adsabs/FOCAL huggingface dataset:
The EFE mentioned in the previous section is due to the fact that the MOND equations (3) and (4) are non-linear and involve the total gravitational acceleration with respect to a pre-defined frame (e.g. the CMB frame). Decomposing the total gravitational field ∇Φ into an internal part $\boldsymbol g$ and an external field $\boldsymbol g_{\rm e}$ and using a similar decomposition for the Newtonian gravitational acceleration ($\nabla \boldsymbol \Phi _{\rm N}=\boldsymbol g_{\rm N}+\boldsymbol g_{{\rm Ne}}$) allows us to solve the equations by taking into account the external field. This must typically be done with a numerical Poisson solver (Wu et al. 2008; Angus et al. 2012; Lüghausen, Famaey & Kroupa 2015). Nevertheless, fits to rotation curves in MOND usually neglect the small corrections due to the non-spherical symmetry of the problem, in order to allow for a direct fit of the rotation curve. In the same spirit, and in order to get a first glimpse of the influence of the EFE on rotation curves, we generalize the one-dimensional solution, by using the following formula to fit rotation curves, namely equation (60) from Famaey & McGaugh (2012):

(6)

\begin{equation}
\boldsymbol g=\nu \left(\frac{|\boldsymbol g_{\rm N}+\boldsymbol g_{{\rm Ne}}|}{a_0}\right)\left(\boldsymbol g_{\rm N} + \boldsymbol g_{{\rm Ne}}\right)-\nu \left(\frac{g_{{\rm Ne}}}{a_0}\right)\boldsymbol g_{{\rm Ne}}\,.
\end{equation}

The 1D version of this formula has been shown to be a good approximation of the true 3D solution from a numerical Poisson solver for a random orientation of the external field, at least for computing the Galactic escape speed (Famaey et al. 2007; Wu et al. 2008). Further work should investigate the range of variation of the actual rotation curve compared to the one obtained in this way, for full numerical solutions of the modified Poisson equation and various orientations of the EFE. As mentioned in Famaey & McGaugh (2012), the EFE is negligible if ge g but can play a significant role when the gravitational field g ∼ ge a0. This condition is always reached at some point in the external part of the galaxies. In this case, the relation (6) shows that the EFE will induce a decrease in the internal gravitational field. In other words, the EFE can lead to a decrease of the external part of the rotation curves. We will study this effect more carefully in Section 3.
Citation: Angus et al. 2012
Citation function: Uses
The two main problems arising when dealing with P are the typically low signal-to-noise ratio of the polarisation signal coming from ERS and the non-Gaussian distribution of its noise statistics. Regarding the former, as mentioned above, the typical polarisation fractions of ERS at frequencies below ∼10 GHz are at most 10%. This means that only a few ERS are bright enough to be detected in polarisation with present-day technology. A standard procedure to avoid false detections in polarisation is to detect sources in total intensity and then to try to estimate their polarisation properties in a non-blind way3. We follow this approach in this paper. Regarding the latter problem, assuming that the Q and U noises are Gaussian-distributed, P would have a non-Gaussian Rice distribution (Rice 1945). Rician distribution has strictly non-negative support and heavy tails, which firstly biases the estimation of the polarisation of the sources and secondly disrupts the intuitive interpretation of signal-to-noise in terms of σ thresholds which is used virtually everywhere else in radio astronomy. Simmons & Stewart (1985) discussed four estimators which attempted to correct for biasing in the degree of linear polarisation in the presence of low signal-to-noise ratios. More recently, Argüeso et al. (2009) studied the problem in the context of CMB astronomy and developed two methods for the detection and estimation of ERS in polarisation data: one that applies the Neyman-Pearson lemma to the Rice distribution, the Neyman-Pearson filter (NPF), and another based on pre-filtering before fusion of Q and U to obtain P, the filtered fusion (FF) method. That work found that under typical CMB-experiment settings, the FF outperforms the NPF both in terms of computational simplicity and accuracy, especially for low fluxes. López-Caniego et al. (2009) applied the FF to the Wilkinson Microwave Anisotropy Probe (WMAP) five-year data. The same method has been used to study the polarisation of the Planck Second Catalogue of Compact Sources (PCCS2, Planck Collaboration XXVI 2016) and of the QUIJOTE experiment wide survey source catalogue (Herranz et al. 2021). Alternatively, a novel method for the estimation of the polarisation intensity and angle of compact sources in the E and B modes of polarisation based on steerable wavelets has been recently proposed by Diego-Palazuelos et al. (2021).
Citation: Simmons & Stewart (1985)
Citation function: Background
The physical processes involved in the formation of massive O-type stars and their feedback mechanisms are still under debate (Zinnecker & Yorke 2007; Tan et al. 2014). The energetics of O-type stars can affect the origin of new low-mass and massive stars (Deharveng et al. 2010). The massive stars are often surrounded by the bubbles/rings/semi-ringlike structures traced at mid-infrared (MIR) 8.0 μm (Churchwell et al. 2006, 2007) and are also associated with the extended radio continuum emission (e.g., Deharveng et al. 2010). Note that the majority of the studies related to the MIR bubbles are mainly carried out for a single H ii region or several H ii regions on scales of a few parsecs (e.g., Zinnecker & Yorke 2007; Deharveng et al. 2010; Rathborne et al. 2011; Kendrew et al. 2012; Simpson et al. 2012; Tackenberg et al. 2012; Thompson et al. 2012; Tan et al. 2014; Dewangan et al. 2015a, 2015b; Xu et al. 2016a). However, to our knowledge, in the Milky Way, there is still a limited detailed multiwavelength study of large-scale systems (>25 pc) of several MIR bubbles/H ii regions containing O-type stars, and hence the origin of such extended systems of H ii regions remains unexplored. These systems could be candidates for “mini-starburst” (such as the W43 “mini-starburst” region; Motte et al. 2003). With the availability of the radio recombination line (RRL) and continuum observations (e.g., Lockman 1989; Condon et al. 1998; Anderson & Bania 2009; Jones & Dickey 2012), the MIR survey (e.g., Benjamin et al. 2003), the dust continuum survey at 870 μm (e.g., Schuller et al. 2009; Urquhart et al. 2018), and the 13CO line survey (e.g., Jackson et al. 2006; Anderson et al. 2009), it appears that the H ii regions located toward the Galactic plane and the inner Galaxy are the promising sites to investigate the extended systems of O-type stars. Such study will enable us to understand the physical conditions in a densely clustered environment linked with the luminous giant H ii regions/massive star-forming complexes/mini-starburst candidates in the Galaxy. However, in particular, in the direction of the inner Galaxy, the investigation of an extended system of H ii regions is often restricted by the near–far kinematic distance ambiguity (e.g., Anderson & Bania 2009; Jones & Dickey 2012; Urquhart et al. 2018). In recent years, significant effort has been devoted to resolving the distance ambiguity for H ii regions in the inner Galaxy (see Urquhart et al. 2018 and references therein). In this work, we aim to observationally investigate a large-scale system/configuration of several H ii regions powered by O-type stars and the origin of such a large system.
Citation: Thompson et al. 2012
Citation function: Compare/Contrast
Optical color-magnitude and near-infrared (NIR) color-color diagrams are used to classify our variable candidates. The 2MASS JHKs data are available for 93 stars, while for the remaining two stars, photometric data are adopted from the UKIDSS Galactic Plane Survey (Lucas et al. 2008). The 2MASS photometry is transformed to the California Institute of Technology (CIT) system using the relations provided on their website3 to compare with the evolutionary models. Figure 6 represents the J − H/H − K CCD based on 2MASS data, typically used to classify the YSOs. The YSOs from Rebull et al. (2011) and Ogura et al. (2002) are overplotted in colored symbols. The sequence of dwarf and giants from Bessell & Brett (1988), and the intrinsic locus of CTT stars (Meyer et al. 1997) are also overplotted. The three parallel lines are the reddening vectors drawn from the tip of the giant branch (left), from the base of the MS branch (middle), and from the tip of the intrinsic CTTSs line (right). The extinction ratios to derive these reddening vectors are 





A

J
/
H
/
K



A
V


=
0.265
/
0.155
/
0.090


$ \frac{A_{J/H/K}}{A_V} = 0.265/0.155/0.090 $


, adopted from Cohen et al. (1981). In general, CTTSs with smaller NIR excess, WTTSs, and field stars (MS and giants) occupy the region between the left and middle reddening vectors. Figure 6 shows that most of the variables that are outliers in the proper motions and lie below the intrinsic CTTSs locus are the MS stars. Two variables (V173 and V177) are members based on their proper motions, but fall below the giant sequence. One of these, V173, does not have kinematic information. The CTTSs with large infrared excess are located in the region between the middle and right reddening vectors, while more moderate CTTSs with smaller infrared excess can also populate the region between left and middle reddening vectors, mixed with reddened WTTSs just above the CTT locus. Some contamination is expected depending on the reddening and IR excess, and also due to variability in single-epoch measurements.
Citation: Bessell & Brett (1988)
Citation function: Uses; Uses
It is harder to evaluate the behaviour of the young stellar population along the line of sight, since radial velocity measurements for our sample of Cepheids, needed for a thorough study, do not exist. Given this deficit, we provide only a simplified estimate using radial velocities of OBA-type stars from Evans & Howarth (2008). Since they belong to the same young population, we assume that they have a similar distance distribution and kinematics as the Cepheids. Fig. 16 shows the massive star sample in the plane of the sky. Except for the northernmost region (δ ≥ −72○), where no data exist, these stars cover a comparable area to the Cepheids (indicated as grey dots in the figure for comparison). The radial velocities show a distinct and well-known gradient across the SMC with higher velocities in the eastern part (see also fig. 5 of Evans & Howarth 2008). Such a gradient in radial velocity is also present in older (few Gyr) RGB stars (see fig. 9 of Dobbie et al. 2014). This gradient is commonly attributed to rotation of the SMC. Based on our results obtained for the Cepheids, we propose a different interpretation: this line-of-sight velocity gradient may instead be caused by the fact that the nearest parts of the galaxy, in the region of the SMC Wing, move with a higher radial velocity compared with the main body of the galaxy. Given the additional differences in tangential velocities, these outer parts might be in the process of being stripped from the SMC. Diaz & Bekki (2012) show in their simulations that tidal effects can produce a velocity gradient that is similar to that of a rotating disc. We stress again that this interpretation is based on the assumption that the Cepheid sample and the OBA-type stellar sample trace a similar three-dimensional distribution. For any conclusive answer, radial velocities of the Cepheid stars are required. Such measurements will be provided by the One Thousand and One Magellanic Fields (1001MC) survey (Cioni et al. 2019), which is a consortium survey with the forthcoming multi-object spectrograph 4MOST that will be mounted on the VISTA telescope.
Citation: Evans & Howarth 2008
Citation function: Compare/Contrast
Citation: Evans & Howarth (2008)
Citation function: Uses; Compare/Contrast
Silicon carbide is the best-characterized presolar mineral. It was identified more than 30 yr ago (Bernatowicz et al. 1987) because it is tagged with noble gases of anomalous isotopic compositions (Lewis et al. 1994). Subsequently, it was found that the major elements C and Si, and numerous minor elements contained in presolar SiC, have highly anomalous isotopic compositions as well, the fingerprints of nucleosynthetic processes in their parent stars. Based on the isotopic compositions of C, N, and Si, SiC was divided into distinct populations (Zinner 2014). This includes the mainstream grains, which account for about 80%–90% of all grains (depending on grain size), and the minor types AB (originally defined as two distinct types A and B), C, X, Y, Z, and (putative) nova grains. The mainstream grains have 12C/13C ratios between 10 and 100 (solar: 89), and the 14N/15N ratios of most of them are higher than the solar ratio of 440, the ratio measured for the solar wind (Marty et al. 2011). In a plot of δ29Si versus δ30Si, the mainstream grains lie along a straight line defined by δ29Si = 1.37 × δ30Si–20 (Zinner et al. 2007), where δxSi = [(xSi/28Si)grain/(xSi/28Si)solar−1) × 1000, and x = 29 or 30, i.e., δxSi is the per mil deviation from the solar xSi/28Si ratio. δ30Si values of mainstream grains vary between about −50‰ and +150‰. The isotopic compositions of heavy elements show the signatures of slow neutron-capture nucleosynthesis (s-process, Käppeler et al. 2011), which points toward low-mass (1.5–3 M⊙) asymptotic giant branch (AGB) stars of about solar or supersolar metallicity as parent stars (e.g., Lugaro et al. 2018, and references therein). The minor type Y and Z grains (a few % of all SiC grains, depending on grain size), which fall to the 30Si-rich side of the Si mainstream line, were also proposed to originate from low-mass AGB stars, but with metallicities lower than solar (Hoppe et al. 1997; Amari et al. 2001b). This low-metallicity scenario, however, was recently questioned (Liu et al. 2019). The type C (∼0.1% of all SiC grains) and X grains (∼1% of all SiC grains) are believed to originate from core-collapse supernovae (CCSNe; Amari et al. 1992; Hoppe et al. 1996b; Nittler et al. 1996; Gyngard et al. 2010). These grains show strong depletions (X grains) or enrichments (C grains) in the heavy Si isotopes. Their 12C/13C ratios span a large range from 10 to >10,000; other characteristic features of X and C grains are enrichments in 15N and high initial 26Al/27Al ratios of typically >0.1. Putative nova grains (∼0.1% of all SiC grains) have low 12C/13C ratios of 10, low 14N/15N ratios of 40, and high initial 26Al/27Al ratios of up to 0.2 (Amari et al. 2001a); their origins in the outflows of nova explosions, however, were questioned and SNe were proposed for at least some of the putative nova grains instead (Nittler & Hoppe 2005; Pignatari et al. 2015; Liu et al. 2017a; Hoppe et al. 2018b).
Citation: Marty et al. 2011
Citation function: Background
The GBHT outburst light curves could be very complicated, and while the so-called ‘the main outburst’ could go through the spectral states described above, some GBHTs also show rebrightening episodes during the outburst decay (Kalemci et al. 2013) and/or an increase in brightness several days after the X-ray flux goes below the detection limits of the most observatories that are sometimes defined as mini-outbursts (Chen et al. 1997). A systematic multiwavelength study of GBHTs in the outburst decay by Kalemci et al. (2013) showed that for most of the systems, a rebrightening (secondary maximum or secondary flare) in OIR occurred ∼1–2 weeks after the soft-to-hard transition. Detection of rebrightening during the outburst decay supports the argument that the formation of a compact jet and its interaction with the accretion environment are imprinted on the multiwavelength behaviour of the GBHTs (Buxton & Bailyn 2004; Kalemci et al. 2005, 2013; Buxton et al. 2012; Dinçer et al. 2012; Corbel et al. 2013). Alternatively, the synchrotron radiation from the hot accretion flow model (Poutanen 1998; Veledina et al. 2013), or the irradiation from the secondary star or outer part of the disc could explain the brightness increase in the OIR bands. In contrast, there are limited number of pointed hard X-ray observations for the mini-outbursts (e.g. XTE J1752 − 223, SWIFT J1745 − 26, and V404 Cyg, Chun et al. 2013; Kalemci et al. 2014; Muñoz-Darias et al. 2017) since they have been observed frequently in the soft X-rays and optical (see Chen et al. 1997 for some historical examples, both in black holes and neutron stars). A recent study by Zhang et al. (2019) attempted a classification of the rebrightenings during/after the main outburst decay based on the the available fluxes and applied this scheme to Swift J1753.5 − 0127, which showed a mini-outburst in radio, optical, and X-rays. It can be seen that different flavours exist depending on whether the source reaches quiescence first. Some sources show multiple mini-outbursts after the initial outburst (e.g. XTE J1650 − 500, MAXI J1535 − 571, Tomsick et al. 2003; Cúneo et al. 2020). Although the origin of the mini-outbursts is still debated, an increased mass accretion triggered by the events during the evolution of the primary outburst through heating of the outer parts of the accretion disc (Ertan & Alpar 2002), or the companion star (Augusteijn et al. 1993), is known to be the likely explanations.
Citation: Buxton et al. 2012
Citation function: Similarities
The Bayesian approach is indeed robust and optimal, within the context mentioned above. It focuses on the reconstruction of the LSS within the framework of the standard model of cosmology and for a given data base. However, most previous studies have not addressed the question how consistent is the assumed cosmological model with the observed data. This is not a trivial issue – the model needs to agree with the data so as to provide a solid foundation for the WF/CRs construction. Ideally, one should have started with establishing the agreement of the model with the data and only then reconstruct the LSS in the manner described above. However, history does not always proceeds in a linear fashion. The aim of the paper is to amend that situation and establish the likelihood of peculiar velocities data bases given the standard model of cosmology. The relevant methodology is straightforward and well established. One needs to calculate the likelihood function of the data given the model – namely the probability of the occurrence of the data within the framework of the assumed model (Jaffe & Kaiser 1995; Zaroubi et al. 1995; Hoffman 2001; Press et al. 2007). The likelihood function establishes the goodness-of-fit (GoF) of the data by the model. In the cosmological case and under the assumption of the linear regime, where the velocity field constitutes a random Gaussian vector field and the observational errors are normally distributed, the likelihood analysis amounts to calculating a χ2 statistics. This approach was indeed applied to velocity data bases (Jaffe & Kaiser 1995; Zaroubi et al. 1997, 2001). The application of the likelihood analysis to actual velocity data bases suffers however from one major drawback. The gravitational dynamics of structure formation induces non-linear contributions to the velocities of galaxies. These non-linear corrections render the parameter estimation and GoF analysis to be rather uncertain. The remedy to the problem involves the filtering of small scales to give linearized data. The likelihood analysis can then be safely applied to the linearized data. Here, we suggest such a small-scales filtering procedure and study the extent by which Cosmicflows-2 (CF2; Tully et al. 2013) is compatible with the Λ cold dark matter (ΛCDM) standard model of cosmology.
Citation: Jaffe & Kaiser 1995
Citation function: Uses
Classical imaging techniques were developed in the field to solve the RI reconstruction problem, such as clean and its multiscale variants (Högbom 1974; Bhatnagar & Corwnell 2004; Cornwell 2008; Stewart, Fenech & Muxlow 2011). In particular, clean builds a model image by iteratively removing point source components from the residuals of the acquired data (at each iteration). clean-based algorithms, however, are typically slow (generally requiring computationally demanding major cycles; cf. Clark clean), requiring fine-tuning and supervision, while providing suboptimal imaging quality (see e.g. Li, Cornwell & de Hoog 2011a; Carrillo, McEwen & Wiaux 2012). Another classical technique is the maximum entropy method (MEM) (Ables 1974; Gull & Daniell 1978), extended to RI imaging by Cornwell & Evans (1985). The MEM approach of Cornwell & Evans (1985) developed for RI imaging considers a regularization problem consisting of a relative entropic prior, a (Gaussian) likelihood term and an additional flux constraint. In principle, MEM requires less fine-tuning and supervision compared to clean and can therefore alleviate part of the shortcomings of clean-based algorithms. However, an optimal metric – expressed as an entropy functional – is not known in advance and therefore needs to be chosen individually (Starck et al. 2001; Maisinger, Hobson & Lasenby 2004). Indeed, it is widely known that MEM fails to reconstruct sharp and smooth image features simultaneously. Recently, the theory of compressed sensing (CS) has suggested the use of sparse representation and regularization approaches for the recovery of sparse signals from incomplete linear measurements (Donoho 2006; Candes & Wakin 2008; Candes et al. 2010), which has shown great success. CS techniques based on sparse regularization were ushered into RI imaging for image reconstruction (Suksmono 2009; Wiaux et al. 2009a,b; Wenger et al. 2010; Li et al. 2011a,b; McEwen & Wiaux 2011; Carrillo et al. 2012; Wolz et al. 2013; Carrillo, McEwen & Wiaux 2014; Dabbech et al. 2015; Garsden et al. 2015; Onose et al. 2016; Dabbech et al. 2017; Kartik et al. 2017; Onose, Dabbech & Wiaux 2017; Pratley et al. 2018) and have shown promising results and improvements compared to traditional approaches such as clean-based methods and MEM. In general, such approaches can recover sharp and smooth image features simultaneously (e.g. Carrillo et al. 2012). While sparse approaches have been shown to be highly effective, the best approach to image different sources remains an open question. Algorithms have been developed to scale sparse approaches to big-data (Carrillo et al. 2014; Onose et al. 2016; Cai, Pratley & McEwen 2017a; Kartik et al. 2017; Onose et al. 2017), such as that anticipated from the Square Kilometre Array (SKA1). However, clean-based methods, MEM, and CS-based methods, unfortunately, do not provide any uncertainty quantification about the accuracy of recovered images.
Citation: Maisinger, Hobson & Lasenby 2004
Citation function: Uses