text:
\section{Introduction} \label{sec:intro}

Neutron stars (NSs) are born very hot in the aftermath of the core-collapse supernova event which brings them into existence, and then progressively cool down through neutrino and photon emission. Their thermal evolution is interwoven with that of their
magnetic field because of the strong dependence on the temperature of the electric and magnetic conductivities. A detailed study of the NS coupled magnetic and thermal evolution is challenging, not the least on the numerical ground, and has been the focus of several investigations over the past 20 years \cite[see e.g.][for reviews and a historical overview]{transport,Pons_2019,2013PhDT.........7V}.
Most recent efforts were devoted to extending previous axially symmetric calculations to three spatial dimensions. This was  done first by considering the evolution of the $B$-field only \cite[][]{2016PNAS} and then addressing the coupled
magnetothermal problem \citep{2020NatAs.tmp..215I,2020ApJ...903...40D,Igoshev_2021}.

A realistic modeling of NS cooling is key in understanding their internal structure and composition, ultimately bearing to the equation of state of ultra dense matter. In this respect, the detection and interpretation of radiation coming from the (cooling) surface of an isolated NS can provide a direct measure of the star radius and offer insights on the topology of the crustal magnetic field. Thermal emission has been indeed observed, mostly in the soft X-ray band, from several different classes of NSs, including radio pulsars (PSRs), soft gamma repeaters (SGRs) and anomalous X-ray pulsars (AXPs; the magnetar candidates), central compact objects in supernova remnants (CCOs) and a handful of radio-quiet X-ray pulsars known as the ``magnificent seven'' \cite[M7 or XDINSs; see e.g.][for reviews]{2009ASSL..357...91B,2009ASSL..357..141T,2017ARA&A..55..261K,De_Luca_2017}. Besides, thermal emission has been detected in the soft X-ray transients, NS sources in binary systems which cool down during the quiescent state when accretion is turned off \cite[see e.g.][]{2017JApA...38...49W,2020arXiv201110490P}.

Thermal X-rays from NSs are pulsed, indicating that emission comes from a limited region, as in the case of PSRs and SGRs/AXPs, or from the entire star surface, as in the M7 and possibly some of the CCOs, but with a inhomogeneous temperature distribution. Actually, the most general occurrence is a mixture of the two, with localized ``hot spots'', believed to be produced by some form of extra heating (backflowing currents or dissipation of magnetic energy in the crust), superimposed to the rest of the cooling surface, the emission of which is often (but not always) undetected.
Pulse profiles are in many cases far from sinusoidal and the pulsed fraction can be very large, pointing to complex shapes of the emitting region and/or to some form of beaming.
Extracting meaningful information from spectral and timing data requires an \emph{a priori} knowledge of the surface temperature map and emission properties. A simple fitting with a single component spectral model, say a blackbody, would, in fact, provide only the radiation radius, i.e. an estimate of the size of the emitting region (which not necessarily coincides with the star radius) and a value of the temperature which mostly reflects that of the hotter region(s).

Three-dimensional magnetothermal models can indeed provide a consistent, detailed surface temperature map at different stages of the NS evolution which can be used to compute synthetic spectra and lightcurves for different emission  mechanisms. These can be then confronted with X-ray (and optical) observations. Such an approach has been applied in the past to different sources, the M7 \cite[][]{2006MNRAS.366..727Z,2011A&A...534A..74H}, the magnetar candidates \cite[e.g.][and references therein]{2020MNRAS.492.5057T} and the PSRs \cite[][]{2019ApJ...872...15R}.

Previous studies, however, dealt with thermal surface distributions which were either derived from a prescribed magnetic topology (usually with high degrees of symmetry, e.g. \citealt{2017MNRAS.464.4390P}), or which was given \emph{a priori} to mimic various crustal heating mechanisms \citep[e.g.][]{2014MNRAS.443...31V}, but with no regard to the actual structure of the $B$-field, as it follows from evolution. Very recently \cite{2020NatAs.tmp..215I} presented 3D magnetothermal simulations of magnetars and computed self-consistent lightcurves for a number of sources in quiescence, although the effects of the heat blanketing envelope (see section \ref{sec:magthermevol}) were accounted for in a simplified way.

Among the diverse classes of isolated NSs the M7 are the most promising target for applying 3D magnetothermal simulations to X-ray spectral modeling. These sources, in fact, exhibit purely thermal emission, most likely originating from the entire star surface, are not variable \cite[with the exception of \zeroseven, see again ][]{2009ASSL..357..141T} and, albeit being sometimes dubbed \emph{X-ray dim isolated neutron stars}, are
quite bright in the soft X-rays. As such, they have been repeatedly observed by all major X-ray telescopes, from {\em ROSAT} to {\em Chandra} and especially {\em XMM-Newton}.

In this work we present models of 3D magnetothermal evolution of isolated neutron stars and  consistently derive their observable properties (phase-dependent spectra, pulse profiles, pulsed fraction). The plan of the paper is as follows. The physics of magnetothermal evolution and the numerical code used for the simulations, together with the tools used to compute the radiation spectrum at infinity, are reviewed in Section \ref{sec:methods}. In Section \ref{sec:results} we present a set of simulations, both in the case of initially axisymmetric and of more complex magnetic configurations. The properties of the former models in connection with those of the brightest of the M7, \eighteen, are discussed in  Section \ref{sec:1856}. Discussion and conclusions follow in Section \ref{sec:conclusions}.

\section{Methods}\label{sec:methods}
\replaced{In this section we briefly describe the tools used in calculating the magnetothermal evolution of isolated neutron stars (INSs) and the radiation spectrum emitted by their cooling surface.}{
The key ingredients for describing the thermal X-ray emission coming from an isolated NS are its surface temperature distribution, which in turn is dictated by the topology of the magnetic field in the crust, and how radiation propagates to the observer, which is greatly influenced by strong gravitational field. In this section, we lay out the tools we employ to compute the thermal and magnetic structure of the crust and its time evolution, and for calculating the thermal flux detected at infinity.
}

\subsection{Magneto-thermal evolution}\label{sec:magthermevol}

{In a magnetized NS, thermal and magnetic evolution are strongly coupled. However, where the star internal magnetic field (mostly) resides is still an open question. In fact, even though it is commonly accepted that the core of a NS is in some sort of superfluid/superconducting state, it is unclear as yet whether the flux expulsion via the Meissner effect is slow enough to allow for some field to be retained in the core over a significant timescale. This reflects in the diverse strategies adopted in previous investigations, which divide into those considering the magneto-thermal evolution of the whole star and the ones focusing on the crust alone. The latter has been the approach of choice when dealing with computations in more than one spatial dimensions \citep[e.g.][see also \citealt{Pons_2019} for a recent review]{2007A&A...470..303P,2013MNRAS.434..123V,2014PhRvL.112q1101G,2014MNRAS.438.1618G}. In this paper we build on the same line, starting from the model presented by \citet{2015PhRvL.114s1101W} to study the crustal magnetic field in three dimensions, but including the thermal evolution of the crust as well. The same approach has been already used in \citet[][in the following DG+20]{2020ApJ...903...40D} and \citet{2020NatAs.tmp..215I}, to which we refer for more details.

The thermal and magnetic evolution of the crust are then described by the induction equation, in the electron MHD regime (eMHD, i.e. in the assumption that only electrons can move), and the heat balance equation
\begin{align}
 \frac{\partial\mathbf{B}}{\partial t} &= -c\,{\boldsymbol{\nabla}}\times\left[\sigma^{-1}\mathbf{J} +\frac{1}{{\rm e} cn_e}\mathbf{J}\times{\mathbf{B}}+ \boldsymbol{G}\cdot{\boldsymbol{\nabla}} T-\frac{{\boldsymbol{\nabla}}\mu}{{\rm e}}\right] \label{eq:Induction}\\
  C_v\frac{\partial T}{\partial t} &= - {\boldsymbol{\nabla}}\cdot\left( T\boldsymbol{G}\cdot\mathbf{J} - \boldsymbol{k}\cdot{\boldsymbol{\nabla}} T - \frac{\mu}{{\rm e}}\mathbf{J}\right) + \mathbf{E}\cdot\mathbf{J}+N_\nu \label{eq:heat}
\end{align}
where $n_e$ is the electron density, $\mathbf{J}=c{\boldsymbol{\nabla}}\times\mathbf{B}/4\pi$ is the current, $\mu$ the chemical potential, $\boldsymbol{G}$ and $\boldsymbol{k}$ are the thermopower and thermal conductivity tensors and $C_v$ is the heat capacity (per unit volume). The term in square brackets in equation (\ref{eq:Induction}) represents the electric field $\mathbf{E}$, as expressed by the generalized Ohm law and $N_\nu$ accounts for energy losses due to neutrino produced by weak processes in the crust. The explicit form we use for $N_\nu$ is detailed in DG+20. However, neutrino emission from the crust is negligible for temperatures below $\approx\SI{e9}{\kelvin}$ \citep{2001PhR...354....1Y}. Since this condition is met for all the models presented in this work, crustal neutrino losses will be not considered in the following. Equations (\ref{eq:Induction}) and (\ref{eq:heat}), written in dimensionless form, were solved in three spatial dimensions by means of the {\sc parody} code (DG+20).

The (numerical) hindrances of a 3D approach force us to introduce a number of simplifying assumptions concerning the microphysical input. These were already discussed in DG+20 but are summarized in the following for the sake of clarity and completeness. We assume that electrons are completely degenerate, so that
\begin{equation}
    \mu= c\hslash (3\pi^2n_e)^{1/3}; \qquad \boldsymbol{G} = -\frac{\pi^2k_B^2T}{{\rm e}\mu}\delta_{ij}
\end{equation}
where $\hslash$ and $k_B$ are the reduced Planck and the Boltzmann constants. Here we only consider the isotropic part of the thermopower tensor, the so-called Seebeck, term which is responsible for the Biermann battery effect. The (scalar) electric and thermal conductivity are taken to be those of electrons,
\begin{equation}
\sigma={\rm e}^2c^2\,\frac{n_e\tau(\mu)}{\mu}; \qquad (\boldsymbol{k}^{-1})_{ij}=\frac{3{\rm e}^2}{\pi^2k_b^2T} \left(\frac{1}{\sigma}\delta_{ij}+\frac{\epsilon_{ijk}B_k}{{\rm e} c n_e}\right)
\end{equation}
where $\tau$ is the relaxation time and $\epsilon_{ijk}$ is the Levi-Civita symbol.
A pure eMHD description of the crust implies that other contributions to the transport properties are neglected; in particular, we do not take into account the isotropic terms in the thermal conductivity due to the lattice and superfluid neutrons. While the former contribution is always subdominant, the latter can become comparable if not greater than the electron one for comparatively high temperatures and densities ($T\approx\SI{e8}{\kelvin}$, $\rho\gtrsim\SI{e12}{\gram\per\cubic\centi\meter}$ \citep[see][]{2009PhRvL.102i1101A}.

The crust is in hydrostatic equilibrium and spherically-symmetric, so that the electron density depends only on the radius, $r$. Following \citet{2004ApJ...609..999C}, we choose the scaling $n_e\propto z^4$, where $z$ is the depth into the crust. More specifically, we take
\begin{align} \label{eq:density}
\mu(r) &= [1 + (1 - r)/0.0463]^{4/3}
\end{align}
with the chemical potential in units of $\mu_0=\SI{2.9e-5}{\erg}$ and $r$ in units of the star radius. This simple expression has been computed by \citet{2014MNRAS.438.1618G} to provide an acceptable fit to a realistic Fe-Ni crustal model with a chosen impurity parameter $Q\simeq3$ based again on \citet{2004ApJ...609..999C}. The density drops from $\rho(r_\text{core})\approx\SI{e14}{\gram\per\cubic\centi\meter}$ to $\rho(r_\text{crust})\approx\SI{e11}{\gram\per\cubic\centi\meter}$ in a $\SI{1}{\kilo\meter}$ thick crust. Although the solid crust can extend down to $\rho\lesssim\SI{e8}{\gram\per\cubic\centi\meter}$, this shallow region is not included in our grid.

 Moreover, we assume that the relaxation time is constant throughout the crust, $\tau=\SI{9.9e-19}{\second}$. This is adequate in the lower crust, but it becomes questionable in the upper layers, where the contribution by phonons becomes important \citep{transport}. The adopted value, however, is such that the conductivity in the upper crust matches the phonon conductivity at a realistic temperature, $T\approx\SI{e8}{\kelvin}$.

Finally, we take the specific heat to be that of the electrons, $C_v=\tau\mu^2T$. This assumption is quite rough, since the (temperature independent) contribution of the ion lattice is dominant or at least of the same order of magnitude under typical NS conditions \citep[see again][and the discussion in DG+20]{transport}. This choice is dictated essentially by computational requirements, since it makes eq. (\ref{eq:heat}) dependent on $T^2$ only (see again DG+20). However, the large conductivity of the crust greatly suppresses the term containing $C_v$ in eq. (\ref{eq:heat}). This implies that the long-term crustal evolution, such as we are considering here, is not too sensitive to the exact form of the specific heat. We are nevertheless aware that this a major limitation and a more realistic expression for $C_v$ will be necessary in investigating impulsive events, like a sudden, localized release of energy in crust (see the discussion in DG+20).}

Since the field is confined within the crust of the NS, the inner boundary conditions are fixed by the requirement that the radial component of the magnetic field and the tangential component of the electric field vanish at the core-crust interface, $r_c$. Since the contribution of the Hall term is negligible at $r_c$, this is tantamount to ask that $B_r(r_c)=0,\ J_t(r_c)=0$ where $J_t$ is the tangential component of the current.
Moreover, we assume that the magnetosphere can only support currents that are negligible with respect to those inside the crust. The outer boundary condition requires then that the field at the top of the crust matches a potential one.

Following again DG+20 (see their Eq. 23), we adopt a simplified time evolution equation for the (isothermal) core temperature, whereas the temperature on the surface of the star is controlled by the properties of the envelope. This is a geometrically thin layer in which a huge temperature gradient is present, and is treated separately. The surface temperature $T_s$ (i.e. that at the top of the envelope) is related to that at the top of the crust, $T_b$, by \added{the relation}
\begin{equation}\label{eq:tsurf}
T_s(T_b, g, \mathbf{B})=T_s^{(0)}(T_b, g)\,\mathcal{X}(T_b, \mathbf{B})
\end{equation}
where $g$ is the gravitational acceleration at the surface. We used the expressions for $T_s^{(0)}$ calculated by \citet{1983ApJ...272..286G} for an iron envelope, with the magnetic correction $\mathcal{X}(T_b,\mathbf{B})$ given by \citet{envelopes}. \added{The latter term describes how the} heat blanketing effect of the envelope is enhanced by the presence of the magnetic field, which thwarts heat transport as field lines get more parallel to the surface.

The solution of equation (\ref{eq:heat}), coupled with equation (\ref{eq:Induction}) and (\ref{eq:tsurf}), provides the thermal map of the surface at any given time. This can be used to simulate the thermal surface emission once a model for radiative processes is specified.
\added{We remark that magnetothermal evolution is computed without taking into account general relativistic effects. Given the limited thickness of the crust, inclusion of GR would result only in a minor change of the magnetic outer boundary condition which has a negligible overall effect \citep[see][DG+20]{2009A&A...496..207P}. Nevertheless, GR crucially affects light propagation from the surface to the observer as discussed in detail in the next section.}

\subsection{Observed spectrum}\label{sec:spectrum}
In order to simulate the emitted radiation from an isolated NS and to reproduce the spectrum as observed at infinity, we exploit the {\sc idl} ray-tracing code originally developed by \citet[see also \citealt{2015MNRAS.454.3254T,2017MNRAS.464.4390P}]{2006MNRAS.366..727Z}. The code starts dividing the star surface into $N_\Theta\times N_\Phi$ angular patches, each one characterized by the co-latitude $\Theta$ and azimuth $\Phi$ of its center in the observer's frame $XYZ$, with the $Z$-axis along the line-of-sight (LOS) and the $X$-axis in the plane of the LOS and the star spin axis $\boldsymbol{\Omega}$. Photons emitted from the surface and propagating along the LOS are then selected, eventually summing together the contributions coming from all the patches which are into view at a given rotational phase $\gamma$.

GR effects are accounted for assuming that the space-time outside the star is described by the vacuum Schwarzschild solution, including both gravitational red-shift and relativistic ray-bending; as a consequence an area larger than an hemisphere is visible at each rotational phase.
The phase- and energy-dependent radiation flux at the observer is then given by
\begin{align} \label{eq:raybending1}
    F_\nu(\gamma)&=(1-x)\frac{R^2_{\rm NS}}{D^2}\int_0^{2\pi}{\rm d}{\Phi}\int_0^1I_\nu{\rm d}u^2\,,
\end{align}
where $x\equiv 2GM_{\rm NS}/c^2R_{\rm NS}$, with $M_{\rm NS}$ and $R_{\rm NS}$ the star mass and radius and $c$ the speed of light, $D$ is the source distance and $u\equiv\sin\bar{\Theta}$, with
\begin{align} \label{eq:raybending2}
    \bar{\Theta}&=\int_0^{1/2}\frac{{\rm d}v\sin\Theta}{[(1-x)/4-(1-2vx)v^2\sin^2\Theta]^{1/2}}\,.
\end{align}

The specific intensity $I_\nu$ follows once a model for the surface emissivity is specified. \added{Here, $\nu$ is the frequency as measured by a static observer at the star's surface, whereas the frequency at infinity is $\nu_\infty=\nu\sqrt{1-x}$.} It depends in general on the photon propagation direction as well as on the magnetic co-latitude $\theta$ and azimuth $\phi$, which label the emission point in the star frame $pqt$, with the $t$-axis along the magnetic field axis. If the field is axially symmetric, the magnetic axis trivially coincides with that of the dipole component, $\boldsymbol{b}_{\rm dip}$, whereas in more complex topologies a choice must be made. In the non symmetric cases presented in section \ref{sec:results}, we took the field axis to be along the axis of the quadrupole component, $\boldsymbol{b}_{\rm quad}$. The  two angles $\theta$ and $\phi$ can be expressed in terms of those in the observer's frame, $\Theta$ and $\Phi$, and of $\chi$ and $\xi$ ($\psi$), the angles that the spin axis makes with the LOS and $\boldsymbol{b}_{\rm dip}$ ($\boldsymbol{b}_{\rm quad}$), respectively \cite[see][for more details]{2015MNRAS.454.3254T}. It can be easily shown that it is $\psi=\xi\pm\Theta_\mathrm q$, where $\Theta_\mathrm q$ is the angle between $\boldsymbol{b}_{\rm dip}$ and $\boldsymbol{b}_{\rm quad}$ (see again section \ref{sec:tilted}). For each configuration, corresponding to different values of the angles $\chi$ and $\xi$ ($\psi$) on a $21\times21$ evenly spaced grid, the code finally returns the observed spectrum as a function of the rotational phase (chosen from 30 evenly spaced values).

This approach has been used to study the spectral and polarization properties of thermal radiation emitted from NS sources accounting for realistic surface emission models \cite[a magnetic condensate, a magnetized atmosphere,][]{2016MNRAS.459.3585G,2017MNRAS.465..492M,2020MNRAS.492.5057T}. Here, however, we assume
that the (local) spectrum is an isotropic blackbody, i.e.
\begin{align} \label{eq:bbody}
    I_\nu(\theta,\phi)=\frac{2h}{c^2}\frac{\nu^3}{\exp[h\nu/kT(\theta,\phi)]-1}\,,
\end{align}
where $h$ is the Planck's constant and $T(\theta,\phi)$ is the temperature map produced by {\sc parody}. This (simplifying) choice is motivated because our main aim is to assess the effects of considering self-consistent thermal maps on a number of observable quantities (pulse profiles, phase-resolved spectra), rather then producing detailed predictions for the spectral distribution. Moreover, the overall X-ray spectra of the M7 are better interpreted in terms of (one or two) blackbody(s) (with the presence of broad absorption features at $\approx 100$ eV in a few sources), even in the case of bright sources, like \eighteen\ for which a large number of counts is available \cite[][]{2009ASSL..357..141T,2014A&A...563A..50P}.

\section{Results}\label{sec:results}
We performed numerical 3D simulations to follow the magnetothermal evolution of an isolated neutron star over some Hall times, defined from the scale values as $\tau_H=4\pi n_0{\rm e} R^2/cB_0\approx\SI{e4}{\year}$, exploring, in particular, different initial conditions for the magnetic field. All models refer to a NS with mass $M_\mathrm{NS}=1.2 M_\odot$ and radius $R_\mathrm{NS}=\SI{12}{\kilo\meter}$. In this phase the evolution is dominated by the non-linear Hall term (see equation \ref{eq:Induction}, second term on the rhs), which, albeit being conservative \citep{2007A&A...470..303P}, can transfer energy between different multipolar components of the $B$-field, until a magnetic configuration dominated by odd modes, the so-called \emph{Hall attractor}, is reached before ohmic dissipation takes over \citep{2014PhRvL.112q1101G}. The latter acts more effectively on higher multipoles, hence the field will eventually go back to a dipole-like configuration. This process, however, acts on the much longer Ohm timescale $\tau_O=4\pi\sigma_0 R^2/c^2\approx\SI{e7}{\year}$, which we do not follow here due to the long computational times required by our 3D code

\begin{figure}
    \centering
    \includegraphics[width=.5\textwidth]{evo_1856.pdf}
    \caption{Evolution of the magnetic energy content in the first seven field multipoles for the axially symmetric run discussed in section \ref{sec:axsym}.}
    \label{fig:Hall}
\end{figure}

The large thermal conductivity of the crust makes equation (\ref{eq:heat}) rather insensitive of the temperature rate of change, so that the star thermal evolution tends to follow the magnetic one: the thermal distribution is influenced by local ohmic dissipation due to currents and by the fact that the electron-mediated heat transport follows the field lines (see {DG+20} and references therein). The magnetic evolution strongly depends on the initial conditions for the $B$-field, so are the latter that actually control the surface thermal map at each evolutionary stage. In this section we present results for a number of cases, starting with axisymmetric initial conditions (section \ref{sec:axsym}) and then moving to more complex magnetic topologies (section \ref{sec:tilted}).

\subsection{Axisymmetric cases}\label{sec:axsym}
\begin{figure}
    \centering
   \subfigure{\includegraphics[width=.5\textwidth]{in_state.png}}
   \subfigure{\includegraphics[width=.5\textwidth]{fin_state.png}}
    \caption{Internal (left) and surface (right) temperature at an early ($t=\SI{2}{\kilo\year}$, top row) and late ($t=\SI{4e5}{\year}$, bottom row) phase of the evolution. The field lines of the poloidal component are superimposed. The width of the crust is enlarged by a factor $4$ to improve visualization.}
    \label{fig:Tevo}
\end{figure}

We consider first a highly symmetric case, starting the evolution from a force-free, purely dipolar field with $B_\text{dip}(0)\approx\SI{3e13}{\gauss}$, which obeys the boundary conditions. Having previously checked that with such an initial condition the field does not develop instabilities and maintains axial symmetry, as well as north-south (anti)symmetry, during the entire evolution (DG+20), here we restrict the spatial integration domain to a wedge encompassing one sixth of the longitudes with periodic boundary conditions in order to save computational time. Moreover, we decided to reduce the parameter space in this case by suppressing core cooling and setting an initial uniform temperature $T=\SI{4.5e7}{\kelvin}$. This value has been chosen so that to produce a maximum surface temperature of \replaced{$\sim \SI{60}{\eV}$}{$\sim \SI{75}{\eV}$ (corresponding to $\sim \SI{60}{\eV}$ for an observer at infinity)} at an age of $\sim\SI{4e5}{\year}$ in view of the application described in Sec. \ref{sec:1856}. We remark that this, however, does not affect the consistency of our thermal maps, since the core thermal evolution sets the overall temperature scale in the crust, but does not affect its topology, which is dictated by the shape of the magnetic field due again to the large conductivity of the crust.

The evolution of the magnetic field is summarized in Figure \ref{fig:Hall}, where the magnetic energy content of the first seven multipolar components is shown. The formation of the Hall attractor, dominated by odd $\ell$ multipoles, is clearly seen before ohmic dissipation starts to substantially reduce the field at an age of $\approx\SI{e5}{\year}$.

A general feature of axially symmetric runs is an enhancement of the magnetic field in the equatorial region of the crust, which also becomes hotter. This is due to the currents circulating there and also to the fact that it is threaded by closed field lines, which inhibit heat conduction towards the surface. This hotter internal belt, however, does not automatically translate into a hotter equatorial zone on the surface, since the surface temperature map follows after accounting for heat transport in the envelope. Near the equator, the field lines are almost parallel to the surface, hence the surface temperature is lower, resulting in the appearance of a \emph{colder} equatorial belt.

\begin{figure}
    \centering
    \includegraphics[width=.5\textwidth]{Lightcurves_1856.pdf}
    \caption{Pulse profiles in the $\num{0.1}-\SI{3}{\kilo\eV}$
    energy band for the axisymmetric case at $t=\SI{4e5}{\year}$ for selected values of the two geometrical angles; each curve is labeled by the corresponding values of $\chi$ and $\xi$ (in degrees) and shown in a different color.}
    \label{fig:LCs}
\end{figure}

This is clearly illustrated in Figure \ref{fig:Tevo} where the thermal structure of the crust, together with the temperature map at the top of the crust and at the surface is shown at two subsequent phases of the evolution. In the early phases, the temperature anisotropy is small enough that magnetic screening dominates, and the surface temperature monotonically decreases from the poles to the equator, giving rise to a thermal distribution close to the well-known one produced by a purely dipolar field on the top of an isothermal crust, i.e. a cold equatorial belt and two hotter polar regions \citep[][see also \citealt{1995SSRv...74..437P, 2017MNRAS.464.4390P}]{1983ApJ...271..283G}. On the other hand, as the evolution proceeds, the poloidal field lines are more tightly wound up near the equator and the ``heat trap'' mechanism described previously becomes effective. As a consequence, an equatorial hot region appears on the surface, with a small low temperature ring exactly on the equator, while the polar regions are at an intermediate temperature.

\begin{figure}
    \centering
    \includegraphics[width=.5\textwidth]{montaggio_r.png}
    \caption{Pulsed fraction as a function of time during the evolution of a NS with axisymmetric field. The three evolution curves correspond to the viewing angles $\chi=\ang{90}$, $\xi=\ang{90}$ (blue, corresponding to the maximum value), $\chi=\ang{36.2}$, $\xi=\ang{31.8}$ (green, see Sec.\ \ref{sec:1856}) and $\chi=\ang{90}$, $\xi=\ang{0}$ (orange). Contour plots show the dependence on the viewing geometry at the selected ages, $\SI{25}{\kilo\year}$ (top-right), $\SI{123}{\kilo\year}$ (bottom-left) and $\SI{265}{\kilo\year}$ (bottom-right). The contour line at $\PF=1.2\%$ corresponds to the value observed for \eighteen\ (see again Sec.\ \ref{sec:1856}).}
    \label{fig:PFevo}
\end{figure}

The thermal maps we obtained were then used as the input for our ray-tracing code in order to get the spectrum received by an observer at infinity as a function of the rotational phase and the two geometrical angles $\chi$ and $\xi$ defined in section \ref{sec:spectrum}. A detailed discussion of the (phase-dependent) spectral distribution is postponed to section \ref{sec:1856}, where an application of our results to the isolated NS \eighteen\ is presented. Here we focus on the pulse profiles and, in particular, on the pulsed fraction and its time evolution. The pulse profiles at an age of $\simeq\SI{4e5}{\year}$ are shown in Figure \ref{fig:LCs} for some representative values of the angles $\chi$ and $\xi$. The pulsation is symmetric around half a period and the profiles are quasi-sinusoidal, with a double-peak structure appearing for those geometries in which the equatorial belt (see Figure \ref{fig:Tevo}) crosses the LOS more than once in a period.

We characterize each lightcurve through its pulsed fraction $\PF$,
\begin{equation}
    \PF=\frac{F_\text{max}-F_\text{min}}{F_\text{max}+F_\text{min}},
\end{equation}
where $ F_\text{max}$ ($F_\text{min}$) is the maximum (minimum) of the flux, integrated over a given energy band, along the pulse profile. Having specified an emission model (a blackbody in the present case, see \ref{sec:spectrum}), the $\PF$ depends on the thermal map, the viewing geometry and the selected energy range. Fig.\ \ref{fig:PFevo} shows the evolution in time of the maximum $\PF$ (i.e. the one for the most favorable viewing geometry; the minimum one is always $\simeq0$), as well as its dependence on the angles $\chi$ and $\xi$. The $\PF$ peaks at an early stage of the evolution ($t\simeq\SI{25}{\kilo\year}$), when the highest temperature anisotropy in the crust is reached, and then slowly decreases as the crust becomes isothermal and the field is pushed back to a pure dipole by ohmic dissipation. The overall value is anyway quite low, $\PF\lesssim 5\%$. This is expected given the high degree of symmetry of the configuration, and is indeed well below the maximum $\PF$ predicted for an axisymmetric model, which can reach $\sim 10\%$ for comparable star mass and radius for an isotropic emission model \citep{1995SSRv...74..437P}.
The north-south symmetry of the temperature maps is reflected in the invariance of the $\PF$ upon the exchange of the $\chi$ and $\xi$ angles, i.e., the symmetry along the $\chi=\xi$ diagonal in the contour plots of Fig.\ \ref{fig:PFevo}.

\subsubsection{An application: the INS \eighteen} \label{sec:1856}
\eighteen\ was the first source discovered among the M7 and it is the brightest of its class. Since its identification in the Rosat All Sky Survey by \cite{1996Natur.379..233W}, it has been the target of many observations with the {\it XMM-Newton} and {\it Chandra} satellites \citep[see][for a comprehensive analysis of existing data]{2012AA...541A..66S}. Emission \eighteen\ is pulsed at a period of $P\sim 7$ s with a very low pulsed fraction, $\PF\sim 1.2\%$ \citep[][]{2007ApJ...657L.101T}. The lack of an accurate measurement of the period derivative $\dot P$ prevented up to now a robust estimate of the $B$-field: \citet{2008ApJ...673L.163V} provided a spin-down value of $B\sim \SI{1.5e13}{\gauss}$, while a lower value, $B\sim 3-\SI{4e12}{\gauss}$, has been inferred from spectral fitting with atmospheric models by \citet{2007MNRAS.375..821H}. The, quite uncertain, spin-down age of \eighteen \ is  $\tau_\mathrm{c}\approx\SI{4}{\mega\year}$ but dynamical estimates, based on the identification of the NS birthplace, give instead $\tau_\mathrm{dyn}\sim\SI{4e5}{\year}$ \citep[][]{2011MNRAS.417..617T,2013MNRAS.429.3517M}.
\eighteen\ exhibits a purely thermal spectrum, with no absorption features. Analyzing a large set of {\it XMM-Newton} data, \cite{2012AA...541A..66S} found that it is best fitted by two blackbodies, with (redshifted) temperatures $T_1=\SI{62.4}{\eV}$, $T_2=\SI{38.9}{eV}$ ($T_2/T_1\simeq0.59$) and radiation radii $R_1=\SI{4.7}{\kilo\meter}$, $R_2=\SI{11.8}{\kilo\meter}$ at an assumed distance of \SI{120}{\parsec}; this yields a ratio between the emitting areas of $A_2/A_1\simeq6.3$.

This simple spectrum, combined with the very low $\PF\sim1.2\%$, suggest that \eighteen\ harbors a simple, symmetric field. In order to assess if our axisymmetric models can indeed bear to observations, we take run  discussed in section \ref{sec:axsym}, for which the initial conditions were selected to match the dipolar magnetic field (here we take $B_\text{dip}\simeq\SI{4e12}{\gauss}$) and the temperature of the hotter spectral component of \eighteen\ at the inferred dynamical age. We then fitted the computed spectra at different epochs with a double BB function
\begin{equation}\label{eq:2BB}
    F(E)=E^3\left[\displaystyle{\frac{A_1}{\exp(E/T_1)-1}}+
    \displaystyle{\frac{A_2}{\exp(E/T_2) -1}}\right],
\end{equation}
where $E$ is the photon energy, $T_1$, $T_2$ the temperatures (all in $\si{\kilo\eV}$) and $A_1$, $A_2$ are the emitting areas.
We find that all our spectra can indeed be interpreted as the superposition of two BB profiles. The ratios $T_2/T_1$ and $A_2/A_1$, as derived from the fits, are shown in Figure \ref{fig:evo_fit} at different epochs.

The fit at a simulation time close to the inferred dynamical age returns a value of  the area of the hotter component which is smaller than that of the colder one. By requiring that the computed pulsed fraction matches the observed one, $\PF\simeq1.2\%$, we get $T_2/T_1\approx0.76$ and $A_2/A_1$ ranging between $6.0$ and $6.7$, according to the selected source geometry. These are indeed in broad agreement with the observations, even if the simplifying assumptions of our model prevent a more quantitative comparison. Figure \ref{fig:spec1D} shows the fit for $\chi=\ang{36.2}$ and $\xi=\ang{31.8}$. This geometry was chosen since it satisfies the $\PF$ requirement and produces a ratio $A_2/A_1=6.3$, which is the closest to observations among the computed ones.

This result is of interest since earlier attempts to reproduce the spectral parameters of \eighteen\ in the framework of the Hall attractor could reproduce the temperature ratio, but finding consistently that the {\it hot} region had the largest area \citep{2017MNRAS.464.4390P}. This is because only the imprint of the magnetic field on the surface temperature was considered, without taking into account the thermal structure of the crust itself. When considering the effects of the coupling of the magnetic field evolution with temperature in the whole crust, we found that efficient heat trapping mechanism with a high degree of symmetry allows small hot structures to form and persist over long enough timescales.

\begin{figure}
    \centering
    \includegraphics[width=.5\textwidth]{evo_fit_log.pdf}
    \caption{Evolution of the $T_2/T_1$ and $A_2/A_1$ ratios extracted by fitting the synthetic spectra with the double BB  at selected times (results are connected through spline curves). The full ranges of values corresponding to all the viewing geometries explored are reported in the plots.}
    \label{fig:evo_fit}
\end{figure}

\begin{figure}
    \centering
    \includegraphics[width=.5\textwidth]{Fits-1D.png}
    \caption{Phase-averaged synthetic spectrum of \eighteen\ (black-solid curve) computed at $t\simeq\SI{4e5}{\year}$ together with the best fitting BB+BB model (yellow-dotted curve, nearly indistinguishable from the calculated spectrum) and the single hotter (red dash-dotted) and hotter (blue dashed) components. The geometrical angles $\chi=\ang{36.2}$ and $\xi=\ang{31.8}$ are chosen in such a way that the observed $\PF\simeq1.2\%$ is reproduced and that the ratio $A_2/A_1=6.3$ is the closest to the observed one.}
    \label{fig:spec1D}
\end{figure}

\subsection{Beyond axial symmetry}\label{sec:tilted}

\begin{table}[]
    \centering
    \begin{tabular}{ccc}
         \toprule
         $\Theta_q$& $\beta$&$\PF_\text{max}$\\
         \midrule
         \ang{45}& 0.75 & 16\%\\
         \ang{45}& 1.25 & 20\%\\
         \ang{45}& 10   & 23\%\\
         \ang{90}& 1    & 4\%\\
         \bottomrule
    \end{tabular}
    \caption{Parameters of the configurations discussed in Sec.\ \ref{sec:tilted}, with the maximum value of the $\PF$ reached in the evolution.}
    \label{tab:rot_cases}
\end{table}

\begin{figure}
    \centering
    \includegraphics[width=.5\textwidth]{Lightcurves_2195.pdf}
    \caption{Same as Fig.\ \ref{fig:LCs} for the case $\Theta_q=\ang{45}$, $\beta=1.25$ at time $t=\SI{9570}{\year}$.}
    \label{fig:LCs_rot}
\end{figure}

\begin{figure*}
\centering
\subfigure[Mollweide projection of the thermal maps at the top of the crust (left) and at the surface (right).]{\raisebox{.8em}{\includegraphics[width=.48\textwidth]{temps_075_rev.png}}}~~
\subfigure[Evolution of the $\PF$ for selected viewing angles, alongside its full dependence on $\xi$ and $\psi$ at selected times.] {\includegraphics[width=.49\textwidth]{PFs_b075_readble.png}}
\caption{Thermal maps and pulsed fractions for the case $\beta=0.75$, $\Theta_q=\ang{45}$, shown at three times $t_1=\SI{6378}{\year}$, $t_2=\SI{9570}{\year}$ and $t_3=\SI{41476}{\year}$. The $\PF$ evolution curves correspond to the viewing geometries with angles $\chi=\ang{90}$, $\psi=\ang{0}$ (blue, corresponding to the maximum overall value), $\chi=\ang{65}$, $\psi=\ang{45}$ (green) and $\chi=\ang{45}$, $\psi=\ang{45}$ (orange).}\label{fig:rot1}
\end{figure*}

\begin{figure*}
\centering
\subfigure[]{\raisebox{.8em}{\includegraphics[width=.48\textwidth]{temps_125_rev.png}}}~~
\subfigure[]{\includegraphics[width=.49\textwidth]{PFs_b125_r.png}}
\caption{Same as in Figure \ref{fig:rot1} for the case $\beta=1.25$, $\Theta_q=\ang{45}$, shown at three times $t_1=\SI{6378}{\year}$, $t_2=\SI{9570}{\year}$ and $t_3=\SI{41476}{\year}$.}\label{fig:rot2}
\end{figure*}

\begin{figure*}
\centering
\subfigure[]{\raisebox{.8em}{\includegraphics[width=.48\textwidth]{temps10_rev.png}}}~~
\subfigure[]{\includegraphics[width=.49\textwidth]{PFs_b10_r.png}}
\caption{Same as in Figure \ref{fig:rot1} for the case $\beta=10$, $\Theta_q=\ang{45}$, shown at three times $t_1=\SI{25637}{\year}$, $t_2=\SI{68900}{\year}$ and $t_3=\SI{169700}{\year}$ (note that the timescale is quite different from the one of Figs. \ref{fig:rot1} and \ref{fig:rot2}). In this case, the maximum $\PF$ corresponds to the viewing angles $\chi=\ang{90}$, $\psi=\ang{90}$ (red curve).}\label{fig:rot3}
\end{figure*}

\begin{figure*}
\centering
\subfigure[]{\raisebox{.8em}{\includegraphics[width=.48\textwidth]{temps90_rev.png}}}~~
\subfigure[]{\includegraphics[width=.49\textwidth]{PFs_90_r.png}}
\caption{Same as in Figure \ref{fig:rot1} for the case $\beta=1$, $\Theta_q=\ang{90}$, shown at three times $t_1=\SI{6378}{\year}$, $t_2=\SI{68900}{\year}$ and $t_3=\SI{115500}{\year}$ (note that the timescale is quite different from the one of Figs. \ref{fig:rot1} and \ref{fig:rot2}).) }\label{fig:rot4}
\end{figure*}

As we pointed out in the previous section, axially symmetric magnetic configurations produce quasi-sinusoidal pulse profiles with a quite modest pulsed fraction. However, $\PF$ values in excess of $\sim 5\%$ are routinely measured in X-ray pulsars and, in particular, in most of the M7. Indeed, the need for thermal maps produced by more complex field topologies to explain the observed pulse profiles in the M7 was recognized long ago \citep[][]{2006A&A...457..937G,2006MNRAS.366..727Z,2007Ap&SS.308..403P}, although early investigations focused on the structure of the $B$-field in the crust (presence of a toroidal component or higher order multipoles) without addressing its evolution, nor its effects on the temperature of the crust. More recently, \citet{2013MNRAS.434.2362P} presented  surface emission models which were derived self-consistently following the star magnetothermal evolution in 2D (axial symmetry).

In order to address this issue within the framework of 3D magneto-thermal evolution, we now turn to initial field configurations which are not axisymmetric. No attempt to a systematic exploration of the parameter space (which contains a countless number of configurations) will be attempted here. Rather, we consider a limited number of simple cases as illustrative examples and, in particular, we take the initial magnetic field as a combination of (force-free) purely dipolar and quadrupolar poloidal components, with axes tilted by an angle $\Theta_q$. Similar configurations were recently studied by \citet{2020MNRAS.497.2883K} in the context of a detailed stationary-state model of heat transport in the envelope. We tested different angles and relative strengths $\beta=B_\text{quad}(0)/B_\text{dip}(0)$, see Table \ref{tab:rot_cases}, with $B_\text{dip}(0)=\SI{e13}{\gauss}$, $T(0)\equiv\SI{e8}{\kelvin}$.

The evolution shows that the magnetic field keeps being dominated by these two components, with odd multipoles still favored during the evolution. The angle $\Theta_q$ undergoes virtually no change ($\lesssim\ang{1}$) over the whole time span for all the cases we examined. On the other hand, the thermal structure of the crust is quite different from the axisymmetric cases. In fact, currents still tend to heat the region near the equator (referred to the dipolar component), but in the presence of a non negligible quadrupolar component the field lines are more tangled, so that the heat trapping mechanism is not as efficient. For this reason, the hot region quickly disappears, and the crust becomes almost isothermal over some Hall times.

Considering the first two cases in Table \ref{tab:rot_cases}, the evolution of which is shown in panel (a) of Figures \ref{fig:rot1} and \ref{fig:rot2},  a hotter region  forms on the equator of the dipole (note that the coordinates of the projection are referred to the axis of the quadrupole). However, it is not symmetric, and a spot-like structure appears in one hemisphere only. The resulting surface map is still dominated by magnetic effects, and a colder ring appears in correspondence to the hot region in the crust, whereas a hotter region is present as well, in correspondence to the crustal hot-spot at early times only.

Now the pulse profiles exhibit a much richer behavior which depends on the degree of asymmetry of the field. An example is shown in Figure \ref{fig:LCs_rot} for the model with $\Theta_q= \ang{45}$, $\beta= 1.25$ at an age of $\sim \SI{10}{\kilo\year}$. As it can be seen, the shape is quite far from sinusoidal for some viewing geometries.
In Figures \ref{fig:rot1} and \ref{fig:rot2}, panels (b), we show the evolution of the pulsed fraction for various geometries, as well as its dependence on the geometry at selected times. The $\PF$ can reach much higher than in the symmetric cases; at early times ($t\lesssim\SI{10}{\kilo\year}$), is has a peak, after which it decays very slowly. The peak value corresponds to the maximum temperature anisotropy in the crust; then, the evolution of the $\PF$ is dictated by the magnetic field only, on top of an almost isothermal crust. The slow decay can be understood as the effect of ohmic dissipation, which eventually brings the field back to a dipole on longer timescales.

The $\PF$ evolution for these two cases is quite similar, but the one with the larger $\beta$ yields a higher $\PF$. One may, then, expect that a very large quadrupole gives much higher $\PF$s. To test this, we ran a case with $\beta=10$, i.e., close to a pure quadrupole (see Fig.\ \ref{fig:rot3}). Its evolution, however, is very different: the role played by the dipole equator in the thermal evolution is now taken by the two nodes of the quadrupole, and a band structure appears on the surface. Hence, an efficient heat trapping mechanism is in place. This results in longer evolution timescales; in particular, the time required for the crust to become isothermal is longer by almost an order of magnitude with respect to the other configurations. This reflects in an increased amplitude of the $\PF$ peak. Moreover, the range of $\PF$s is wider, and the maximum $\PF$ is just comparable to the one reached with $\beta=1.25$, while values $\lesssim10\%$ are also reached.

Finally, we tested a different geometry, setting $\Theta_q=\ang{90}$ with $\beta=1$ (see Fig.\ \ref{fig:rot4}). This case is still somewhat symmetric, so that the $\PF$ values are in general low ($\lesssim4\%$), and comparable to the purely symmetric cases. Again, the effect of the quadrupole is to isothermalize the crust, which in this case happens on a timescale $\approx\SI{100}{\kilo\year}$, corresponding to the plateau of the $\PF$ profile.

\section{Discussion and conclusions}\label{sec:conclusions}

In this work, we presented self-consistent models of the magnetothermal evolution of isolated NSs, focusing in particular on the predicted observable timing and spectral properties at different ages. We have explored the effects of diverse initial magnetic configurations, namely, a purely dipolar field and more complicated topologies, consisting of a dipole plus a (tilted) quadrupole.

The initial dipolar field evolves, keeping its axial symmetry, towards the so-called \emph{Hall attractor} \citep{2014PhRvL.112q1101G}. As the evolution proceeds, the equatorial region of the crust becomes hotter, owing to the local amplification of the magnetic field and to the formation of closed field lines. The star surface, however, is actually colder near the equator, because heat can not be effectively transported through the envelope where the field lines are nearly parallel to the surface. This leads to the appearance of two hotter bands (one for each magnetic hemisphere) at intermediate latitudes, topped by a colder polar region and joined by an even colder equatorial belt. Assuming that the star surface emits isotropic blackbody radiation at the local temperature, we found that the predicted pulsed fraction is quite small ($\lesssim 5\%$) for all possible orientations of the line-of-sight and of spin axis wrt the magnetic axis. Moreover, the pulsed fraction decreases with age, as the crust becomes more isothermal and ohmic dissipation drives the field back to a dipole. Pulse profiles are both single- and double-peaked, depending on the viewing geometry, and quite sinusoidal (see Section \ref{sec:axsym}).

The spectrum can be described as a superposition of two blackbody components with different temperatures and emitting areas. This holds at every epoch, although the temperatures and areas vary in time. A quite general feature of these models is that the area of the hotter blackbody component becomes smaller than that of the colder one when the source is older than a few thousands yr. A model with initial dipolar field is in general agreement with the observed properties of the brightest of the M7, \eighteen. The spectral parameters and the pulsed fraction are recovered when the model evolved for  $\sim \SI{4e5}{\year}$, close to the inferred dynamical age of the source, and the dipolar field decayed to about $B_\text{dip}=\SI{4e12}{\gauss}$, a value compatible with that derived by  \citet{2007MNRAS.375..821H} but a factor $2$--$3$ smaller than the spin-down measure. Given the present uncertainties and the hindrance of comparing an inherently multipolar model with estimates derived assuming a dipolar field, we chose to use the value inferred from spectral fitting to investigate the spectral properties. Other runs with different initial field values produce  qualitatively similar results. In particular, the spectrum is always well described by a BB+BB fit with the ratio $A_2/A_1$ eventually getting above unity. Simulations with a much stronger initial field, however, have a high computational cost in the long term, since they not only have to fulfill a more demanding Courant condition, but tend to develop instabilities that call for extremely fine grids.

As we already pointed out, highly symmetrical configurations imply rather low ($\lesssim5\%$) pulsed fractions. Even restricting to NS sources in which emission reasonably comes from the entire star surface, the measured pulsed fraction can be fairly larger: in the M7 it reaches $\sim 30\%$. This suggests that the thermal map in these sources reflects  a more complex (e.g. non-axially symmetric) field configuration. To test this, we considered models in which the initial field consists of a dipole plus a misaligned quadrupole field (the simplest choice for higher order multipole). Indeed, these models exhibit a pulsed fraction as large as $\sim 25\%$ and a much richer behavior of the pulse profiles, which can be asymmetric and skewed, as indeed observed in some sources, e.g. the M7  RX J0420.0-5022 \citep{2004A&A...424..635H}.
We found, however, that in these cases the crust tends to become isothermal rather quickly, so that the late time observed properties are controlled by the structure of the magnetic field only. Albeit being based on a simplified envelope model, our thermal maps are in qualitative agreement with those produced by the detailed model of \citet{2020MNRAS.497.2883K}. We finally note that, when studying magnetic field configurations that do not allow long-term heat retention, the study of the coupling of the thermal evolution to the magnetic one may be not necessary. More M7-like isolated NSs are expected to be revealed by eROSITA \citep{2018IAUS..337..112P}, likely including younger, hotter objects. This will allow to further constrain magneto-thermal evolutionary models.

We remark that these configurations are by no means exhaustive, and other options to increase the $\PF$ and to produce non-sinusoidal pulse profiles are possible. Recently, \citet{2020arXiv200103335G} and \citet{2020NatAs.tmp..215I} investigated models in which the field has a strong toroidal component and/or develops instabilities, which are inherently asymmetric, during the evolution. Moreover, the $\PF$ can be enhanced when considering inherently anisotropic emission such as that of a magnetized atmosphere or a condensed surface, \citep[see e.g.][for a review]{2014PhyU...57..735P}, or even more general models with a prescribed beaming pattern \citep[as in e.g.][for isolated NSs and magnetars]{2013MNRAS.434.2362P,2015MNRAS.452.3357G}. In such cases a much higher $\PF$ can be obtained even for quite symmetric temperature distributions. Given that the main goal of this paper is to investigate how magnetothermal evolution impacts on the surface temperature map of a INS, we preferred to limit ourselves to a simple blackbody emission. More detailed emission mechanisms will be considered in future works \citep[as it has been done in e.g.][for \eighteen\ and magnetars, respectively]{2017MNRAS.464.4390P,2020MNRAS.492.5057T} in order to get a  more comprehensive comparison with observed spectra and lightcurves. In this respect, we note that a direct application to observations requires to include interstellar absorption  and the detector response function, although these are likely not to alter dramatically the expected spectral shape and pulse profiles \citep{1996ApJ...473.1067P}, and possible effects due to the NS magnetosphere. Even more important, it would require some information about the source geometry.

Viewing angles (i.e. the inclination of the line-of-sight and the star magnetic axis wrt the spin axis) are typically hard to determine in radio-quiet sources like the M7, due to the inherent degeneracy which affects spectroscopy alone. A natural way to solve this problem is by exploiting the additional observables provided by polarization measurements, which are already accessible in the optical band and will be available in the near future at X-ray energies with new generation satellites like {\it XPP} \citep{2019BAAS...51g.181J}. A first constraint for the viewing geometry of \eighteen\ has been put from observations in the optical band by comparing the $\PF$ profile with the predicted and the observed polarization fraction as functions of the viewing angles \citep[][]{2017MNRAS.465..492M}. These estimates, however, are based on a purely dipolar field and cannot be directly compared to the model presented in this work. A model of polarized emission taking into account a consistently evolved multipolar field may in the future provide new insights on this matter.

\added{Another issue when dealing with strongly multipolar fields is the computation of the spin period evolution. For example, taking our axisymmetric model and using the usual spin-down formula \citep[e.g.][]{1983bhwd.book.....S}, with an initial period of $10$--$\SI{50}{\milli\second}$ we get period of $\approx \SI{1}{\second}$, quite shorter than the ones measured in the M7 of the same estimated age, $P\sim3-\SI{10}{\second}$ (\eighteen\ has $P\simeq\SI{7}{\second}$). These values may be reproduced only if the initial period is of the same order of the present one (such long initial periods have been proposed, e.g., by \citet{2012A&A...537L...1H} for SXP~1062). Nevertheless, other factors to account for in this respect may be an underestimate of the initial field (reflecting in a too low $B_\text{dip}(0)$), but also that spin-down losses themselves should be computed self-consistently. A complete model taking into account the full structure of the magnetosphere, akin to the one presented by \citet{2006ApJ...648L..51S} for a dipolar field, should be used to assess the effects of the strong multipolar components on the spin-down.}

\replaced{Finally, we warn that our results have been obtained within the present microphysical input of the PARODY code. In particular, a simple crustal equation of state adapted from \cite{2014PhRvL.112q1101G}, see again {DG+20}, and (iron) envelope composition model was used. A different (and more detailed) framework can alter the thermal transport properties, as well as the timescales of the magnetic evolution.
This has a direct impact when drawing comparisons between our results and observations.}
{
Finally, we stress again that our results have been obtained within the present microphysical input of the PARODY code. In particular, a simple crustal equation of state with no chemical stratification (adapted from \cite{2014PhRvL.112q1101G}, see again DG+20) and an iron only envelope model was used. Moreover, we did not consider the contribution to the thermal conductivity by superfluid neutrons, which can reduce the temperature anisotropy in the crust. In this respect, we note that in all our models the crustal temperature barely exceeds $\SI{e8}{\kelvin}$ in the hottest regions, which are not located in the innermost layers of the crust (see e.g. Fig. \ref{fig:Tevo}); hence, we expect this effect not to be substantial.
This has to be borne in mind when drawing comparisons between our results and observations, which must we kept on a qualitative ground.}

In any case, we expect the deviations related to the microphysics to be \replaced{only}{mostly} quantitative, rather than qualitative, but a complete exploration of the huge number of possibilities is beyond the scope of this work, \added{in which the focus was on the effects of the magnetic field}.

\acknowledgments
Simulations were run at CloudVeneto, a HPC facility jointly owned by the University of Padova and INFN, and at UCL Grace HPC facility (Grace@UCL). The authors gratefully acknowledge the use of both facilities and the associated support services. RT and RT acknowledge financial support from the Italian MUR through grant PRIN 2017LJ39LM. SP has been supported by the Interdisciplinary Scientific and Educational School of Lomonosov Moscow State University ``Fundamental
and Applied Space Research''.

\vspace{5mm}

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The Conqueror Approach
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045 - Kute Blackson | The Magic of Surrender and Finding the Courage to Let Go | The Conqueror Approach
A beloved inspirational speaker and transformational teacher, Kute Blackson offers a fresh, bold look at spiritual awareness for a whole new generation. Born in Ghana, West Africa, Kute's multicultural upbringing as the child of a Japanese mother and a Ghanaian father has spanned four different continents. His unique lineage lay the foundation for his approach to breaking down barriers and unlocking an individual's true gifts and greatness.
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Q: PhoneGap build command not working after updating to Yosemite I am developing an application in PhoneGap. Before updating my iMac to OSX Yosemite the phonegap was working perfectly the build commands and all that. But after updating to OSX Yosemite, whenever I run the build command I get this error:
phonegap build ios
[phonegap] detecting iOS SDK environment...
[phonegap] using the local environment
[phonegap] compiling iOS...
Unknown option: n
Usage: head [-options] <url>...
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    -H <header>   send this HTTP header (you can specify several)

    -u            Display method and URL before any response
    -U            Display request headers (implies -u)
    -s            Display response status code
    -S            Display response status chain
    -e            Display response headers
    -d            Do not display content
    -o <format>   Process HTML content in various ways

    -v            Show program version
    -h            Print this message

    -x            Extra debugging output
Cordova can only run in Xcode version 4.6 or greater.
{ [Error: /Volumes/Macintosh HD 2/Aleem Data/Projects On Mac/IPhone Application Projects/Growing Feet/New Version Test/GrowingFeet/growingfeet/platforms/ios/cordova/build: Command failed with exit code 2] code: 2 }
   [error] /Volumes/Macintosh HD 2/Aleem Data/Projects On Mac/IPhone Application Projects/Growing Feet/New Version Test/GrowingFeet/growingfeet/platforms/ios/cordova/build: Command failed with exit code 2

I am using Xcode 6.1 and OSX Yosemite and I have updated my version to the latest version of Phonegap which is: 3.6.0-0.21.19 but still it gives the same error.

redpajama_set_name: RedPajamaStackExchange


text:
Q: RadListView - "load more items" is always visible with IncrementalLoadingMode="Explicit" Using RadListView from Telerik with IncrementalLoadingMode="Explicit", but then the "load more items" button is always visible, even when there are no items in the listview instance.
Is there any way to hide the "load more items" button when there are no items? Makes no sense to have the button there when there are no items

A: The "load more items" is actually the DataGridLoadDataControl in Telerik, you could try to find it in the UI visual tree by VisualTreeHelper, and then set it to invisible. For example (grid is the name of RadDataGrid control):
private void btnloadcompleted_Click(object sender, RoutedEventArgs e)
{
    IEnumerable<DataGridLoadDataControl> items = FindVisualChildren<DataGridLoadDataControl>(grid);
    foreach (DataGridLoadDataControl item in items)
    {
        item.Visibility = Visibility.Collapsed;
    }
}
private static IEnumerable<T> FindVisualChildren<T>(DependencyObject depObj) where T : DependencyObject
{
    if (depObj != null)
    {
        for (int i = 0; i < VisualTreeHelper.GetChildrenCount(depObj); i++)
        {
            DependencyObject child = VisualTreeHelper.GetChild(depObj, i);
            if (child != null && child is T)
            {
                yield return (T)child;
            }

            foreach (T childOfChild in FindVisualChildren<T>(child))
            {
                yield return childOfChild;
            }
        }
    }
}


text:
Q: How to count remaining days in MySQL My goal is to make a column in phpMyAdmin, which counts down the remaining days of a trial period (or something like that).
So for example when I set remainingDays to 30, I want the database to execute the query every 24 hrs
Is it possible to make something like this with only phpMyAdmin in hand, or do I have to put some code onto my website to send MySql Commands to subtract it?
Any help is greatly appreciated.

A: Are you familiar with datediff()?  Something like:
select datediff(target_date, curdate()) as days_remaining
from t;

That is, you can do this in a SQL query.

A: A better approach would be to have a startDate column compute the remaining days during query execution with something like:
select 30-datediff(now(),startDate) from...


Minutes of the Annual Parish Meeting held on Thursday 4th April 2019 @ 7.30 pm at 'Westlow' Mere Fisheries, Hulme Walfield, Congleton.
Mr Alastair Lewis – Project Manager GRAHAM, Mr Dan Cawthra- Stake Holder and Communication Officer GRAHAM.
19 members of the public attended.
Chairman's Introduction: The Chairman opened the meeting, welcomed the public to the Annual Parish meeting and introduced the Parish Councillors. He summarised the last twelve months and reminded everybody of the amazing 'turn out' to vote for the Neighbourhood Plan referndum last year at over 50%. The Congleton Link Road was now in progress and was lots of evidence throughout the Parish due to the removal of hedgerows and the new bypass track on Giantswood Lane. The Parish Council were still trying to progress improvements along the rural lanes, but the cost involved from Cheshire East had been more than anticipated. They were involved in the process now though. He went on to thank the two residents from Giantswood Lane who had supported the existing homes on the lane to build a relationship with the Alderley Gate, Bloor home development. The relationship and regular meetings had proved invaluable.
The communication links within the Parish had improved vastly over the past two years and he wanted to thank the website administrator as she had played a large part in this progress.
GRAHAM were the appointed contractors for the CLR, and in the process of trying to build a positive relationship within the community. DC was having monthly meetings with the Clerk to resolve any issues that were arising but if anybody had any pressing issues his details were on the website. GRAHAM employed 2,200 employees, their turnover was in excess of £767m a year and there was £1.1bn on their order books plus over 100 live projects. Their head office was in Hillsborough, County Down, Northern Ireland. There were over 30 staff on this project, and they were using local contractors to assist. The scope of the work was obviously to bypass Congleton town. They explained the route and the stages there were at currently. The residents will have noticed the 'by pass' track they had established on G/Wood Lane which was due to be opened later this month with traffic lights so they could commence the bridge. It would be wider than a single carriageway to accommodate cyclists/walkers with the traffic. G/Wood Lane is currently 60 mph and was due to be reduced to 40 mph during the process. It was due to be extend form where it ended towards Manchester Road The bridge was discussed in detail, it will be high sided and will accommodate horses (the parapet will be 1.8m deep.) The soil being removed was planned to be utilised in the embankment at Eaton and will be moved long the line not on the network. The bridge will be on a 35-degree skew and the lane will be realigned back. The drainage issues were discussed in relation to the water table. The water table was very high on Chelford Road and this bridge was going to be quite complex with drainage.
The major constructional challenge was building the bridge over the River Dane. This bridge would be 15m wide and the river was the second highest rising river in England. They have made some amendments to the original plans and it was now bigger and heavier. The bridge would most likely arrive overnight with traffic management and constructed on the ground. There was a large difference in height from the east side of the river to the west, it needs to be 25m high on the west and 4m high on the east side. The total length was 87m. The road surface was tarmac but it wold be noise resistant.
There was a land scaping management plan which involved protecting all the wildlife especially the native newts. If residents saw the plastic thigh high black fencing around certain areas this was to keep the newts preserved. There was a replanting programme that was planned for 25/50 years. GRAHAM was trying to replant existing hedgerows, but this was not always successful. Wildlife surveys on bats/owls/newts/birds/kingfishers had being taking place since 2014.
The four phases of completion were explained Back Lane was a priority to get open as there were two housing developers needing access. G/Wood lane bridge would be completed in phase 2 together with the Sandbach road roundabout. Phase 3 would be the underpass on Chelford Road. The road would be opened in its entirety and not phased in March 2020 if they were on schedule as planned. There would be very little street lightening and no laybys along the road.
There were employment opportunities due to the construction of the CLR and if you contacted DC he would give you further information.
The Chairman thanked everybody for attending and the speakers for being so informative.


text:
CGWIC
China launches rideshare mission, develops new engine, and loses contact with Mars rover
by Adrian Beil January 19, 2023
written by Adrian Beil
In what will probably be the last Chang Zheng launch before the Chinese new year, a Chang Zheng 2D recently lifted 14 payloads to a Sun-synchronous orbit. The rocket lifted off at 03:14 UTC on Sunday, Jan. 15, and was confirmed to have completed its mission successfully. The launch comes at the end of a week that has also seen news about a reusable YF-100 engine, while China has still been unable to make contact with its Zhurong Mars rover.


We know that life is busy. We also know that some of the best ways to connect with one another is around the dinner table, sharing a delicious meal and the events of the day.
Nicole has long had a vision to help busy families, of all sizes, enjoy dinner time with out the extra stress of shopping, cooking and then cleaning up! Stirred at Home is the fulfillment of her vision.
Each week, beginning Tuesday evening, you can go online and order your meals for the following week. Each week we will have three entrees and several delicious sides for you to choose from. You can order anytime up to the end of day on Sunday. Your order will be prepared and packaged by our Stirred Crew and you can pick it up the following Tuesday 2:00 - 4:00 pm. Everything will be ready to be warmed, served and enjoyed!
***There is a glitch in our online ordering system that allows you to choose any time to come in and pick up your order. Orders are only available for pick up the following Tuesday after 2:00 pm.
Click the link below to begin your Stirred at Home order!


High Point Academy is seeking educators inspired to reach, empower, and achieve greatness.
High Point Academy is a charter school serving students preschool through 8th grade. Located in Aurora, CO, just north of Green Valley Ranch (10 minutes from Denver International Airport), HPA serves an ethnically diverse student population which includes 26% linguistically diverse students and 54% of students that qualify for Free or Reduced Lunch. HPA is an award-winning wellness school whose curriculum and classes promote healthy lifestyle choices.
All employees of High Point Academy work together to achieve HPA's mission. In addition to the duties and responsibilities listed below, we seek teachers who are collaborative with colleagues, empathetic in their relationships with students and families, and willing to work above and beyond their job description in order to ensure success for students. HPA teachers possess a school-wide focus and are able to see beyond their classroom in order to create a unified HPA community.
Conducts an organized and professional classroom.
Fluent written and spoken Spanish and the ability to teach native Spanish speakers.
Strong knowledge in the area of developing Spanish lessons and curriculum that will meet the needs of individual students.
Has an unwavering belief that all children can and want to learn.
Implements rigorous and highly engaging standards-based instruction.
Supports all students including students who are linguistically diverse and who have an IEP or 504 plan.
Develops and implements curriculum to ensure student mastery of Colorado state standards.
Maintains curriculum to ensure the needs of students are met.
Collaborates with other faculty in delivery of appropriate instructional approaches, working to serve the various learning styles and needs of all students.
Models and fosters independent thinking skills, creative problem solving, and abstract reasoning.
Shows empathy and understanding of students.
Creates a safe learning environment where each child excels.
Supports students and families by developing strong relationships to ensure student success.
Assesses student performance frequently and objectively to drive instruction.
Communicates consistently and effectively with students and parents.
Follows policies established by the High Point Academy governing board and administration.
Participates in and contributes to programs and activities that enhance High Point Academy outside of instructional hours, such as extracurricular activities, leadership positions, and/or the enrollment process.
Provides instruction in Visual Arts following Common Core standards-based curriculum.
Teaches students to recognize and use visual arts as a form of creativity and communication.
Helps students explore the application of materials, tools, techniques, technologies, and processes; and relate visual arts to various historical and cultural traditions.
Teaches students the creative process by modeling creative thinking and provides opportunities for students to grow their creativity and problem-solving skills.
Showcases and displays student work throughout the building and prioritizes opportunities for students to engage in real world art work.


They now have motion pictures you can rent but much more importantly, films that you can watch for free.
So let's get to the function and dig some entertainment sources to streaming motion pictures on-line for cost-free on phones and laptops.
This blurring of the lines can be confusing, specifically when exploring choices on how to watch complete length films online.
Popcornflix is a legal web site exactly where you can watch full-length streaming movies for free of charge in the each the U.S.
Be positive to check out their weblog to help you locate the totally free on-line motion pictures that are most common and critically-acclaimed.
Save your favored theaters and films to knowledge a customized Fandango just for you.
Select the genre, release date, and video format you want, and we'll display a list of motion pictures and Television shows that fit your criteria.


text:
Q: Using malloc(0) and memcpy I read somewhere: Dereferencing a pointer returned by a "new" allocation of size zero is UB.
Is it same in C?
If yes, is the following code UB? (assuming size = 0)
 a->object[index].data = malloc(size);
 memcpy(a->object[index].data, bytes, size);

To my understanding: NO. Just wanted to double check.

A: When you pass 0 as an argument to malloc, then it free the allocated memory to the pointer which malloc returns to.
Result is implementation defined.
C11: 7.22.3 Memory management functions:

[...] If the size of the space requested is zero, the behavior is implementation-defined: either a null pointer is returned, or the behavior is as if the size were some nonzero value, except that the returned pointer shall not be used to access an object.

Also standard says:

The free function causes the space pointed to by ptr to be deallocated, that is, made available for further allocation. If ptr is a null pointer, no action occurs.

So, in either case of implementation defined behavior, freeing will not invoke undefined behavior.
Now moving to another part of the question.
7.1.4 Use of library functions:

If an argument to a function has an invalid value (such as a value
  outside the domain of the function, or a pointer outside the address space of the program,
  or a null pointer, or a pointer to non-modifiable storage when the corresponding
  parameter is not const-qualified) or a type (after promotion) not expected by a function
  with variable number of arguments, the behavior is undefined.

C11: 7.24.1  p(2):

Where an argument declared as size_t n specifies the length of the array for a
  function, n can have the value zero on a call to that function. Unless explicitly stated
  otherwise in the description of a particular function in this subclause, pointer arguments on such a call shall still have valid values, as described in 7.1.4. On such a call, a function that locates a character finds no occurrence, a function that compares two
  character sequences returns zero, and a function that copies characters copies zero
  characters.

A: According to my reading of the current standard (or n1570, the final public draft of it), the code has Undefined Behaviour:

7.24.1 String function conventions

*Where an argument declared as size_t n specifies the length of the array for a function, n can have the value zero on a call to that function. Unless explicitly stated otherwise in the description of a particular function in this subclause, pointer arguments on such a call shall still have valid values, as described in 7.1.4.

7.1.4 Use of library functions

*

*Each of the following statements applies unless explicitly stated otherwise in the detailed descriptions that follow: If an argument to a function has an invalid value (such as a value outside the domain of the function, or a pointer outside the address space of the program, or a null pointer, or a pointer to non-modifiable storage when the corresponding parameter is not const-qualified) or a type (after promotion) not expected by a function with variable number of arguments, the behavior is undefined.

(Emphasis added.)

A:  size_t size = 0;
 a->object[index].data = malloc(size);
 memcpy(a->object[index].data, bytes, size);

Technically, it is undefined behavior.
malloc may return a null pointer for an allocation of zero bytes and passing a null pointer to memcpy is undefined behavior (even if ìts third argument is 0).
From the mighty C Standard (emphasis mine):

(C99, 7.1.4p1) "[...] unless explicitly stated otherwise in
          the detailed descriptions that follow: If an argument to a
          function has an invalid value (such as a value outside the
          domain of the function, or a pointer outside the address space
          of the program, or a null pointer, or a pointer to
          non-modifiable storage when the corresponding parameter is
          not const-qualified) or a type (after promotion) not expected
          by a function with variable number of arguments, the behavior
          is undefined"


The locals still don't believe that there are people able to cover this distance during daylight hours. This distance has kept the best of the best for the best: impressive views and obstacles providing the same deepness of emotions. After you separate from 30k distance runners, the real fun will begin. Up and down, in the forest and out, here is one picturesque landscape, here is another. Oops! There's a ford. Not deep but refreshing, oh, here is another one… We can't tell you the exact number. It will depend on the amount of precipitations during the previous weeks. To make it more interesting we will add a couple of autonomous sections of about 15-20k. Pitstops every 5k is for the weak which is definitely not you. The cut off time is 17h. If you are late at any check point, you will stay chilling with the volunteers before you are picked up. If you finish, feel free to be proud of yourself. We will definitely be. Quite frankly we expect less than a half to finish. If we are wrong, the distance will be increased to 100k in 2018.


Mayo Clinic doctors are experienced in evaluating and treating people who've had a traumatic brain injury, including concussions. Mayo Clinic doctors trained in neurology, physical medicine and rehabilitation (physiatry), and psychiatry and psychology will work with you and your family to develop your treatment plan if you have had a concussion.
Mayo Clinic experts evaluate and treat more than 1,300 people with concussion each year.
The experts at Mayo Clinic use advanced technology and detailed imaging tests to determine the cause of your symptoms and diagnose concussion. They can work with you to determine the most appropriate treatment and advise you on how to best recover from your concussion to avoid further injury.
Researchers at Mayo Clinic are leaders in the field of concussion and traumatic brain injury research and treatment. You may have the opportunity to participate in a clinical trial as part of your treatment at Mayo Clinic.
Mayo Clinic experts trained in neurology, physical medicine and rehabilitation (physiatry), and psychiatry and psychology have extensive expertise in diagnosing and treating concussion. Mayo Clinic experts evaluate and treat more than 1,300 people with concussion each year.
Researchers at Mayo Clinic have a long history of innovation in brain injury research, including developing the Mayo Classification System for Traumatic Brain Injury Severity, which can help plan for clinical care following a brain injury.
Mayo Clinic researchers continue this tradition and are actively engaged in several clinical trials and studies of concussion and other types of brain injury.


The OverBoard approach is simple, we believe that wherever you go, whatever you do, there's an OverBoard product for you. Not only do we regularly test all our products in our laboratory using our 4 Phase Test process, we test our equipment in the real world, with our athletes, in extreme climates and on expeditions. We even send our gear to testing partners Intertek for independent rigorous product and ingress testing too.
Temperature Test: The materials used in our OverBoard waterproof tech bags and cases are heated up to +40°C to simulate use in very hot climates. They are then placed in 1 meter of moderately warm shallow water to simulate surface water capabilities to check for leaks, floatation, humidity and durability. We also test for accelerated frost resistance by freezing our cases to -20°C to check for cracking, elasticity pliancy, and snow ingress. Now we don't recommend you do the same with your teach for prolonged periods - it won't damage the product, but condensation might build up inside the case and your electronics could become inoperable if they get too hot or cold!
Depth Test: Water ingress protection is our speciality and our tech cases are submerged down to 7 meters for 1.5 hours to see if they can defend against leaks and pressure. We're pleased to say that they all passed with flying colours - but don't forget that these are extreme test conditions so we don't advise you do the same with your tech. The deeper you go underwater the more pressure there is which can crack the screen on your phone, tablet or electronic device which is why we have approved our cases for use down to 6m/19ft for 60 minutes only.
Strength Test: Before any gear can roll off the production line, it undergoes Break Strength Testing – We literally test our products and their components to breaking point using specialised hydraulic equipment. The things we look out for are maximum load at break, deflection at maximum load, load break and deflection at break for all our straps, clips, buckles, Velcro, stitching, zippers, welds and webbing.
Dust, Sand and Dirt Test: Our tech cases are also tested in a controlled environment using Norwegian talcum powder – the finest man-made dust available. The case is exposed to these minute dust particles in an irregular, multi-directional manner and afterwards, the cases are then inspected for any ingress. It's a messy job but our cases don't mind, they're dust, dirt and sand proof too.
Dunk Test: Sometimes the simplest tests are the most effective, at the end of production, we fill our cases with compressed air and we check them for holes, leaks, waterproofing, colour fastness, dust defence and decay by dunking our gear in all sorts of dirt and liquids.
Weld Pressure Test: We like to batch-test our gear by filling our waterproof dry tubes, bags and backpacks with compressed air and then squeezing them really hard in our hydraulic compression tester. This forces compressed air in all directions making sure every seam and stich-free high frequency weld has been fused correctly making them 100% waterproof.
Load Break Test: If we say our backpacks can hold 20kgs, we want to make sure that every strap, weld and seam can handle it so we use a high-capacity sheer tension testing process where we stretch, twist, flex, bend and pull everything apart to make sure it won't break its promises.
Repetitive Stress Test: We open and close our cases for hours at a time to test for component fracture and fatigue using slow-speed static testing and high-frequency dynamic fatigue testing to make sure our clips, buckles, Velcro and zips can withstand a lifetime of daily use.
For further information on our testing programme, please Email technical@overboard.com.


According to Information Resources International, in 1993, Doritos earned $1.3 billion in retail sales, one-third of the total Frito-Lay sales for the year. This made the chip the leading seller in the snack category, which also comprises cookies, crackers, cakes, and candies.
Beer is the world's oldest and most widely consumed alcoholic beverage and the third most popular drink overall after water and tea.
Flavor or flavour is the sensory impression of a food or other substance, and is determined mainly by the chemical senses of taste and smell.


You can password protect your web pages without having access to a cgi-bin or .htaccess files. You're allowed an unlimited number of user name and password combinations.
Doesn't support PayPal IPN and not flexible enough. Not enough automation.
I had no problems with it. It was just what I was looking for!
I checked every script in this category and this is the best! It's the only one that hides the URL, is fast and easy-to-use!
This thing works great -- I've been wanting to set up a members area for my site for quite some time, and now I can. I like the fact that it hides my URL, too.


When Do You Get Charged?
After a campaign is sent, you will be charged the actual amount of how many successful emails are sent.
Every time you send a campaign, you will be given an estimate on how much the campaign will be. Once the campaign is sent, you will be charged the actual price of the campaign (depending on how many emails are sent successfully).


Despite having a population of only 40 million compared with the UK's 65 million California's economy has surpassed that of the United Kingdom to become the world's fifth largest, according to new federal data made public last Friday. California's gross domestic product rose by $127 billion from 2016 to 2017, surpassing $2.7 trillion, the data said. Meanwhile, the UK's economic output slightly shrunk over that time when measured in U.S. dollars, due in part to exchange rate fluctuations. The data demonstrates the sheer immensity of California's economy: a thriving technology sector in Silicon Valley; the world's entertainment capital in Hollywood and; the nation's salad bowl in the Central Valley agricultural heartland.


text:
Als Deskriptor (Plural Deskriptoren) oder Schlagwort (Plural Schlagwörter) bezeichnet man Bezeichnungen, die zur inhaltlichen Beschreibung eines Objektes oder Dokuments ausgewählt werden können. Nach DIN 31 623 sind Deskriptoren Benennungen, die für sich allein verwendbar, eindeutig zur Inhaltskennzeichnung geeignet und im betreffenden Dokumentationssystem zugelassen sind. Die Vergabe von Deskriptoren wird auch als Verschlagwortung (in Österreich Beschlagwortung) oder Indexierung bezeichnet. Im Gegensatz zu Stichwörtern – wichtigen Wörtern, die in einem Text vorkommen – entstammen Deskriptoren einem kontrollierten Vokabular, in dem festgelegt ist, welche Wörter für welche Sachverhalte verwendet werden sollen. Beispiele für solche Vokabulare sind Normdateien und Thesauri. Die Vergabe von Deskriptoren ist Bestandteil der inhaltlichen Erschließung von Dokumenten, zum Beispiel in Bibliotheken und Dokumentationsstellen.

Die Bezeichnung Descriptor wurde im Zusammenhang der Informationsrückgewinnung etwa Anfang der 1950er-Jahre von dem US-amerikanischen Mathematiker Calvin Mooers eingeführt.

Arten von Deskriptoren
Einige Dokumentationssysteme enthalten sogenannte Nicht-Deskriptoren, die ausdrücklich nicht zur Verschlagwortung verwendet werden sollen, aber dem Nutzer den Zugang zu den Deskriptoren ermöglichen. Zu den Nicht-Deskriptoren zählen abweichende Schreibweisen und Synonyme.

Ein Allgemeindeskriptor ist ein Deskriptor, der allein in der Regel keinen Aussagewert hat, z. B. "Kosten" (von was? Für wen? Welchen Geschmack?).

Werden einzelne Deskriptoren für bestimmte Personen verwendet, spricht man von Personenschlagwörtern im Gegensatz zu Sachschlagwörtern.

Deskriptoren aus einer künstlich basierten Dokumentationssprache (z. B. Schlüssel der Universellen Dezimalklassifikation) nennt man Notation.

Bei der freien Verschlagwortung (auch "Tagging") werden Deskriptoren nicht aus einem vorgegebenen Vorrat ausgewählt, sondern frei vergeben. Der Nachteil einer freien Sacherschließung ist die fehlende Kontrolle. Die Erschließungsarbeit wird zum Teil auf den Suchenden verlagert, der sämtliche verschiedene Schreibweisen, verschiedene Fälle (z. B. Einzahl–Mehrzahl), Synonyme etc. zu suchen und Homonyme auszuschließen hat.

Schlagwort vs. Klassifikation
Inhalte von Objekten wie Aufsätze oder Monographien können beschrieben werden durch Zuordnung von Schlagwörtern zum Haupt- oder zu dem Teilinhalt(en) jenes Objekts (dieser Vorgang wird "Verschlagworten", Indexierung, schw. und österr. "Beschlagworten" genannt) oder durch Zuordnung von einzelnen Klassen einer bestimmten Klassifikation zu den Haupt- oder Teilinhalten des Objektes (dieser Vorgang wird "Klassieren" oder "Klassifizieren" genannt). Mit der Klassifikation wird der Fach- oder Themenbereich angegeben, innerhalb dessen die Inhalte behandelt werden, die die Schlagwörter angeben.

Literatur
 Jutta Bertram: Einführung in die inhaltliche Erschließung. Econ-Verlag, Würzburg 2005, ISBN 3-89913-442-7.

Siehe auch
 Lemma (Lexikographie)
 Schlagwortkatalog
 Simple Knowledge Organisation System

Dokumentationssprache

redpajama_set_name: RedPajamaWikipedia


text:
Q: compare input to an object arraylist I would like to compare the input from a JTextField to all the elements in a string arraylist. If the input is equal to an element in the list I would like the program to acknowledge by saying "This is in my vocabulary.", and if it is not, I would like the program to say "This is NOT in my vocabulary." In my code, I have tried getting this to work buy I always get the message "This is NOT in my vocabulary." even if the input matches an element in my list. How can I get this to work properly?
Here is my code, in it AI is where the list that is being compared is.
package Important;

import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import javax.swing.JTextField;
import AI.*;

public class TextActions implements ActionListener{

private String hero;
private Vocabulary vocab1 = new Vocabulary();

public void actionPerformed(ActionEvent e) {

    e.getSource();
    hero = e.getActionCommand();

    if (vocab1.Adjectives.equals(hero)){
        System.out.println("This word is in my vocab");
    }else{
        System.out.println( hero + " is not in my vocab");
    }
    //CompareWords(hero);
}

public void CompareWords(String readme){

    if (vocab1.Adjectives.contains(readme)){
        //System.out.println("This word is in my vocab");
    }
}

}

Here is the Vocabulary class as requested.
package AI;

import java.util.*;
public class Vocabulary {
//String[] thoughts;
public List<String> Adjectives = new ArrayList<String>();

public void AddWord(int ArrayListNumber, String WordEntered){

    if(ArrayListNumber == 1){
    Adjectives.add(WordEntered);
    }
}

}

A: You are creating new object
Vocabulary vocab1 = new Vocabulary();

This would contain an empty Adjectives  list.
So, you have to first populate the Adjectives  list before you do the checking as follows
vocab1.Adjectives.contains(hero)

and use contains instead of equals.


music alert from the multi talented Nigerian Dance hall music artiste popularly know as "Horlawan", Horlawan is out again this time with a world class hit single titled " Komalobe". Komalobe is just the kind of tune I can't explain but in one word overwhelming, you would probably love the great concept he has on this new tune kindly Download, Listen and Enjoy below. For Bookings,inquiries of Horlawan Twitter:-@horlawan Instagram:-@iam_Horlawan Call or WhatsApp:- +234 708 277 1623.


text:
Palm oil has huge potential in Turkey, Pakistan, Iran
MELAKA: Malaysia's palm oil export market has huge potential to be expanded to Turkey, Pakistan and Iran due to the high utilisation of the commodity in the three countries.
Deputy Primary Industries Minister Datuk Seri Shamsul Iskandar Mohd Akin said during a recent palm oil, economic, promotion and investment mission to the three countries, it was found that Karachi (Pakistan) used more than one million tonnes of palm oil annually, while Istanbul (Turkey) used 700,000 tonnes and Tehran (Iran) used 600,000 tonnes per annum.
He said the efforts to explore new markets was a way to expand the palm oil market to new territories following the proposed ban by the European Union (EU).
"This is also part of our efforts to stop the EU which has been going all out in its effort to discriminate against palm oil.
"I believe with the strategy undertaken by the ministry, both domestically and globally, and being directly involved with industry players in those countries, we hope there will be an increase in the purchase of palm oil and other downstream products," he said.
He told Bernama this after attending the Ponggal Festival, organised by the Hang Tuah Jaya Keadilan Youth Wing in Peringgit here on Sunday.
Shamsul Iskandar said the ministry was also intensifying the "Love MY Palm Oil" campaign which was launched in January to maximise the use of the oil in Malaysia since the domestic consumption is only at 70 per cent, currently.
"The government will be increasing its efforts and will conduct more programmes to increase the people's awareness and understanding to reach the 100 per cent palm oil usage target.
"We are also focusing on promoting other downstream health food products which are seen as having anti-cancer and antioxidant capabilities," he added. – Bernama