adsabs/FOCAL huggingface dataset:
The data produced by the HMI instrument are of high quality; however, there are known uncertainties, limitations and systematic errors present that affect the measurement of magnetic flux. These include a sinusoidal variation in the total magnetic flux with a periodicity of 12 and 24 hr, due to a Doppler shift present in the Fe spectral line (Hoeksema et al. 2014). The main contribution to this shift is the geosynchronous orbit of SDO. The daily variation of ±3 km s−1 in spacecraft orbital velocity causes a sinusoidal variation in the total flux measured. This affects weak and strong magnetic fields in the LoS magnetograms differently, with the daily variation remaining less than 30 G for field strengths below 1000 G and less than 75 G for field strengths below 2250 G. On average during a day this is roughly ±35 G (Couvidat et al. 2015). Nevertheless, the strength of these instrumental and observational effects does not account for the strong flux cancellation we observe in AR 11226 prior to eruption. The leading edge of the positive polarity of AR 11226 reaches ∼60° from central meridian on June 6. Due to the spatially dependent sensitivity of HMI the noise level increases as a function of the center-to-limb angle and the spacecraft’s orbital velocity. This increases the value of pixels in low and moderate fields (between 250 and 750 G) by a few tens of percent and manifests itself as broad peaks that are centered at ∼±60° in the magnetic flux. This could be responsible for the increase in flux seen in Figure 5 at this time. However, the increase also coincides with the emergence of the two anti-Hale bipoles and so it is difficult to disentangle these effects. The proximity of AR 11226 to the limb on June 6 means that the magnetic flux was not measured right up until the time of the eruption but only until approximately a day beforehand. Therefore, these results provide a lower limit to the total flux canceled in the lead-up to the eruption. Furthermore, due to the fact that cancellation persists for several days, we can extrapolate that, if the cancellation process continued at the same rate (2.0 × 1019  Mx hr−1) as we observed in the period from June 1 09:00 UT to June 5 00:00 UT up until eruption, then an extra 1.1 × 1021 Mx could have been canceled. This would therefore result in a total amount of 2.8 × 1021 Mx flux canceled between two consecutive CMEs.
Citation: Couvidat et al. 2015
Citation function: Uses; Compare/Contrast
The values rinf, ρinf, and σinf of equations (9) and (10) were computed assuming a bulge mass profile. Unlike other works that use isothermal sphere or Dehnen profiles (see e.g Volonteri, Haardt & Madau 2003; Sesana 2010; Sesana & Khan 2015; Bonetti et al. 2018b; Volonteri et al. 2020), here we decided to use a Sérsic model. This choice is motivated by observational studies that found it to be a good approximation for fitting the bulge light distribution of different galaxies (Drory & Fisher 2007; Drory & Alvarez 2008; Gadotti 2009). The analytical expressions for the Sérsic model are taken from Prugniel & Simien (1997) (see also Terzić & Graham 2005):
(11)$$\begin{eqnarray*}
\rm \rho (\mathit {r}) = \rho _0 \left(\frac{\mathit {r}}{{\it R}_e}\right)^{-{\it p}} \mathit {\rm e}^{-{\it b}\left({\mathit {r}}/{{\it R}_e}\right)^{1/{\it n}}},
\end{eqnarray*}$$(12)$$\begin{eqnarray*}
\rm \sigma ^2(\mathit {r}) &amp;=&amp; \frac{4 \pi G \rho _0^2 \mathrm{{\it R}_{\rm e}}^2 n^2 b^{2\mathit {n}(p-1)}}{\rho (\mathit {r})} \nonumber\\&amp;&amp;\times \, \int _Z^{\infty } \mathcal {Z}^{-\mathit {n}(p+1)-1} {\rm e}^{-\mathcal {Z}} \gamma (\mathit {n}(3-p),\mathcal {Z}) {\rm d}\mathcal {Z},
\end{eqnarray*}$$where $\rm {\it R}_e$ is the bulge effective radius,8 ρ0 is the central bulge density, and n is its Sérsic index. This index correlates with the central concentration of the bulge, being the bulges with smaller n, the ones less centrally concentrated. Finally, the variable γ represents the incomplete gamma function, whereas Z, p, and b are three different quantities that depend on the bulge properties: $\rm {\it Z} = {\it b}(\mathit {r}/{\it R}_e)^{1/{\it n}}$, $p = 1 - 0.6097 n^{-1} + 0.05563 n^{-2}$, and $\mathrm{\it b} = 2n - 0.33 + 0.009\,876 n^{-1}$. This Sérsic model causes that smaller MBHs spend more time in the hardening phase than the most massive ones. To guide the reader, for an MBHB system with total mass $\rm {\it M}_{bin} = 10^9\, M_{\odot }$, $q = 1$, and $e_{\rm BH} = 0.3$, the hardening time-scale is $\rm {\sim }0.2\, Gyr$. For the same system but with $\rm {\it M}_{bin} = 10^6\, M_{\odot }$, the time increases up to $\rm 10\, Gyr$. For further details, we refer to Biava et al. (2019), where a detailed study of hardening time-scales in different bulge profiles was performed.
Citation: Terzić & Graham 2005
Citation function: Uses
Steady and smooth decline: Since falling from the peak of the 2012b event, SN 2009ip has only continued to fade and is now the faintest it has ever been in the optical. Immediately after the 2012 event (around day 200), it was declining somewhat slower than the rate of 56Co decay for a 56Ni mass of 0.04 $\, {\rm M}_{\odot }$ (shown by the dashed grey line in Fig. 2). During that time, its light curve and spectral properties were consistent with those of late-time SNe IIn, and it had an underlying broad-line spectrum similar to that of SN 1987A (Graham et al. 2014; Smith et al. 2014). Up to about day 1000 it continued to fade smoothly at a slower rate around 0.003 mag d−1, and spectroscopically it continued to resemble late-time interaction in SNe IIn (Fox et al. 2015; Smith et al. 2016b; Graham et al. 2017). Our new HST photometry shows that from about day 1000 to day 3000, SN 2009ip has continued to fade smoothly and steadily in the optical, at an even slower rate. While the HST cadence is obviously sparse at these late times, the filters with more than two observations (F555W and F814W) show no significant deviation from a steady decline; there is no evidence of any rebrightening or irregularity in the fading rate. From 2015 to 2021, the decline rates in the various optical filters are 0.00051 ± 0.00001 mag d−1 in F555W, 0.00068 ± 0.00002 mag d−1 in F606W, 0.00092 ± 0.00001 mag d−1 in F657N, and 0.00050 ± 0.00001 mag d−1 in F814W. (The UV is an exception, as discussed below.) While this decline is much slower than radioactive decay, such slow decline rates are not at all unusual for SNe IIn with late-time CSM interaction. SNe IIn span a wide diversity of late-time decay rates, ranging from some SNe IIn that have essentially flat light curves for many years, like SN 2005ip (Smith et al. 2009, 2017; Stritzinger et al. 2012; Fox et al. 2020), down to those that have only weak CSM interaction and faster decline rates that are difficult to distinguish from radioactive decay or light echoes. Some SNe IIn even rebrighten at late times, like SN 2006jd (Stritzinger et al. 2012). In any case, it seems as if SN 2009ip is levelling off and approaching a constant V absolute magnitude of −7.5 or so. In all three broad continuum filters, the object is now fainter than the progenitor, and the light curve has not exhibited any additional eruptive variability since the 2012b event.
Citation: Smith et al.; 2017
Citation function: Background; Background
Fermi–LAT (Atwood et al. 2009) is a pair conversion telescope, with a field of view (FoV) of above 2 sr, operating in the energy range from 20 MeV to 300 GeV. It is the most sensitive instrument available in this energy range (Ackermann et al. 2012). A few months after the launch in 2008 June, Fermi–LAT started to operate in all sky survey mode. The telescope scans the whole sky in 3 h (Atwood et al. 2009). For this paper we have analysed the Pass81 data from 2010 February 13 to 17. We analysed the data for Mrk 421 using the latest Fermi Science Tool2 software package version v10r0p5. In order to determine the flux and the spectrum of the source, maximum likelihood optimization has been used (Abdo et al. 2009). The data selection and quality checks have been made using the gtselect tool.3 Since the telescope is sensitive to γ-rays from the interactions of cosmic rays with the ambient matter, we set our maximum zenith angle at 105 deg to remove the background γ-ray events from Earth’s limb. The analysis included all photons from a circular region of 10 deg around Mrk 421, which we call the region of interest (ROI). Only photons of energy above 100 MeV were considered for further analysis. The latest LAT instrument response function ‘P8R2_SOURCE_V6’ has been used. The third Fermi–LAT catalogue (3FGL catalogue: Acero et al. 2015) has been used to include the contributions of sources inside the ROI. The spectral model of the source has been considered as a simple power law of the form $\mathrm{ d}N(E)/\mathrm{ d}E = N_0 (E/E_0)^{-\Gamma _{\mathrm{ ph}}}$, where N0 is called the prefactor, Γph is the index, and E0 is the scale in energy. The spectral parameters of the sources including Mrk 421 inside the ROI are kept free, whereas the spectral parameters of the sources beyond 10 deg from Mrk 421 are kept fixed to the values according to the 3FGL catalogue. The unbinned likelihood4 method has been used in order to estimate the detection significance of the sources. The test statistics parameter determined from the aforementioned method is given by TS = 2Δlog(L), where L denotes the likelihood function between the model with the source and without the source. According to the definition TS = 9 corresponds to a detection significance of ∼3σ (Mattox et al. 1996). All the sources with TS  9 are excluded from the likelihood analysis. In order to model the spectrum of sources, we used the latest Galactic diffuse emission model ‘gll_iem_v06’ and the isotropic background model ‘iso_P8R2_SOURCE_V6_v06’. We estimated the corresponding butterfly plots for the source using the methods mentioned in the Fermi–LAT webpage.5 VERITAS observed the high-flux state of Mrk 421 for ∼6 h. In order to obtain quasi-simultaneous data with VERITAS, we also analysed the Fermi–LAT data for this state by taking 12 h around the VERITAS observation period. In Fig. 2(d), we show the butterfly plots for both 24 and 12 h by closed butterfly (grey) and open butterfly with cross at the edges (blue), respectively, for the high-flux state.
Citation: Acero et al. 2015
Citation function: Uses; Uses
To solve equations (9)−(11), the pulsar rotation rate Ω0, the long-term spin-down rate $\dot{\Omega }_\infty$, the initial lag δΩ0, the mutual-friction coefficients $\mathcal {B}_{\operatorname{\text{f}}}$ and $\mathcal {B}_{\operatorname{\text{pin}}}$, and the ratios $I_{\operatorname{\text{n}}}^{\operatorname{\text{f}}}/I$ and $I_{\operatorname{\text{n}}}^{\operatorname{\text{pin}}}/I$ need to be specified. In what follows, Ω0 and $\dot{\Omega }_\infty$ are directly taken from pulsar timing. The coefficient $\mathcal {B}_{\operatorname{\text{f}}}$ in the non-pinned region is given by $\mathcal {B}_0$, and the corresponding drag-to-lift ratio by equation (8). In the pinned region, the coefficient $\mathcal {B}_{\operatorname{\text{pin}}}$ is given by equation (6), with the prescription (7) and suitable parameters. Typical values for the underlying parameters are: $\varepsilon _{\operatorname{\text{p}}}^{\operatorname{\text{pin}}}\simeq 0.05-0.2$, $\varepsilon _{\operatorname{\text{p}}}^{\operatorname{\text{f}}}\simeq 0.1-0.5$ (see e.g. Chamel & Haensel 2006; Sourie, Oertel & Novak 2016), $x_{\operatorname{\text{p}}}^{\operatorname{\text{pin}}} \simeq 0.05 - 0.1$, $x_{\operatorname{\text{p}}}^{\operatorname{\text{f}}} \simeq 0.05 - 0.4$, $\rho _{\operatorname{\text{pin}}} \simeq (0.5-2) \rho _0$, and $\rho _{\operatorname{\text{f}}} \simeq (2-6) \rho _0$, ρ0 ≃ 2.7 × 1014 g cm−3 being the nuclear saturation density (see e.g. Pearson et al. 2018). The ratios $I_{\operatorname{\text{n}}}^{\operatorname{\text{pin}}}/I$ and $I_{\operatorname{\text{n}}}^{\operatorname{\text{f}}}/I$ are computed using the relations $I_{\operatorname{\text{n}}}^{_X} /I^{_X} = 1-x_{\operatorname{\text{p}}}^{_X}$ (assuming uniform densities in each region), where $I^{_X}$ is the total moment of inertia of region X, and $I^{\operatorname{\text{f}}} = I-I^{\operatorname{\, \text{cr}}}-I^{\operatorname{\text{pin}}}$, $I^{\operatorname{\, \text{cr}}}$ denoting the crustal moment of inertia of the star. Typical values are: $I^{\operatorname{\, \text{cr}}}/I\simeq 0.01-0.05$ (Delsate et al. 2016) and $I^{\operatorname{\text{pin}}}/I\sim 0.05$ (Gügercinoğlu & Alpar 2014). Unlike the previous quantities, both the initial lag δΩ0 and number $N_{\operatorname{\text{p}}}$ of pinned fluxoids are essentially unknown. As shown in the next section, the large range of possible values for $N_{\operatorname{\text{p}}}$ could account for the very different spin-up behaviours in the Crab and Vela pulsars.
Citation: Sourie, Oertel & Novak 2016
Citation function: Uses
The KN coincident with GW170817 showed a rapidly fading EM transient in the optical and infrared bands. The term kilonova was historically coined from the perception of its brightness being a thousand times larger than a nova (Li & Paczyński 1998; Rosswog 2005; Metzger et al. 2010). We discuss in this work that, even if far from such a standardized luminosity, clear dependencies on physical BNS quantities can be extracted. For AT 2017gfo, the observed spectral evolution is suggested to arise from a mixed composition of r-process elements in the ejected material (Gillanders et al. 2022); while early-time spectra are consistent with light r-process elements (nuclear masses A ∼ 90 − 140), later spectra require intermediate composition, producing even heavier elements such as lanthanides. An alternative scenario, such as dust formation in the KN that could also explain such a blue-red evolution, has been ruled out (Gall et al. 2017). In addition, a broad feature observed at ∼0.7 − 1 μm has been interpreted as due to Sr II (Watson et al. 2019; Domoto et al. 2021; Gillanders et al. 2022). Since then, no other KN has been firmly detected (see e.g., Coughlin 2020 and references therein for a summary of the follow-up efforts during LIGO and Virgo’s third observing campaign). Another merger candidate is linked to GW190814, located farther away at ∼240 Mpc, whose origin remains uncertain. However, it lacks of any EM counterpart and could likely be caused by a binary black hole merger (Essick & Landry 2020; Tews et al. 2021). GW190425 was the first BNS candidate in O3. The LALInference localization pipeline (Veitch et al. 2015) provided a 90% credible region of 7461 deg2, estimated luminosity distance of 156 ± 41 Mpc, much larger than that for GW170817, which complicated the search campaign resulting in no EM counterpart identified. The inferred merger parameters from the GW analysis published in Abbott et al. (2020a) for chirp mass 



1
.

44

−
0.02


+
0.02




M
⊙



$ 1.44^{+0.02}_{-0.02}\,M_{\odot} $


 are the following. Total mass 




M
1

+

M
2

≃
3
.

4

−
0.1


+
0.3




M
⊙



$ M_{1}+M_{2} \simeq 3.4_{-0.1}^{+0.3}\,M_{\odot} $


, with M1 ∈ (1.62, 1.88) M⊙, M2 ∈ (1.45, 1.69) M⊙, and 




Λ
∼

≤
600


$ \tilde{\Lambda} \leq 600 $


 for low spin prior, or M1 ∈ (1.61, 2.52) M⊙, M2 ∈ (1.12, 1.68) M⊙, and 




Λ
∼

≤
1100


$ \tilde{\Lambda} \leq 1100 $


 for high-spin prior. Note that for the other confirmed BNS event, GW170817, the inferred total mass is 




M
1

+

M
2

≃
2
.

73

−
0.01


+
0.04




M
⊙



$ M_{1}+M_{2} \simeq 2.73_{-0.01}^{+0.04}\,M_{\odot} $


 with M1 ∈ (1.36, 1.60) M⊙, M2 ∈ (1.16, 1.36) M⊙, and 




Λ
∼

=

300

−
230


+
420




$ \tilde{\Lambda} = 300_{-230}^{+420} $


 for low-spin prior (Abbott et al. 2019).
Citation: Gall et al. 2017
Citation function: Background
The LoTSS survey, homogeneously covering the whole northern sky complete down to the sub mJy limit will overcome statistical limitations due to shot noise. The large galaxy number density and large sky coverage will substantially reduce cosmic variance in cosmological analysis. The radio galaxies, tracing the background dark matter, will constrain the shape of power spectrum, i.e., the early universe physics, dark matter, baryon, density of neutrinos, the inflation power spectrum, and the degree of non-Gaussianity in density fluctuations. The upcoming LoTSS catalogs, covering a large sky area, will help us to explore further regarding large-scale anomalies (de Oliveira-Costa et al. 2004; Ralston & Jain 2004; Schwarz et al. 2004; Tiwari & Aluri 2019) and the current puzzling dipole signal observed with radio catalogs (Blake & Wall 2002; Singal 2011; Gibelyou & Huterer 2012; Rubart & Schwarz 2013; Tiwari & Jain 2015; Tiwari et al. 2015; Tiwari & Nusser 2016; Colin et al. 2017; Siewert et al. 2021). Furthermore, LoTSS will significantly improve on present low-frequency radio catalogs, e.g., TIFR GMRT Sky Survey (TGSS; Intema et al. 2017) and GaLactic and Extragalactic All-sky MWA (GLEAM; Hurley-Walker et al. 2017), and analyses based on these surveys (Dolfi et al. 2019; Rana & Bagla 2019; Tiwari 2019; Tiwari et al. 2019; Choudhuri et al. 2020). Unfortunately, the link between the galaxy and total matter power spectra depends on some unknowns from astrophysics, such as the galaxy bias factor, which depends on galaxy type and is quite different for radio AGNs and star-forming galaxies. The LoTSS population is a mixture of AGNs and star-forming galaxies, and therefore understanding galaxy bias, relative number densities, and luminosity evolution is nontrivial. The purpose of this work is to present a detailed cosmological analysis of LoTSS galaxies and study the effect of survey footprint, shot noise, and other systematics. We have produced galaxy mocks for the survey and have customized and calibrated the data pipeline for galaxy clustering statistics recovery.
Citation: Tiwari & Nusser 2016
Citation function: Future Work; Future Work
A new result brought by our work is the role of incident polarization on the reflected spectral outcome. Although some X-ray polarization of the primary radiation is expected to be due to Comptonization of thermal radiation inside the corona, general estimates for the polarization degree of the primary source are rather low ($\lesssim 10\,{\rm {per \, cent}}$) according to the recent analysis in Beheshtipour et al. (2017), Tamborra et al. (2018), and Beheshtipour (2018). If some polarization was present, then, for symmetric reasons, vertically or horizontally polarized light should be dominant in case of extended coronal models (Dabrowski & Lasenby 2001; Niedzwiecki & Zycki 2008; Schnittman & Krolik 2010) at low heights. In case of lamp-post models (Matt, Perola & Piro 1991; Martocchia & Matt 1996; Henri & Petrucci 1997; Martocchia, Karas & Matt 2000; Dovčiak, Karas & Yaqoob 2004a; Miniutti & Fabian 2004) general-relativistic effects will rotate the polarization position angle along null geodesics from the corona towards the disc (Connors et al. 1980) and the situation becomes more general for incident disc irradiation, i.e. any incident state of polarization is possible. Our computations, apart from the unpolarized case, assumed two extreme cases of initial $p = 100\,{\rm {per \, cent}}$ polarization in order to estimate its possible effects in comparison with the completely unpolarized light and in order to test that the code adheres to the stated orientation conventions. Having appended these two initially polarized cases to our tables, it also allows for interpolation of reflection results for any input polarization state from this basis of the three computed independent polarization states, which will be necessary in future construction of global spectropolarimetric models. We aim to address any impact of light bending and other relativistic effects for a distant observer in our future works that will introduce the stokes local tables integrated over the accretion disc with some adopted global geometry.
Citation: Henri & Petrucci 1997
Citation function: Compare/Contrast; Compare/Contrast; Compare/Contrast
Now we turn to the question of whether there are any general trends or strong correlations between the degree of HSP compliance, the average Fidx, and the average Φ derived from the AR samples contained in the defined HRs. As shown in the scatter plot of the average Fidx versus the HSP (Figure 5(a)), we find a weak tendency that HRs with lower degrees of HSP compliance show larger values of the average Fidx, with the linear Pearson correlation coefficient (PCC) of −0.55. In the scatter plot, the anti-HSP region with the largest average Fidx can be considered as an extreme case, which lies far away from both the vertical and horizontal dashes lines used to separate data points of the five lowest HSP and the five largest average Fidx, respectively. On the other hand, a positive correlation exists between the average Φ and the average Fidx with the linear PCC = 0.65 (refer to Figure 5(b)). Such correlation of Φ with flaring activity in individual ARs has been reported in many previous studies (e.g., Leka & Barnes 2003, 2007; Park et al. 2010; Liu et al. 2017; Lee et al. 2018), but it is reported here for the first time on this larger spatial scale of the HRs over a much longer period of solar cycle 24. As shown in Figure 5(c), a negative, although weak, correlation appears between the HSP and the average Φ with the linear PCC = −0.36. In contrast, a weak trend was reported in Paper I that ARs with larger values of Φ show a higher HSP. These two contrasting trends of the HSP with the average Φ are mainly due to the different ways of dividing the same AR samples into smaller subsets. The AR subsets in this study were selected based on heliographic locations of the AR samples in the defined Carrington longitude–latitude plane, while those in Paper I as a function of Φ values. The two highest flare-productive HRs with the average Fidx ≥15 have the average Φ values ranked in the top two as well as lower degrees of HSP compliance (i.e., one with the lowest HSP and the other with the HSP in the bottom 20%). Meanwhile, the two highly flare-productive regions can be considered as obvious outliers, compared to the positive trend of the HSP with respect to the average Φ in Paper I. This may indicate that the HSP for those regions is obscured by vigorous turbulent convective flows interacting with rising flux tubes therein. As mentioned earlier, the two X-class flaring ARs, NOAA 12673 and NOAA 12192, are located at the two HRs, respectively. Even excluding these two influential ARs, however, all of the trends as described in Figure 5 remain the same, although the correlations become less strong (i.e., the linear PCCs of −0.25, 0.51, and −0.27 for the cases in Figures 5(a), (b), and (c)).
Citation: Leka & Barnes; 2007
Citation function: Similarities