adsabs/FOCAL huggingface dataset:
Recently, Sezestre et al. (2017) investigated this scenario in a quantitative way, using numerical simulations with test particles. The model is relatively straightforward and makes a minimal number of assumptions. It assumes grains released at a given distance of the star andat several epochs. The dynamical behavior of the grains is ruled by the ratio of the pressure to gravitational forces (β). In the case of AU Mic, the stellar wind exceeds the radiation pressure, so that β scales with the stellar mass loss. The authors considered two situations, one where the source of dust was fixed in the system, and one where it was in Kepleriancircular orbit. To match the positions of the features as well as their projected speeds, the grains must be characterized by high β values of atleast 6, which points to a combination of small grains (a few tenths of m) and large stellar mass loss (a few hundreds of 

$\dot{M_{\odot}}$





M
⊙


.



), which is in rather good agreement with previous estimations (Fitzgerald et al. 2007; Schüppler et al. 2015). Although several geometries (position of the source, direction of emission, and periodicity) can still match the observations given that only three epochs were available, the fit of the model to the data indicates that the source of this dust production should be located at ~ 8–28 au from the star, that is, within the belt of planetesimals, the “birth ring”. To introduce the aim of this paper, we present in Fig. 1 a sketch of the hypothetical distribution of the features in the system as pictured from the first observations (Boccaletti et al. 2015), and we assume that they originate from an orbiting parent body. An alternative explanation is proposed by Chiang & Fung (2017), in which the fast-moving features would originate from a collisional avalanche site at the intersection of two belts: the main belt, and a belt resulting from the catastrophic disruption of a large asteroid-likebody. Small dust particles would be released from this place and expelled by the stellar wind. This theory involves several assumptions to qualitatively match the observations, but the dynamical behavior of the grains once released is quite similar to the case of a fixed source as proposed in Sezestre et al. (2017). From the photometry of the HST image, Chiang & Fung (2017) roughly estimated that one dust feature should contain ~ 4 ×10−7 M⊕.
Citation: Fitzgerald et al. 2007
Citation function: Similarities
From these two observational campaigns, the inference on the nature of Sgr A* has been reached on the ground of novel theoretical understandings. A recent important result has been obtained in Matsumoto, Chan & Piran (2020) (see also Tursunov et al. 2020), by re-considering the flare emissions around Sgr A*, emphasizing both, that their motion is not purely geodesic, and establishing a limit on the spin of a putative Kerr BH mass of |a|  0.5. Soon after, in Becerra-Vergara et al. (2020), it was introduced an alternative model to the classical BH in Sgr A* by re-interpreting it as a high concentration of quantum self-gravitating DM made of fermions of about 56 keV c−2 rest mass. This alternative approach can explain the astrometric data of both the S2-star and the G2 object with similar accuracy than the Schwarzschild BH scenario, but without introducing a drag force on G2 which is needed in the BH case to reconcile it with the G2 post-pericentre passage velocity data. An underlying assumption about the nature of such a DM quantum core is its absence of rotation, which is well supported by recent upper bounds on the spin of the central BH of a  0.1, based on the spatial distribution of the S-stars (Ali et al. 2020; Fragione & Loeb 2020; Peißker et al. 2020). The first results obtained in Becerra-Vergara et al. (2020) within the DM scenario have been further extended in Becerra-Vergara et al. (2021) by considering the 17 best resolved stars orbiting Sgr A*, achieving an equally good fit than in the BH paradigm. Remarkably, such a dense DM core is the central region of a continuous distribution of DM whose diluted halo explains the Galactic rotation curves (Argüelles et al. 2018; Becerra-Vergara et al. 2020, 2021). Core-halo DM distributions of this kind are obtained from the solution of the Einstein equations for a self-gravitating, finite-temperature fluid of fermions in equilibrium following the Ruffini–Argüelles–Rueda (RAR) model (Ruffini, Argüelles & Rueda 2015; Argüelles et al. 2016, 2018, 2019, 2021; Gómez et al. 2016; Gómez & Rueda 2017; Becerra-Vergara et al. 2020, 2021; Penacchioni et al. 2020; Yunis et al. 2020). These novel core-halo DM profiles, as the ones applied in this Letter, have been shown to form and remain stable in cosmological time-scales, when accounting for the quantum nature of the particles within proper relaxation mechanisms of collisionless fermions (Argüelles et al. 2021). There are other alternative scenarios for Sgr A* involving a compact object of quantum nature, e.g. a boson star composed of ultralight scalars (see e.g. Torres et al. 2000). However, unlike the ∼50–345 keV c−2 fermionic DM RAR solutions, those boson stars do not explain the Galaxy rotation curves.
Citation: Peißker et al. 2020
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By combining observational constraints on the dynamics in galaxies with constraints from the Solar system, Milgrom (1983a) corrected the theory of gravitation at low acceleration, which could be a consequence of the quantum vacuum (Milgrom 1999; Pazy 2013; Smolin 2017; Verlinde 2017). In analogy with Newtonian dynamics, a non-relativistic Milgromian gravity theory (MOND) can be constructed by setting up a Lagrangian which, upon extremization of the action, yields a generalized Milgromian Poisson equation. Two such Lagrangians have been proposed, called AQUAL (Bekenstein & Milgrom 1984) and QUMOND (Milgrom 2010). The latter, which we adopt hereafter, yields the following generalized Poisson equation,
(1)$$\begin{eqnarray}
\Delta \Phi (\vec {x}) = 4\pi G\rho _{\rm b} (\vec {x}) + \vec {\nabla } \cdot [\tilde{v}(\left|\vec{\nabla } \phi \right|/a_0)\vec {\nabla } \phi (\vec {x})],
\end{eqnarray}$$or,
(2)$$\begin{eqnarray}
\Delta \Phi (\vec {x}) = 4\pi G [\rho _{\rm b} (\vec {x}) + \rho _{\rm ph}(\vec {x})],
\end{eqnarray}$$where $\rho _{\rm b}(\vec{x})$ is the baryonic density, $\phi (\vec{x})$ is the Newtonian potential that fulfils the standard Poisson equation, $\Delta \phi (\vec{x})$  = 4πG$\rho _{\rm b}(\vec{x})$ and Milgrom’s constant a0$\approx \rm 1.2 \times 10^{-10} \ ms^{-2} \approx 3.8 \ pc \ Myr^{-2}$. The phantom dark matter (PDM) density, $\rho _{ph}(\vec{x})$, is not a real density distribution but a mathematical function that arises out of the non-linearity of the Poisson equation. $\Phi (\vec{x})$ is the total gravitational potential from which the accelerations follow, $\vec{a} = -\vec{\nabla } \vec{\Phi }$, and $\tilde{v}(y)$ is a transition function characterizing the theory (see Milgrom 2008, 2010, 2014; Famaey & McGaugh 2012; and Banik & Zhao 2022 for detailed reviews on the theory). $\tilde{v}(y)$ has the limits,
(3)$$\begin{eqnarray}
\tilde{v}(y) \rightarrow 0 \,\,\rm {for}\,\, \it y\,\, \gg \rm 1 \,\,\rm {and}\,\, \it \tilde{v}(\it y)\,\, \rightarrow \it y^{\rm -1/2}\,\, \rm {for}\,\, \it y\,\, \ll \rm 1.
\end{eqnarray}$$The above formulation deals only with linear differential equations and is shown to emerge as a natural modification of a Palatini-type formulation of Newtonian gravity. It is a member of a larger class of bipotential theories (quasi-linear formulation of MOND; QUMOND Milgrom 2010). Bekenstein & Milgrom (1984) also noted a correspondence with some theories of quark confinement using a different form of the function $\tilde{v}$.
Citation: Milgrom 2010
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Citation: Milgrom; 2010
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Citation: Milgrom 2010
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When considering only spaxels with S/N > 5 for each emission line contributing to a given BPT diagram, we are left only with spaxels on the galaxy discs of CGCG097–079 and CGCG097–073 and their immediate surroundings where the emission line flux is high enough to obtain robust line ratios in individual spaxels. We present these results in Fig. 8. The top panel shows the distribution of individual spaxels in the aforementioned BPT diagrams. Each spaxel is colour coded by its distance from the lines separating the region dominated by photo-ionization from the one dominated by active galactic nuclei (AGNs) or shocks, following the separation of Kauffmann et al. (2003). The distributions of line ratios from nuclear spectra of a sample of 50 000 SDSS galaxies at 0.03  z  0.08 whose emission lines are detected at S/N > 5 (Fossati et al. 2016) are shown with grey contours. The innermost to outermost contours include the 25, 50, 75, and 98 per cent of the full data set, respectively. However, this SDSS sample only represents the nuclear properties of galaxies which might be different from their outskirts which are likely providing most of the stripped gas. To overcome this possible issue, we add to the diagnostic diagrams the same density contours from a sample of individual spaxels from the DR17 of the Mapping Nearby Galaxies at APO (MaNGA) IFU survey of ∼10 000 galaxies (Abdurro’uf et al. 2021). For each BPT diagram, we selected spaxels outside the effective radius (R > 1 Re) of each individual galaxy whose emission lines are detected at S/N > 5. This sample includes roughly half a million spaxels in the BPT diagram using the fainter [O i] line and roughly 2 million spaxels in the other two BPT diagrams. Density contours from this sample (at the same levels mentioned above) are shown in pink in Fig. 8. We also verified that by using spaxels from the entire galaxy discs, the density contours would appear very similar to the SDSS sample, due larger weight given to the inner parts of the discs. Despite the differences seen in these two reference samples, the BPT diagnostic made using [O i]/H α shows enhanced [O i]/H α in the RPS tails that appear not to be typical neither of the galaxy nuclei nor of their disc outskirts. We will discuss this point in a more quantitative fashion in Section 5.1. In the middle and bottom panels, we show the spatial distribution of the spaxels from the two galaxies, with points colour coded as above.
Citation: Fossati et al. 2016
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Small fluctuations δ in the distribution of dark matter grow, as long as they are in the linear regime |δ| ≪ 1, according to the growth function D+(a) (Linder & Jenkins 2003; Wang & Steinhardt 1998),
(3)
\begin{equation}
\frac{\mathrm{d}^2}{\mathrm{d}a^2}D_+(a) + \frac{2-q}{a}\frac{\mathrm{d}}{\mathrm{d}a}D_+(a) - \frac{3}{2a^2}\Omega _\mathrm{m}(a) D_+(a) = 0,
\end{equation}
and their statistics is characterized by the spectrum $\langle \delta (\boldsymbol {k})\delta ^*(\boldsymbol {k}^\prime )\rangle = (2\pi )^3\delta _{\rm D}(\boldsymbol {k}-\boldsymbol {k}^\prime )P_\delta (k)$. Inflation generates a spectrum of the form $P_\delta (k)\propto k^{n_s}T^2(k)$ with the transfer function T(k) (Eisenstein & Hu 1999, 1998) which is normalized to the variance $\sigma _8^2$ smoothed to the scale of 8 Mpc h−1,
(4)
\begin{equation}
\sigma _8^2 = \int _0^\infty \frac{k^2\mathrm{d}k}{2\pi ^2}\, W^2(8\,{\rm }\mathrm{Mpc}\, h^{-1}\times k)\,P_\delta (k),
\end{equation}
with a Fourier-transformed spherical top-hat W(x) = 3j1(x)/x as the filter function. From the CDM spectrum of the density perturbation, the spectrum of the Newtonian gravitational potential Φ can be obtained,
(5)
\begin{equation}
P_\Phi (k; \chi ) = \left(\frac{3 \Omega _\mathrm{m} H_0^2}{2} \right)^2 k^{-4} P_\delta (k; \chi ) \propto \left(\frac{3\Omega _\mathrm{m}H_0^2}{2}\right)^2\,k^{n_s-4}\,T(k)^2,
\end{equation}
by applying the comoving Poisson equation $\Delta \Phi = \frac{3 \Omega _\mathrm{m}H_0^2}{2} \delta$ for deriving the gravitational potential Φ from the density δ. With equation (3) yielding a solution for the homogeneous growth of the density contrast. It should be noted that velocities at linear order are obtained from the continuity equation,
(6)
\begin{equation}
\boldsymbol {\nabla } \cdot \boldsymbol {\upsilon } = - a \dot{ \delta },
\end{equation}
such that in Fourier space,
(7)
\begin{equation}
\boldsymbol {\upsilon }_{\rm k} = a H(a) \frac{\mathrm{d}\ln ( D_+)}{\mathrm{d}\ln (a)} \frac{ \boldsymbol {k}}{k^2} \boldsymbol { \delta }_{\rm k}.
\end{equation}
Citation: Eisenstein & Hu 1999
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The observed X-ray emission from AGNs may be modified by line-of-sight obscuration, resulting in lower observed X-ray fluxes than those expected from the α
OX–L
2500 Å relation. A common approach to parameterize the amount of X-ray weakness uses the Δα
OX parameter, defined as the difference between the observed α
OX value and the α
OX value expected from the α
OX–L
2500 Å relation; Δα
OX = − 0.3838 thus corresponds to a factor of X-ray weakness of 10 at rest-frame 2 keV. Type 2 AGNs are generally X-ray obscured, likely due to the dusty “torus” (e.g., Netzer 2015; Hickox & Alexander 2018). Type 1 AGNs may also have X-ray obscuration from largely dust-free gas.
13


13
Similar obscuration from dust-free gas might also be present in some of the type 2 AGNs, though usually not distinguishable from the torus obscuration. For example, broad absorption line (BAL) quasars, which are characterized by blueshifted broad UV absorption lines (e.g., C iv
λ1549), generally show weak X-ray emission (e.g., Gallagher et al. 2002, 2006; Fan et al. 2009; Gibson et al. 2009). One frequently adopted physical model for BAL quasars is the disk wind model, where the observed BALs originate from an outflowing equatorial wind launched from the accretion disk and radiatively driven by UV-line pressure (e.g., Murray et al. 1995; Proga et al. 2000; Matthews et al. 2016). This model usually invokes “shielding” gas between the wind and nucleus or a clumpy wind (e.g., Baskin et al. 2014; Matthews et al. 2016; Giustini & Proga 2019) to provide obscuration of the nuclear extreme-UV (EUV) and X-ray radiation, which might otherwise overionize the wind and hamper radiative acceleration. BAL quasars are considered generally to have larger inclination angles than non-BAL quasars, with the line of sight to the UV continuum region of the accretion disk intersecting the wind, leading to the observed BALs. The line of sight to the X-ray-emitting corona, though not necessarily the same as the UV line of sight, is likely also through the shielding gas or the clumpy wind, resulting in the often-observed X-ray weakness (e.g., Figure 1 of Luo et al. 2013). Besides BAL quasars, a small fraction (5.8% ± 0.7%) of non-BAL type 1 quasars have been found to be X-ray weak, likely due to absorption (e.g., Pu et al. 2020). They may share a similar nature to the BAL quasars; they do not show any UV BALs, probably due to geometric effects (e.g., small inclination angles) or a low velocity of the wind along the UV line of sight (e.g., Giustini & Proga 2019).
Citation: Gibson et al. 2009
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Citation: Gallagher et al.; 2006
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The recently observed ultra-diffuse galaxy NGC 1052-DF2 with a dark matter mass 400 times smaller than theoretically expected based on an internal velocity dispersion of 




σ
intr

=
3
.

2

+
5.5


−
3.2




$ \sigma_\mathrm{{intr}}=3.2_{+5.5}^{-3.2} $


 km s−1, seems to support the existence of dark matter-free galaxies in our Universe (van Dokkum et al. 2018a). van Dokkum et al. (2018b) derived a revised internal velocity dispersion of 




σ
intr

=
7
.

8

+
5.2


−
2.2




$ \sigma_\mathrm{{intr}}=7.8_{+5.2}^{-2.2} $


 km s−1 using ten GCs surrounding this galaxy. Danieli et al. (2019) measured a stellar velocity dispersion of 




σ
stars

=
8
.

5

+
2.3


−
3.1




$ \sigma_\mathrm{{stars}}=8.5_{+2.3}^{-3.1} $


 km s−1 with the Keck Cosmic Web Imager (KCWI). The high relative velocity to the nearby massive elliptical galaxy NGC 1052 underpins the theory that this observed dark matter-lacking galaxy is indeed a TDG. However, Martin et al. (2018) revised the internal velocity of NGC 1052-DF2 to a 90 percent upper limit of 17.3 km s−1 corresponding to a mass-to-light ratio of M/LV   8.1 Υ⊙, consistent with many Local Group dwarf galaxies. Emsellem et al. (2019) obtain M/LV in the range 3.5−3.9(±1.8) Υ⊙ using the Jeans model if located at D = 20 Mpc. This result would be close to the 2σ upper limit of the study from Martin et al. (2018). The lack of dark matter and the unusual high luminosity of ten globular cluster-like objects surrounding this galaxy only holds if NGC 1052-DF2 is located at a distance of around 20 Mpc (van Dokkum et al. 2018a). Danieli et al. (2019) confirmed that DF2 is dark matter deficient and concluded that it is an outlier to dwarf galaxies of the Local Group. In contrast to that, Trujillo et al. (2019) derived a revised distance to NGC 1052-DF2 of D = 13.0 ± 0.4 Mpc based on five redshift-independent measurements including the tip of the red giant branch and the surface brightness fluctuation method. Thus, NGC 1052-DF2 would be a dwarf galaxy with an ordinary dark matter content Mhalo/Mstellar >  20 and a normal globular cluster population. Meanwhile, van Dokkum et al. (2019) reported that the dwarf galaxy NGC 1052-DF4 also lacks dark matter and is found at a distance of D = 20 Mpc.
Citation: Danieli et al. (2019); Danieli et al. (2019)
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An estimate of a sputtering cross-section can be inferred from our measurements with σs ≈ V∕d, where V is the volume occupied by 

${Y}_{\textrm{s}}^{\infty}$Ys∞
 molecules and d the depth of sputtering. 

$\sigma_{\textrm{s}}\approx {Y}_{\textrm{s}}^{\infty}/l_{\textrm{d}}/\textrm{ml}$σs≈Ys∞/ld/ml
, where ml is the number of CO or CO2 molecules cm−2 in a monolayer (about 6.7 × 1014 cm−2 and 5.7 × 1014 cm−2, respectively,with the adopted ice densities). As is shown in Table 1, the sputtering radius rs would therefore be about 1.26 to 2.12 times larger than the radiolysis destruction radius rd in the case of the CO2 ice, and 2.03 to 2.36 for CO in the considered energy range (~0.5-1 MeV/u). The net radiolysis is the combined effect of the direct primary excitations and ionisations, the core of the energy deposition by the ion, and the so-called delta rays (energetic secondary electrons) travelling at much larger distances from the core; that is, several hundreds of nanometres at the considered energies in this work (e.g. Mozunder et al. 1968; Magee & Chatterjee 1980; Katz et al. 1990; Moribayashi 2014; Awad & Abu-Shady 2020). The effective radiolysis track radius that we calculate is lower than the sputtering one, which points towards a large fraction of the energy deposited in the core of the track. The scatter on the ratio of these radii is due to the lack of more precise data. It nevertheless allows to put a rough constraint on the estimate of Nd in the absence of additional depth measurements, with 

${N}_{\textrm{d}} \lesssim {Y}_{\textrm{s}}^{\infty}/\sigma_{\textrm{d}}$Nd≲Ys∞/σd
. If the rs∕rd ratio is high, a large amount of species come from the thermal sublimation of an ice spot less affected by radiolysis, and the fraction of ejected intact molecules is higher. The aspect ratio corresponding to these experiments evolves between about ten and twenty for CO2 and CO, whereas for water ice at a stopping power of Se ≈ 3.6 × 103eV∕1015 H2 O molecules cm−2, we show that it is closer to one (Dartois et al. 2018). The depth of sputtering is much larger for CO and CO2 than for H2O at the same energy deposition, not only because their sublimation rate is higher, but also because they do not form OH bonds. For complex organic molecules embedded in ice mantles dominated by a CO or CO2 ice matrix, with the lack of OH bonding and the sputtering for trace species being driven by that of the matrix (in the astrophysical context), the co-desorption of complex organic molecules present in low proportions with respect to CO/CO2 cannot only be more efficient, but will thus arise from deeper layers.
Citation: Mozunder et al. 1968
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Citation: Dartois et al. 2018
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Bolometric magnitudes, 





, are estimated as the sum of the 





-band magnitudes, 





, bolometric correction (





), and DMs, i.e., 





 = 





−





+





-DM. 





 are adopted from the work of Levesque et al. (2005), which is based on MARCS models. The new temperature scale by Davies et al. (2013) agrees within ±100 K with that of Levesque et al. (2005). Errors in the 





 values are calculated by propagation. 





 magnitude errors are provided in the 2MASS catalog (0.02 mag in average); errors in 





 are described in Section 3.2 (0.02 mag on average); errors in 





 are conservatively assumed to be 0.5 mag—the difference between the 





 values provided by Levesque et al. (2005) for an M0Iab and M2Iab star amounts to ≈0.1 mag, while the typical difference between their 





 values is 0.5 mag (e.g., Verhoelst et al. 2009); rare supergiant Ia can be more than 1 mag brighter. Adopted distance moduli, DMs, are those of Messineo et al. (2016), who estimated distances of 68 (out of 94) targets using extinction as indicator of distance, and calibrating the extinction–distance relation with clump stars surrounding the target (see also Drimmel et al. 2003; Messineo et al. 2014). Errors in the DM values range from 0.12 to 0.36 mag; they have been estimated as a sum of three terms: the uncertainty of the absolute magnitude of clump stars (≈0.11 mag), the error of the centroid of the Gaussian (0.04–0.25 mag, 





 of the Gaussian divided by the square-root of the number of enclosed stars), and the uncertainty in the reddening of clump stars (





 ≈ 0.06 mag, taken as the half-width of the J − K bin times 0.537); only CMDs with a well visible trace were considered. To verify these bolometric magnitudes, which are based only on one magnitude (





) plus the bolometric corrections by Levesque et al. (2005), we calculated estimates of bolometric magnitudes (





) by directly integrating under their stellar energy distribution with the collected infrared measurements (see also Ortiz et al. 2002; Messineo et al. 2004, 2014). We extrapolated to zero the flux on the blue part (from 0 to 1.2 μm) of the spectrum with a blackbody, and to the red part (beyond 12–25 μm) with a linear fit passing through the last two available flux measurements. The differences between the two estimates of bolometric magnitudes yield an average of 0.09 mag with a σ = 0.03 mag. We obtained that the red extrapolation contributed only −0.004 to 0.002 mag to the total 





; the blue extrapolation added −0.85 mag (for the direct integration only JHKs magnitudes were used and not the DENIS I magnitudes). When including the DENIS I magnitudes, i.e., blue from 0 to 0.8 μm and green from 0.8 to 12–25 μm, we obtained that the contribution of the blue extrapolation to the total 





 would drop to −0.18 mag—extinction in the I-band 





 is assumed to be 6.8 times 





(Messineo et al. 2005). Table 7 lists the inferred values of 





, bolometric magnitudes, and adopted DM values.
Citation: Messineo et al.; 2014
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Citation: Messineo et al. 2014
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