adsabs/FOCAL huggingface dataset:
An outlier is defined to be an anomalous event or observation that arises from a process that differs from the majority of the data generation. Outlier detection has always been an indispensable part of data analysis; contaminated data sets without proper outlier treatment can increase modelling uncertainties and produce misleading results. A common mitigation strategy is to model the data as a Gaussian mixture of inlier and outlier distributions with differing variance (Hogg, Bovy & Lang 2010; Vallisneri & van Haasteren 2017). For example, assume a model with an inlier data model, yi = μi + ϵi, where yi is the i-th observation, μi is the mean, and ϵi is Gaussian random noise with variance $\sigma _i^2$. We can then account for possible outlier contamination in the data collection by modelling such fluctuations with $\epsilon _\mathrm{out}\sim \mathcal {N}(0, \sigma _\mathrm{out}^{2})$, where our full data model now includes a latent outlier indicator zi for each observation, where zi = 1 for an outlier and 0 otherwise. This indicator is modelled with a certain prior outlier probability, θ, e.g. zi ∼ Bernoulli(θ). This data model is a mixture of two Gaussians with different mean and different variances, which can be expressed in the form
(1)$$\begin{eqnarray}
y_i = (1-z_i) \mu _i +(1-z_i) \epsilon _i + z_i \epsilon _\mathrm{out}.
\end{eqnarray}$$Incorporating the outlier indication parameter zi allows us to assess the possibility of an individual measurement being an outlier and to formulate the likelihood as a mixture of two Gaussians that respectively model the inlier and outlier distributions:
(2)$$\begin{eqnarray}
p \left(y_{i} \mid \mu _{i}, z_{i}, \sigma _{i}, \sigma _{\mathrm{out }}\right)=\left\lbrace \begin{array}{l{@}{\quad}l}\mathrm{e}^{-\left(y_{i}- \mu _{i}\right)^{2} /\big(2 \sigma _{i}^{2}\big)} / \sqrt{2 \mathrm{\pi} \sigma _{i}^{2}}, &amp; \text{for } z_{i}=0 \\
\mathrm{e}^{-y_{i}^{2} /\big(2 \sigma _{\mathrm{out }}^{2}\big)} / \sqrt{2 \mathrm{\pi} \sigma _{\mathrm{out }}^{2}}, &amp; \text{for } z_{i}=1 .\end{array}\right. \\
\end{eqnarray}$$We use this model for the toy sine wave example in Section 2.3.
Citation: Vallisneri & van Haasteren 2017
Citation function: Uses
As expected, the final luminosity (LV) of our model dwarfs strongly correlates with the shape of their formation histories. We divide our models into three categories dependent on their LV range. In the following, we will refer to them as sustained, extended and quenched. A few representative cases of each of these three categories are shown in Fig. 9. The strength of the UV-background heating is indicated by the dotted black curve. It represents the hydrogen photo-heating rate due to the UV-background photons following the model of Haardt & Madau (2012).

(a)LV > 108 L⊙, sustained: the star formation rate of those massive and luminous dwarfs increases over 1 to 2 Gyr. This period is followed by a rather constant SFR plateau. These systems are massive enough to resist the UV-background heating and, once formed, to form stars continuously. This sustained star formation activity that lasts up to z = 0 results from the self-regulation between stellar feedback and gas cooling (Revaz et al. 2009; Revaz & Jablonka 2012).
(b)106 L⊙ LV  108 L⊙, extended: in this luminosity range, the star formation is clearly affected by the UV-background. After a rapid increase, the star formation activity is damped owing to the increase of the strength of the UV-heating. However, at the exception of the h070 halo which is definitively quenched after 6.5 Gyr, the potential well of those dwarfs is sufficiently deep to avoid a complete quenching. The star formation activity extends to z = 0, however, at a much lower rate than the original one.
(c)LV  106 L⊙, quenched: the potential well of those galaxies is so shallow that the gas heated by the UV - photons escape the systems. Star formation is generally rapidly quenched after 2 or 3 Gyr. Only halo h064 shows signs of activity up to 4 Gyr. Those galaxies may be considered as true fossils of the re-ionization in the nomenclature of Ricotti & Gnedin (2005). They are all faint objects with only old stellar populations.
Citation: Haardt & Madau (2012)
Citation function: Uses
In order for simulations to play a role in improving our understanding of the formation and dynamics of the CGM, particularly given the complex, multiphase picture emerging from the latest observations (Tumlinson et al. 2011; Werk et al. 2014), the level of detail and sophistication in stellar feedback models must improve. In this work, we analyse the outflowing (and infalling) gas seen in the galaxies and CGM of the Feedback in Realistic Environments (FIRE) simulations,1 first presented in Hopkins et al. (2014). Unlike the subgrid recipes which involve kinetically prescribed decoupled winds and cooling-suppressed blastwaves, the FIRE simulations solve the ‘overcooling’ problem by explicitly modelling the radiation pressure, stellar winds, and ionizing feedback from young stars as taken directly from the population synthesis code starburst99 (Leitherer et al. 1999). These ‘early feedback’ mechanisms act before SNe, heating and stirring the surrounding ISM which is necessary to match conditions in star-forming regions such as Carina (Harper-Clark & Murray 2009) and 30 Dor (Lopez et al. 2011; Pellegrini, Baldwin & Ferland 2011). SNe are implemented by taking into account their energy and momentum input. When the cooling radius of SNe is resolved, SN energy injected is free to expand and generate momentum in the ISM before too much energy is radiated away. When this scale is poorly resolved, momentum accumulation from SN remnant evolution below the resolution scale is added to the surrounding gas. This model is physically realistic when it is applied on the scale of giant molecular clouds, meaning that a resolution of several to tens of parsecs is required. The physical feedback implementation in FIRE successfully regulates mass accumulation in galaxies and provides a physical explanation for the inefficiency of star formation in galactic discs (Kennicutt 1983, 1998; Genzel et al. 2010). We stress that we allow hydrodynamical interactions and cooling of all gas at all times, unlike in typical subgrid models. This is critical to make meaningful predictions for the phase structure of circumgalactic gas.
Citation: Leitherer et al. 1999
Citation function: Uses
Once He core burning finishes the core contracts and hydrogen burning starts, the radius of the hot subdwarf expands beyond its Roche radius, and mass transfer starts at an orbital period close to the observed orbital period. Mass transfer will continue for ≈1 Myr at a rate exceeding 10−9 M⊙ yr−1 until hydrogen shell burning is finished and the star contracts to become a carbon–oxygen WD with a thick helium layer and a small residual layer of hydrogen. The high accretion rate will heat the accreting WD significantly (Townsley & Bildsten 2003). Models predict a Teff ≈ 50,000 K for accretion rates of 10−9 M⊙ yr−1 (Burdge et al. 2019) consistent with the high blackbody temperature of the accretor observed in ZTF J2055+4651. Accretion onto the WD companion at this rate will cause unstable hydrogen ignition after ≈10−4 M⊙ accumulates, leading to classical novae eruptions (Nomoto 1982; Nomoto et al. 2007; Wolf et al. 2013). This accretion rate predicts a recurrence time of order 105 yr for a total of approximately 10 novae. Our binary model suggests that this system is within the first ≈10% of the 1 Myr accretion phase. At the current state the orbit will shrink with 





 s s−1, which will be detectable after a few years of monitoring. The right panel of Figure 5 shows the evolution of the donor through this mass transfer phase. After accretion has ceased, the orbit of the system will continue to shrink due to the radiation of gravitational waves and the system will merge in ≈30 Myr. Our models predict that there is a substantial He layer of ≈0.05 M⊙ left in the former hot subdwarf and the total mass of the system is relatively high (Mtotal ≈ 1.1 M⊙). Recent models predict that such a system explodes as a subluminous thermonuclear supernova (Perets et al. 2019; Zenati et al. 2019). If the system avoids a thermonuclear supernova it will merge and could evolve into a rapidly rotating single high-mass carbon–oxygen WD (Saio 2008; Clayton 2012; Schwab 2019).
Citation: Townsley & Bildsten 2003
Citation function: Background
We have also considered early radio emission from gamma-ray bursts (GRBs), which can have higher brightness temperatures at early times than blazars, owing to their ultrarelativistic velocities. They can therefore be brighter and easier to measure while still at small angular sizes, and are consequently observed to show interstellar scintillation in their first days at ${\sim } 5\, \mbox{GHz}$ (Granot & van der Horst 2014). Before deceleration to Lorentz factor Γ  1/θj (before the ‘jet break’ for a jet of opening half-angle θj), the projected source angular size θ at (earth) time T after explosion of a GRB at redshift $z$ is θ ∼ 2cT Γ/DM($z$), where DM($z$) = DA($z$)(1 + $z$) is the proper motion distance, and DA($z$) the angular diameter distance. The Blandford–McKee blast wave of the ultrarelativistic shock moving into a medium of uniform external density ρ0 has radius R ≃ 2cT Γ2/(1 + $z$) and explosion energy per unit solid angle E/Ω ≃ ρ0R3Γ2c2, which gives Γ ≃ 9(Eiso, 53/n0)1/8(T/[(1 + $z$)day])−3/8, where $E=10^{53}\, \mbox{erg}(\Omega /4\pi)E_{iso,53}$ and n0 is the external density in cm−3 (Granot et al 2002, cf.). At DM($z$ = 1) = 3.3 Gpc, $\theta = [0.2,\, 1,\, 4]\, \mu \mbox{as}$ at $T=[0.1,\, 1,\, 10]\, \mbox{d}$. Thus at $\lambda \lt 4\, \mbox{cm}$ (the transition wavelength below which Milky Way scintillation becomes unimportant), the GRB will be smaller than our fiducial scattering angle $\theta =20\,\mu \mbox{as}(\lambda /30\, \mbox{cm})^{11/5}\lt 0.25\,\mu \mbox{as}$ for less than 0.1 d. During this time, the scintillation time-scale will be set by the rapidly expanding source, expanding across the refractive screen at a projected speed of ∼ΓcDl/Ds. This is many times c for our cosmological lenses with Dl ∼ 0.5Ds (but less than $1\, \mbox{km s}^{-1}$ for Milky Way interstellar plasma at $D_l\sim 100\, \mbox{pc}$, so Milky Way scintillation time-scales are dominated by gas motions in the Milky Way, not the apparent source expansion). The refractive scintillation time-scale is thus the same as the time-scale for the source to expand to a size larger than the refractive scale – i.e. the source will have only about 1 speckle before becoming too large to display refractive scintillation. This would be difficult to convincingly detect in a GRB.
Citation: Granot et al 2002
Citation function: Uses
We calculate the corresponding γ-ray spectrum constructed from the photons arriving at the observer within the observation time of MAGIC and plot it in the bottom panel of Fig. 5. Although it is possible to explain the very fast variability of the emission even with a moderate Lorentz factor of the blob, strong constraints are put by the level of the observed flux. If the emission region has a radius of Rb = 3 × 1014 cm, and is moving with a Lorentz factor of γb = 100, we require an energy density of ρE = 20 erg cm−3 (measured in the blob's frame of reference) to reproduce the flux observed by MAGIC and Fermi-LAT (see the bottom panel of Fig. 5). Note that such large values of the Lorentz factor of the emission region in the jet have been already postulated in terms of other models in order to explain extremely short flares observed in this source (Ackermann et al. 2014) or in the other sources, e.g. PKS 2155−304 (Aharonian et al. 2007). Such large Lorentz factors of the blob find also some observational support from the observations of the superluminal motion in PKS 1510−089 which represents similar type of blazar (Jorstad et al. 2005). We can estimate the power of the blob in the observer's reference frame on $L_{\rm blob} = \pi R_{\rm b}^2c\rho _E \gamma _{\rm b}^2\approx 1.7\times 10^{45}$ erg s−1. On the other hand, the Eddington luminosity of the black hole in PKS 1222+21, with the mass 6–8 × 108 M⊙, is LEdd = 1.3 × 1047M9 ≈ 8–10 × 1046 erg s−1. Therefore, the blob has to contain about ∼2 per cent of the Eddington power. This is quite demanding but seems not to be excluded, especially if Rb ≈ R⊥. Lower values of γb require a much higher energy density in the blob (e.g. ρE = 340 erg cm−3 for γb = 50 and Rb = 3 × 1014 cm). The strong dependence on the γb is a combined result of the transformation of the energy density to the reference frame of the observer and the beaming of the emission in a narrower cone. Note that a larger radius of the blob will lower the energy density constraint, e.g. for Rb = 1015 cm we obtain ρE = 4.9 erg cm−3 for γb = 100 and ρE = 80 erg cm−3 for γb = 50, at the assumption that there is no competing energy loss process of the electrons at such a large distance from the star.
Citation: Ackermann et al. 2014
Citation function: Similarities
Thermal motions of atoms produce a Doppler broadening of spectral lines with a Gaussian profile. Other unresolved velocities of a random nature are usually described as a turbulence broadening with a Gaussian or Lorentzian profile (see Rutten 2003, for a detailed description). The instrumental broadening encompasses the broadening caused by the finite spectral resolution of the instrument and is commonly approximated by a Gaussian. When other line broadening mechanisms are negligible, the total line broadening is the convolution of the line broadening profiles for the thermal and turbulence motions as well as the instrumental profile (Sect. 10.5 in  Böhm-Vitense 1989). In other words, the velocity equivalent of the observed line width, Wobs = c × Δλ/λ, at 1/e of the peak intensity results from instrumental, Doppler, and turbulence (non-thermal) broadenings by (1)\begin{equation} W_{\rm{obs}}^2 = \left(c\times \frac{\Delta\lambda}{\lambda}\right)^2 = W_{\rm{instrumental}}^2 + W_{\rm{Doppler}}^2 + W_{\rm{turbulence}}^2, \end{equation}Wobs2=c×Δλλ2=Winstrumental2+WDoppler2+Wturbulence2,assuming that all three line broadening components have a Gaussian profile (Eq. (4.17) of  Stix 2002). The POLIS instrumental width is less than 2 km s-1 (Beck 2006; Rezaei 2008; Beck et al. 2013a), while that of the Echelle spectrograph is of the same order. Assuming a generic chromospheric temperature of 104 K, we estimate a turbulence velocity using Eq. (2), (2)\begin{equation} \label{eq:one}  \Delta\lambda=\frac{\lambda}{c}\sqrt{2\,k_{\rm B}\,T/m+ W_{\rm{turbulence}}^2\,\,+\,\,W_{\rm{instrumental}}^2 }, \end{equation}Δλ=λc2 kB T/m+Wturbulence2  +  Winstrumental2,where Δλ is the observed line width, m is mass of the calcium atom, c the speed of light, and kB is the Boltzmann constant (Tandberg-Hanssen 1960). Using the measured width of Ca ii H & IR lines of 1.0 and 0.7 Å, respectively (Sect. 4), we estimate a turbulence velocity of about 45 km s-1 for Ca ii H and 24 km s-1 for Ca ii IR lines (we also note that the H1 minima of the EB profile is about 1 Å   wider than in the quiet Sun profile). The width of the emission peaks on either side of the Hα line (1 Å) amounts to a turbulence velocity of 15 km s-1. Attributing the line width to the temperature and the instrumental profiles (omitting the turbulence broadening), we get a temperature of about 5 ×  105 K, which is too hot for chromospheric heights. An increased turbulence velocity as a function of height in the chromosphere is part of standard models, either in the quiet Sun or sunspots (Kneer & Mattig 1978; Vernazza et al. 1981; Lites & Skumanich 1982). Our measured values, however, are larger than the turbulence velocity in an average atmosphere. The estimated turbulence velocity changes from one profile to another, but the general result remains the same: the observed width of the emission peaks is far in excess of any instrumental or thermal Doppler profile and to the first order has to have a turbulent nature. The Doppler width of a calcium line at 1–2 × 104 K is only about 2–3 km s-1, far from the observed widths of >20  km s-1.
Citation: Stix 2002
Citation function: Uses
As mentioned above, molecular oxygen was used to calibrate the magnetic field applied. A total of 155 Zeeman components (for the three transitions considered) was measured, with the magnetic field varied from B = 2.3 G (Itot = 0.2 Amp) to B = 113.5 G (Itot = 10 Amp). Figure 5 shows the Zeeman spectrum for the N,J = 3, 2 ← 1, 2 transition when a magnetic field of 5.7 G is applied. The fit was carried out with the program described in the previous section, with the spectroscopic parameters and g factors fixed at the values of Yu et al. (2012) and Christensen & Veseth (1978), Evenson & Mizushima (1972), respectively; the only free parameter was the correction factor to be applied to the theoretical magnetic field (see Eq. (1)). The fit reproduces in a satisfactory manner the measured Zeeman components, with a standard deviation of 73 kHz (the uncertainty for the measured frequencies was in most cases set to 70 kHz). Moving to SO, for the seven transitions considered, a total of 353 Zeeman components were measured, with the magnetic field varied from B = 5.7 Gauss (Itot = 0.5 Amp) to B = 124.8 Gauss (Itot = 11 Amp), and fitted as described above. In the fitting procedure the spectroscopic parameters (i.e., the rotational, centrifugal distortion, and fine structure constants) were kept fixed at the values derived by Lattanzi et al. (2015). The g factors resulting from the fit are given in Table 4 together with the best-estimated values discussed above, while the complete set of the measured Zeeman components is available in the Supplementary Material. Alternative fits were carried out: In the first fit, the three g factors, gs, gl, and gr, were fitted. In a second step, three different fits were carried out by fixing one of the three g factors and fitting the other two. In the last fit, only gs was determined. We note that in the first fit, based on the comparison with theory, the gs value is overestimated and the gl value is underestimated; the two terms therefore seem to be correlated. For this reason, we performed the additional fits described above. We note that in all cases, gr is determined with a limited accuracy, that is, with a relative uncertainty of ~20%. We also note that, if we fix gs at the best computed value, a gl value in good agreement with theory is obtained. However, by fixing gl at the best estimate, the resulting gs is still slightly overestimated. Simulations using values of gs in the 2.0020−2.0030 range show that the Zeeman splittings only change by a few tens of kHz, that is, in most cases within the typical uncertainty affecting the frequency measurements. The last comment concerns the standard deviation of the fits that, in all cases, is about 50 kHz.
Citation: Lattanzi et al. (2015)
Citation function: Uses
Table 3 shows the best-fit model parameters for the baseline fit for the three observations. We note that we did not find any statistically significant neutral or ionized absorption intrinsic to the source. On the addition of an ionized absorption model generated using the latest atomic data with the photoionization modeling code CLOUDY (Ferland et al. 2013; Laha et al. 2016c, 2016b, 2017, 2019b), we did not detect any improvement in the fit, as also found in previous works on this source (Rivers et al. 2011). Two blackbody components were necessary to describe the soft excess. We detected a narrow FeKα emission line in the Suzaku observation at an energy E = 6.41 ± 0.01  keV, while a marginally broad line (σ = 0.35 ± 0.08  keV) was required in the XMM-Newton and NuSTAR observations. We detected a neutral reflection hump at energy E > 10  keV with Suzaku that was modeled with pexrav, with an improvement  Δχ2 = 32 for one additional degree of freedom. The pexrav model assumes an exponentially cutoff power-law spectrum reflected from neutral material (Magdziarz & Zdziarski 1995). The output spectrum is the sum of the cutoff power law and the reflection component. However, the reflection component alone can be obtained by setting the relative reflection value negative. The power-law cutoff energy for pexrav is assumed to be 300  keV, the abundance of the reprocessor set to solar value, and we allowed the inclination angle of this model to vary between 0° and 45° (being a Seyfert 1 galaxy). We have tied the power-law photon index normalization of pexrav to that of the primary power-law component. The pexrav reflection fraction is 0.17 ± 0.03. Note that throughout the text, we refer to the positive value of the reflection fraction. We did not detect any significant neutral reflection component in the XMM-Newton+NuSTAR spectra. Table 2 shows the fluxes of the soft excess, power law, FeKα emission line, and hard X-ray excess. In XSPEC notation, the best-fit baseline model is written as constant × tbabs × (powerlaw+bbody+pexrav+Gaussian(s)). We note that we required an emission line at 0.56  keV for XMM-Newton observation, which corresponds to O vii emission and is found in several bright AGNs, and we did not need that model for Suzaku and NuSTAR, as they do not cover that energy range.
Citation: Magdziarz & Zdziarski 1995
Citation function: Uses
The remaining six parameters are less constrained. They are ϵe, ϵB, n0, L (where L = ηL0), κ and Ek. We apply constraints to the range of allowed values for these parameters. ϵB has been found to be as low as 10−8 (Barniol Duran 2014; Santana, Barniol Duran & Kumar 2014) and as a fraction can be as high as 1. In practice, ϵe tends towards higher values than ϵB. We set an upper limit of 1, noting that ϵe actually refers to the electron population that is emitting synchrotron radiation, rather than the electron population as a whole, and set a lower limit of 10−3 (Kumar 2000). n0 is limited between 10−5 and 100 cm−3, in line with what has been found in these sources (Cenko et al. 2011). The upper limit of L is set by the argument in equation (5), and values of this parameter below ∼1047 erg s−1 are never energetic enough to match the data, so we set the lower limit as 1047 erg s−1. Within these limits for L, we find that EE ceases to have any influence on the light curve if κ ≲ 10−2. If EE is isotropic, and the observed luminosity is only 1 per cent of the true energy (i.e. the conversion efficiency of kinetic to potential energy in the internal shocks is 1 per cent), then the energy delivered to the synchrotron shock front could be up to 100 times higher than observed in the light curve. In practice, however, the emission is (a) unlikely to be fully isotropic, (b) likely to shock more efficiently than 1 per cent, and (c) certain to be less than 100 per cent efficient at delivering its energy to the synchrotron shock front. For these reasons, we set the upper limit of κ at a still fairly generous factor of 10. Finally, we limit the energy in the shock from prompt emission to 1048 erg  Ek  1052 erg. The arguments for these limits are identical to those used for κ, except that the prompt emission is known to be beamed (Sari, Piran & Halpern 1999; Frail et al. 2001) so the upper limit is lower, and because the injected energy at early times is negligible, Ek dominates the early light curve so the lower limit can be much less energetic before its influence vanishes. These limits are summarized in Table 3.
Citation: Cenko et al. 2011
Citation function: Uses