adsabs/FOCAL huggingface dataset:
In our study, the central engine of GRB 100814A is assumed to be a newborn magnetar with spin evolution. The early-time optical shallow decay phase and X-ray plateau come from the initial spin-down process and the late-time optical rebrightening results from the enhanced energy injection generated by the spinning up of the magnetar. When calculating the dynamic process of the multi-band afterglow of GRB 100814A, we use the Equations for beamed GRB outflows developed by Huang et al. (1999, 2000) considering continuous energy injection from the central magnetar with spin evolution. The bulk Lorentz factor (γ) of the shocked interstellar medium is described by the following differential Equation (for details, see Huang et al. 1999):
6





where Mej is the initial ejecta mass, m is the swept-up interstellar medium mass, and  is the radiative efficiency. When the energy injection due to the magnetic dipole radiation from the central magnetar is taken into account, the above differential Equation can be modified to be (Kong & Huang 2010; Geng et al. 2013)
7





where 





 can be calculated from Equation (1). In our calculations, several effects, such as lateral expansion, electron synchrotron cooling, and equal arrival time surfaces, have been incorporated. In the absence of electron synchrotron cooling, the comoving frame distribution of the shock-accelerated electrons is usually assumed to be a power-law function, 





, where p is the power-law index. After considering the electron synchrotron cooling effect, the distribution function will be changed to 





 for electrons above a critical Lorentz factor 





 (Sari et al. 1998). For detailed description of electron distribution, see Huang et al. (2000) and Huang & Cheng (2003). We neglect the adiabatic pressure and energy losses due to adiabatic expansion, which might also have a minor effect on the dynamical evolution of the blast wave (van Eerten et al. 2010; Pe’er 2012; Nava et al. 2013). For radiative process, the multi-band afterglow emission mainly comes from synchrotron radiation of the shock-accelerated electrons due to their interaction with the magnetic field (Sari et al. 1998; Sari & Piran 1999). We present our numerical results below.
Citation: Geng et al. 2013
Citation function: Uses; Uses
For the first step, we adopted the nucleosynthesis calculation for around 4070 nuclei performed by Fujimoto et al. (2007), which was cooled using the adiabatic expansion modeled from Freiburghaus et al. (1999) to provide the elemental composition ratios of nuclei for Y
e = 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, and 0.45. This estimation assumes that the initial environment has a temperature of 9 × 109 K, a radius of 100 km, entropy per baryon of 10 k
B, where k
B is the Boltzmann constant, and a velocity of 2 × 109  cm s−1, along with the initial abundances of the 4070 nuclei in nuclear statistical equilibrium. As a result, the calculation provides the mass fractions at t = 1 yr evaluated with the nuclear reaction network (network A in Fujimoto et al. 2007), by using Y
e = 0.10–0.45 in steps of 0.05. To set up the mass distribution of nuclei for the NSMs at t = 1 yr, we blended the nuclei with the mass fraction using the Y
e provided in Wanajo et al. (2014). Specifically, the fractions are 4.54%, 4.85%, 14.6%, 29.7%, 10.3%, 25.1%, 10.5%, and 0.33% for Y
e = 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, and 0.45, respectively. Note that this Y
e-fraction model by Wanajo et al. (2014) describes a slightly less neutron-rich environment than those by the recent dynamical-ejecta models after the kilonova observations of the gravitational event GW170817, such as four models in Kullmann et al. (2022) under two kinds of equations of state, density dependent 2 (DD2; Hempel & Schaffner-Bielich 2010; Typel et al. 2010), and SFHo (Steiner et al. 2013). In this paper, we adopted the first one by Wanajo et al. (2014) as a pessimistic case for the r-process site, but changing the Y
e-fraction models does not change the conclusions from the gamma-ray spectra as tested in Section 3. Figure 1 shows the mass fraction of multiple nuclei at t = 1 yr generated in an NSM case, information that is given in the table of nuclides (neutron number N versus atomic number Z). Using the same data set, Figure 2 summarizes the distribution of nuclei with mass number A at t = 1 yr, showing the contributions of Y
e. This plot demonstrates that the environment with lower Y
e contributes to the generation of heavier elements.
Citation: Fujimoto et al. (2007)
Citation function: Uses; Uses
Citation: Fujimoto et al. 2007
Citation function: Uses; Uses
In this section, we study the feasibility of detecting non-thermal SZ with future CMB experiments. The distortion in intensity Iν of CMB at a frequency ν and towards a localized concentration of hot electrons can be written as,
(19)$$\begin{eqnarray*}
\Delta I_{\nu }=\Delta I_{\rm {y}}+\Delta I_{\rm {\mu }}+\Delta I_{\rm {kSZ}}+\Delta I_{\rm {rSZ}}+\Delta I_{\rm {NT}},
\end{eqnarray*}$$where ΔIy is the typically dominant non-relativistic y distortion, ΔIμ is the μ distortion, ΔIkSZ is the temperature shift of the CMB blackbody due to kSZ effect (Sunyaev & Zeldovich 1980), ΔIrSZ is the relativistic SZ signal from a massive galaxy cluster, and ΔINT is the non-thermal SZ distortion. The expression for ΔIy, ΔIμ, and ΔIkSZ are given by (Zeldovich & Sunyaev 1969; Sunyaev & Zeldovich 1970; Illarionov & Siuniaev 1975),
(20)$$\begin{eqnarray*}
\Delta I_{\rm {y}}=y\frac{2\rm {h}{\nu }^3}{\rm {c^2}}\frac{x\rm {e^x}}{(\rm {e^x}-1)^2}\left[x\frac{\rm {e^x}+1}{\rm {e^x}-1}-4\right]
\end{eqnarray*}$$(21)$$\begin{eqnarray*}
\Delta I_{\rm {\mu }}=\mu \frac{2\rm {h}{\nu }^3}{\rm {c^2}}\frac{\rm {e^x}}{(\rm {e^x}-1)^2}\left[\frac{x}{2.19}-1\right]
\end{eqnarray*}$$(22)$$\begin{eqnarray*}
\Delta I_{\rm {kSZ}}=\left(\frac{\Delta T}{T}\right)\frac{2\rm {h}{\nu }^3}{\rm {c^2}}\frac{\rm {e^x}}{(\rm {e^x}-1)^2}
.
\end{eqnarray*}$$The y-distortion can have contribution from both pre-recombination Universe as well as post-recombination Universe while μ-distortion can only be created at redshifts greater than 2 × 105. The SZ spectrum from electrons with energy ≳keV is obtained by including Klein–Nishina corrections for Compton scattering which can be calculated perturbatively as an expansion in $\frac{T_{\rm {e}}}{m_{\rm {e}}}$ (Challinor & Lasenby 1998; Itoh, Kohyama & Nozawa 1998; Sazonov & Sunyaev 1998; Dolgov et al. 2001). For example, the temperature of massive galaxy cluster with mass 1014 times solar mass can be ∼5 keV (Erler et al. 2018), and with a typical y ∼ 10−5.
Citation: Illarionov & Siuniaev 1975
Citation function: Uses; Uses
Stars with masses 130 M
⊙ ≲ M
ZAMS ≲ 250 M
⊙ are subject to the pair instability, which disrupts them completely, and hence no BH forms. Stars with M
ZAMS ≳ 250 M
⊙ can collapse directly to IMBHs with a mass ≳135 M
⊙. Thus, in the standard picture, there should be an upper stellar-mass BH gap in the range [65, 135] M
⊙, and any BHs observed in this range (e.g., the primary BH of GW190521) have to form via other formation channels—for example, through hierarchical coalescence of smaller BHs or direct collapse of a stellar merger between an evolved star and a main-sequence companion (e.g., Quinlan & Shapiro 1989; Portegies Zwart & McMillan 2000; Ebisuzaki et al. 2001; Miller & Hamilton 2002; O’Leary et al. 2006; Gerosa & Berti 2017; Antonini et al. 2019; Di Carlo et al. 2019, 2020; Rodriguez et al. 2019; Gayathri et al. 2020a; Kimball et al. 2021; Mapelli et al. 2021). However, the exact mass boundaries of the gap depend on parameters that are uncertain. For example, the 12C(α, γ)16O nuclear reaction rate, which converts carbon to oxygen in the core, can affect the boundary significantly (Takahashi 2018; Farmer et al. 2020; Costa et al. 2021; Woosley & Heger 2021). Here, to better determine whether future GW observations will be able to observe BHs in the mass gap, we recompute the mass-gap boundaries with updated 12C(α, γ)16O reaction rates and increased mass and temporal resolution. The complexity of this system has made a reliable analysis of the reaction a decades-old challenge.
7


7
The reaction rate for 12C(α, γ)16O is determined by the quantum structure of the compound nucleus 16O as an α cluster system. It is characterized by the interfering ℓ = 1 waves of the J

π
 = 1− resonances and sub-threshold levels defining an E1 component for the reaction cross section as well as by the ℓ = 2 components and interference from broad J

π
 = 2+ resonances and the nonresonant E2 external capture to the ground state of 16O. In addition to these two main E1 and E2 ground-state components, transitions to higher lying excited states occur that also add to the total cross section (see, e.g., Buchmann & Barnes 2006; deBoer et al. 2017). The rapidly declining cross section at low energies has prohibited a direct measurement of the reaction at stellar temperatures, and the reaction rate is entirely based on the theoretical analysis and extrapolation of the experimental data toward lower energies. The rate newly derived by deBoer et al. (2017), using a multichannel analysis approach, derives for the first time a reliable prediction for the interference patterns within the reaction components by taking into account all available experimental data sets that cover the near-threshold energy range of the 12C(α, γ)16O process.
Citation: Rodriguez et al. 2019
Citation function: Background
Citation: Mapelli et al. 2021
Citation function: Background; Background
Another possible explanation for the peculiar solar composition is that some of the dust in the pre-solar nebula was radiatively cleansed by luminous hot stars in the solar neighbourhood before the formation of the Sun and its planets. This dust-cleansing scenario is supported by the finding that the open cluster M67 seems to have a chemical composition closer to the solar composition than most solar twins (Önehag et al. 2011, hereafter O11 and Önehag, Gustafsson & Korn 2014, hereafter O14). They suggested that the proto-solar nebula was dust-cleansed by massive stars, similar to what happened for the proto-cluster cloud of M67, while the majority of solar twins in the field would presumably have formed in less massive clusters where no nearby high-mass star (≥15 M⊙) was formed. M67 offers the possibility for studying the solar-type stars in a dense cluster environment. This cluster has about solar metallicity ([Fe/H] in the range −0.04 to +0.03, e.g. Hobbs & Thorburn 1991; Yong, Carney & Teixera de Almeida 2005; Randich et al. 2006; Pasquini et al. 2008). The age of M67 is also comparable with that of the Sun: 3.5–4.8 Gyr (Yadav et al. 2008). Pasquini et al. (2008) listed 10 solar-twin candidates in M67, including M67-1194 which hosts a hot Jupiter with a period of 6.9 d and a minimum mass of 0.34 MJup (Brucalassi et al. 2014). M67-1194 was studied by O11 and re-visited by O14. They found that unlike nearby solar twins, which were systematically analysed by Meléndez et al. (2009) and Ramírez, Meléndez & Asplund (2009), the chemical composition of M67-1194 is more solar-like and therefore suggested that the Sun may have been formed in a similar cluster environment, perhaps even in M67. While this scenario is plausible when considering chemical abundances and ages, the dynamics are problematic: the Sun has an orbit close to the Galactic plane, while M67 is presently some 450 pc above the plane. The probability that the Sun, if formed in M67 with an orbit similar to the present cluster orbit, was scattered or diffused out of the cluster into the present solar orbit, is found to be quite low, if the existence of the outer planetary system is taken into account (Pichardo et al. 2012). Gustafsson et al. (2016) suggested that the high-altitude metal-rich clusters (such as M67) were formed in orbits close to the Galactic plane and later scattered to higher orbits by interaction with giant molecular clouds and spiral arms. Thus, it is possible, though not very probable, that the Sun formed in such a cluster before scattering occurred. Currently, only one solar twin in M67 (M67-1194) was spectroscopically analysed with high precision (∼0.02 dex). It is thus crucial to analyse the chemical composition of additional solar-type stars in M67 of very high precision.
Citation: Yadav et al. 2008
Citation function: Compare/Contrast
Let us consider a SMBH with mass MBH kicked with velocity vk from the galactic centre (r = 0). The SMBH will be ejected from the galactic halo if vk exceeds the escape velocity of the system:

(33)

\begin{eqnarray}
v_{\rm esc}= \sqrt{2G\left( \frac{M_{\rm BCG}}{r_{\rm H}} + c \,g_{\rm c} \frac{M_{\rm DM}}{r_{\rm v}}\right)} \,.
\end{eqnarray}

If vk  vesc, the SMBH will stop at a distance rmax from the centre. Gualandris & Merritt (2008) showed that the maximum displacement rmax can be estimated simply through energy conservation neglecting star friction (see their fig. 2):

(34)

\begin{eqnarray}
\frac{1}{2} v_{\rm k}^{2}+\phi (0)=\phi (r_{\rm max})\,.
\end{eqnarray}

The initial displacement is reached in a time which is typically 100 times smaller than the sinking time-scale (Gualandris & Merritt 2008) and will be therefore neglected. Here, we estimate the time needed to sink back to r = 0 integrating the DF equation on quasi-circular orbits. The frictional force exerted on to the black hole is given by (e.g. Binney & Tremaine 1987)

(35)

\begin{eqnarray}
F(r)=\frac{4 \pi G^2 M_{\rm BH}^2 \rho (r)\,\xi (r) \ln \Lambda }{v_{\rm c}^2(r)}\,,
\end{eqnarray}

where $v_{\rm c}(r)=\sqrt{r\, {\rm d}\phi /{\rm d}r}$ is the circular velocity, ln Λ is the Coulomb logarithm and the factor ξ(r) depends on the stellar velocity distribution. We take ln Λ = 2.5, as observed by Gualandris & Merritt (2008) in the very first phase of their simulated orbits (see also Escala et al. 2004). We assume the velocity distribution to be locally Maxwellian, with velocity dispersion σ(r). Although not exact, the Maxwellian distribution is approached as a consequence of collisionless relaxation processes (Lynden-Bell 1967). Under this assumption, the ξ factor in equation (35) reads (Binney & Tremaine 1987)

(36)

\begin{eqnarray}
\xi (r) = {\rm erf}\left[\frac{v_{\rm c}(r)}{\sqrt{2} \sigma (r)}\right] - \sqrt{\frac{2}{\pi }}\frac{v_{\rm c}(r)}{\sigma (r)}\exp \left[-\frac{v_{\rm c}^2(r)}{2\sigma ^2(r)}\right]\,.
\end{eqnarray}

The velocity dispersion σ(r) is computed from our galactic potential using the expression provided by Binney (1980) when isotropy is assumed. The frictional force F(r) is tangential and directed opposite to the SMBH velocity. The SMBH angular momentum L(r) = MBHrvc(r) is lost at the rate dL(r)/dt = −rF(r) by Newton's third law, causing the SMBH to slowly inspiral while remaining on a quasi-circular orbit. The DF time-scale, over which the SMBH sinks back to the galactic centre r = 0 from its initial position rmax , is thus given by6
(37)

\begin{eqnarray}
t_{\rm DF}=-\int _{r_{\rm max}}^0 \frac{\mathrm{d} L(r)}{\mathrm{d}r} \frac{1}{r F(r)} \mathrm{d}r\,.
\end{eqnarray}
Citation: Binney & Tremaine 1987
Citation function: Uses; Uses
Citation: Binney & Tremaine 1987
Citation function: Uses; Uses
We consider the MW satellites with parallax and proper-motion measurements from Gaia DR2 (Gaia Collaboration et al. 2018c) and the corresponding galactocentric coordinates and velocities computed and documented by Riley et al. (2019, their Table A.2; see also Li et al. 2020) and Vasiliev & Belokurov (2020). Of these, we only consider the satellites with known dynamical mass estimates (Simon & Geha 2007; Bekki & Stanimirović 2009; Łokas 2009; Erkal et al. 2019). Adopting the initial conditions for galactocentric positions (R, z, ϕ) and velocities (v

R
, v

z
, v

ϕ
) as the median values quoted by Riley et al. (2019) and Vasiliev & Belokurov (2020), we simulate the orbits of the galaxies in the combined gravitational potential of the MW halo, disk, and bulge, which are respectively modeled by a spherical NFW (Navarro et al. 1997) profile (virial mass M

h
 = 9.78 × 1011
M
⊙, scale radius r

h
 = 16 kpc, and concentration c = 15.3), a Miyamoto−Nagai (Miyamoto & Nagai 1975) profile (mass M

d
 = 9.5 × 1010
M
⊙, scale radius a = 4 kpc, and scale height b = 0.3 kpc), and a spherical Hernquist (1990) profile (mass M

b
 = 6.5 × 109
M
⊙ and scale radius r

b
 = 0.6 kpc).
5


5
Our MW potential is similar to GALPY MWPOTENTIAL2014 (Bovy 2015) except for the power-law bulge, which has been replaced by an equivalent Hernquist bulge. The total mass of our fiducial MW model is thus 1.08 × 1012
M
⊙. We evolve the positions and velocities of the satellites both forward and backward in time from the present day, using a second-order leap-frog integrator. For simplicity, we ignore the effect of dynamical friction.
6


6
Dynamical friction might play an important role in the orbital evolution of massive satellites like the Large Magellanic Cloud (LMC) and Sgr, pushing their orbital radius farther out in the past. From each individual orbit, we note the time, t
cross, when the satellite crosses the disk (i.e., crosses z = 0) and record the corresponding distance, x
P, from the Sun, which we integrate backward/forward in time using a purely circular orbit up to t
cross. We also record the velocity, 



vP=vR2+vz2+vϕ2

, and the angle of impact with respect to the disk normal, 



θP=cos−1(vz/vP)

. Finally, we compute the disk response to the satellite encounter using Equation (49). Results are summarized in Table 1 and Figures 6 and 7.
Citation: Miyamoto & Nagai 1975
Citation function: Uses; Uses; Uses
One type of radio transient expected to be found in image plane transient searches is flares from stars and stellar systems (see e.g. Osten 2008, for a summary). Radio flare stars are usually M-type dwarf stars that emit coherent radio bursts on time-scales of minutes to hours. Recently, Villadsen & Hallinan (2019) detected 22 coherent radio bursts from M dwarfs using the VLA at 300 MHz and 1–6 GHz, and Zic et al. (2019) detected several pulses from the M-dwarf UV Ceti with ASKAP. As well as flare stars, binary systems such as RS Canum Venaticorum (RS CVn), cataclysmic variables (CVs), and symbiotic binaries are known to flare in the radio. RS CVn are binary systems consisting of a late-type giant or sub-giant star with a late-type main-sequence star companion (e.g. Hall 1976; Craig et al. 1997; García-Sánchez, Paredes & Ribó 2003). RS CVn are chromospherically active and the giant or sub-giant rotates quasi-synchronously with the orbital period. Periods for RS CVn are typically 1–20 d, and radio flares on RS CVn systems have been observed to last up to a few days (e.g. Walter et al. 1987; Trigilio, Umana & Migenes 1993). RS CVn emit in both the radio and X-ray while in quiescence (e.g. Gunn 1996). CVs are binary systems with a white dwarf primary accreting matter from Roche lobe overflow of the secondary star, usually a main-sequence star (e.g. Coppejans et al. 2016). Dwarf novae from magnetic CVs have been observed to exhibit radio outbursts that can last for weeks, with rapid radio flaring on time-scales less than an hour (Mooley et al. 2017). Symbiotic binaries also have a white dwarf primary, but the companion is a red giant star and the orbit is wide. In these systems, mass is accreted on to the white dwarf via stellar winds (O’Brien et al. 2015). Radio variability over time-scales of a few hours have been detected on symbiotic binaries, for example RX Puppis (Seaquist 1977). AR Scorpii is another stellar binary that is observed in the radio, it consists of a white dwarf primary and an M-dwarf companion. AR Scorpii has an orbital period of 3.56 h, is observed to pulsate in the optical, radio and X-ray with a period of 1.97 min (Marsh et al. 2016; Takata et al. 2018), and is highly polarized (e.g. Buckley et al. 2017). Radio flaring stellar systems vary on a variety of time-scales, making it difficult to detect when these systems are in outburst (e.g. Osten & Bastian 2008). This means that wide-field monitoring is an important method for discovering and investigating these sources in the radio.
Citation: Trigilio, Umana & Migenes 1993
Citation function: Background
Citation: Osten 2008
Citation function: Background; Background
Citation: Villadsen & Hallinan (2019)
Citation function: Background; Background
Citation: Zic et al. (2019)
Citation function: Background; Background
Citation: Hall 1976
Citation function: Background
Citation: Gunn 1996
Citation function: Background
Citation: Coppejans et al. 2016
Citation function: Background
Citation: Mooley et al. 2017
Citation function: Background
Citation: O’Brien et al. 2015
Citation function: Background
Assuming that some or the entire detected high-energy neutrino flux originates from cosmic rays accelerated in structure-formation accretion shocks, we find the corresponding gamma-ray flux and determine its contribution to the EGRB for different assumed cosmic-ray spectra and plot these results in Figure 1. Panels on the left show SFCR curves after normalization to the αν = 2.0 neutrino spectrum from Aartsen et al. (2014b), and panels on the right use normalization to the latest αν = 2.46 neutrino spectrum from Aartsen et al. (2015). Top panels represent SFCR curves (dot–dashed line) derived for the case of strong shocks, i.e., for cosmic-ray spectral index α = 2.0, which matches that of neutrinos from Aartsen et al. (2014b). Normalization to the αν = 2.0 neutrino spectrum from Aartsen et al. (2014b) yields an upper limit to the SFCR contribution of ≈46% of the EGRB observed by Fermi, which is around the contribution of some of the major components, such as unresolved star-forming galaxies contributing ≲50% (Fields et al. 2010; dashed line), or blazars contributing ≈16% (Abdo et al. 2010a; dotted line). If, for this same SFCR model, the attenuation of highest-energy gamma-ray photons by extragalactic background light (EBL; Gilmore et al. 2012) is included (thin red solid line), we find that this reduces the SFCR contribution to ≲18% of the observed EGRB. The sum of all components is shown with a thick blue solid line. Using the latest neutrino spectrum with αν = 2.46 (Aartsen et al. 2015) as the upper limit constraint, we find that for SFCRs accelerated in strong shocks, i.e., with spectral index α = 2.0, their contribution to the EGRB can be ≈29%, or ≲12% after the EBL attenuation was included. However, SFCRs with such a spectrum cannot explain the entire detected high-energy neutrino flux, and additional sources would be needed. If, on the other hand, SFCRs are assumed to have softer spectra with indices α > 2.0, their resulting fluxes would quickly violate the Fermi EGRB observations. The middle panels of Figure 1 show SFCR gamma-ray fluxes for source spectra α = 2.3, while the bottom panels correspond to α = 2.6. Here we point out that using the latest neutrino fluxes with spectrum  αν = 2.46 (Aartsen et al. 2015) is more constraining in the sense that it does not allow for this entire neutrino flux to be of the SFCR origin because the accompanying gamma-ray flux quickly violates the observed EGRB, as we can see in the bottom two panels on the right side of Figure 1. Such a soft neutrino spectrum, together with gamma-ray observations from Fermi, allows for only a small fraction of its flux to be made by SFCRs with hard spectra α ≲ 2.2.
Citation: Gilmore et al. 2012
Citation function: Uses; Uses
Citation: Aartsen et al. (2015)
Citation function: Uses
Citation: Aartsen et al. 2015
Citation function: Uses; Uses
Citation: Aartsen et al. 2015
Citation function: Compare/Contrast; Compare/Contrast
Citation: Aartsen et al. (2014b)
Citation function: Uses
Citation: Aartsen et al. (2014b)
Citation function: Similarities
Citation: Aartsen et al. (2014b)
Citation function: Uses; Uses