adsabs/FOCAL huggingface dataset:
Various strategies have been devised to identify modes. One can, for instance, search for frequency patterns appropriate for rapid rotation. The background for this search is the discovery of asymptotically uniform frequency spacings in the numerically computed spectra of uniformly rotating polytropic models (Lignières et al. 2006; Reese et al. 2008) and differentially rotating realistic self-consistent field (SCF) models (Reese et al. 2009a). These uniform spacings have also been modelled through asymptotic semi-analytical formulas (Pasek et al. 2012). In observed spectra, recurrent frequency spacings that may correspond to the large separation or half its value have been found in some stars (García Hernández et al. 2009; García Hernández et al. 2013; Paparó et al. 2016). Moreover, García Hernández et al. (2015) show that mean density estimates based on this type of spacings (obtained via a scaling relation similar to the one in Reese et al. 2008, but based on SCF models) are compatible with independent mass and radii measurements obtained for δ Scuti stars in binary systems. Nonetheless, it is expected that various effects may contribute to hide these regular frequency patterns. First, as mentioned before, the full spectrum is a superposition of sub-spectra corresponding to different classes of modes and some of the uniform spacings only concern one class. This complicates their detection in the full spectrum. Also, owing to their asymptotic nature, these spacings might not be relevant to analyse the low to moderate (up to radial order n ~ 10) frequency domain, typical of most rapidly rotating pulsators. A third effect that may come into play is the presence of mixed modes in evolved stars and/or sharp sound speed gradients since they can potentially modify the regular spacings. Finally, mode selection effects that are due to the non-linearly determined intrinsic mode amplitudes could affect the detectability of the regular patterns. As a first attempt, Reese et al. (2009b) developed a strategy to find these frequency spacings but ran into difficulties when including chaotic modes, which come from another class of modes. Lignières et al. (2010) addressed the same question with encouraging results but their analysis was restricted to the asymptotic regime and relied on simplifying assumptions regarding the spectrum of chaotic modes and the mode visibilities. In this paper, our first goal is to search for regular frequency spacings in the most realistic synthetic spectra available, using relevant frequency ranges and accurate visibility calculations. While they can provide guidance to a similar search in real data, we already know that these results must be taken with caution since the intrinsic mode amplitudes used in this paper are not realistic, but based on ad-hoc prescriptions.
Citation: García Hernández et al. 2013
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Spectral energy distributions in accordance with the physical parameters of the best-fit spectra were generated with FASTWIND, to provide the flux density per surface unit through our studied bands. The composite flux measured at Earth from a binary at a distance d, at a wavelength λ, reddened to extinction A(λ), is given by \begin{eqnarray*} f_{\lambda}=\dfrac{1}{d^2}\left(R_{1}^{2}F_{1,\lambda}+R_{2}^{2}F_{2,\lambda}\right) \times 10^{-0.4A(\lambda)} \end{eqnarray*}fλ=1d2(R12F1,λ+R22F2,λ)×10−0.4A(λ)where R1,2 and F1,2 are the radii and the surface fluxes of the components, respectively. The composite SED was reddened according to the new family of optical and near-infrared extinction laws for O-type stars provided by Maíz Apellániz et al. (2014), which constitute an improvement of the widely used extinction laws by Cardelli et al. (1989). We ran a fitting algorithm over a wide range of distances with a step of 0.05 kpc, setting free the monochromatic parameters R5495 and E(4405 − 5495) for the type and amount of extinction, respectively, and the best-fit values were considered to be those that minimized the weighted-χ2. To estimate the uncertainty of our measurements, we used a Monte Carlo approach. In particular, we ran the fitting procedure 1000 times using sets of randomly selected parameters (photometry and radii) within their uncertainties assuming a Gaussian distribution is used. The corresponding values of distance are shown in Table 6 for every set of radii and temperatures determined from the four different fit models. Our adopted radii measured with ELC yielded d = 3.52 ± 0.08 kpc, E(4405 − 5495) = 3.66 ± 0.06 mag, R5495 = 3.26 ± 0.04 and A5495 = 11.9 ± 0.1 mag, based on a photometric Teff2 ~ 36 kK. Assuming a spectroscopic Teff2 = 37 kK, the distance changed slightly to d = 3.55 ± 0.08 kpc. Having three degrees of freedom, the reduced-χ2 of our resulting fits was measured to be \hbox{$\chi^2_\textrm{red}\sim11$}χred2~11.
Citation: Cardelli et al. (1989)
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NASA’s Kepler mission has unveiled a wealth of new planetary systems (e.g. Borucki et al. 2010). These systems offer new insights into the process of planet formation and evolution. One of Kepler’s key findings is that the most common planets in our Galaxy, observed to date, are between 1 and 4 R⊕, i.e. larger than Earth but smaller than Neptune (Fressin et al. 2013; Petigura, Marcy & Howard 2013). Further observations revealed a transition in average densities at planet sizes ∼1.5 R⊕ (Marcy et al. 2014; Rogers 2015), with smaller planets having densities consistent with rocky compositions while larger planets having lower densities indicating significant H/He envelopes. In addition, Owen & Wu (2013) noticed a bimodal distribution of observed planet radii. Since then, refined measurements have provided strong observational evidence for the sparseness of short-period planets in the size range of ∼1.5–2.0 R⊕ relative to the smaller and larger planets, yielding a valley in the small exoplanet radius distribution (e.g. Fulton et al. 2017; Fulton & Petigura 2018). For example, the California-Kepler Survey reported measurements from a large sample of 2025 planets, detecting a factor of ∼2 deficit in the relative occurrence of planets with sizes ∼1.5–2.0 R⊕ (Fulton et al. 2017). Studies suggest that this valley likely marks the transition from the smaller rocky planets: ‘super-Earths’, to planets with significant H/He envelopes typically containing a few per cent of the planet’s total mass: ‘sub-Neptunes’ (e.g. Lopez & Fortney 2013, 2014; Owen & Wu 2013; Rogers 2015; Ginzburg, Schlichting & Sari 2016). Furthermore, the location of this valley is observed to decrease to smaller planet radii, Rp, with increasing orbital period, P. In a recent study involving asteroseismology-based high precision stellar parameter measurements for a sample of 117 planets, a slope $\text{d log} R_\mathrm{ p}/ \text{d log} P = -0.09^{+0.02}_{-0.04}$ was reported for the radius valley by Van Eylen et al. (2018). A similar value for the slope of $-0.11^{+0.03}_{-0.03}$ was reported by Martinez et al. (2019).
Citation: Rogers 2015
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Citation: Rogers 2015
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Following the original BGK kinetic-theoretical scheme (Bernstein et al. 1957), we transform the above equations to the energy frame, defined as
5



w=12v2+ϕ.

In the energy frame, the ion distribution transforms into
6



fi(w)=Γ(κi)πκi−3/2Γ(κi−1/2)1+2wκi−3/2−κi,

where
7



f(x,v)dv=f(w)dw/2w−ϕ.

Here, the total energy (w) is normalized with 



mvth,i2

, i.e., 2k

B

T

i
. As the ions encounter a negative potential well (a pulse), depending on their respective velocities, some of them will become trapped and some of them will pass through. Hence two types of population exist: a trapped population, and a passing population. We assume the passing populations to follow the initial distribution function - a kappa distribution function. In addition, we also assume the form of the potential in which particles are trapped to be prescribed. Spacecraft observations show that wave potential structures of Gaussian form are common in space and astrophysical plasmas (Matsumoto et al. 1994; Williams et al. 2006). A negative wave potential well acts as a perturbation capable of trapping ions in it. We assume this potential well to have Gaussian form, given by
8



ϕ(x)=−ψexp−x22δ2,

where ψ (>0) denotes the amplitude, and δ is the width of the perturbation, respectively. More precisely, δ is actually the distance where the potential decreases to 0.6065 times the maximum amplitude of ψ. The FWHM of the perturbation is actually given by Δ = 2.35δ. The net charge density can thus be expressed as
9



d2ϕdx2=1−Hne−ni,p−ni,tr+H,

where n

i,p
 is the passing ion density, and 



ni,tr

 is the trapped ion density. Particles with suitable velocities falling in the potential range 



−−ϕ,+−ϕ

 will become trapped, and the rest will pass through. Thus, the range of integration for both passing and trapped ion distributions is given by
10



ni,p=∫−∞−−ϕfp(x,v)dv+∫+−ϕ∞fp(x,v)dv.

As the passing ions follow the kappa distribution, we obtain the passing ion density as
11



ni,p=1−2AB−ϕ2F1[κi,1/2,3/2;ϕ/B],

where 2
F
1 is the hypergeometric function of the first kind. Now that we have obtained the passing ion density, we move on to the derivation of the trapped ion density. In terms of distribution function, the trapped ion density is given by
12



ni,tr=∫−−ϕ+−ϕftr(x,v)dv.

We may now derive the trapped ion density by rearranging Equation (9) as
13



ni,tr=1−Hne−ni,p−d2ϕdx2+H.

Substituting from Equation (11) and differentiating the potential in Equation (8) twice, in Equation (13), we obtain the trapped electron density as
14



ni,tr=1−H1−Trϕ(κe−3/2)0.5−κe+2ϕlog−ϕψδ2+ϕδ2−1+2AB−ϕ2F1[κi,1/2,3/2;+ϕ/B]+H.

For convenience, we make a transformation − ϕ = ∣ϕ∣ → ρ, (>0), and we obtain the trapped ion density as
15



ni,tr=1−HρTrκe−32+10.5−κe−2ρlogρψδ2−ρδ2−1+2ABρ2F1[κi,1/2,3/2;−ρ/B]+H.
Citation: Williams et al. 2006
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Quasi-periodic pulsations (QPPs) often refer to the quasi-periodic intensity variations during solar/stellar flares (see Zimovets et al. 2021, for a recent review). In many observations, the flare QPPs were found to show a nonstationary property in the time series integrated over the whole Sun/star or over the oscillation region, for instance, each pulsation has an anharmonic and symmetric triangular profile shape (e.g., Kolotkov et al. 2015; Nakariakov et al. 2019). The signature of flare QPPs can be detected in flare light curves across a broad band of the electromagnetic spectrum, i.e., radio/microwave emissions (Ning et al. 2005; Reznikova & Shibasaki 2011; Nakariakov et al. 2018; Yu & Chen 2019), UV/EUV wavelengths (Shen et al. 2018; Hayes et al. 2019; Reeves et al. 2020; Miao et al. 2021), SXR/HXR and γ-ray channels (Nakariakov et al. 2010; Ning 2017; Hayes et al. 2020; Li et al. 2020c), and the Hα (Srivastava et al. 2008; Kashapova et al. 2020; Li et al. 2020b) or Lyα (Van Doorsselaere et al. 2011; Milligan et al. 2017; Li 2021) emissions. The quasi-periods of these QPPs were reported from subseconds to tens of minutes (e.g., Tan et al. 2010; Shen et al. 2013, 2019; Kolotkov et al. 2018; Karlický & Rybák 2020; Clarke et al. 2021). It should be stated that the observed periods are generally related to the specific channels or flare phases (Tian et al. 2016; Dennis et al. 2017; Pugh et al. 2019), suggesting that the various classes of QPPs could be produced by different generation mechanisms (e.g., Kupriyanova et al. 2020). In the literature, the flare-related QPPs were most often explained by magnetohydrodynamic (MHD) waves, more specifically sausage waves, kink waves, and slow waves (Li et al. 2020a; Nakariakov & Kolotkov 2020; Wang et al. 2021), or by a repetitive regime of magnetic reconnection that could be spontaneous (i.e., self-oscillatory process) or triggered owing to external MHD oscillations (Thurgood et al. 2017; Yuan et al. 2019; Clarke et al. 2021). They can also be interpreted in terms of the LRC-circuit oscillation in current-carrying loops (Tan et al. 2016; Li et al. 2020b) or caused by the interaction between supra-arcade downflows and flare loops (Xue et al. 2020; Samanta et al. 2021).
Citation: Hayes et al. 2019
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Our ideas about which systems may survive spiral-in and produce WR X-ray binaries were triggered by the realization that the peculiar X-ray binary SS433 has avoided going into CE evolution, and that the donor star in this system is transferring mass to the compact star by stable Roche lobe overflow (RLOF; King & Begelman 1999; King, Taam & Begelman 2000). By analysing the properties of this system we realized that it is the high mass of the compact star in this system [4.3(±0.8)  M⊙] in combination with the relatively low mass of its donor star [12.3(±3.3) M⊙] (Hillwig & Gies 2008), which allowed it to avoid CE evolution and enables it to gently spiral in without ever coalescing with its donor. As we consider SS433 to be a ‘keystone’ for understanding the formation of the WR X-ray binaries, we give in Section 2 a brief overview of its properties and evolutionary state. The avoidance of its going into CE evolution is – as we will argue – a consequence of the donor star having a radiative envelope (King et al. 2000), in combination with the donor star and accretor having a mass ratio less than 3.5. In Section 3, we then examine for which donor masses, mass ratios and orbital periods HMXBs will, when they start Roche lobe overflow, avoid going into CE evolution and may survive as WR X-ray binaries with short orbital periods. We also examine under which conditions they may still survive after having gone into CE evolution. In this section, some examples are given on how a number of well-known observed WR+O binaries with relatively short orbital periods are expected to evolve in the future, and are expected to produce WR X-ray binaries and, as a final evolutionary state, close double BHs. This model for producing double BHs is different from the ones proposed by Belczynski et al. (2016), Marchant et al. (2016) and de Mink & Mandel (2016). In Section 4, we attempt to estimate the birth rate of WR X-ray binaries in the Galaxy on the basis of our model, and find it to be still higher than observed and discuss possible ways to minimise this discrepancy. In Section 5, we discuss the results and estimate the possible birth rate of double BHs based on our model.
Citation: King et al. 2000
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We calculated the dependence of the width of the profiles on the pulse period, considering the different frequencies separately. We note that the pulse width is not a direct reflection of the beam size or diameter (i.e. 2ρ, where ρ is beam radius). For a visual representation of the geometry see for instance Maciesiak et al. (2011) and Bilous et al. (2014). In fact, only if the observer’s line of sight cuts the emission centrally for magnetic inclination angles, α, that are not too small (i.e. α>  ~ 60°), w ≈ 2ρ. In such a case, when the emission beam is confined by dipolar open field lines, we would expect a P− 1 / 2 dependence, which has indeed been observed when correcting for geometrical effects by transforming the pulse width into a beam radius measurement (see Rankin 1993; Gil & Krawczyk 1996; Maciesiak et al. 2012). For circular beams, profile width and beam radius are related by the relation first derived by Gil et al. (1984): (5)\begin{equation} {\rho_{10}} = 2\sin^{-1} \left[\sin{\alpha}\sin{(\alpha+\beta)}\sin^2\left(\frac{w_{10}}{4}\right)+\sin^2\left(\frac{\beta}{2}\right)\right]^{1/2}\cdot \end{equation}ρ10=2sin-1sinαsin(α+β)sin2w104+sin2β21/2·The angle β is the impact angle, measured at the fiducial phase, φ, which describes the closest approach of our line of sight to the magnetic axis. This equation is derived under the assumption that the beam is symmetric relative to the fiducial phase. Typically, widths are measured at a certain intensity level (e.g. 50% or 10%, as here), and ρ values are derived accordingly. In many cases, profiles are indeed often asymmetric relative to the chosen midpoint, or become so as they evolve with frequency. We note that for a central cut of the beam (β = 0) and for an orthogonal rotator (α ~ 90°) the equation reduces to ρ = w/ 2 as expected, while in a more general case, where β = 0 and α ≫ ρ the relation reduces to ρ = (w/ 2)sinα. In principle, it is possible to determine α and β with polarisation measurements. However, in reality the duty cycle of the pulse is often too small to obtain reliable estimates (see Lorimer & Kramer 2004). Alternatively, at least for α, the relation reported by Rankin (1993) can be used: (6)\begin{equation} \label{eqn:w50} w_{50,{ \rm core}}(1~{\rm GHz}) = 2.45^\circ \cdot P^{-0.5\pm 0.2}/\sin(\alpha), \end{equation}w50,core(1GHz)=2.45◦·P−0.5±0.2/sin(α),calculated from the observed width dependency on period for the core components of pulsars (see Sect. 5.1), which is intrinsically related to the polar cap geometry. Equation (6) is valid at 1 GHz, but can be applied at LOFAR frequencies, maintaining the same dependence, if the impact angle β ≪ ρcore; sinα should be ignored for orthogonal rotators. Additionally, Rankin (1993), Gil et al. (1993), Kramer et al. (1994), Gould & Lyne (1998) suggested that “parallel” ρ − P relations are found if the radio emission of the pulsar can be classified and separated into emission from “inner” and “outer” cones, which seem to show different spectral properties (see Sect. 5.1 for details).
Citation: Maciesiak et al. 2012
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It is well known that there exists an anticorrelation between the cyclic variations of GCR intensity and SSN (Forbush 1954), and the time lag in this relationship has also been reported by Forbush (1958). The time lag in solar modulation of GCRs should be closely related to the transport of solar wind plasma with its embedded HMF through the modulation region. This effect has been considered in numerical models of GCR modulation to study the long-term modulation mechanism (e.g., Le Roux & Potgieter 1990; Ferreira & Potgieter 2004; Bobik et al. 2012; Potgieter et al. 2014; Qin & Shen 2017). Moreover, the delay time in odd solar cycles was found to be longer than that in even ones (e.g., Nagashima & Morishita 1980; Mavromichalaki & Petropoulos 1984; Usoskin et al. 1998; Mavromichalaki et al. 2007; Ross & Chaplin 2019). Drift theory has predicted that positively charged particles mainly drift inward through the polar region of the heliosphere during the A > 0 solar magnetic cycle, while they predominantly participate in the heliosphere along the wavy heliospheric current sheet when A  0 (Jokipii et al. 1977; Jokipii & Thomas 1981). Thus, positively charged particles will take a longer time to reach Earth when A  0, and such modulation mechanism may cause a longer delay time in odd cycles (Van Allen 2000; Cliver & Ling 2001). In addition, the time lag varies with the energy/rigidity of the particle, which is easy to understand: the higher the particle’s energy is, the shorter its propagation time in the modulation region. Such phenomenon is implied from several theoretical (O’Gallagher 1975; Strauss et al. 2011) and observational (Burger & Swanenburg 1973; Nymmik & Suslov 1995) studies. Meanwhile, the difference in the energy dependence of the time lag in odd and even solar cycles was also shown by Nymmik & Suslov (1995). However, in the correlation studies of Ross & Chaplin (2019), an obvious rigidity dependence on the delay time between SSN and GCR intensity recorded by NMs was not found. Thus, we focus on the GCR data from spacecraft rather than those from NMs in this work.
Citation: Potgieter et al. 2014
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Otherwise (i.e. if there is insufficient mass left in the sub-grid gas reservoir), the mass deficit $m_\mathrm{BH} + \Delta m - m_\mathrm{BH}^\mathrm{dynamical}$ (the last term denotes the dynamical mass of the SMBH) is drawn from the surrounding gas particles. In eagle, this was done by stochastically swallowing individual gas neighbours. This is not an ideal approach: the momentum imparted on the SMBH from the swallowed gas particle may artificially dislodge it from its position, particularly without instantaneous repositioning (as also discussed by Steinborn et al. 2015). The mass of a gas particle is also typically much greater than Δm, so that the dynamical mass of SMBH particles remains systematically above its sub-grid mass. Both issues become more severe when individual gas particles have been enriched to masses well above their initial value due to stellar outflows, which is particularly common in massive, gas-poor galaxies. Instead of swallowing entire particles, we therefore transfer a (typically very) small fraction of mass from all gas neighbours to the SMBH simultaneously, with the mass δmi ‘nibbled’ from each neighbour i weighted in analogy to their contribution to the gas density at the location of the SMBH,
(4)$$\begin{eqnarray}
\delta m_i = (1-\epsilon _\mathrm{r}) \Delta m \left[\frac{w_i m_i}{\sum _j (w_j m_j)}\right],
\end{eqnarray}$$where wi is the kernel weight of particle i, mi its mass, and the sum is over all neighbours; as above, the factor of (1 − ϵr) accounts for the mass converted to energy. In addition to mass, a fraction δmi/mi of the momentum of neighbour i is also transferred to the SMBH. To prevent individual gas particles from becoming too light, we exclude any neighbour that would be reduced to less than half its initial mass and accept that the dynamical mass of the SMBH grows slightly less than desired in this case. In practice, we have found that this limit is never reached in the simulations presented here, because stars typically inject far more mass into gas particles than is drained by SMBHs.
Citation: Steinborn et al. 2015
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Lenticular galaxies seems to have a wider range of properties compared to ellipticals that resemble more the old definition of ETGs. However, even in ellipticals, large differences prevail. Recent observations of elliptical galaxies with Spitzer and Herschel (Temi et al. 2005, 2007a, 2007b, 2009; Smith et al. 2012; Agius et al. 2013; Mathews et al. 2013) have revealed that the far-infrared (FIR) luminosity LFIR from these galaxies can vary by ∼100 among galaxies with similar optical luminosity. The 70 μm band luminosities (from Temi et al. 2007a, 2009), is a good example of such a huge scatter in the FIR luminosity of elliptical galaxies. Some of the high L70 galaxies are members of a small subset of ellipticals having radio detections of neutral and molecular gas. A few others may be S0 galaxies which, because of their rotationally supported disks, often contain large masses of cold gas and dust. Ellipticals containing large excess masses of dust and cold gas probably result from significant galaxy mergers in the past. However a fraction of elliptical galaxies appear to be completely normal but L70 in these galaxies still ranges over a factor of ∼30, far larger than can be explained by uncertainties in the estimate of the FIR spectral energy distribution (SED) due to local stellar mass loss. While a significant fraction of the cold gas mass in low- to intermediate-mass ETGs is thought to have an external, merger-related origin (e.g., Davis et al. 2011), in the most massive ETGs the cold gas phases are presumably generated internally (Davis et al. 2011; David et al. 2014; Werner et al. 2014). Mergers with gas- and dust-rich galaxies have often been suggested for the origin of dust in all elliptical galaxies (e.g., Forbes 1991). Although the merger explanation is almost certainly correct in some cases, mergers cannot explain most of the observed scatter in L70. A crucial element in our understanding of the evolution of galaxies toward ETGs is the mutual role played by the major merging of galaxies and the secular star formation quenching. Neither of these scenarios yet accounts for all the observational evidence, and one could assume both contributing to some extent.
Citation: Temi et al. 2007a
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Citation: Temi et al.; 2007a
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