adsabs/FOCAL huggingface dataset:
Several optical/near-UV surveys have targeted the CDF-S and its flanking fields, with the main purpose of photometrically and spectroscopically calculating the redshifts of the detectable sources. In the context of the ESO imaging survey (EIS, Arnouts et al. 2001) project, multi-colour (six broad band filters, U′UBVRI) photometric measurements of about 75 000 sources have been provided to observe the Extended-CDF-S (E-CDF-S) through the Wide Field Imager (WFI, Baade et al. 1998, 1999) at the MPG/ESO 2.2 m telescope on La Silla. By means of the same telescope and instrument, a nearly coincident area of 31.5 × 30 arcmin2 has been observed in 17 passbands (350–930 nm) within the COMBO-17 survey, obtaining a catalogue of more than 60 000 objects including astrometry, classification, and photometric redshifts, with around 10 000 galaxies identified at RVega 24 (Wolf et al. 2004, 2008). Another optical and near-IR multi-wavelength survey has been developed by Cardamone et al. (2010) as part of the Multi-Wavelength Survey by Yale-Chile (MUSYC, Gawiser et al. 2006), combining the Subaru 18-bands imaging (400–900 nm) to 14 other available ground-based and Spitzer images: about 80 000 galaxies are catalogued at R  ≤  27, and about 30 000 redshifts are computed. The Great Observatories Origins Deep Survey (GOODS, Giavalisco et al. 2004), instead, covers a 320 arcmin2 region in the CDF-S (GOODS-S) by using the Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS, Ford et al. 2003), through the filters F435W,F606W,F775W, and F850LP; it catalogued about 29 600 objects, at m ≤ 27. Moreover, an 11 arcmin2 region within the GOODS-S (Hubble Ultra Deep Field, UDF, Beckwith et al. 2006) has been deeply observed by the ACS in the same bands, reaching a uniform limiting magnitude m ~ 29 for point sources. Voyer et al. (2009) also presented the U-band observations of the same area, achieved through the HST Wide-Field Planetary Camera 2 (WFPC2)/F300W filter (λmax ~ 300 nm) and providing a catalogue of 96 objects. The Arizona CDFS Environment Survey (ACES, Cooper et al. 2012) spectroscopically targeted the E-CDF-S by means of the Inamori-Magellan Areal Camera and Spectrograph on the Magellan-Baade telescope (565–920 nm), yielding more than 5000 redshifts for R ≤ 24.1 sources; it widens therefore previous sets of spectroscopic redshift estimates of CDF-S sources (e.g. Szokoly et al. 2004; Le Fèvre et al. 2005; Ravikumar et al. 2007; Popesso et al. 2009; Balestra et al. 2010; Silverman et al. 2010), for a total of about 1300 ACES objects with comparison published redshifts. All the publicly available spectroscopic redshift estimates in the CDF-S have been compiled in the ESO CDF-S Master Catalogue, version 3.01.
Citation: Cardamone et al. (2010)
Citation function: Background; Background; Background
The theory of LK migration with STs involves two important time-scales. The first is the time-scale for quadrupole LK eccentricity oscillations, tLK, given by 
(40)
\begin{eqnarray*}
t_{\rm LK} &amp;=&amp; \left(\frac{10^6}{2\pi }\,\text{yr}\right)\left(\frac{M_\mathrm{ b}}{\rm{ M}_\odot }\right)^{-1}\left(\frac{M_*}{\mathrm{ M}_\odot }\right)^{1/2}\left(\frac{a_0}{1\, \text{au}}\right)^{-3/2}\nonumber \\
&amp;&amp;\times \, \left(\frac{a_{\rm b,eff}}{100\, \text{au}}\right)^{3} , 
\end{eqnarray*}
where a0 is the initial semimajor axis of the planet’s orbit, Mb is the mass of the (stellar) companion, and 
(41)
\begin{eqnarray*}
a_{\rm b,eff} \equiv a_{\rm b} (1-e_{\rm b}^2)^{1/2} , 
\end{eqnarray*}
with ab and eb the semimajor axis and eccentricity of the companion’s orbit, respectively. The time that the planet spends near the maximum eccentricity, emax, is of the order of (e.g. Anderson et al. 2016) 
(42)
\begin{eqnarray*}
\Delta t(e_{\rm max}) \sim (1-e_{\rm max}^2)^{1/2} t_{\rm LK}. 
\end{eqnarray*}
The second important time-scale is that of orbital decay due to STs given by (Alexander 1973; Hut 1981). 
(43)
\begin{eqnarray*}
t^{-1}_{\rm ST} &amp;=&amp; \left|\frac{\skew4\dot{a}}{a}\right|_{\rm ST} = (6 k_{2\mathrm{ p}} \Delta t_{\mathrm{ L}}) \frac{M_*}{M_\mathrm{ p}} \left(\frac{R_\mathrm{ p}}{a}\right)^{5}\frac{n^{2}}{(1-e^2)^{15/2}} \nonumber \\
&amp;&amp;\times \, \left[f_1(e)\ - \frac{f_2^2(e)}{f_5(e)}\right], 
\end{eqnarray*}
where k2p is the tidal Love number of the planet, ΔtL is the lag time, f1(e) = 1 + 31e2/2 + 255e4/8 + 185e6/16 + 25e8/64, and f2(e) and f5(e) are given in equations (30) and (31), respectively. (We have assumed that the planet has a pseudo-synchronous spin rate.) Tidal dissipation is most efficient near the maximum eccentricity. Since the planet only spends a fraction (${\sim } \sqrt{1-e_{\rm max}^2}$) of the time near emax, the effective orbital decay rate during LK migration is 
(44)
\begin{eqnarray*}
t^{-1}_{\rm ST,LK} &amp;=&amp; \left(\left|\frac{\skew4\dot{a}}{a}\right|_{\rm ST} \sqrt{1-e^2}\right)_{e_{\rm max}} \nonumber \\
&amp;\approx&amp; \frac{1.27}{{\rm Gyr}} \left(\frac{k_{\rm 2p}}{0.37}\right) \left(\frac{\Delta t_{\rm L}}{1 {\rm s}}\right)\left(\frac{M_\mathrm{ p}}{\mathrm{ M}_{\odot }}\right)^2 \left(\frac{M_\mathrm{ p}}{M_\mathrm{ J}}\right)^{-1} \nonumber \\
&amp;&amp;\times \; \left(\frac{R_\mathrm{ p}}{R_\mathrm{ J}}\right)^5\left(\frac{a_0}{1\, {\rm au}}\right)^{-1} \left(\frac{r_{\rm p, min}}{0.025\, {\rm au}}\right)^{-7} \,,
\end{eqnarray*}
where rp, min = a0(1 − emax) is the minimum pericentre distance (in the second of the above equalities, we have used emax = 0.96). Successful migration within a few Gyr requires rp, min ≲ 0.025 au, corresponding to a final (circularized) planet semimajor axis aF ≲ 0.05 au. A planet would need to be more dissipative than Jupiter (larger ΔtL)5 to become an HJ with a larger aF.
Citation: Anderson et al. 2016
Citation function: Uses; Uses
Citation: Hut 1981
Citation function: Uses; Uses
Figure 5 shows that, toward the Galactic plane,
            ⟨ B⊥
            ⟩ is mostly oriented along the plane, corresponding to a polarization
          angle close to 0°. This is
          especially the case toward the outer MW regions. There are a few exceptions, in particular
          toward lines of sight that are tangent to spiral arms (Cygnus X, ℓII ≃ 81°,
            bII ≃
            0°; Carina, ℓII ≃ 277°, bII ≃ −9°),
          where the polarization signal is actually the smallest in the plane because in those
          regions the large-scale magnetic field is parallel to the LOS. This was already noted by
            Heiles (1996) (and references therein) and Benoît et al. (2004). We also note that the homogeneity
          of the field orientation being parallel to the plane extends away from the plane and up to
            | bII | ≃
            10° in many regions (in particular the Fan). At intermediate latitudes,
          the field orientation follows a few of the well known filamentary intensity structures of
          the local ISM. In particular, this is the case for the Aquila Rift and most of Loop I
          (outside the latitude range bII ≃ 50°−60°), where the structure of
            ⟨ B⊥
            ⟩ follows the intensity flare and loop elongation. As addressed
          earlier, this orientation of ⟨
                B⊥ ⟩ in those regions was
          already noted in the synchrotron polarized maps of WMAP (Gold et al. 2011). Other regions, however, show a variety of relative
          orientations between the field projection and intensity structures, which can also be
          orthogonal in some instances. Thus studies with Planck submillimetre
          polarization (Planck Collaboration Int. XXXII 2015;
            Planck Collaboration Int. XXXIII 2015) hold
          promise as a valuable complement to optical and near infrared polarization studies of the
          relative orientation of the magnetic field and structure (e.g., Goodman et al. 1990; Chapman et al.
            2011).
Citation: Benoît et al. (2004)
Citation function: Similarities; Similarities
Blazars are the subclass of active galactic nuclei (AGNs) characterized by a relativistic jet that is aligned close (≤10°) to the observer's line of sight (Urry & Padovani 1995). The Doppler-boosted non-thermal emission from the relativistic jets is highly variable at all observed timescales over essentially the entire electromagnetic spectrum. Variability seen over a timescale of less than a day is called intraday variability (IDV), or microvariability (Wagner & Witzel 1995), variations over a few days to months are often called short-term variability (STV), and fluctuations observed over several months to years, or even decades, are known as long-term variability (LTV; Gupta et al. 2004). The two classical subclasses of blazars are BL Lacertae objects (BL Lacs), which have no detectable, or very weak (EW  5Å), optical emission lines (Marcha et al. 1996), and flat spectrum radio quasars (FSRQs), which have the usual strong quasar emission lines in their optical spectra. The two broad bumps seen in the broadband spectral energy distributions (SEDs) of blazars indicate two different emission mechanisms. The low-energy peak is well understood to be caused by the synchrotron emission from relativistic electrons in the jet. However, the origin of the high-energy peak is still under debate. In the leptonic model, the high-energy component is interpreted as the inverse Compton (IC) scattering of synchrotron photons themselves (synchrotron-self Compton, SSC; e.g., Bloom & Marscher 1996), or external photons (external Compton, EC; e.g., Blandford & Levinson 1995) by the same electrons responsible for the synchrotron emission. In the alternative hadronic models, processes such as proton and muon synchrotron emission are thought to be responsible for the high-energy bump (e.g., Böttcher 2007). Blazars are also classified through the value of the peak frequency of the synchrotron component. It typically lies in the infrared to optical region in the low-frequency peak blazars (LBL), while in the high-frequency peaked blazars (HBL) it is located at FUV to X-ray energies (Padovani & Giommi 1995). The high-energy components of blazar SEDs peak at GeV energies in LBLs and at TeV energies in HBLs, but some LBLs and the intermediate-peaked blazars (IBLs) have still been detected at TeV energies.
Citation: Marcha et al. 1996
Citation function: Background
Now we estimate the average number of strong lensing systems within the region of possible GW sky location ($\mathbf {\delta \Omega }$), and capable of reproducing the observed ΔtGW and RGW. The probability for an object at redshift zs being strongly lensed by a foreground galaxy with redshift in [zl, zl + dzl] and velocity dispersion in [σv, σv + dσv] is 
(2)$$\begin{eqnarray*}
{\rm d}\tau = \frac{{\rm d}n(\sigma _v,z_l)}{{\rm d}\sigma _v}S_{cr}(\sigma _v,z_l,z_s)\frac{{\rm d}V(z_l)}{{\rm d}z_l}{\rm d}\sigma _v{\rm d}z_l.
\end{eqnarray*}$$Here n(σv, zl) is the comoving number density of the lens galaxies per unit velocity dispersion σv at redshift zl. $S_{cr}(\sigma _v,z_l,z_s)=\pi \theta _E^2$ is the cross-section for a lens of velocity dispersion σv at zl and a source at zs. V(zl) is the comoving volume within zl. For simplicity and consistency with previous research on detection rate of SLGWs for ET (Piórkowska et al. 2013; Biesiada et al. 2014; Li et al. 2018), we ignore the redshift dependence of n(σv, zl), and adopt the following Schechter distribution function 
(3)$$\begin{eqnarray*}
\frac{{\rm d}n(\sigma _v,z_l)}{{\rm d}\sigma _v} = n_*\left(\frac{\sigma _v}{\sigma _{v*}}\right)^\alpha \exp \left[-\left(\frac{\sigma _v}{\sigma _{v*}}\right)^\beta \right]\frac{\beta }{\Gamma (\alpha /\beta)}\frac{1}{\sigma _v},
\end{eqnarray*}$$where $(n_*,\sigma _{v*},\alpha ,\beta)=(8.0\times 10^{-3}\, h^3\, {\rm Mpc^{-3}},161\, {\rm km\, s}^{-1}, 2.32$, $2.67)$ comes from the galaxy sample of SDSS DR5 (Choi, Park & Vogeley 2007). Γ(α/β) is the Gamma function. Integrating equation (2), one obtains the probability for an object at redshift zs being strongly lensed. It is (Piórkowska et al. 2013) 
(4)$$\begin{eqnarray*}
\tau (z_s)=\frac{8}{15}\pi ^3(1+z_s)^3d_s^3\left(\frac{\sigma _{v*}}{c}\right)^4n_*\frac{\Gamma (\frac{4+\alpha }{\beta })}{\Gamma (\alpha /\beta)}.
\end{eqnarray*}$$To estimate the expected number of strongly lensed galaxies in redshift range (zs, zs + δzs), we need the redshift distribution of source galaxies. Here we approximate it by (Holz & Hughes 2005) 
(5)$$\begin{eqnarray*}
\frac{{\rm d}N}{{\rm d}r}=N_0r^a\exp (-(r/r_*)^b),
\end{eqnarray*}$$where (a, b, r*) = (1, 4, c/H0) and r is the comoving distance (Kaiser 1992; Hu 1999). The normalization factor N0 is chosen to satisfy $\int \frac{{\rm d}N}{{\rm d}r} {\rm d}r=40 \, \rm galaxies\, arcmin^{-2}$, corresponding to several important survey projects in the future like LSST, WFIRST, and Euclid (Yao et al. 2017). Then the expected number of strongly lensed galaxies in redshift range (zs, zs + δzs) will be 
(6)$$\begin{eqnarray*}
N_{\rm lg} = \int _{z_s}^{z_s+\delta z_s} \tau (z)\frac{{\rm d}N}{{\rm d}r}\frac{{\rm d}r(z)}{{\rm d}z}{\rm d}z.
\end{eqnarray*}$$The normalized differential distribution of the expected number of the lensed galaxies is shown as Fig. 1. It shows that most of lensed galaxies distribute in the range of redshift (0.5, 2.5) and the distribution peaks at z ≈ 1.5.
Citation: Piórkowska et al. 2013
Citation function: Uses; Uses
Citation: Piórkowska et al. 2013
Citation function: Uses; Uses
The PWN morphology depends on the pulsar’s Mach number 





, where v is the pulsar’s velocity and cs is the speed of sound in the ambient medium. Because even the transverse velocity of B0656+14, 





 km s−1 (Brisken et al. 2003)—where i is the angle between the velocity vector and the line of sight—exceeds the typical speed of sound in the ISM, 





–30 km s−1, the pulsar moves supersonically and the interaction of its wind with the ISM should produce a bow-shock PWN. X-ray emission from such a PWN is due to synchrotron radiation from the shocked pulsar wind outside the termination shock (TS). For large 





 and small values of the magnetization parameter σ of the preshock isotropic wind (Kennel & Coroniti 1984), the TS acquires a bullet-like shape (Bucciantini et al. 2005) with a distance 





 between the pulsar and bullet head, where 





 dyn cm−2 is the ram pressure, 





 is the mass density of the ambient medium, 





 (in units of cm−3), and 





. The bullet’s cylindrical radius is 





 and the distance of its back surface from the pulsar is 





. The shocked wind outside the TS is confined by the contact discontinuity (CD) surface, which has an approximately cylindrical shape behind the bullet, with a radius 





. The shocked wind flows along and past the bullet, reaching very high flow velocities: ∼(0.1–0.3)c in the “inner channel” (





) and up to (0.8–0.9)c in the “outer channel” (





) of the collimated outflow. The appearance of such a PWN depends on the velocity orientation angle i. For i close to 90°, the PWN would look like a bow-shock structure accompanied by a tail of collimated wind outflow. However, for small 





 the PWN would look nearly round because of the projection effect. Because the emission from the nearly relativistic flow is predominantly directed along the flow velocity, the apparent PWN radius 





 is smaller, 





, in the case of approaching pulsar than in the case of receding pulsar, when 





.
Citation: Kennel & Coroniti 1984
Citation function: Uses
For the clustering measurements, we use the sample of galaxies compiled in Data Release 11 (DR11) of the SDSS-III project. The SDSS-III is a spectroscopic investigation of galaxies and quasars selected from the imaging data obtained by the SDSS (York et al. 2000) I/II covering about 11,000 deg2 (Abazajian et al. 2009) using the dedicated 2.5 m SDSS Telescope (Gunn et al. 2006). The imaging employed a drift-scan mosaic CCD camera (Gunn et al. 1998) with five photometric bands (





 and z; Fukugita et al. 1996; Smith et al. 2002; Doi et al. 2010). The SDSS-III (Eisenstein et al. 2011) BOSS project (Ahn et al. 2012; Dawson et al. 2013) obtained additional imaging data of about 3000 deg2 (Aihara et al. 2011). The imaging data was processed by a series of pipelines (Lupton et al. 2001; Pier et al. 2003; Padmanabhan et al. 2008) and corrected for Galactic extinction (Schlegel et al. 1998) to obtain a reliable photometric catalog. This catalog was used as an input to select targets for spectroscopy (Dawson et al. 2013) for conducting the BOSS survey (Ahn et al. 2012) with the SDSS spectrographs (Smee et al. 2013). Targets are assigned to tiles of diameter 3° using an adaptive tiling algorithm designed to maximize the number of targets that can be successfully observed (Blanton et al. 2003). The resulting data were processed by an automated pipeline which performs spectral classification, redshift determination, and various parameter measurements, e.g., the stellar-mass measurements from a number of different stellar population synthesis codes which utilize the photometry and redshifts of the individual galaxies (Bolton et al. 2012). In addition to the galaxies targeted by the BOSS project, we also use galaxies that pass the target selection but have already been observed as part of the SDSS-I/II project (legacy galaxies). These legacy galaxies are subsampled in each sector so that they obey the same completeness as that of the CMASS sample (Anderson et al. 2014).
Citation: Doi et al. 2010
Citation function: Uses; Uses
Equation (1) describes the departure of the system from a ‘background’, time-independent state of exact corotation, where this departure is driven by $\dot{\boldsymbol {\Omega }}$. As a consequence, all quantities appearing in (1) are perturbations with respect to the corotating state. For instance, the magnetic field can be decomposed into a fixed background part, $\boldsymbol {B}_0$, plus a small, spin-down-induced perturbation, $\boldsymbol {b} \equiv \delta \boldsymbol {B}$, i.e.

(4)

\begin{equation}
\boldsymbol {B} \approx \boldsymbol {B}_0 + \boldsymbol {b}.
\end{equation}

The magnetic force can therefore be expressed to leading order

(5)

\begin{equation}
\boldsymbol {F}_{\rm mag} \approx - \nabla \left(\frac{\boldsymbol {B}_0 \cdot \boldsymbol {b} }{4\pi } \right) + \frac{1}{4\pi } \left[ (\boldsymbol {b} \cdot \nabla ) \boldsymbol {B}_0 + (\boldsymbol {B}_0 \cdot \nabla ) \boldsymbol {b} \right].
\end{equation}

The nature of the coupling force, $\boldsymbol {F}_{\rm cpl}$, is determined by the interaction between the superfluid's quantized vortices and the other components of the star (e.g. protons, electrons, the magnetic field). The simplest form for this force is provided by the Hall & Vinen mutual friction force (Hall & Vinen 1956a,b)

(6)

\begin{equation}
\boldsymbol {F}_{\rm cpl} = 2\Omega _{\rm n}\rho _{\rm n}\left\lbrace {\cal B}\left[ \hat{\boldsymbol {z}} \times (\hat{\boldsymbol {z}} \times \boldsymbol {w}) \right]+ {\cal B}^\prime (\hat{\boldsymbol {z}} \times \boldsymbol {w}) \right\rbrace ,
\end{equation}

where $\boldsymbol {w}= \boldsymbol {v}_{\rm n}-\boldsymbol {v}_{\rm p}$ is the velocity lag between the neutrons and the charged particles, ${\cal B}$ and ${\cal B}^\prime$ are mutual friction coefficients (which we take to be uniform throughout the star) and a ‘hat’ denotes a unit vector. This form of the force assumes a vortex array aligned with the common spin axis. According to our setup of the problem we have,

(7)

\begin{equation}
\boldsymbol {w} \approx \varpi (\Omega _{\rm n}-\Omega _{\rm p}) \hat{\varphi } \equiv \varpi \Omega _{\rm np}\hat{\bf {\varphi }},
\end{equation}

where ϖ = rsin θ is the usual cylindrical radius. The mutual friction coupling force becomes

(8)

\begin{equation}
\boldsymbol {F}_{\rm cpl} = -2\varpi \rho _{\rm n}\Omega _{\rm n}\Omega _{\rm np}\left({\cal B}\hat{\varphi } + {\cal B}^\prime \hat{\varpi}\right).
\end{equation}

The most commonly considered mutual friction mechanism in neutron star cores is the scattering of electrons by the magnetic field of individual vortices, in which case ${\cal B}^\prime \ll {\cal B}\sim 10^{-4}$ (Alpar et al. 1984; Andersson, Sidery & Comer 2006).
Citation: Hall & Vinen 1956a
Citation function: Uses; Uses
The importance of obtaining high-fidelity constraints on ΩK cannot be overstated. The sign and value of ΩK play an important role in determining the future evolution of the universe. From the model-building side, constraints on ΩK have important consequences for models of inflation, most of which predict an universe that is spatially flat to the level of 





 (see, e.g., Kazanas 1980; Starobinsky 1980; Guth 1981; Mukhanov & Chibisov 1981; Sato 1981; Albrecht & Steinhardt 1982; Linde 1982). Conversely, detecting ∣ΩK∣ ≠ 0 at the 





 level or larger could be a problem for most models of inflation (Linde 2008; Guth & Nomura 2012; Kleban & Schillo 2012), although others (see, e.g., Bull & Kamionkowski 2013) have argued that this might not be as problematic. It is generally simpler to construct inflationary models in a spatially open universe (see, e.g., Coleman & De Luccia 1980; Gott 1982; Ratra 1994; Ratra & Peebles 1995, 1994; Bucher et al. 1995; Linde 1995; Yamamoto et al. 1995; Linde 2008; Guth & Nomura 2012; Kleban & Schillo 2012), whereas achieving the same result in a spatially closed universe might require more fine-tuning (see, e.g., Ratra 1985; Hartle & Hawking 1987; Linde 2003; Ratra 2017). In any case, the importance of spatial curvature in modern cosmology is the reason why a huge number of works have been devoted to providing and forecasting constraints on ΩK from current and future cosmological observations.6

6
For an inevitably incomplete list of such works, see, e.g., Vardanyan et al. (2009), Carbone et al. (2011), Li & Zhang (2012), Bull et al. (2015), Takada & Dore (2015), Di Dio et al. (2016), Leonard et al. (2016), Rana et al. (2017), Ooba et al. (2018a), Jimenez et al. (2018), Ooba et al. (2018b), Park & Ratra (2018, 2019a, 2019b, 2019c, 2020), Denissenya et al. (2018), Bernal et al. (2019), Li et al. (2020), Wang et al. (2020), Zhai et al. (2020), Geng et al. (2020), Heinesen & Buchert (2020), Gao et al. (2020), Khadka & Ratra (2020), Nunes & Bernui (2020), Liu et al. (2020), Chudaykin et al. (2021), Benisty & Staicova (2020), Shimon & Rephaeli (2020), Tröster et al. (2020), Di Valentino et al. (2021), and Qi et al. (2020).
Citation: Kleban & Schillo 2012; Kleban & Schillo 2012
Citation function: Motivation; Motivation