise in each arm (Larson, Hiscock & Hellings 2000). We calculate the GW amplitudes A(f) of NS–WD binaries using the phenomenological (PhenomA) waveform model in the Fourier domain (Ajith et al. 2007; Robson et al. 2019). A(f) is expressed as
(31)$$\begin{eqnarray*}
A(f) = \sqrt{\frac{5}{24}}\frac{G^{5/6}\mathcal {M}^{5/6}}{\pi ^{2/3}c^{3/2}R_{\rm b}}f^{-7/6}\, {\rm Hz}^{-1},\,\,\,\it f\lt f_{\rm m},
\end{eqnarray*}$$
 (32)$$\begin{eqnarray*}
f_{\rm m} = \frac{0.2974\zeta ^{2}+0.04481\zeta +0.09556}{\pi (GM/c^{3})}\, {\rm Hz},
\end{eqnarray*}$$
 (33)$$\begin{eqnarray*}
\zeta = m_{1}m_{2}/M^{2},
\end{eqnarray*}$$where $\mathcal {M} \equiv m_1^{3/5} m_2^{3/5}/(m_1+m_2)^{1/5}$, and fm is the GW frequency at the point of merging. If f > fm, the index of the power-law relation between A(f) and f changes (Ajith et al. 2007) and is beyond the scope of this study. The power spectral density of total detector noise $P_{\rm n}=\frac{1}{L^{2}}\left[P_{\rm o}+2(1+\cos ^{2}(f/f_{\ast }))\frac{P_{\rm a}}{(2\pi f)^{4}}\right]$, where f* = c/(2πL), L = 2.5 × 109 m is the armlength of the detector, $P_{\rm o}=2.25\times 10^{-22} \,\rm m^{2}\left(1+(\frac{2\,mHz}{\it f})^{4}\right) \,\, \rm Hz^{-1}$ is the single-link optical metrology noise, and $P_{\rm a}=9.0\times 10^{-30} \,\rm (m\,s^{-2})^{2}\left(1+(\frac{0.4\,mHz}{\it f})^{2}\right)\left(1+(\frac{\it f}{8\,\rm mHz})^{4}\right) \,\,Hz^{-1}$ is the single test mass acceleration noise (LISA Science Study Team 2018; Robson et al. 2019). R(f) is the transfer function numerically calculated from Larson et al. (2000). The effective noise power spectral density can be defined as Sn(f) = Pn(f)/R(f). For Taiji and Tianqin, we use the sensitivity curve data in Ruan et al. (2020) and Wang et al. (2019), respectively.


In this model, the pulsar associated with the PWN loses its rotational energy via a pulsar wind composed of magnetic and high-energy particles to power the high-energy physical process inside the nebula (Atoyan & Aharonian 1996; Fang & Zhang 2010). The relativistic wind of particles driven by the pulsar is blown into the ambient medium and generates a termination shock wave, which accelerates the electrons to relativistic energy. These relativistic electrons interact with the magnetic field and low-energy background photons (the synchrotron, thermal, FIR, and microwave background radiation), and generate the multiband nonthermal photons with energies ranging from radio to high-energy gamma-ray bands (Zhang et al. 2008; Fang & Zhang 2010; Lu et al. 2017). According to the review of the leptonic model (see, e.g., Zhang et al. 2008; Venter & de Jager 2007; Torres et al. 2013), the electrons injected into PWNe are accelerated by the pulsar magnetosphere and the termination shock. Therefore, the relativistic particles injected into the PWNe are also assumed as two different power-law components from the pulsar magnetosphere and shock acceleration, respectively. The injected spectrum of relativistic electrons inside PWNe is described as
1

Q(Ee,t)=Q0(t)Ee/Ecut−α1ifEeEcutQ0(t)Ee/Ecut−α2ifEe≥Ecut,

where the Q
0 can be determined by the ∫Q(E

e
, t)E

e

dE

e
 =η
L(t); η is the conversion efficiency from spin-down power into electron luminosity. The maximum energy of the electrons was express as

Emax(t)≈ε0L(t)L0

, and L
0 is initial spin-down power. The electron energy distribution was given by
2

dN(Ee,Tage)dt=∫0TageQ(Ee,t)exp−Tage−tτeffdt,

where the

τeff−1=τesc(t)−1+τsyn(t)−1

, τ

esc
(t) is the escape timescale, and τ
syn(t) is the lifetime of the relativistic electron of the synchrotron emission loss. The details of temporal evolution about the electron in the PWNe are discussed by the Zhang et al. (2008; also see the version of Fang & Zhang 2010; Lu et al. 2017).


Douchin & Haensel (2001; DH) formulated a unified EoS for NS on the basis of the SLy4 Skyrme nuclear effective force (Chabanat et al. 1998), where some parameters of the Skyrme interaction were adjusted to reproduce the Wiringa et al. calculation of neutron matter (Wiringa et al. 1988) above saturation density. Hence, the DH EoS contains certain microscopic input. In the DH model the inner crust was treated in the CLDM approach. More recently, unified EoSs for NS have been derived by the Brussels-Montreal group (Chamel et al. 2011; Pearson et al. 2012; Fantina et al. 2013; Potekhin et al. 2013). They are based on the BSk family of Skyrme nuclear effective forces (Goriely et al. 2010). Each force is fitted to the known masses of nuclei and adjusted among other constraints to reproduce a different microscopic EoS of neutron matter with different stiffness at high density. The inner crust is treated in the extended Thomas-Fermi approach with trial nucleon density profiles including perturbatively shell corrections for protons via the Strutinsky integral method. Analytical fits of these neutron-star EoSs have been constructed in order to facilitate their inclusion in astrophysical simulations (Potekhin et al. 2013). Quantal Hartree calculations for the NS crust have been systematically performed by (Shen et al. 2011b,a). This approach uses a virial expansion at low density and a RMF effective interaction at intermediate and high densities, and the EoS of the whole NS has been tabulated for different RMF parameter sets. Also recently, a complete EoS for supernova matter has been developed within the statistical model (Hempel & Schaffner-Bielich 2010). We shall adopt here the EoS of the BSk21 model (Chamel et al. 2011; Pearson et al. 2012; Fantina et al. 2013; Potekhin et al. 2013; Goriely et al. 2010) as a representative example of contemporary EoS for the complete NS structure, and a comparison with the other EoSs of the BSk family (Chamel et al. 2011; Pearson et al. 2012; Fantina et al. 2013; Potekhin et al. 2013) and the RMF family (Shen et al. 2011b,a) shall be left for future study.


Most of these observations are consistent with the general understanding that, for increasing distance from the Sun, the turbulent power-law spectrum expands toward larger scales (Bavassano et al. 1982; Bruno & Carbone 2013; Chen et al. 2020). However, spectral properties may be misleading, as it is not possible to unequivocally ascribe the Kolmogorov-like power-law scaling to the presence of a turbulent cascade. For example, it is universally observed that turbulence is associated with intermittency (Kolmogorov 1962), as is routinely observed in solar wind measurements (Sorriso-Valvo et al. 1999; Bruno & Carbone 2013). A standard way for characterizing the intermittency of a field ϕ (ϕ being, for example, a velocity or magnetic field component) is by means of the scale-dependent increments Δϕ = ϕ(t + Δt) − ϕ(t), which account for the presence of gradients on a timescale Δt (Anselmet et al. 1984). Intermittency is related to the scale-dependent shape of the probability distribution function of the increments Δϕ (Castaing et al. 1990). This, additionally, implies the existence of nonvanishing odd moments. In particular, a scaling law can be derived for the third-order moment directly from the dynamical MHD equations, as the conservation law of the appropriate inviscid invariants (de Karman & Howarth 1938; Danaila et al. 2001). Such a relation, known in the MHD description as the Politano–Pouquet (PP) law (Politano & Pouquet 1998; Carbone et al. 2009), establishes that under the hypothesis of homogeneity, stationarity, local isotropy, and incompressibility, in the turbulent inertial range the mixed third-order moment of the increments of velocity (v) and magnetic field (in velocity units,

b
=
B

/

4
π
ρ

, with B the magnetic field vector and ρ the plasma mass density) is a linear function of the scale Δt. Moreover, the proportionality coefficient is related to the mean energy transfer rate of the turbulent cascade. This can be written as
1

Y
(
Δ
t
)

≡

〈
Δ

v

R

(
∣
Δ
v

∣

2

+
∣
Δ
b

∣

2

)

−
2
Δ

b

R

(
Δ
v
·
Δ
b
)
〉
=

4

3

ε

V

sw

Δ
t
.

Here Δv and Δb are scale-dependent vector increments of the plasma velocity and magnetic field, as defined above; ΔvR = vR(t + Δt) − vR(t) and ΔbR = bR(t + Δt) − bR(t) are velocity and magnetic field longitudinal increments measured in the sampling direction R; ε is the mean energy transfer rate; and brackets indicate ensemble average. Note that the solar wind speed Vsw is used for switching between space scales, ℓ, and timescales, Δt, through the Taylor hypothesis, ℓ = VswΔt (Taylor 1938). This also results in the reversal of the sign in the left-hand side of Equation (1) with respect to the traditional formulation in terms of spatial increments. The PP law is a fundamental relation for MHD turbulence, since it describes the energy cascade and ultimately allows us to estimate the energy that will be dissipated at small scales. It is particularly relevant for solar wind turbulence, where the collisionless processes responsible for removing the energy at the bottom of the nonlinear cascade are not yet fully understood (Chen et al. 2019; Sorriso-Valvo et al. 2019; Matthaeus et al. 2020; Smith & Vasquez 2021). The linear relation (1) has been observed in various regions of the heliosphere, for different conditions of the space plasma, confirming the turbulent nature of their dynamics and providing an estimate of the energy transfer rate (MacBride et al. 2005; Sorriso-Valvo et al. 2007; Marino et al. 2008; Smith et al. 2009; Stawarz et al. 2010; Coburn et al. 2012; Bandyopadhyay et al. 2018; Hadid et al. 2018; Andrés et al. 2019; Bandyopadhyay et al. 2020; Sorriso-Valvo et al. 2021).


Diffuse synchrotron emission associated with ultrarelativistic particles and magnetic fields in the intracluster medium (ICM) primarily consists of radio haloes and radio relics (see Ferrari et al. 2008; Brüggen et al. 2012; Feretti et al. 2012; Brunetti & Jones 2014 for recent reviews). It is thought that radio haloes are caused by cluster-wide post-merger turbulence (see e.g. Brunetti et al. 2001; Petrosian 2001), secondary electrons from proton–proton interactions (see e.g. Dennison 1980; Blasi & Colafrancesco 1999) or a combination of the two mechanisms (see Brunetti & Blasi 2005; Brunetti & Lazarian 2011; Pinzke, Oh & Pfrommer 2015), whereas radio relics are apparently associated with localized, post-merger shock-fronts (Ensslin et al. 1998). However, the non-detection of gamma-ray emission by the Fermi satellite (see e.g. Brunetti et al. 2012; Zandanel & Ando 2014; Ackermann et al. 2015) disfavours a purely hadronic model for the origin of radio haloes and challenges standard diffuse shock acceleration to explain radio relics (see e.g. Brunetti & Jones 2014; Vazza & Brüggen 2014). Additionally, the variety of the observed properties of cluster-scale radio emission is becoming increasingly difficult to describe within the current theoretical picture. For example: whilst in the ‘Sausage’ cluster (CIZA J2242.8+5301) van Weeren et al. (2010) observe a textbook example of an arc-like radio relic related to a shock; in ZwCl 2341.1+000 Ogrean et al. (2014) observe no X-ray shock at the position of a relic, and in the Bullet cluster (Shimwell et al. 2015), PLCKG287.0+32.9 (Bonafede et al. 2014b) and the Coma cluster (Ensslin et al. 1998) an apparent link is seen between radio galaxies and radio relics. Furthermore, whilst radio haloes are statistically detected in merging clusters (e.g. Cassano et al. 2013), the role of the cluster mass and its dynamical state is difficult to disentangle with current observations (see Cuciti et al. 2015). For example, in CL1821+643 Bonafede et al. (2014a) detect a giant radio halo in a cool core cluster with no obvious merging activity and Russell et al. (2011) observe no diffuse radio emission in Abell 2146, which is a less massive cluster, but a clear merging system. Recently upgraded and new facilities have significantly improved sensitivity to diffuse radio emission from the ICM and are already beginning to reveal increasingly complex phenomena (e.g. Owen et al. 2014) which may shed light on the connection between haloes and relics and further challenge a univocal interpretation of these sources. One such instrument is the Low-Frequency Array (LOFAR; van Haarlem et al. 2013) which can produce deep, high-resolution, high fidelity, low-frequency radio images.


The kinetic energy stored in the CO shell can be estimated as $E_{\rm kin} = 0.5\, M_{\rm shell}\, V^2_{\rm exp}$, where Vexp is the expansion velocity of the shell and Mshell is the total (molecular, atomic, and ionized) shell mass. Adopting an expansion velocity equal to half the velocity interval where the structure is observed, Vexp = 7.0 ± 1.3 km s− 1 , the molecular mass given in Table 1 and the atomic and ionized masses estimated by Cichowolski et al. (2001), 1450 and 3000 M⊙, respectively, we obtain Ekin = (2.5 ± 1.0) × 1049 erg, assuming a 40 per cent error for the masses.. Although Cichowolski et al. (2001) concluded that WR 130 could have alone created the observed structure, it is important to note that they did not take into account the molecular mass present in the shell, which considerably increases the kinetic shell energy. Thus, we can compare now the new value obtained for Ekin with the mechanical energy deposited in the ISM by the wind of the WR star, Ew = (0.7–2.2) × 1050 erg (Cichowolski et al. 2001). We obtain ϵ = Ekin/Ew = 0.007–0.5. The ratio ϵ measures the energy conversion efficiency in the shell, and according to evolutionary models ϵ ≤ 0.2 (Koo & McKee 1992). Thus, not all the possible values of ϵ are compatible with the scenario where the energy injected during the WR phase is enough to create the structure. In this case, the contribution of the energy injected during the O-star phase and/or other massive stars, should be considered. As mentioned in the Introduction, WR 130 is a WNH star, and according to Smith & Conti (2008) its age would be of about 2–3 Myr and its initial mass of at least 60 M⊙. A rough estimation of the energy injected by such a star during its main sequence yields Ew = (2.5–3.5) × 1050 erg (de Jager, Nieuwenhuijzen & van der Hucht 1988), which would be enough to create the observed structure. We have nevertheless looked for the presence of other massive stars in the region. We queried the available catalogues such as the Galactic O-Star Catalog (Maíz Apellániz et al. 2013), the Early-Type Emission-Line Stars Catalogue (Wackerling 1970), the Catalogue of Be stars (Jaschek & Egret 1982), the H-alpha Stars in the Northern Milky Way Catalogue (Kohoutek & Wehmeyer 1997), and the Catalog of Galactic OB Stars (Reed 2003), for early-type and emission stars. No stars were found in any catalogue. The only massive star located nearby is, as mentioned by Cichowolski et al. (2001), an OB star, which has an uncertain spectral type and no distance estimate (Stock, Nassau & Stephenson 1960). It is located in projection not in the centre of the structure but on to the shell (there is a second OB star mentioned by Cichowolski et al. 2001 but its location is actually outside the structure, see fig. 1 of Cichowolski et al. 2001). Although we cannot completely rule out the possibility that the OB star may be playing a role in creating the shell structure, we think that the action of WR 130 is sufficient and most likely dominant in the region.


Consider a space–time scale invariance of the equations of motion under the consideration of the transformation in Minkowsky space (Milgrom 2009a; see also Milgrom 2014a,b):
(3)

\begin{equation}
(t,{\boldsymbol r}) \rightarrow (\lambda t,\lambda {\boldsymbol r}),
\end{equation}

where t and ${\boldsymbol r}=(x,y,z)$ are time and Cartesian coordinates, respectively, and λ is a positive number. The Newtonian gravitational acceleration for a spherically symmetric system,

(4)

\begin{equation}
g_{\rm N} = \frac{GM_{\rm b}}{r^2},
\end{equation}

then transforms as gN → λ−2gN, whereas the kinematical acceleration, $g\equiv {\rm d} \dot{x} / {\rm d} t$, scales as g → λ−1g. Here Mb(  r) is the enclosed baryonic mass within r. As a result, the Newtonian gravitational acceleration and the kinematical acceleration scale differently under equation (3). Linking purely gravitational interactions to symmetries such as defined in equation (3) suggests deeper physics and constitutes a motivation for viewing MOND as much more than a mere phenomenological description of galactic dynamics (Milgrom 2009c). In order to assure that both the gravitational and the kinematical accelerations scale symmetrically under equation (3), i.e. in order to maintain the invariant symmetry, the gravitational acceleration, g, has to scale proportionally to $g_{\rm N}^{1/2}$. In order to obtain the correct dimension, a constant with the unit of acceleration, needs to be introduced. This constant is referred to as a0, such that

(5)

\begin{equation}
g=(a_0g_{\rm N})^{1/2},
\end{equation}

i.e. g2 = a0gN. Thus g = (GMba0)1/2/r, and the circular velocity, which follows from the centrifugal acceleration g = v2/r, is

(6)

\begin{equation}
v = (GM_{\rm b}a_0)^{1/4}={\rm constant},
\end{equation}

which is exactly the BTFR (Milgrom 1983a, 2009a, 2014b; McGaugh et al. 2000; Famaey & McGaugh 2012). We refer to gravitational dynamics which thus conforms to low-acceleration scale invariance (equation 3) as low-acceleration SID. SID beautifully reproduces the deep MOND equations of motion. It is rather remarkable that such a simple principle as SID and discovered by Milgrom leads to one of the most important scaling relations which real galaxies are observed to obey. Note that equation (6) implies that each baryonic galaxy is surrounded by a logarithmic non-particle (and thus phantom) DM halo potential, which is however not a real halo as it is only evident if Newtonian dynamics is applied to the galaxy. If SID is true, then a Newtonian observer would thus deduce that each baryonic galaxy is surrounded by a PDMH the mass of which is proportional to radial distance (equation 27 below).


For variable star classification, both convolutional neural networks (CNNs; LeCun, Bengio & Hinton 2015) and recurrent neural networks (RNNs; Hochreiter & Schmidhuber 1997; Cho et al. 2014) have been shown to be competitive to the traditional RF-based methods. Naul et al. (2018) used an RNN autoencoder network to learn low-dimensional representations of period-folded light curves in an unsupervised fashion. This representation was then, in a supervised context, used as feature inputs to an RF classifier. They showed that the learned features are at least as good as, and often better than, two sets of state-of-the-art hand-crafted features (Richards et al. 2011; Kim & Bailer-Jones 2016), in terms of downstream classification accuracy. Becker et al. (2020) used an RNN for which instead of period-folding, each input light curve is grouped with a moving time-sample window of size 50 and stride 25. Although period-folding improves performance (Naul et al. 2018), Becker et al. (2020)’s time-space RNN does not require the period to be calculated, and is thus less computationally expensive in terms of preprocessing. Again, they found similar performance to an RF classifier with the Nun et al. (2015) features over three data sets, although lower accuracy was seen for many sub-classes with the OGLE data set (Table 2; see Section 3.3 for data description). More recently, Jamal & Bloom (2020) systematically benchmarked the performance of different configurations of RNN and CNN network architectures on variable star classification. Aside from other work (e.g. Aguirre, Pichara & Becker 2018; Tsang & Schultz 2019) evaluating neural network (NN) performance retrospectively on previously labelled data sets, Dékány & Grebel (2020) used an RNN classifier to identify a new sample of fundamental-mode RR Lyrae (RRab) stars. Similarly, Dékány et al. (2019) found Classical and Type II Cepheids with a CNN classifier, also using the VISTA Variables in the Via Lactea (VVV) survey (Minniti et al. 2010) and using period-folded light curves.


AGN-driven outflows. Another possible effect of the AGN activity on the molecular gas is through outflows. This possibility is supported by observations of individual objects: For example, Carniani et al. (2017), Brusa et al. (2018) and Loiacono et al. (2019) find low gas fractions in powerful AGN at cosmic noon hosting high-velocity molecular and ionized outflows (but see also Herrera-Camus et al. 2019). AGN feedback in action in these targets could be depleting the molecular gas reservoir (Brusa et al. 2015). Förster Schreiber et al. (2019), studying outflows in a large sample of 0.6  z  2.7 galaxies through integral field spectroscopy of the Hα emission line, find that incidence, strength, and velocity of AGN-driven winds are strongly correlated with the stellar mass. In particular, they find that high-velocity (∼1000–2000 km s−1) AGN-driven outflows are commonly detected at masses above log(M*/M⊙) = 10.7, and present in up to 75% of the population for log(M*/M⊙) > 11.2. Interestingly, above this stellar-mass threshold we find a significant CO luminosity deficit in our AGN sample with respect to inactive galaxies (Fig. 3, bottom). Moreover, our AGN show on average gas fractions 0.57 dex (by using uniform assumptions, Sect. 4) lower than inactive galaxies at the 2.2σ level. Quantitatively, this translates into Mgas, mol/M* ≈ 0.3 for AGN (0.16 if we use r31 = 0.92; Kirkpatrick et al. 2019) and ≈1 in inactive galaxies. This representative value for our AGN is in line but not as low as previous work targeting extremely powerful sources (e.g., Mgas, mol/M*  0.05 in Brusa et al. 2018). Our team is performing a systematic investigation of ionized gas outflows with SINFONI as part of the SUPER survey, and 11 targets of our ALMA sample have complementary good quality SINFONI data (Kakkad et al. 2020; Perna et al., in prep.). For some of them we measured [O III] line widths larger than 600 km s−1, interpreted as a clear signature of the presence of an AGN-driven outflow in these objects (Kakkad et al. 2020). A detailed comparison between outflow and CO properties for these targets will be presented in a future work. Distinguishing among the scenarios described above is challenging with the current dataset. AGN feedback could proceed in different ways and different mechanisms likely overlap in shaping the properties of the molecular gas reservoir. For example, AGN radiation could both heat and/or dissociate CO molecules. In this case, AGN would produce a feedback mechanism that does not require outflows but would potentially work toward inhibiting further star formation. As for AGN-driven outflows, they could impact the gas content by ejecting material out of the galaxy (e.g., Travascio et al. 2020), or they could produce CO heating or dissociation due to shocks. Additionally, numerical simulations predict that AGN-driven outflows may heat via shocks a significant quantity of the gas in the ISM, reaching the high temperatures required for the excitation of high-J CO transitions (Costa et al. 2018). To reach a deeper understanding of the impact of AGN on the molecular gas reservoir, also on longer timescales, predictions from simulations providing the spatial scales and effects of AGN activity on CO properties as a function of cosmic time are needed.


This work is the second in a series of works aimed at understanding the effect of residual gain errors in different power spectrum estimations in the presence of strong foreground and exploring potential mitigation techniques. In this work, we have not investigated the different possibilities for the presence of residual gain errors and chosen the values of σR and σI same as σg for most of the discussions. In general, the standard deviation of the real and imaginary parts can be different. We observe here that it is essential to assess the time dependence of the gain accurately, as its inaccurate estimation leads to the time-correlated residual gain errors. In this work, we do not consider the effect of frequency correlation in gain error, and all our estimations are done for correlating visibilities in the same frequency channel. Furthermore, this work also uses the foreground subtraction technique, where we expect to have accurate knowledge of the foreground emissions (Jelić et al. 2008; Ghosh et al. 2012). An alternative method, more regularly exercised in literature, is foreground avoidance. It has been established that the foregrounds to the redshifted 21-cm emissions remain correlated across relatively larger bandwidth (Platania et al. 1998; Santos et al. 2005; Ali et al. 2008; Jelić et al. 2008; Chakraborty et al. 2019b), whereas the H i signal decorrelates faster (Bharadwaj & Pandey 2003; Bharadwaj & Ali 2005). As a result, when the power spectrum is observed as a function of (k∥, k⊥), the foreground emission remains concentrated near the low k∥, inside the ‘wedge’ (Datta et al. 2010; Morales et al. 2012; Vedantham et al. 2012). Note that the smaller frequency separation in multifrequency angular power spectrum contributes to larger k∥ modes of the power spectrum. Hence, the effect of frequency-independent residual gain we see here at zero frequency separation may contribute to bias in the power spectrum beyond the wedge. Moreover, the antenna-based gains are functions of both time and frequency; the residual gain is expected to have correlated frequency dependence. Such frequency-correlated calibration errors couple the foreground power beyond the foreground wedge into the EoR window region of the 2D power spectrum space (Barry et al. 2016; Ewall-Wice et al. 2017; Byrne et al. 2019; Pal et al. 2021). At present, we are working towards expanding the formalism presented in this paper to estimate bias and variance in power spectrum estimate when visibility correlation in different frequencies is considered. Here, we also consider that the gain errors arising from the different antennae are uncorrelated. Though this is a fairly good assumption for the gain arising from electronics in the antenna system itself, the ionospheric effects may introduce correlated gains across the antenna. Furthermore, as the calibration procedure uses baseline-dependent gains to solve for the antenna dependent gains, calibration errors can lead to correlated residual gain errors across the antenna. Moreover, asymmetry in the telescope aperture, mechanical fatigue of telescope structure, etc., can lead to parts of the gain errors correlated across different antennae and even across different days of observations. We are investigating these effects, and the result will be presented in future work. Though the demonstrations here are done with the uGMRT as a model for the interferometer, a similar analysis can be carried out for any telescope of concern, and a prior assessment of the effect of the gain errors can be made using the analytical expression presented here with minimum computation cost. Furthermore, this work emphasizes the importance of estimating and establishing the gain statistics for a given interferometer. Though we use a simple model for the residual gain error here, the calculations that lead to the analytical expression can be readily expanded for a more complicated gain error model. We believe that this work provides significant direction in understanding and planning observations to detect redshifted 21-cm power spectrum.


Many efforts have thus been devoted to the correction of surface effects, either from theoretical modelling (e.g., Gabriel et al. 1975; Balmforth 1992b; Houdek 1996; Rosenthal et al. 1999; Grigahcène et al. 2005) or through empirical formulae (e.g., Kjeldsen et al. 2008; Christensen-Dalsgaard 2012; Ball & Gizon 2014; Sonoi et al. 2015). Some aspects, however, are very complicated to model, and existing models make use of assumptions that can barely be justified, if at all. For instance, turbulent pressure modulations are usually described in the Gas-Γ1 (GGM) or reduced-Γ1 (RGM) approximations (Rosenthal et al. 1999), which amounts to neglecting the effects of turbulent dissipation and buoyancy on the mode (Belkacem et al. 2021). Another problem is the use of time-dependent mixing-length formalisms (Unno 1967; Gough 1977) to account for modal surface effects (e.g., Gabriel et al. 1975; Houdek 1996; Grigahcène et al. 2005; Sonoi et al. 2017; Houdek et al. 2017, 2019). While useful for the bulk of the convective region, the mixing-length hypothesis is no longer valid in the superadiabatic region just beneath the surface of the star, as shown by 3D hydrodynamic simulations of stellar atmospheres (see Nordlund et al. 2009, for a review). Finally, such formalisms require that the oscillations be separated from the convective motions, thus yielding separate equations. This is done either by assuming a cut-off in wavelength space, with oscillations having much shorter wavelengths than turbulent convection (Grigahcène et al. 2005), or by using 3D hydrodynamic simulations and separating the oscillations from convection though horizontal averaging (Nordlund & Stein 2001). The necessity to separate the equations for oscillations and convection is fundamentally problematic as there is no rigorous way to disentangle the two components, mainly because, in solar-type stars, they have the same characteristic lengths and timescales (Samadi et al. 2015). This is even truer if one wishes to model their mutual coupling.


Strong gravitational lensing systems are a powerful tool for cosmology. They have been used to study how dark matter is distributed in galaxies and clusters (e.g., Kochanek 1991; Hogg & Blandford 1994; Broadhurst et al. 2000; Koopmans & Treu 2002; Bolton et al. 2006; Koopmans et al. 2006; Bradač et al. 2008; Huang et al. 2009; Vegetti & Koopmans 2009; Jullo et al. 2010; Grillo et al. 2015; Shu et al. 2015, 2016, 2017; Meneghetti et al. 2020) and are uniquely suited to probe the low end of the dark matter mass function and test the prediction of the cold dark matter (CDM) model beyond the local universe (e.g., Vegetti et al. 2010, 2012; Hezaveh et al. 2016; Ritondale et al. 2019; Diaz Rivero & Dvorkin 2020; Caǧan Sengül et al. 2020, 2021; Gilman et al. 2021). Multiply lensed supernovae (SNe) are ideal for measuring time delays and H
0 because of their well-characterized light curves, and in the case of Type Ia, with the added benefit of standardizable luminosity (Refsdal 1964; Treu 2010; Oguri & Marshall 2010), provided microlensing can be accurately characterized (Yahalomi et al. 2017; Foxley-Marrable et al. 2018). Furthermore, SNe have the benefit of fading, so for these systems lens models can be validated using images that are uncontaminated by bright point sources (Ding et al. 2021). In recent years, strongly lensed SNe, both core-collapse (Kelly et al. 2015; Rodney et al. 2016) and Type Ia (Quimby et al. 2014; Goobar et al. 2017; Rodney et al. 2021), have been discovered. Time-delay H
0 measurements from multiply imaged SNe (e.g., Goldstein & Nugent 2017; Shu et al. 2018; Goldstein et al. 2018, 2019; Pierel & Rodney 2019; Suyu et al. 2020; Huber et al. 2022), combined with measurements from distance ladders (e.g., Freedman et al. 2019, 2020; Riess et al. 2019, 2022) and lensed quasars (e.g., Suyu et al. 2010, 2013; Treu & Marshall 2016; Bonvin et al. 2017; Birrer et al. 2020; Millon et al. 2020; Wong et al. 2020), can be an important test of the tension between H
0 measured locally and the value inferred from the cosmic microwave background (CMB; Planck Collaboration et al. 2020).


The 17 GHz polarization reversal during this CRF can be a yet unknown feature inherent to the fan–spine structure, where magnetic polarity around null point (NP) varies so rapidly as to affect the propagation of microwave polarization. A way to possibly explain this polarization change is to view it as a mode-coupling phenomenon, the process by which the rays reverse their original sense of polarization while passing through a quasi-transverse field region along the line of sight from the radiation source to the observer, depending on the degree of mode coupling there (Cohen 1960; Zheleznyakov 1970; Melrose 1975; White et al. 1992). This is an attractive scenario for a fan–spine structure, because the fan surface may well act as a quasi-transverse layer for the rays emitted underneath. To think about an ideal fan–spine structure with a flux rope inside, in this configuration, the magnetic fields above the fan surface are all in the negative magnetic polarity, and the rays emitted from either magnetic polarity underneath will be observed as LHCP everywhere. Therefore, the LHCP observed everywhere before the flare can simply be due to the fan–spine structure, without any strong mode-coupling phenomenon. On the other hand, if a magnetic flux rope rises to reconnect with the overlying fan field, the fan surface may partially open up to let the flux rope erupt out. Such a change of magnetic field structure can explain the instant reversal of the 17 GHz polarization at t3 more naturally. The reconnection between the magnetic fields inside and outside of the fan will occur across a current sheet, the so-called breakout current sheet (BCS), and the newly open field lines amount to the lower part of the rising and expanding BCS (see, e.g., Lynch et al. 2016; Karpen et al. 2017). A sustained BCS over the active region might affect the microwave polarization, as mode coupling across a current sheet is still a debatable issue (Zheleznyakov et al. 1996; Lee et al. 1998; Lee 2007). We here offer only the simplest interpretation, according to which the change from LHCP to RHCP of the 17 GHz emission over the inner ribbon is not just a signature for any magnetic field perturbation, but may indicate a specific form of a breakout eruption out of the closed fan structure. The implied magnetic field reconfiguration is in line with the recently reported decay of the coronal magnetic field at the flare site by Fleishman et al. (2020).


To emphasize it again, one may suggest accordingly that several low-m modes of moderately growing collective oscillation with different amplitudes, number of spirals and pitch angles (radial wavelengths), including the most interesting m = 1 mode, may co-exist in the solar neighbourhood. The so-called lopsidedness, or the m = 1 azimuthal asymmetry, is often seen in the distribution of stars and gas in the outer discs of many disc galaxies (Zaritsky & Rix 1997; van Eymeren et al. 2011). Generally, there is no azimuthal symmetry, at least far from their centres, in multi-arm galaxies (Efremov 2011). As for us the spiral pattern of the Galaxy is not a single m model but a superposition of modes as suggested theoretically in the late 1970s (Bertin et al. 1977; Lin & Lau 1979; Bertin 1980; see also Griv & Wang 2014). The overall pattern is thus basically multiple armed. In addition, we argue that the Galaxy is the azimuthally asymmetric spiral system (cf. Levine et al. 2006). The system therefore may exhibit a complicated asymmetric, multi-arm, not well-defined spiral structure as seen, for instance, in the face-on spiral galaxy M101 (Fig. 13). Interestingly, many spiral structures in galaxies do not appear to be well-organized grand designs. Galaxies dominated by a single and symmetric pattern are exceedingly rare.

The pitch angle of the spiral pattern seems to be relatively small for all models considered, |tan p| ≪ 1. Thus, the original Lin–Shu approximation of tightly wound gravity perturbations used throughout the theory does not fail.
The relative amplitude of the surface density $\widetilde{\Sigma }_0/\Sigma _{\mathrm{basic}} \gtrsim 1$ for all models considered. The latter means that the non-axisymmetric variation found in the relative amplitude of the surface density does not represent a small perturbation in the basic equilibrium state of the Galaxy that is axisymmetric in the mean.
The above mentioned results are in agreement with our previous determinations (Griv et al. 2013, 2014, 2015a,b,c).


Tol1247 was imaged with the HST (see Fig. 3) in the optical using the Wide Field Ultraviolet-Visible Channel (UVIS) of its Wide Field Camera 3 (WFC3). For UV imaging, the Advanced Camera for Surveys' Solar Blind Channel (ACS/SBC) was used. Seven filters were utilized in total, allowing to apply laxs – the Lyman alpha eXtraction software (Hayes et al. 2009) – to produce continuum-subtracted Lyα, Hα and Hβ images, corrected for underlying stellar absorption and contamination from [N ii] λ6548, 6584. The latter one is based on the spectroscopic line ratio ${[\mathrm{N}\,\small {II}]}/{\mathrm{H}\alpha }=0.0605$ published by Terlevich et al. (1993). The imaging strategy and data reduction methodology for Tol1247 is very similar to that of the Lyman Alpha Reference Sample (LARS; Hayes et al. 2014; Östlin et al. 2014; Duval et al. 2015) and the basic data reduction for this data set is done in the same way as for LARS. Flat-field-corrected frames were obtained from the Mikulski Archive for Space Telescope. The charge transfer inefficiency (CTE) correction for the ACS data was performed by the pipeline, whereas CTE losses in WFC3/UVIS (Anderson & Bedin 2010) were treated manually using the tools supplied by STScI.3 We then stacked the individual data frames and drizzled them to a pixel scale of 0.04 arcsec pixel−1 using DrizzlePac version 1.1.16 (Gonzaga et al. 2012). Further pre-processing of the data includes additional masking of cosmic rays in the drizzled frames and matching the point spread functions (PSFs) for the different filters. In order to match the PSF, we first construct PSF models for all of the filters used in the study. For the optical filters, we use TinyTim models (Krist, Hook & Stoehr 2011), re-sampled to a pixel scale of 0.04 arcsec pixel−1. However, for the FUV filters, TinyTim is not accurate enough, particularly in the wings. Therefore, the PSF models for the FUV filters are instead built from stacks of stars obtained in calibration observations; see Hayes et al. (2016) for details. All of the PSF models are then normalized by peak flux and stacked by maximum pixel value. We then proceed to calculate convolution kernels that match the PSFs for all of the filters to the maximum width model. Each kernel is built up from a set of delta functions and we find the optimum matching kernel by least-squares optimization; see also Becker et al. (2012) and Melinder et al. (in preparation). The drizzled and registered images are convolved with the kernel found for each filter, which result in a set of images matched to a common PSF.


Guo et al. (2015) used an automated “blob finder” to identify star-forming regions in the HST/ACS images for 3,239 log M*/M⊙  10.6 galaxies in CANDELS (GOODS-S and UDS fields) at 0.5  z  3. They defined clumps as blobs which contribute more than 8% of the total UV light of their host galaxies. In contrast to our results, they find that a much higher fraction of SFGs are clumpy (as much as ∼60% at z ∼ 2), and also that higher mass bins have lower clumpy fractions. It is worth pointing out that clumpy galaxy fractions are highly sensitive to methodology and clump definition and vary widely in the literature (e.g., Ravindranath et al. 2006; Elmegreen et al. 2007; Wuyts et al. 2012; Guo et al. 2015), so we should not expect complete agreement. Comparing their observed clumpy galaxy fractions (as a function of redshift) to fractions derived from the K15 classification scheme, Guo et al. (2015) find that their results agree best with clumpy fractions derived using both the clumpiness and patchiness flags from the K15 data release (see their Appendix A) rather than either the clumpy or patchy flags alone. This is because the blob finder does not account for the light concentration of the blobs. The inclusion of patches may help explain why their clumpy fractions are generally higher than ours. Guo et al. (2015) also exclude very small (01) and elongated (axis ratio 0.5) galaxies from their sample. Our inclusion of such galaxies could easily lead to lower clumpy fractions given that many galaxies with half-light radius 01 are Spheroids (see Figure 13), which rarely possess clumps. We also include edge-on disks whose clumps may be obscured by dust. The inclusion of galaxies with unresolved or obscured clumps may imply that we are underestimating the clumpy fractions. However, we do include the contribution from non-disky compact or irregular SFGs which would be excluded by the Guo et al. (2015) cuts. The contribution from such galaxies is not insignificant, especially at z ∼ 2, so our looser selection is not without merit. Even if we do underestimate our clumpy fractions, our consistent sample selection and methodology ensures that they should be similarly underestimated at all redshifts, preserving the general evolutionary trends.


The major difference between the axisymmetric case and the asymmetric approach is that we need to derive the 3D, asymmetric gravitational potential of luminous baryons beforehand. We thus computed the potential in Cartesian coordinates (x,y,z), which enables us to derive both radial and azimuthal forces at any desired z. This can be derived independently for each stellar or gaseous contribution. The gravitationtal potential Φ of the mass distribution is in principle deduced from the convolution of the volume mass density by the Green function, namely (11)\begin{equation} \Phi = -G \iiint\frac{{\rm d}\rho'}{|\vec{r}-\vec{r}'|}, \label{eq:pot} \end{equation}Φ=−G$dρ′|r−r′|,where G is the gravitational constant. However, the Green function written by 1/ | r−r′ |  =  [(x−x′)2 + (y−y′)2 + (z−z′)2] − 1/2, is well known to diverge at each point where x = x′, y = y′ and z = z′. This function renders any direct estimate of Φ inaccurate and generally encourages modelers to incorporate a softening length to bypass the divergence. Here, we use the new formalism presented in Huré (2013) who showed that the Newtonian potential is exactly reproduced by using an intermediate scalar function ℋ, namely \hbox{$\Phi = \partial_{xy}^2 {\cal H}$}Φ=∂xy2ℋ. In 3D, this hyperpotential is written as (12)\begin{equation} {\cal H}(x,y,z) = -G \iiint_{\Omega'}{\rho(x',y',z')} \kappa^{xy}(X,Y,Z){\rm d}x'{\rm d}y'{\rm d}z' , \end{equation}ℋ(x,y,z)=−G$Ω′ρ(x′,y′,z′)κxy(X,Y,Z)dx′dy′dz′,with X = x−x′, Y = y−y′ and Z = z−z′. The κ function is a hyperkernel defined by (13)\begin{equation} \kappa^{xy}(X,Y,Z) = -Z \arctan \frac{XY}{Z |\vec{r}-\vec{r}'|}+Y \ln \frac{X+|\vec{r}-\vec{r}'|}{\sqrt{Y^2+Z^2}}\cdot \label{eq:k} \end{equation}κxy(X,Y,Z)=−ZarctanXYZ|r−r′|+YlnX+|r−r′|Y2+Z2·This approach is particularly simple and efficient for 2D or 3D distributions since ℋ is, in contrast to Φ, the convolution of the surface or volume density with a regular, finite amplitude kernel. The methodology thus does not make use of a softening length in the derivation of the potential. In practice, this convolution is performed using the second-order trapezoidal rule and the mixed derivatives are estimated at the same order from centered finite differences. Furthermore, the volume density of the tracer are deduced from a surface density map, considering that the vertical density follows a sech-squared or exponential law of constant scaleheight with radius. The precision of these schemes is sufficient for the present purpose.


We have developed the simplest spherical void lens model based on the recently developed embedded lens theory. We have assumed a uniform mass profile for the void, compensated by a thin bounding shell. The infinitesimally thin bounding shell was chosen for convenience (Maeda & Sato 1983a, 1983b). To investigate other void profiles such as a non-uniform void interior or a finite-thin bounding ridge (Colberg et al. 2005; Lavaux & Wandelt 2012; Pan et al. 2012; Sutter et al. 2012; Hamaus et al. 2014; Kantowski et al. 2015) is straightforward; one has only to evaluate the Fermat potential of Equation (1) or equivalently the potential part of the time delay of Equation (4). It is also possible to build embedded void lens models with non-spherically symmetric density profiles given that the lowest-order embedded lens theory is applicable to any distributed lens (Kantowski et al. 2013). It is well accepted by the lensing community that small overdensities attract light, whereas small underdensities repel light. This fact can be rigorously proved using general relativistic perturbation theory (Sachs & Wolfe 1967) assuming

. However, the repulsive nature of lensing by a large and deep underdense region (i.e., cosmic voids) as described by the rigorously derived but simply implemented embedded lens formalism did not appear until Kantowski et al. (2013). In the case of large density contrasts, i.e.,

 approaching its lower bound −1 for cosmic voids, the repulsive lens equation follows naturally from the embedded lensing theory. This theory is based on Swiss cheese models (Einstein & Straus 1945), which are exact solutions of Einstein’s field equations containing inhomogeneities with large density contrasts (Chen et al. 2010, 2011, 2015; Kantowski et al. 2010, 2012, 2013). The void-lensing community takes void repulsive lensing as granted (e.g., Amendola et al. 1999; Das & Spergel 2009), whereas the galaxy/cluster strong-lensing community has ignored embedding effects, i.e., the repulsive lensing caused by the large underdense regions surrounding the central overdense lens. Besides correctly predicting repulsive lensing by cosmic voids, our Fermat potential formulation can be used to compute the void-lensing time delay effects, including the ISW effect caused by voids; see Equation (5).


One has to be sure to rule out cases where inorganic chemistry can mimic the presence of life (“false positives”). Potential abiotic ozone production on Venus- and Mars-like planets has been discussed by Schindler & Kasting (2000, and references therein). While this is based on photolysis of e.g., CO2 and H2O and is thus limited in extent, a sustainable production of abiotic O3 which could build up to a detectable level has been suggested by Domagal-Goldman & Meadows (2010) for a planet within the habitable zone of AD Leonis with a specific atmospheric composition. Indeed, other studies confirm that abiotic buildup of ozone is possible (e.g., Hu et al. 2012; Tian et al. 2014); however, detectable levels are unlikely if liquid water is abundant, as e.g. rainout of oxidized species would keep atmospheric O2 and O3 low (Segura et al. 2007), unless the CO2 concentration is high and both H2 and CH4 emissions are low (Hu et al. 2012). False-positive detection of molecules such as CH4 and O3 is discussed by von Paris et al. (2011). Seager et al. (2013) present a biosignature gas classification. Since abiotic processes cannot be ruled out for individual molecules (e.g. for O3), searches for biosignature molecules should search for multiple biosignature species simultaneously. It has been suggested that the simultaneous presence of O2 and CH4 can be used as an indication for life (Sagan et al. 1993, and references therein). Similarly, Selsis et al. (2002) suggest a so-called “triple signature”, where the combined detection of O3, CO2 and H2O would indicate biological activity. Domagal-Goldman & Meadows (2010) suggest to simultaneously search for the signature of O2, CH4, and C2H6. Of course, care has to be taken to avoid combinations of biosignature molecules which can be generated abiotically together (see e.g. Tian et al. 2014). The detectability of biosignature molecules is discussed, e.g. by von Paris et al. (2011) and Hedelt et al. (2013). In particular, the simulation of the instrumental response to simulated spectra for currently planned or proposed exoplanet characterization missions has shown that the amount of information the retrieval process can provide on the atmospheric composition may not be sufficient (von Paris et al. 2013).


RFs can propagate from the magnetotail to Earth over a long distance more than 10 R
E together with BBFs behind them (Runov et al. 2009; Cao et al. 2010). Studies have suggested that RFs are crucial regions for particle acceleration, pitch-angle evolution, wave–particle interactions, and electromagnetic energy conversion during their Earthward propagation. For instance, rapid increases in energy fluxes of electrons and ions from tens to hundreds of keV are a typical feature of RF events (Khotyaintsev et al. 2011; Liu et al. 2013, 2018c, 2021a, 2022b; Zhou et al. 2018; Liu & Fu 2019; Gabrielse et al. 2021), pitch-angle distribution of suprathermal electrons can evolve dramatically around RFs (Runov et al. 2013; Liu et al. 2020), strong particle and wave activity can occur in the vicinity of RFs (Ono et al. 2009; Zhou et al. 2009, 2014; Fu et al. 2014; Breuillard et al. 2016; Greco et al. 2017; Yang et al. 2017), and RFs are associated with energy conversion from electromagnetic fields to particles (Sitnov et al. 2009; Huang et al. 2015; Khotyaintsev et al. 2017; Liu et al. 2018a, 2022a). The energetic plasma in the vicinity of RFs plays a key role in connecting the magnetotail with the inner magnetosphere because they carry a large amount of energy and can be injected into the inner magnetosphere to affect the ring current and radiation belt (Gabrielse et al. 2012; Duan et al. 2014; Turner et al. 2014). Possible mechanisms responsible for the energization of particles around RFs have been widely investigated based on both spacecraft observations and numerical simulations during the past decade. The strong convection electric field induced by the strong magnetic field gradient of RFs provides significant adiabatic acceleration of the ambient particles (Birn et al. 2004, 2013, 2015; Gabrielse et al. 2012, 2014, 2016; Ganushkina et al. 2013; Liu et al. 2016; Turner et al. 2016). Nonadiabatic effects, caused by particle reflection ahead of the RFs (Zhou et al. 2018), resonance with RFs (Ukhorskiy et al. 2013, 2017), and scattering by wave emissions (Zhou et al. 2009; Greco et al. 2017), are also significant for particle energization. These above studies usually assumed that the RF surface has a planar boundary at a typical thickness comparable to the ion gyroradius and below (Nakamura et al. 2002; Sergeev et al. 2009; Zhou et al. 2009; Schmid et al. 2011; Liu et al. 2013; Vapirev et al. 2013). Divin et al. (2015b) revealed that the RF surface is unstable to instabilities ranging from electron scales to ion scales. Simulation studies found that RFs can be unstable to interchange instability and that finger-like structures on ion–electron hybrid scales can develop at the RF (Vapirev et al. 2013). Such finger-like structures are found to play a role in modulating the electron acceleration process (Wu et al. 2018). Bai et al. (2022) also reported significant ion trapping acceleration at the RF with ion-scale ripples. Unlike these surface structures with ion or ion–electron hybrid scales, Liu et al. (2018b) recently reported that the RF layer has electron-scale density gradients, currents, and electric fields, based on the MMS mission, which consists of four spacecraft separated by 30 km. Such electron-scale ripple structure can be generated by lower hybrid drift instability (Divin et al. 2015b; Pan et al. 2018). Liu et al. (2021c) presented a detailed investigation of energy flux densities at two RFs with/without the electron-scale surface ripples and indicated that surface ripples may play an important role in the particle dynamics. But how such electron-scale RF structure impacts the electron energization and transport still remains unknown. In this paper, with the aid of observation-based test-particle simulation, we aim to investigate in detail the effect of the front surface ripples on the local electron dynamics.


To perform a statistical analysis of the average quiescent fraction of satellites around our sample of massive galaxies, we use a statistical background subtraction technique (e.g., Kauffmann et al. 2010; Tal et al. 2012; Wang & White 2012; Kawinwanichakij et al. 2014). We detect objects within fixed apertures centered on our central galaxies and satisfying Equation (2). These apertures include physically associated galaxies as well as chance alignments of foreground and background galaxies. We estimate and correct for the contamination due to chance alignments by placing random apertures across the field. We adapt this procedure by restricting the placement of the random apertures to regions near the centrals, as demonstrated by Chen et al. (2006). This accounts for the bias due to contaminating galaxies that are physically associated with the centrals but are not satellites (i.e., the 2-halo term of the correlation function; see Chen et al. 2006).15

15
The contaminating galaxies that are physically associated with the central galaxies in our sample are expected to have marginally different properties than truly random field galaxies due to the fact that they exist in biased regions of the universe. There may be an additional effect due to large-scale 2-halo conformity. If 2-halo conformity exists, our procedure effectively corrects for it.
 We therefore place the random apertures within annuli with inner and outer radii equal to 1 and 3 cMpc from each central galaxy for the UDS and UltraVISTA. Parenthetically, our tests showed that the restriction on the location of the background apertures has only a small effect on the conformity signal. Relative to apertures that are placed randomly through the field, this correction increases the quiescent fractions of background galaxies by 0.4%–10%. For the smaller ZFOURGE fields, placing the random apertures within annuli is too restrictive, and for this survey we randomly place the apertures across the fields. We do note that the ZFOURGE fields are small enough that even these randomly placed apertures trace the same large-scale environment as the centrals. Additionally, we find that when we restrict the background apertures to be

 cMpc from the centrals, it changes the measured quenching efficiencies (see Section 4 below) by 10%, and none of our conclusions would be changed.


Variability in observed emission can be considered a defining characteristic of active galactic nuclei (AGNs), and for the roughly 10% of AGNs that are radio-loud (e.g., Jiang et al. 2007) the majority of this variable emission is understood to arise from the relativistic flows of plasma along two oppositely directed jets (e.g., Urry & Padovani 1995). When viewed at small angles to the jet direction the Doppler boosting makes the emission from the approaching jet appear dramatically brighter and also shortens the observed timescales with respect to those in the emitted frame, thereby explaining many of the properties of blazars (e.g., Blandford & Rees 1978; Lister 2001; Gopal-Krishna et al. 2003). Multiband radio studies and very long baseline interferometry (VLBI), coupled with theoretical models, have provided extremely strong evidence for the presence of both moving and standing shocks in these jets (e.g., Marscher & Gear 1985; Hughes et al. 1991; Lister et al. 2001, 2009; Marscher et al. 2008, 2010), indicating significant changes in the fluid flow and/or the density of material ejected into the jets; it is now accepted that the largest flares arise from the production and relativistic propagation of new components seen as radio knots. Changes in the overall direction of the inner portions of the jet, or at least its brightest portions, have also been demonstrated via VLBI (e.g., Biretta et al. 1986; Ros et al. 2000; Piner et al. 2003; Caproni & Abraham 2004). Even modest changes in direction (e.g., Camenzind & Krockenberger 1992; Gopal-Krishna & Wiita 1992) have long been recognized as one way to produce significant changes in the flux and polarization (e.g., Gopal-Krishna & Wiita 1993; Piner et al. 2008). It is to be expected that turbulence is produced within these jets, at least in the vicinity of shocks, and thus some of the variations should arise from such smaller scale motions as has been suggested theoretically (Marscher & Travis 1991; Marscher 2014, Calafut & Wiita 2015) and strongly supported by observations of blazars (e.g., Marscher et al. 2008, 2010; Bhatta et al. 2013). In addition, there is the possibility that portions of the jet are moving much faster than other portions, and such misaligned mini-jets could also produce some extremely rapid fluctuations (Giannios et al. 2009; Biteau & Giebels 2012). Variability on a wide range of timescales can be produced within the accretion disks feeding the central black holes (e.g., Czerny 2006). This presumably dominates the variations from radio-quiet AGNs though not those of radio-loud ones because the special relativistic boosting of the jet emission is so important in the latter (Urry & Padovani 1995). Some of the variations in the jet emission might be traced to plasma fluctuations in the disk being advected into the base of the jets (e.g., Wiita 2006) but the exact origins of the initial fluctuations are not addressed in this work. Here we address the question of whether variations in the bulk flow of a propagating relativistic hydrodynamic (RHD) jet along with sub-grid mildly relativistic turbulence can produce light curves and power spectra resembling those of radio-loud AGNs.


Given the quite strong surface magnetic field of the M7, thermal radiation is expected to be polarized, either if emission is from a bare surface or from an atmosphere (see Turolla et al. 2004; Potekhin 2014). The polarization properties are quite different in the two cases, although there are still uncertainties, especially at optical/ultraviolet (UV) wavelengths. One of the first predictions of quantum electrodynamics (QED), even before it was properly formulated, was vacuum birefringence, and, in particular, that a strong magnetic field affects the propagation of light through it (Heisenberg & Euler 1936; Weisskopf 1936). In thermally emitting INSs, radiation comes from a region comparable with the entire star surface, over which the magnetic field direction changes substantially. In the absence of QED vacuum polarization effects, this would produce a drastic depolarization of the radiation collected at infinity (Heyl, Shaviv & Lloyd 2003, see also Taverna et al. 2015; González Caniulef et al. 2016 and references therein). Vacuum birefringence dramatically increases the linear polarization of the observed radiation, from a level of a few  per cent up to even ∼100 per cent, depending on the viewing geometry and the surface emission mechanism (Heyl & Shaviv 2000, 2002; Heyl et al. 2003; Taverna et al. 2015; González Caniulef et al. 2016). Detecting polarization in the thermal emission from the surface of an INS will be therefore extremely valuable. First, and independently on the physical conditions of the emitting region, the detection of a large degree of linear polarization in the signal would constitute the observational evidence of QED vacuum polarization effects in the strong-field regime. Secondly, the polarization observables can be compared with emission models and help to uncover the physical conditions of INS surfaces and atmospheres, ideally complementing spectral observations (Taverna et al. 2014; González Caniulef et al. 2016).


There is now renewed interest in the literature concerning these transitions, because some of the O iv and S iv intercombination lines, together with the Si iv resonance lines, are routinely observed with the Interface Region Imaging Spectrograph (IRIS; De Pontieu et al. 2014) at much higher spectral, spatial and temporal resolution than previously. For example, Peter et al. (2014) used the intensities of the O iv vs. Si iv lines to propose that very high densities, on the order of 1013 cm-3 or higher, are present in the so-called IRIS plasma “bombs”. Line ratios involving an O iv forbidden transition and a Si iv allowed transition have been used in the past to provide electron densities during solar flares and transient brightenings (e.g. Cheng et al. 1981; Hanssen 1981). However, the validity of using O iv to Si iv ratios has been hotly debated because these ratios gave very high densities compared to the more reliable ones obtained from the O iv ratios alone (see, e.g. Hayes & Shine 1987). In addition, Judge (2015) recalled several issues that should be taken into account when considering the Si iv/O iv density diagnostic. The main ones were: (1) O iv and Si iv ions are formed at quite different temperatures in equilibrium and hence a change in the O iv/Si iv ratio could imply a change in the temperature rather than in the plasma density (2) the chemical abundances of O and Si are not known with any great accuracy and could be varying during the observed events (3) density effects on the ion populations could increase the Si iv/O iv relative intensities by a factor of roughly three to four. Judge (2015) has also mentioned the well known problem of the “anomalous ions”, that is, the observed high intensities of the Li- and Na-like (as Si iv) ions (see also Del Zanna et al. 2002). Another important aspect to take into account is the effect of non-equilibrium conditions on the observed plasma diagnostics. It is well known that strong variations in the line intensities are obtained when non-equilibrium ionisation is included in the numerical calculations (see, e.g. Shen et al. 2013; Raymond & Dupree 1978; Mewe & Schrijver 1980; Bradshaw et al. 2004). In particular, Doyle et al. (2013) and Olluri et al. (2013) investigated the consequences of time-dependent ionization on the formation of the O iv and Si iv transition region lines observed by IRIS. In addition, Dudík et al. (2014) showed that non-Maxwellian electron distributions in the plasma can substantially affect the formation temperatures and intensity ratios of the IRIS Si iv and O iv lines. These authors also suggested that the observing window used by IRIS should be extended to include S iv. Recent IRIS observation sequences have indeed included the S iv line near 1406 Å. The S iv line ratios have a higher limit for density sensitivity than the O iv line ratios and are thus particularly useful for diagnosing high densities which might occur in flares. Previous flare studies have in fact reported line ratios involving O ions which lay above the density sensitivity range, indicating an electron density in the excess of 1012 cm-3 (e.g. Cook et al. 1995; Polito et al. 2016).


Accreting stellar-mass black holes in binary systems regularly display quasi-periodic oscillations (QPOs) in their X-ray flux with frequencies drifting from ∼0.1–10 Hz (e.g. Van der Klis 1989). Three main components can be identified in the spectrum of these sources: disc blackbody emission, power-law emission from the inner accretion flow, and a reflection spectrum from photons reflected off the disc (Done, Gierlinski & Kubota 2007). So-called Type-C low-frequency QPOs (Casella, Belloni & Stella 2005) are believed to originate from the inner accretion flow/corona that is associated with the Comptonized power-law component of the X-ray spectrum, as this component shows a much larger variability amplitude than the blackbody disc component (Sobolewska & Zycki 2006; Axelsson, Hjalmarsdotter & C. 2013). Since currently no consensus on the origin of QPOs exists, we can generally divide QPO models into two broad categories: geometric and intrinsic models. In the former, the X-ray emission is constant but an oscillating accretion geometry quasi-periodically alters the observed flux. A possible origin for these geometric oscillations could be Lense–Thirring precession of the Comptonizing medium, due to misalignment of the black hole spin and the binary orbit (Stella & Vietri 1997; Stella, Vietri & Morsink 1999; Ingram, Done & Fragile 2009). Alternatively, in intrinsic models the emitted luminosity itself varies, for example due to changes in mass accretion rate (Tagger & Pellat 1999; Cabanac et al. 2010) or due to a standing shock in the accretion flow (Chakrabarti & Molteni 1993). Recently, Heil, Uttley & Klein-Wolt (2015) and Motta et al. (2015) confirmed that the QPO amplitude depends on the inclination of the binary orbit, strongly suggesting a geometric origin (Schnittman, Homan & Miller 2006). Ingram & Van der Klis (2015) found that the iron line equivalent width changes over a QPO cycle in GRS 1915+105, also strongly pointing towards a geometric origin.