adsabs/FOCAL huggingface dataset:
First, we discuss the discrepancy of the distribution scale of the radio core positions based on the discussions of the internal shock model (Koyama et al. 2015; Niinuma et al. 2015). As is discussed there, the radio cores in Mrk 501 and Mrk 421 observed at 43 or 22 GHz can usually be considered as the internal shocked regions owing to the convex shape of the radio spectrum peaking around 10 GHz (Giroletti et al. 2008; Sokolovsky et al. 2010; Lico et al. 2012; Blasi et al. 2013). The standard internal shock model of blazars considers that the discrete ejecta with higher speeds (with Lorentz factor Γf) catch up with the preceding slower ejecta (with Lorentz factor Γs), and the collision leads to the nonthermal emission (e.g., Spada et al. 2001; Tanihata et al. 2003; Guetta et al. 2004; Kino et al. 2004; Ghisellini et al. 2005). Based on the model, the distribution scale of the internal shocks (ΔDIS in Figure 7, defined as the difference between the largest distance between the internal shock and the central engine DIS,max and the closest one DIS,min) can be explained as the variation of the Lorentz factors of the ejecta (Koyama et al. 2015; Niinuma et al. 2015), by assuming the Lorentz factor ratio (Γf/Γs) and the initial separation of the ejecta (IIS). The core stable within 200 μas constrained by the VERA can be explained by Lorentz factors within a factor of two variation for the slower ejecta, i.e., 8 ≤ Γs ≤ 17, by assuming a minimum value of 8 (e.g., Kino et al. 2002), Γf/Γs ≤ 1.01 (Tanihata et al. 2003), and IIS ∼ 1 Rs (Koyama et al. 2015). This time we refined the distribution scale of the radio core within 42 μas along its main jet axis, or 4.6 × 103 Rs deprojected (see Figure 7). Based on the same assumptions as in Koyama et al. (2015), to explain the further stable distribution scale of the internal shocks, the variation of Lorentz factors of the slower ejecta is constrained to be much smaller, within 30% or 8 ≤ Γs ≤ 10. On the other hand, the radio core wandering of ΔDIS ∼ 2.6 × 105 Rs in Mrk 421 can be explained by the maximum value as Γs ∼ 60 (with different assumptions; Niinuma et al. 2015). Even by applying the same assumptions to Mrk 421 as those for Mrk 501, the maximum of the slower Lorentz factor is estimated to be Γs ∼ 50, which is still a few times as large as that of Mrk 501. Therefore, even during the X-ray and VHE γ-ray active states in 2012, the maximum Lorentz factors that explain the stability of Mrk 501's core are roughly a few times smaller than those for Mrk 421's wandering core, based on the internal shock model.
Citation: Tanihata et al. 2003
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Citation: Tanihata et al. 2003
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Star formation from molecular cloud cores collapse is a chaotic process that is expected to result in initially misaligned and warped discs (Bonnell & Bastien 1992; Bate, Lodato & Pringle 2010; Offner et al. 2010; Bate 2018). We expect this to be the general case for circumbinary discs as well as circumstellar ones. Indeed, some misaligned circumbinary discs have already been reported (e.g. KH 15D Chiang & Murray-Clay 2004; Winn et al. 2004; Lodato & Facchini 2013; Smallwood et al. 2019; Fang et al. 2019; Poon, Zanazzi & Zhu 2021, GG Tau A Köhler 2011; Andrews et al. 2014; Aly, Lodato & Cazzoletti 2018, IRS 43 Brinch et al. 2016, L1551 NE Takakuwa et al. 2017, and HD 98800B Kennedy et al. 2019). Misaligned discs around binaries experience a gravitational torque that leads to radially differential precession, which causes disc warping and twisting. For the gas component, warps are expected to propagate in a wave-like manner in thicker discs with low viscosity that are more relevant in protoplanetary contexts (Papaloizou & Lin 1995; Nelson & Papaloizou 1999; Facchini, Lodato & Price 2013), as opposed to the diffusive warp propagation that occurs in more viscous, thinner discs expected around black holes (Papaloizou & Pringle 1983; Ogilvie 1999; Lodato & Pringle 2007; Lodato & Price 2010). The final state of gas discs precessing around binaries depends on the binary parameters; for circular and low-eccentricity binaries, the disc will align with the binary plane, either in a prograde or retrograde sense depending on the initial misalignment (King et al. 2005; Nixon et al. 2011). For eccentric binaries, discs with high initial misalignments will align in a polar configuration around the binary eccentricity vector (Farago & Laskar 2010; Aly et al. 2015; Martin & Lubow 2017; Zanazzi & Lai 2018). Either way, the disc is susceptible to breaking when the binary torque is larger than the viscous torque and the disc communicates the precession more slowly than it occurs (Nixon, King & Price 2013; Doǧan et al. 2018).
Citation: Kennedy et al. 2019
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The spectral evolution of an ensemble of stars of various masses can be combined through an IMF and followed over time. Such spectral synthesis codes are valuable tools for ultraviolet spectral libraries (Robert etÂ al. 1993; Rix etÂ al. 2004; Leitherer etÂ al. 2014) and stellar population synthesis codes such as Starburst99 (Leitherer etÂ al. 1999). FigureÂ 12 shows a series of spectra for a cluster starburst containing 105âM in which the stars follow a Salpeter IMF (0.1 â©½ m â©½ 120). The two panels show model spectra at times t = 0, 1, 3, 5, and 7âMyr after a coeval burst of star formation, using evolutionary tracks with rotation, at solar metallicity (Z = 0.014 from EkstrÃ¶m etÂ al. 2012) and at sub-solar metallicity (Z = 0.014 from Georgy etÂ al. 2013). These models were created by a Monte Carlo sampling of stars for each mass for which we have an evolutionary track (m = 20, 25, 32, 40, 60, 85, 120). For the Salpeter differential mass distribution, Î¾(m) = KmâÎ± with Î± = 2.35, the fraction of stars above mass m is given by
8The constant K is normalized to the total cluster mass M = 5.862âK, and the total number of stars N = 16.582âK for mass limits mmin = 0.1 and mmax = 120. For M = 105âM, we expect a mean number  stars and mean stellar mass â©mâª = M/N = 0.354 M. In many of our Monte Carlo samples the numbers fluctuate about this value, with small numbers at the high-mass end of the IMF. The mean numbers of stars at the high-mass end are N(> 60âM) â 30 and N(> 100âM) â 5. If the upper mass was extended to mmax = 200, we would expect 40 stars above 60 M and 15 stars above 100 M. As discussed earlier, the existence of these very massive stars is controversial, owing to resolution effects. Moreover, the LyC from stars at m > 100 M may not escape the embedded cloud from which they formed, or from the dense gas produced in mass-loss episodes or binary mergers (Smith 2014). We therefore do not consider stars above the 120 M track.
Citation: EkstrÃ¶m etÂ al. 2012
Citation function: Uses
Fast radio bursts (FRBs) are bright, cosmological origin, and millisecond-duration bursts in radio wavelengths (Lorimer et al. 2007; Thornton et al. 2013; Bassa et al. 2017; Macquart et al. 2020). After the discovery of the first FRB (Lorimer et al. 2007), a number of dedicated facilities have been conducted to search FRBs, such as the Parkes telescope (e.g., Bhandari et al. 2018), the updated Molonglo Observatory Synthesis Telescope (e.g., Farah et al. 2018), the Australian Square Kilometre Array Pathfinder (e.g., Shannon et al. 2018), the Canadian Hydrogen Intensity Mapping Experiment (CHIME; The CHIME/FRB Collaboration et al. 2018), the Deep Synoptic Array (Kocz et al. 2019; Ravi et al. 2019), the Green Bank Telescope (Masui et al. 2019), Arecibo (Spitler et al. 2014; Patel et al. 2018), and the Five-hundred-meter Aperture Spherical radio Telescope (FAST; Nan et al. 2011; Li et al. 2019). All these efforts result in an increasing rate of new FRB detections. Among them, more than 20 repeating FRBs have been reported. Particularly, the physical origin of the repeating FRB 20121102A was identified to be with a low-metallicity star-forming dwarf galaxy at a redshift 0.19273 (Bassa et al. 2017; Tendulkar et al. 2017). Another repeating FRB 20190523A was found to be associated with a more massive but low specific star formation rate (Ravi et al. 2019). The identification of the counterpart of the brightest radio bursts from SGR 1935+2154 as a magnetar in our Galaxy by HXMT (Li et al. 2021) and INTEGRAL (Mereghetti et al. 2020) with short-duration X-ray bursts suggests that at least a fraction of FRBs are connected with newborn magnetized neutron stars (e.g., Weltman & Walters 2020; Zhang 2021). More bursts with similar characteristics need to be detected in the future to confirm this conclusion. Recently, a new large sample with 535 FRBs was presented by CHIME/FRB Collaboration et al. (2021) that were detected by the CHIME survey, including 61 bursts from 18 previously reported repeating sources and 474 one-off bursts. Though an increasing catalog of theories and models is developing to explain the physical nature of FRBs (e.g., see the review of Platts et al. 2019; Xiao et al. 2021), the origin of FRBs remains a mystery.
Citation: Nan et al. 2011
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We then allow the synthetic single or binary system to evolve until present time, adopting for our reference model a thin disc age of 10 Gyr (Cojocaru et al. 2014) and a thick disc age of 12 Gyr. This is motivated by the findings of Feltzing & Bensby (2009), who presented a sample of very likely thick disc candidates with ages, on average, well above 10 Gyr and of Ak et al. (2013), who found that thick disc cataclysmic variables have ages up to 13 Gyr. If the synthetic star is single and has time to become a white dwarf, it evolves following the cooling tracks detailed in the following section. If that is the case, the mass of the white dwarf is obtained from the initial-to-final mass relation (IFMR) according to the prescription from Hurley, Tout & Pols (2002). If the object is member of a binary system and the primary star has time to become a white dwarf, then the pair can evolve through two different scenarios. In the first scenario, the binary evolves without mass transfer interactions as a detached system and the primary star evolves into a white dwarf that subsequently cools down following the cooling sequences described in the next section. In this case, the mass of the white dwarf is also calculated from the IMFR of Hurley et al. (2002). The second scenario involves mass transfer episodes and the evolution of the binary is obtained following the prescriptions of the bse package (Hurley et al. 2002), following the parameter assumptions detailed in Camacho et al. (2014). If the system evolves though the common envelope phase, we use the α-formalism as described in Tout et al. (1997), with αCE being the efficiency in converting orbital energy into kinetic energy to eject the envelope (assumed to be 0.3 in our reference model). This implementation also takes into account the αint parameter (assumed to be 0.0 in our reference model), first presented in Han, Podsiadlowski & Eggleton (1995), describing the fraction of the internal energy (thermal, radiation and recombination energy) used to eject the envelope. As described in Camacho et al. (2014), the αint parameter is used to include the effects of the internal energy in the binding energy parameter λ, which is thus not taken as a constant, but computed using a specific algorithm (Claeys et al. 2014) in bse. In the current version of the code, provided that a positive value is used, the parameter αint represents the fraction of recombination energy that contributes to eject the envelope. It is important to note that the thermal energy of the envelope is always taken into account (using the virial theorem) even if αint is set to zero. For a more detailed discussion on how this is implemented in the latest version of BSE and important comments on the correct use of BSE and the notations used in the code itself, we direct the reader to Zorotovic, Schreiber & Parsons (2014a), mentioning that the notations αint or αrec are, in our case, equivalent.
Citation: Hurley et al. (2002)
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Citation: Hurley et al. 2002
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It has been thought that QPOs originate from the innermost part of an accretion disc, which is associated with strong gravity, so that we might detect general relativistic effects. Miller et al. (1998) proposed beat-frequency models and estimated the parameters of NSs using this model. Stella & Vietri (1999) developed the relativistic precession model. In the last 20 years, disc-oscillation and resonance models and wave models have been proposed (e.g. Osherovich & Titarchuk 1999; Abramowicz & Kluźniak 2001; Abramowicz et al. 2003; Zhang 2004; Li & Zhang 2005; Erkut, Psaltis & Alpar 2008; Shi & Li 2009, 2010; Shi 2011; Shi, Zhang & Li 2014, 2018; de Avellar et al. 2018). Shi & Li (2009, 2010) obtained the twin modes of MHD waves in LMXBs (including NS LMXBs and black hole LMXBs), which are considered as the sources of high-frequency QPOs. Shi, Zhang & Li (2014, 2018) also considered the waves produced by the two MHD oscillation modes at the magnetosphere radius as the origin of kHz QPOs. A relationship between the frequencies of the twin-peak kHz QPOs and the accretion rate, in which parallel tracks can be explained, was obtained (Shi, Zhang & Li 2018). Recently, many simulations on the oscillations of accreting tori in the accretion process of NS LMXBs (e.g. Kulkarni & Romanova 2013; Parthasarathy, Kluźniak, Čemeljić 2017) have been performed, and almost every model can reproduce some of the observed characteristics of QPOs. However, most models cannot fit the observed data perfectly, the observed data. Belloni, Méndez & Homan (2005) suggested that the twin kHz QPOs showed no intrinsically preferred frequency ratio, and this weakened support for the resonance models. Morsink & Stella (1999) were able to fit the overall NS data with different masses and spins of NSs using the relativistic precession model; however, Belloni, Méndez & Homan (2007) found that there were deviations between the expected and the observed trends. Recently, Török et al. (2016b, 2018) identified the observed QPO frequencies with the frequencies of the epicyclic modes of torus oscillations, and suggested that the relationship between the strong modulation of the X-ray flux and high values of QPO frequencies is connected to the orbital motion in the innermost part of an accretion disc. In addition, there are studies that compared a large set of models with the data of many sources in a complex manner (Lin et al. 2011; Török et al. 2012, 2016a).
Citation: Shi & Li; 2010
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Citation: Shi & Li; 2010
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Early 15 GHz images using the very long baseline interferometry (VLBI) technique obtained from the very long baseline array (VLBA) indicated a twisted morphology with jet bending on a scale of ∼20 mas (Kellermann et al. 1998), and multi-epoch 43 GHz observations show jet knots with complex kinematics involving a mixture of apparent superluminal motion and as well as stationary components (Jorstad et al. 2001, 2005). Multi-frequency (15 and 43 GHz) multi-epoch observations during the 2006 radio flare (Fromm et al. 2013a) inferred a possible association between a jet component ejection event at the end of 2005 and a strong radio flare in 2006 April. The authors interpreted the 2006 radio flare as a result of the interaction between a propagating shock and a stationary shock at a de-projected distance of 18 pc from the core. Temporal variability studies during the 2012 September–October multi-band flaring period found a near-simultaneous γ-ray and optical flaring behavior, inferring a co-spatial origin (Cohen et al. 2014; Larionov et al. 2016). The latter study in addition suggested that the measured Stokes parameter variations is consistent with a bright jet knot moving along a helical trajectory. A multi-wavelength polarimetric study during the same flaring phase (Casadio et al. 2015) detected a co-spatial origin from the near-simultaneous variability and identified the passage of a superluminal radio knot coincident with the γ-ray flare. Further evidence, including an intra-day optical polarization variability and clockwise rotation of the electric vector position angle (EVPA, 





, where U and Q are Stokes components) during the flaring phase, is consistent with a jet knot passing a region hosting helical magnetic fields. A study of γ-ray–optical variability in flux density and polarization between prominent flares during the end of 2016 (Larionov et al. 2017) finds no time lag between the light curves indicating co-spatial origin of synchrotron (optical) and inverse-Compton (γ-ray) flux, and a smaller viewing angle (more energetic, emission closer to jet base) compared to a flare in 2012 when interpreted in terms of a blob or shock wave on a helical trajectory. From the above studies, the γ-ray flares may be associated with optical flux and polarization variability, and the jet kinematics and polarization properties may be described in terms of a helical jet.
Citation: Larionov et al. 2016
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On 2017 November 24 the MMS orbit allowed us to collect measurements in the pristine solar wind, well outside the Earth's magnetosheath and the bow shock, for a long period (i.e., a few times longer than the typical correlation scale) of approximately 1 hour from 01:10 to 02:10 UT. Figure 1 (upper panel) displays an overview of the magnetic field measurements collected by the FIELDS instrument suite (Torbert et al. 2016) on board of MMS1 with a temporal resolution Δt = 128 samples s−1 (Russell et al. 2016). The period of interest is a typical example of slow solar wind stream (V ∼ 377 km s−1), with an average magnetic field 〈B〉 ∼ 6.6 nT and a mean plasma density 〈n〉 ∼ 9 cm−3 (Roberts et al. 2020a, 2020b). This means that the average Alfvén speed is VA ∼ 50 km s−1, while the ion inertial length and gyroradius are di ∼ 76 km and ρi ∼ 96 km, respectively (Chhiber et al. 2018), with the corresponding timescales τd ∼ 1.3 s and τρ ∼ 1.6 s, respectively. As reported in previous works (Bandyopadhyay et al. 2018; Chhiber et al. 2018; Roberts et al. 2020a, 2020b) this interval is characterized by two different spectral scalings: a typical inertial range ∼ τ5/3 is found at large scales (i.e., τ > τb), while a steeper scaling ∼ τ7/3 is found at small scales (i.e., τ τb), with τb ∼ 2.4 s (Roberts et al. 2020a). Furthermore, the magnetic field spectrum flattens near τnoise ∼ 0.2 s, due to the instrumental noise floor near ∼5 Hz (Russell et al. 2016). Finally, a decrease at shorter timescales (e.g., τ ∼ 0.1 s) is due to an anti-aliasing filter of nonphysical origin (Russell et al. 2016; Roberts et al. 2020a). Taken together, this interval is particularly suitable for testing our formalism with respect to processes of both physical and nonphysical origin. The presence of an instrumental noise floor allows us indeed to assess our formalism with respect to purely stochastic processes, while the existence of two spectral regimes (i.e., the MHD/inertial and the kinetic/dissipative) allows us to investigate small- versus large-scale processes and their possible coupling in a dynamical system framework.
Citation: Chhiber et al. 2018
Citation function: Uses; Uses
One of the key model ingredients that determines the TDE rates is the distribution of stars in galactic nuclei (Magorrian & Tremaine 1999; Wang & Merritt 2004). Depending on the merger history of the galaxy and the efficiency of feedback on star formation, the stellar density profile can develop either a core or a cusp. For simplicity, we adopt a singular isothermal sphere density profile ρ(r) = σ2/2πGR2 with σ being the constant velocity dispersion and R the halo virial radius. For a galaxy of halo mass Mh, the relation between the halo mass and the velocity dispersion is simply Mh = 2σ2R/G; while the velocity dispersion can be directly related to the black hole mass using the MBH–σ relation (Kormendy & Ho 2013; McConnell & Ma 2013; Baldassare et al. 2015; Saglia et al. 2016; Thomas et al. 2016)
(1)
\begin{equation}
M_{{\rm BH}} = 0.309\times 10^9\times \left(\sigma /200\ \rm{km\,\,s}^{-1}\right)^{4.38}\ \mathrm{M}_{\odot },
\end{equation}
which holds for a wide range of black hole masses from 5 × 104 M⊙ (Baldassare et al. 2015) to 1.7 × 1010 M⊙ (Thomas et al. 2016) in galaxies with a bulge (Guillochon & Loeb 2015). Assuming the isothermal stellar distribution, Wang & Merritt (2004) derived TDE rates for galaxies with a single central black hole, while Chen et al. (2009) report the rates in a case of a black hole binary. As we discuss in Section 2.2, for MBH with masses in the range MBH ∼ 105–108 M⊙, the TDE rates per halo computed using the isothermal stellar distribution are similar (within tens of percent) to more realistic estimates based on a large galaxy sample (Stone & Metzger 2016), which justifies our assumption. The error in the rate estimation due to the idealized stellar density profile is small compared to other uncertainties, e.g. introduced by the poorly constrained occupation fraction of IMBHs in low-mass galaxies, which amounts to one–two orders of magnitude uncertainty in the derived volumetric TDE rates.
Citation: McConnell & Ma 2013
Citation function: Uses