text:
\section{Introduction}

The emission mechanism at the origin of the observed signal during the prompt phase of GRBs
remains unknown. Among the prime contenders are photospheric emission, released when the plasma becomes optically
thin \citep{Goo86,Pac86,MR00,DS02}, and synchrotron emission produced by relativistic particles accelerated by
shocks or magnetic reconnection once the flow is optically thin \citep{RM94,SNP96,DM98,ZY11}. In addition, protons may also contribute, either directly by synchrotron emission, or indirectly by emission from the secondaries produced in photo-hadronic and photo-pair processes \citep{AIM09,CK13,FPM21}.

When comparing models to spectral data, the most crucial difference between the aforementioned models are the
prediction for the low energy spectral slope $\alpha$, usually associated with the low-energy slope of the
Band model \citep{BMF93}. For photospheric emission models, the slope is expected to be around $\alpha = 0.4$
\citep{Bel10, PR11, BSV13, PL18}, unless the ejecta becomes transparent during the acceleration phase
\citep{Goo86, Pac86, BV14, RLA17}, in which case a steeper slope up to $\alpha = 1$ can be achieved. Slopes
shallower than $\alpha = 0.4$ can be obtained when considering geometrical effects such as emission from a
structured jet \citep{LPR13}, or subphotospheric dissipation \citep{PW05,Gia06,VB16}. Observationally, the footprint
of photospheric emission is seen in many GRB spectra, see \textit{e.g.} \cite{RP09, ARP20, DPR20}. Moreover, analysis
of GRB 090902B strongly supports a model where the emission is produced at the photosphere of a highly
relativistic outflow \citep{RAZ10,PZR12}. In the past years, photospheric models have been directly fitted to data
achieving good agreement \citep{ALN15, VGG17,SLR21}.

Synchrotron models predict a low energy slope to be $\alpha = -2/3$
in the slow cooling regime and $\alpha = -3/2$ in the fast cooling regime. Slightly steeper slopes could be
obtained when considering the effects of inverse Compton cooling in the Klein-Nishina regime \citep{BDB09, NAS09,DBG11}.
Yet, most GRB spectra fitted with the Band function \citep{BMF93} are found incompatible with a synchrotron model:
this is known as the ''synchrotron line-of-death'' \citep{PBM98}. Recently, it was found that fitting a synchrotron model
directly to GRB spectra alleviates this problem\footnote{The spectral width was also proposed as a criteria to
further rule out synchrotron models \citep{AB15, YVG15}, but it was shown that the argument does not hold when
synchrotron models are fitted directly to the data \citep{Bur17}.} \citep{BBB19, ARP20}. The main reason for the disagreement
is that the Band function is a poor approximation of the synchrotron emission around the peak, giving poor
constraints when comparing the fitted results to the expectations from synchrotron models in a limiting energy window.
In addition, two independent analysis using \textit{Swift} X-ray \citep{ONG18} and optical
data \citep{ONG19} showed that the spectra of several GRBs require an additional break around
observed energy $\simeq 1$ keV, leading to the straightforward identification of the injection and cooling frequencies
of a synchrotron model. The spectral slopes below and between the breaks were also found compatible
with the expectation from synchrotron models with power-law distributed charged particles.

The closeness of the two identified breaks requires, within the framework of synchrotron models, that the emitting particles
be in the marginally fast cooling regime, with their cooling Lorentz factor $\gamma_{\rm c}$ nearly equal to their
injection Lorentz factor $\gamma_{\rm m}$. This requirement is difficult to account for if the radiating particles
are electrons \citep{BBG18}. Possible solutions include
the jet in jet model \citep{NK09,ZZ14,BBG18} or emission in a time dependent magnetic field \citep{UZ14b}.

Alternatively, it was proposed by \cite{GGO19} that protons could be the particles radiating synchrotron and
producing the main prompt MeV-peak. The observed requirement of marginally fast cooling is then
naturally fulfilled for emission radius in the order of
$10^{13}-10^{14}~$cm and bulk Lorentz factor of a few hundreds \citep{GGO19}, as expected for optically thin emission
models of GRBs \citep{RM94,DM98}. On the other hand, proton synchrotron models do not explain the observed spectral peak energy
clustering \citep{vMP20} and require a large magnetic luminosity $L_{\rm B} \gtrsim 10^{55}~$erg s$^{-1}$ \citep{FPM21}.

Synchrotron emission from protons and from the secondaries produced by photo-pion ( $p\gamma \rightarrow p + \pi^0$,
$p\gamma \rightarrow n+\pi^+$ and other channels producing two or more pions \citep{MER00,LLM07,HRS10}) and BeHe
($p\gamma\rightarrow p e^+ e^-$) interactions
was thoroughly studied in connection with ultra-high energy cosmic ray acceleration \citep{BD98, Tot98, RDF10},
high-energy PeV neutrino production \citep{Pet14} and high energy photon component observed by LAT and more recently by HESS and MAGIC \citep{GZ07,AIM09, CK13,SF20}.
However, all those studies have in common the leptonic origin of the main MeV peak component, when it is not set to be a fiducial Band model.

\citet{FPM21} numerically studied a proton synchrotron model as the source of the main MeV peak similar to the one proposed by \cite{GGO19}. They concluded that emission from the secondaries produced
by either the BeHe-process or photo-pion interactions would be too bright to account for the optical constraints.
This is especially important since this result is inconsistent with
the claim that optical observations support synchrotron emission models \citep{ONG19}.
However, the bursts used by \cite{ONG19} and afterwards by \cite{FPM21} are very long duration bursts ($T_{90} > 70-80$s),
which is required to have simultaneous optical observations. Thus, this small subset of bursts is not necessarily
representative of the full GRB population, nor of the emission mechanism producing the early episodes of a GRB.
Indeed, it was suggested that the emission mechanism might change throughout the burst episodes
(\textit{e.g.} \cite{ZZC18, Li19}).
It is therefore interesting to find predictions of proton synchrotron models that do not rely on optical data,
to be able to test the model on shorter duration bursts.

In this paper, we assume that the prompt emission is due to proton synchrotron and derive constraints on the model.
We present analytical estimates of the effect of BeHe pair production and the pairs subsequent radiation. We
identify two emission regimes: 1) proton synchrotron dominated emission regime with little contribution from other processes,
2) BeHe pair dominated emission regime, leading to a spectrum incompatible with observations. We further describe the transition between these two extreme regimes in which a subdominant power-law from the BeHe pair synchrotron radiation appears across the MeV band, as observed in some GRBs (\textit{e.g.} \cite{VGG17,CPB20}).

The paper is organized as follows. In Section
\ref{sec:2}, we identify the parameter space for each of the three regimes mentioned above by comparing the timescales
of synchrotron emission to that of BeHe pair production. Section \ref{sec:3} details the modification to the spectrum
due to synchrotron radiation from the pairs produced by the BeHe process. Discussion with an emphasis on GRB 190114C is
given in Section \ref{sec:4}.

\section{Constraining proton synchrotron emission models by Bethe-Heitler cooling}
\label{sec:2}

In this section, we compare the timescale of proton synchrotron emission to that of BeHe pair production. If the protons
cool too quickly from BeHe pair creation, the secondary emission from the pairs can greatly affect the observed spectrum.
The valid parameter space for proton synchrotron models can thus be constrained.

Consider an emission region expanding relativistically with Lorentz factor $\Gamma$, emitting radiation at a distance
$r$ from a central engine, and threaded by a magnetic field of comoving strength $B$. The comoving dynamical
time is given by $t_{\rm dyn} = r/(\Gamma c)$, where $c$ is the speed of light. In a marginally fast cooling scenario,
relativistic particles, here protons, are assumed to be steadily injected into a power-law with index $-p$ above some
injection Lorentz factor $\gamma_{\rm p,m}$. We present our results for $p = 2.5$ and $p = 3.5$. On the one hand, the
value of $p \sim 2.5$ is expected in many dissipation and acceleration scenarios (\textit{e.g.} \citet{BO98, KGG00}),
albeit softer values can also be obtained from simulations \citep{SSA13, CCM19,CSS20}. On the other hand, synchrotron
fits to the GRB spectra require an average value of $p = 3.5$ \citep{BBB19}. Marginally fast cooling implies that
$\gamma_{\rm p,m} \sim \gamma_{\rm p,c}$, where $\gamma_{\rm p,c}$ is the characteristics proton cooling Lorentz factor.
We write $\gamma_{\rm p,m} = \xi \gamma_{\rm p,c}$. In this paper, we assume $\xi \gtrsim 1$, i.e., the protons are
fast cooling albeit marginally. This implies that protons efficiently radiate most of their energy, while satisfying
the observed spectral constraints.

The comoving cooling time for protons with Lorentz factor $\gamma_{\rm p}$ emitting synchrotron radiation is
\begin{align}
t_{\rm synch} = \frac{6\pi c m_{\rm p}}{B^2 \gamma_{\rm p} \left (\frac{m_{\rm e}}{m_{\rm p}} \right)^2 \sigma_T},
\end{align}
and the frequency of the synchrotron spectral peak is   $
\nu_{\rm peak} = (4/3) \Gamma q \gamma_{\rm p,m}^2 B /(\pi c m_{\rm p})$,
where we used $\nu_{\rm peak}$ as the frequency without redshift correction, \textit{i.e.} in the frame of the burst.
The observed frequency is $\nu^{\rm obs} = \nu_{\rm peak}/(1+z)$. In those equations, $m_{\rm p}$ and $m_{\rm e}$ are the proton and
electron masses, $q$ is the elementary charge and $\sigma_{\rm T}$ is the Thompson cross section.

Setting the dynamical timescale and the cooling timescale equal, $t_{\rm dyn} \sim t_{\rm synch}$, gives the magnetic
field and the proton cooling Lorentz factor
\begin{align}
B &= \frac{2 \sqrt[3]{6\pi q} c m_{\rm p}^{\frac{5}{3}}}{ m_{\rm e}^{\frac{4}{3}}  \sigma_{\rm T}^{\frac{2}{3}}} \frac{\Gamma \xi^{\frac{2}{3}} }{r^{\frac{2}{3}}\sqrt[3]{\nu_{\rm peak}}} \sim  3.3 \times 10^6 ~{\rm G}  ~\frac{\Gamma_2 \xi^{\frac{2}{3}} }{r_{14}^{\frac{2}{3}} \nu_{\rm MeV}^{\frac{1}{3}}},  \\
\gamma_{\rm p,c} &= \frac{\sqrt[3]{6\pi m_{\rm e}^2 \sigma_{\rm T}}}{4 \sqrt[3]{m_{\rm p} q^2}} \frac{\sqrt[3]{r \nu_{\rm peak}^2}}{\Gamma \xi^{\frac{4}{3}}} \sim 1.4 \times 10^4 ~ \frac{r_{14}^{\frac{1}{3}} \nu_{\rm MeV}^{\frac{2}{3}}}{\Gamma_2 \xi^{\frac{4}{3}}},
\end{align}
where we have replaced $\gamma_{\rm p,m}$ by $\xi \gamma_{\rm p,c}$ and have used the notation
$Q_x = Q/10^x$. Here, $\nu_{\rm MeV} = h\nu_{\rm peak}/1~$MeV is the peak energy from the proton
synchrotron, normalised to the value 1 MeV in agreement with observations, and
$h$ is Planck's constant.

The comoving photon peak energy is $h\nu_{\rm m} = h\nu_{\rm peak}/(2\Gamma) = 5.0 ~{ \rm  keV  } ~\nu_{\rm MeV} \Gamma_2^{-1}$.
Most of the accelerated protons\footnote{Our model only describes the non-thermal population of protons. Colder protons
are also present in the flow, but we discard their contribution to the overall emission process.} have Lorentz factor
$\gamma_{\rm p,c}$. Therefore, for the bulk number of accelerated protons interacting with photons at the peak,
one gets
\begin{align}
\gamma_{\rm p,c} \, h\nu_{\rm m} = 67.5 ~{ \rm MeV} ~ \frac{r_{14}^{\frac{1}{3}} \nu_{\rm MeV}^{\frac{5}{3}}}{\Gamma_2^2 \xi^{\frac{4}{3}}}, \label{eq:prod_gps_nup}
\end{align}
which satisfies the threshold requirement for the BeHe-process ($\gamma_{\rm p,c} \, h\nu_{\rm m} > 2 m_ec^2$) unless $r_{14}^{\frac{1}{3}} \nu_{\rm MeV}^{\frac{5}{3}} < 0.015 \times \Gamma_2^2 \xi^{\frac{4}{3}}$. We note
that the lowest energy protons cannot satisfy the energy threshold for photo-pion interaction
$\gamma_{\rm p,c} \, h \nu_{\rm m}^{'} < 135~ {\rm MeV}$, and it is therefore expected that neutrino production in this
model be small. We comment further on the relevant cooling times in the discussion section.
The model can be further constrained by the tight constraints from the IceCube \citep{AAA17} and Antares \citep{AAA17_Antares} experiments, as shown by \cite{FPM21} and \cite{PTP21}.

Having verified that all accelerated protons are energetic enough to satisfy the threshold
of BeHe pair creation, we now estimate the cooling of proton by the BeHe. This timescale is a function
of the comoving photon spectrum near the peak of their distribution, which itself depends on the comoving proton density\footnote{In principle, the analysis
can be done without computing the proton density, as the photon density can be directly expressed in terms of luminosity,
radius, Lorentz factor and peak energy. This does not change the dependency on the parameters. Here, we chose to make
explicit use of the proton density. }. Let $L^{\rm obs}$ be the observed isotropic photon luminosity of the burst.
Assuming the main emission mechanism is proton synchrotron, the number of radiating protons $N_{\rm p}$ is
\begin{align}
N_{\rm p} \sim \frac{L^{\rm obs}}{P_{\rm synch}^{\rm obs} (\gamma_{\rm p,m})} = \frac{L^{\rm obs}}{\frac{4}{3} c \gamma_{\rm p,m}^2 \Gamma^2 u_{\rm B} \sigma_{\rm T} \left ( \frac{m_{\rm e}}{m_{\rm p}}\right )^2} \sim 1.64 \times 10^{48} ~ \frac{L_{52} r_{14}^{\frac{2}{3}}}{\Gamma_2^2 \nu_{\rm MeV}^{\frac{2}{3}} \xi^{\frac{2}{3}}},
\end{align}
where $P_{\rm synch}^{\rm obs} (\gamma_{\rm p,m})$ is the observed synchrotron power emitted by a single proton with Lorentz
factor $\gamma_{\rm p,m}$ and $u_{\rm B} = {B}^2/(8\pi)$ is the comoving magnetic energy density.

For the comoving volume, we use $V = 4 \pi r^2 (r/\Gamma)$ (\textit{e.g.} \cite{Pee15}), and therefore, the comoving density
of radiating protons is given by
\begin{align}
n_{\rm p} \sim \frac{N_{\rm p}}{V} = & 1.3 \times 10^{7} ~ {\rm cm}^{-3} ~ \frac{L_{52}}{\Gamma_2 r_{14}^{\frac{7}{3}} \nu_{\rm MeV}^{\frac{2}{3}} \xi^{\frac{2}{3}}}, \label{eq:proton_density}
\end{align}
To normalise the photon spectrum, it is assumed that the whole power radiated by protons with Lorentz factor $\gamma_{\rm p,m}$
is emitted at $\nu_{\rm m}$. Thus, the peak spectral energy density is
\begin{align}
u_{\nu_m} \sim \frac{n_{\rm p} P_{\rm synch}(\gamma_{\rm p,m})}{\nu_{\rm m}} t_{\rm dyn} =  2.2 \times 10^{-10} ~ {\rm  erg}~ {\rm cm^{-3}}~ {\rm Hz^{-1}}~L_{52} \Gamma_2^{-1} r_{14}^{-2} \nu_{\rm MeV}^{-1}, \label{eq:spectral_energy_density_synchrotron_proton}
\end{align}
where $P_{\rm synch} = \Gamma^{-2} P_{\rm synch}^{\rm obs}$. Since protons with Lorentz factor $\gamma_{\rm p, m}$
mostly interact via BeHe process with photons close to the peak, only the shape of the photon spectrum around the
peak affects the cooling rate by the BeHe process. The photon distribution close to the peak is well
approximated by the synchrotron radiation of the protons even when $t_{\rm BeHe}\sim t_{\rm synch}$,
where $t_{\rm BeHe}$ is the BeHe cooling timescale.
This can be understood because the photons produced by the BeHe pairs are at different energies (see section \ref{sec:3}),
where the cross-section is smaller. Furthermore, when $t_{\rm BeHe}\sim t_{\rm synch}$, the proton distribution
function is not strongly changed below $\gamma_{\rm p, m}$.
Therefore, in the marginally fast cooling scenario considered in this paper $(\xi \geq 1)$, the comoving
photon spectrum around the peak is obtained as
\citep{SPN98}
\begin{align}
n_\nu =& \frac{1}{h \nu} u_{\nu_{\rm m}} \left \{
\begin{aligned}
& \left ( \frac{\nu}{\nu_{\rm c}} \right )^{\frac{1}{3}} \left ( \frac{\nu_{\rm c}}{\nu_{\rm m}} \right )^{-\frac{1}{2}} & & \nu < \nu_{\rm c},\\
& \left ( \frac{\nu}{\nu_{\rm m}} \right )^{-\frac{1}{2}} & & \nu_{\rm c} < \nu < \nu_{\rm m}, \\
& \left ( \frac{\nu}{\nu_{\rm m}} \right )^{-\frac{p}{2}} & & \nu_{\rm m} <  \nu .
\end{aligned} \right.  \label{eq:synch_spectrum_fast_cooling}
\end{align}
where $p$ is the index of the proton spectrum.

In Appendix \ref{app:appendix_BeHe_cooling_rate_simplification}, we obtain the cooling rate of protons by BeHe pair production ($p\gamma\rightarrow p e^+ e^-$)
following the prescription of \citet{CZS92}. The cooling is a function of photon energy in the proton rest frame, thus,
one has to integrate the photon distribution over energy and angle. This is done when generating the figures, which therefore show exact results in the case of an isotropic photon distribution. Here, we present approximate analytical estimates to demonstrate how the cooling varies with the parameters. Using Equations \eqref{app:eq_dgammadt_BeHe}
and \eqref{app:eq_BeHe_cooling}, and assuming  $\xi =1$ for simplicity, the BeHe timescale is given by
\begin{align}
t_{\rm BeHe}^{-1} = -\left. \frac{1}{\gamma_{\rm p}} \frac{d\gamma_{\rm p}}{dt} \right |_{\rm BeHe} = \left \{ \begin{aligned}
&  8.3 \times 10^{-2}  ~ {\rm s^{-1}} ~ \Gamma_2^{-\frac{2}{3}} L_{52} r_{14}^{-2} \gamma_{\rm p}^{-\frac{1}{3}} \nu_{\rm MeV}^{-\frac{4}{3}} & ~~~~~ & 2 x_{\rm m} \gamma_{\rm p} > \kappa_0,  \\
&  4.8 \times 10^{-7} ~ {\rm s^{-1}} ~   L_{52} \gamma_{\rm p}^{\frac{5}{4}} \nu_{\rm MeV}^{\frac{1}{4}} r_{14}^{-2} \Gamma_2^{-\frac{9}{4}}  & ~~~~~ & {\rm else,}
\end{aligned} \right.
\label{eq:t_BeHe}
\end{align}
where $x_{\rm m} = h \nu_{\rm m}/(m_e c^2)$ and $\kappa_0 = 40$ is found to provide an adequate approximation
for the cooling rate, see Appendix \ref{app:appendix_BeHe_cooling_rate_simplification}. The parameters $\kappa_0$ is introduced to simplify the expression for the BeHe cooling. It is roughly the photon energy (in the proton rest frame) corresponding to the maximum cooling rate by the BeHe process.  To obtain the numerical
value in the bottom expression, $p$ was set to 2.5. The expression and numerical value for a different value of
$p$ can be obtained by using
Equations \eqref{app:eq_dgammadt_BeHe} and \eqref{app:eq_BeHe_cooling}. The first line of Equation \eqref{eq:t_BeHe}
is for protons that mostly interact with photons below $\nu_{\rm m}$, while the second line describes
protons interacting with photons with frequency higher than $\nu_{\rm m}$. An estimate of the ratio between
the BeHe cooling time and the synchrotron cooling time at the injection Lorentz factor $\gamma_{\rm p,m}$ is given by
\begin{align}
\left. \frac{t_{\rm BeHe}}{t_{\rm synch}}\right |_{\gamma_{\rm p,m}} = \left \{
\begin{aligned}
& 8.57  ~ r_{14}^{\frac{10}{9}} \nu_{\rm MeV}^{\frac{14}{9}} \Gamma_2^{\frac{4}{3}} L_{52}^{-1} & ~~~~~ & 2 x_{\rm m} \gamma_{ \rm  p, m} > \kappa_0,  \\
& 4.3 \times 10^{-1} ~  \Gamma_2^{\frac{9}{2}} r_{14}^{\frac{7}{12}} \nu_{\rm MeV}^{-\frac{13}{12}} L_{52}^{-1} & ~~~~~ & {\rm else,}
\end{aligned}
\right.
\label{eq:ratio_cooling_at_gamma_m}
\end{align}
where we used the fact that $t_{\rm synch} = t_{\rm dyn}$ for $\gamma_{\rm p,m}$. This results therefore indicates
similar timescale for fiducial parameters. As noted above, the similarities of the time scales implies that the peak of the proton synchrotron is not substantially modified by the BeHe process.

Figure \ref{fig:cooling_comparison} shows the ratio of cooling times at $\gamma_{\rm p,m}$ assuming $\xi = 1$ for
different parameter choices. It is obtained by direct integration of Equation \eqref{app_eq:dgp_dt}. In computing
this figure, we have assumed that the proton distribution function is only modified by synchrotron losses. This
assumption breaks when BeHe cooling strongly dominates in the lowest domain of each panel in Figure
\ref{fig:cooling_comparison}. From top to bottom, the emitted luminosity is $10^{54}$, $10^{53}$, and $10^{52}$
erg s$^{-1}$ and from left to right the observed spectral peak energy is $100$ keV, $300$ keV, and 1 MeV,
respectively. Figure \ref{fig:cooling_comparison} is made with $p = 2.5$. A softer value of $p$ increases
the timescale ratio for the high-energy branch, \textit{i.e.}, it only affects the left-most part in the
panels in Figure \ref{fig:cooling_comparison}. For $p = 3.5$ as compared to $2.5$, the timescale ratio
increases by a factor $\sim 2$ for an order of magnitude decrease in radius.

From this figure, as well as from Equation
\eqref{eq:ratio_cooling_at_gamma_m}, one can identify two extreme regimes. For low luminosities $L^{\rm obs}$, high
Lorentz factor $\Gamma$ and large radius $r$, the protons are largely unaffected by BeHe pair creation (yellow
region in Figure \ref{fig:cooling_comparison}).
In this scenario, the observed spectrum is due to the synchrotron emission from the marginally fast
cooling protons as described in \citet{GGO19}, without any modification by BeHe. This shows
that explaining GRB prompt spectra with proton synchrotron requires high bulk Lorentz factor $\Gamma \gtrsim 300$,
in agreement with the analysis of \cite{FPM21} who used optical constraints. On the other end, when
$\Gamma$ and $r$ are small and/or $L$ is high, the BeHe process dominates the cooling
(dark region in Figure \ref{fig:cooling_comparison}).
In this regime, the synchrotron photons from the very fast cooling pairs quickly outnumber the
proton synchrotron photons, leading to even more rapid BeHe pair creation. Therefore, most of the available
proton energy is extracted by the BeHe pairs. The cooling Lorentz factor of the pairs is
$\gamma_{\pm, {\rm c}} \sim 1$, corresponding to a cooling break in the observed spectrum at $\sim 10~$eV, whereas
the $\nu F_\nu$-peak energy associated to the synchrotron from the created BeHe pairs is at $\sim 100~$MeV (see Equation \eqref{eq:ratio_peak_energy}). Thus, the
observed spectrum consists of a single power-law with $F_\nu \propto \nu^{-1/2}$ between these two
energies, clearly incompatible with observed GRB spectra. In between the two extreme regimes when
the cooling timescales are comparable, signatures from both processes can be seen in the spectrum,
and we explore this scenario in Section \ref{sec:3}.

\begin{figure}
\centering
\includegraphics[width=0.99\textwidth]{cooling_param_new.pdf}
\caption{Comparison of cooling rate between the BeHe and synchrotron processes at $\gamma_{\rm p,m}$. From top to bottom the emitted luminosity is $10^{54}$, $10^{53}$ and $10^{52}$ erg s$^{-1}$, while from left to right the observed spectral peak frequency is $100$ keV, $300$ keV and 1 MeV. The purple, red and black thick lines correspond to $t_{\rm BeHe} = t_{\rm synch}$, $t_{\rm BeHe} = 0.1 t_{\rm synch}$, and $t_{\rm BeHe} = 10 t_{\rm synch}$ respectively. The thin black lines show the variability time expected from the Lorentz factor and radius $t_{\rm var} \sim r/(\Gamma^2 c)$ for selected variability time $10^{-2}$s, $10^{-1}$s, $1$s and $10$s. The figure is made with $p = 2.5$. A value of $p = 3.5$ slightly increases the valid parameter space for proton synchrotron models by increasing the timescale ratio $t_{\rm BeHe}/t_{\rm synch}$ at small radii. }
\label{fig:cooling_comparison}
\end{figure}

\section{Spectral signature of Bethe-Heitler pairs}
\label{sec:3}

In this section, we obtain predictions for the comoving pair distribution and their emission spectrum in the case where the cooling via synchrotron and BeHe are comparable. In this situation, the proton distribution at $\gamma_{\rm p,m}$ is only marginally affected by BeHe cooling. This implies that the photon spectrum at the peak energy around 1 MeV (which is the optimal photon energy for BeHe pair creation; see Equation \eqref{eq:prod_gps_nup} and Appendix \ref{app:appendix_BeHe_cooling_rate_simplification}) is not strongly modified by synchrotron radiation from the secondaries. If the secondary emission from the pairs do substantially contribute to the BeHe cooling of the protons, the BeHe pair creation becomes exponential in time and we are instead in the regime where BeHe dominates. Here, we use the proton synchrotron photons as targets to compute the rate at which pairs are created, namely in the case $t_{\rm BeHe} \raisebox{-0.3ex}{\mbox{$\stackrel{>}{_\sim} \,$}} t_{\rm synch}$.

A proton with Lorentz factor $\gamma_{\rm p}$ produces electrons and positrons with typical Lorentz factor
$\gamma_\pm = \kappa_{\rm e} (m_{\rm p}/m_{\rm e})\gamma_p$, where $\kappa_{\rm e}$ is the inelasticity. The
dependence of the inelasticity on $\gamma_{\rm p} x$, where $x$ is the target photon energy in units of
electron rest mass, can be found in \cite{MPK05}. For photons at the peak energy, $\gamma_{\rm p} x$ is
given by Equation \eqref{eq:prod_gps_nup} and is of the order of a few to a few hundreds. Looking at Figure 1
of \cite{MPK05} for those values of $\gamma_{\rm p} x$, the inelasticity is found to vary
between $10^{-3}$ and $10^{-4}$, giving an average pair Lorentz factor between $\gamma_\pm \sim 2\gamma_{\rm p}$
and $\gamma_\pm \sim \gamma_{\rm p}/5$. Considering that most of the protons have Lorentz factor
$\gamma_{\rm p,m} \sim \gamma_{\rm p,c}$, we consider that all pairs are created with Lorentz factor
$\gamma_{\pm,{\rm m}} \equiv \kappa_{\rm e} (m_{\rm p}/m_{\rm e})\gamma_{\rm p,m}$. In other words, we
neglect the contribution of higher energy protons in the creation of pairs with higher energies. This
effect only changes the very high energy photon spectrum, which is likely to be absorbed by pair creation.
In addition, since the pairs are fast cooling, which follows as the protons are marginally fast cooling,
they obtain a Lorentz factor much smaller than their initial Lorentz factor in one dynamical timescale
$\gamma_{\pm,c} \ll \gamma_{\pm,{\rm m}}$, and therefore the exact details of their injection is lost via
their cooling.

The pair production rate by BeHe is given by \cite{CZS92}, but cannot be analytically integrated for a general
photon spectrum. Analytical estimates in some specific cases were provided by \cite{PM15b}.
We provide the integral expression used in our numerical computation in Appendix \ref{app:appendix_pair_production_rate_simplification}.
In order to get analytical estimates of the number of pairs, we write the ratio between the synchrotron power
and BeHe power to be equal to the ratio of their timescales:
\begin{align}
    \frac{P_{\rm BeHe}^{\rm tot}}{N_{\rm p} P_{\rm synch}} = \left (\frac{t_{\rm BeHe}}{t_{\rm synch}} \right )^{-1},
\label{eq:power_ratio}
\end{align}
where $P_{\rm BeHe}^{\rm tot}$ it the power emitted by all BeHe pairs. Using $P_{\rm BeHe}^{\rm tot} = \gamma_{\pm,{\rm m}} m_{\rm e} c^2 \dot n_\pm V$, which is valid since the pairs are fast cooled, one obtains
\begin{align}
    \dot n_\pm = n_{\rm p}
    \left (\frac{t_{\rm BeHe}}{t_{\rm synch}} \right )^{-1} \frac{P_{\rm synch}}{\gamma_{\pm,{\rm m}} m_{\rm e} c^2} = \left \{
    \begin{aligned}
    & 4.6 \times 10^8 ~ {\rm cm }^{-3} {\rm s}^{-1} ~ L_{52}^{2} \Gamma_2^{-\frac{4}{3}} r_{14}^{-\frac{40}{9}} \kappa_{\rm e, -4}^{-1} \nu_{\rm MeV}^{-\frac{20}{9}}  & ~~~~~ & 2 x_{\rm m} \gamma_{\rm p, m} > \kappa_0, \\
    & 9.2 \times 10^9 ~ {\rm cm }^{-3} {\rm s}^{-1} ~ L_{52}^{2} \nu_{\rm MeV}^{\frac{5}{12}} \Gamma_2^{-\frac{9}{2}} r_{14}^{-\frac{47}{12}} \kappa_{\rm e, -4}^{-1} & ~~~~~ & {\rm else.}
    \end{aligned}\right.
\label{eq:n_pm_dot}
\end{align}
We note the very strong dependence on the parameters, specifically the radius and the peak energy. This means
that in principle both scenarios with high and low pair yield are possible.

Assuming that all pairs are produced at Lorentz factor $\gamma_{\pm,{\rm m}}$ and that pair annihilation
is negligible (see Section \ref{sec:4}), the continuity equation for
the pairs can be solved to obtain the pair distribution. This computation is done
in Appendix \ref{sec:appendix_pair_spectrum}, and gives
\begin{align}
n_\pm (\gamma_{\rm e}) = \frac{m_{\rm e} c^2 \dot n_\pm}{P_{\rm e}(\gamma_{\pm,{\rm m}})} \left( \frac{\gamma_{\pm,{\rm m}}}{\gamma_{\rm e}} \right )^{2} H(\gamma_{\pm,{\rm m}} - \gamma_{\rm e}), \label{eq:pair_production_rate}
\end{align}
namely a single power-law with index $-2$ extending from $\gamma_{\pm,{\rm m}}$ down to $\gamma \sim 1$.
Here, $P_{\rm e}$ is the synchrotron power emitted by an electron and $H$ is the Heaviside function. We note that
at low energies the pair distribution should substantially deviate from this power-law because of strong
synchrotron self-absorption heating and pair annihilation. Our analysis also neglects the electrons originally present in the flow (see the discussion in Section \ref{sec:4}).

We now estimate the emerging spectrum. The emitted synchrotron spectrum from the pair distribution
in Equation \eqref{eq:pair_production_rate} is a fast cooling power-law with $F_\nu \propto \nu^{-1/2}$.
It extends from an observed peak frequency of
\begin{align}
\nu_{ {\rm m}, \pm} = \left(\frac{\gamma_{\pm,{\rm m}}}{\gamma_{\rm p,m}}\right)^{2} \left(\frac{m_{\rm p}}{m_{\rm e}}\right) \nu^{\rm obs} = 61.9 ~{\rm MeV}~ \kappa_{\rm e,-4}^2 \nu_{\rm MeV} \label{eq:ratio_peak_energy}
\end{align}
down to sub-keV energies. The synchrotron frequency of the pairs linearly depends on the observed peak frequency.
It also indirectly depends on the other model parameters via the value of the inelasticity. Larger values of
$\kappa_{\rm e}$ results from smaller values of $\gamma_{\rm p,m} \nu_{\rm m}$, i.e., larger Lorentz factor
and peak frequency, and/or smaller radius and luminosity, see Equation \eqref{eq:prod_gps_nup}. The shape of
the spectrum above $\nu_{\pm,{\rm m}}$ depends on the shape of the proton distribution function and of the pair
injection details. Since we are only giving analytical estimates, it is out of the scope of this paper to
account for a detailed analysis at those energies. We note however that emission at GeV and eventually TeV
energies are constrained by the LAT instrument on-board Fermi (\textit{e.g.} \cite{GPW11}). The normalization
of the spectrum is either obtained from the pair distribution function in Equation \eqref{eq:pair_production_rate},
or by considering the ratio of the synchrotron power to the BeHe power in Equation \eqref{eq:power_ratio}.
Indeed, the value and parameter dependence of the ratio between
the proton synchrotron peak and the BeHe peak, $\nu_{\rm m} F_{\nu_{\rm m}}/\nu_{\pm, {\rm m}} F_{\nu_{\pm, {\rm m}}}$,
are well described by the ratio of the timescales given in Equation \eqref{eq:ratio_cooling_at_gamma_m}. This is true as long as $t_{\rm synch}$ is not much larger than $t_{\rm BeHe}$, so that the target photons for the BeHe process are those produced by proton synchrotron.

Figure \ref{fig:spectrum_synchrotron_dominated} shows an example spectrum when the two timescales are comparable.
A subdominant power-law extends from $\sim 100$ MeV all across the observation window. This extra component is
solely due to synchrotron radiation from the BeHe pairs and it is simultaneous to the main MeV emission.
It is potentially detectable at low energy (few tens of keV) and in the LLE data. In making this figure, we assumed
$r_{14} = 1$, $\Gamma_2 = 1$, $\nu_{\rm MeV} = 1$, $L_{52} = 10$, $\xi =1$ and $p = 2.5$ (left) or $p = 3.5$ (right).
They both correspond to $t_{\rm BeHe}/ t_{\rm synch} \sim 1.9$ (the approximate expression in Equation
\eqref{eq:ratio_cooling_at_gamma_m} gives $t_{\rm BeHe}/ t_{\rm synch}\sim 0.85$). The figure was made with BeHe inelasticity
$\kappa_{\rm e} \sim 10^{-4}$ to determine $\nu_{{\rm m},\pm}$. This value of $\kappa_{\rm e}$ is appropriate
when $\gamma_{\rm p,m} h \nu_{\rm m}/(m_{\rm e} c^2) \sim 100 $, as obtained for this choice of parameters.
The total number of pairs was calculated using the integral formulation of \cite{CZS92} (see Appendix \ref{app:appendix_pair_production_rate_simplification}).

In this example, the overall synchrotron spectrum is strongly modified at low and high energies by an extra
power-law produced by the synchrotron emission of the BeHe pairs. This is a clear spectral signature of
the proton synchrotron emission model, which can help to differentiate proton synchrotron models from electron synchrotron models.
Several properties of this power-law are well determined and weakly sensitive to the parameter of
the model. First, its slope is set to be $\alpha = -1.5$
since it is produced by electrons and positrons in the fast cooling regime. Second, it extends from low (sub-keV)
energy to high energy with a peak at few tens or hundreds of MeV. Therefore, this component crosses the entire
GBM energy window. Third, the maximum energy of this component is linearly correlated with the peak frequency of the MeV
component, as shown by Equation \eqref{eq:ratio_peak_energy}. Finally, the intensity of this component does not
have a strong dependence on the uncertain value of the proton index $p$, but strongly depends on the luminosity, Lorentz factor and emission
radius. The combination of all those characteristics provides a clear smoking-gun of proton synchrotron model.

\begin{figure}
\centering
\begin{tabular}{cc}
\includegraphics[width=0.45\textwidth]{photon_spectrum_total_synchrotron_marginally_dominant_1.pdf} &
\includegraphics[width=0.45\textwidth]{photon_spectrum_total_synchrotron_marginally_dominant.pdf}
\end{tabular}
\caption{Photon spectrum in marginally dominant synchrotron cooling regime with $t_{\rm synch} \sim t_{\rm BeHe}$. Parameters are $r_{14} = 1$, $\Gamma_2 = 1$, $\nu_{\rm MeV} = 1$, $L_{52} = 10$, $\xi = 1$ and $p = 2.5$ (left) or $p = 3.5$ (right). Blue - proton synchrotron component. Green - BeHe synchrotron component. Red - total. It is clear that the emission from the secondary BeHe pairs greatly affect the overall shape of the spectrum at low ($\lesssim 30$ keV) and high ($\gtrsim 10$ MeV) energies . The frequency of the second peak is independent on the power-law index. Above the photon peak at $\sim 100~$MeV, the photon spectrum is not specified by our analysis as it depends on the details of the pair injection spectrum, and as such on the exact shape of the proton distribution function above $\gamma_{\rm p,m}$. This is represented by a dashed line. }
\label{fig:spectrum_synchrotron_dominated}
\end{figure}

\section{Discussion and conclusion}
\label{sec:4}

Proton synchrotron models are an attractive solution to explain marginally fast cooling spectra from GRBs
\citep{GGO19}.
We have performed a detailed investigation of the effect of BeHe cooling on the protons and of the subsequent
radiation of the BeHe pairs.  For high bulk Lorentz factor $\Gamma$, large radius $r$ and low luminosity
$L^{\rm obs}$, proton synchrotron emission dominates and no BeHe pair signature is expected. Conversely,
synchrotron emission from the BeHe pairs dominates when the luminosity is high, and $\Gamma$ and $r$ are relatively
low. This constitutes an additional test for the model: if no pair signature is observed in high
luminosity bursts, large radii and high Lorentz factors are necessary. The magnetic luminosity is given by
\begin{align}
L_{\rm B} = \pi c r^2 \Gamma^2 \frac{B^2}{8\pi} = 4.43 \times 10^{53} {\rm erg}~{\rm s}^{-1} r_{14}^{\frac{8}{3}} \xi^{\frac{4}{3}} t_{\rm v}^{-2} \nu_{\rm MeV}^{-\frac{2}{3}}
\label{eq:magnetic_luminosity}
\end{align}
where we have replaced the Lorentz factor $\Gamma$ by the variability time $t_{\rm v} = r/(c \Gamma^2)$ normalised
to 1s. The large dependence on the radius and variability time implies a very large magnetic luminosity if
no BeHe pair signature is observed.
For instance, for a variability timescale of the order a few seconds as observed in the burst sample of \cite{BBB19},
an observed luminosity of $L^{\rm obs} = 10^{54}~$erg s$^{-1}$ requires that $r\sim 10^{15}$
cm to suppress the BeHe pair creation (see Figure \ref{fig:cooling_comparison}). Using Equation
\eqref{eq:magnetic_luminosity}, this implies a magnetic luminosity of a few $10^{56}$ erg s$^{-1}$.
Such a high magnetic luminosity suggests that the jet is magnetically dominated, leading to an
acceleration rate with $\Gamma \propto r^{1/3}$ \citep{DS02, BPL17}, and possibly magnetic reconnection as the
energy dissipation mechanism, see \textit{e.g.} \cite{LB01,GU19}.

In between the two regimes outlined above, we expect a parameter space where both signatures can be
observed simultaneously in the MeV band (see Figure \ref{fig:spectrum_synchrotron_dominated}).
This component might have already been observed in several GRBs. Indeed, it is
reminiscent of the population of bursts whose spectra seems to have two components: a main emission peak
together with a subdominant component well approximated by a power-law observed from a few keV to several
tens of MeV \citep{AAA10_Ferm_090510,GKD15}. This sub-dominant power-law can be interpreted as
the radiation from BeHe pairs, identified in our work as the spectral signature of proton synchrotron models.

Most notably, the spectra of GRB 190114C detected by MAGIC \citep{MAA20} are
composed of two components in the energy range 1keV - 1 GeV\footnote{Three when considering the TeV emission.},
with low energy slopes seemingly compatible with slow $\alpha = -2/3$ and fast $\alpha = -3/2$ cooling
synchrotron radiation in some time bins (\citet{CPB20}, however see \citet{AAA20_190114C}). In addition,
a spectral cut-off component at energies between $50$ to $100$ MeV was reported in \citet{CPB20}. We
speculate that this burst might possess the clear signature of proton synchrotron with BeHe cooling
discussed in this paper: 1) one main peak produced by proton synchrotron in the slow cooling regime,
2) a second component compatible with fast cooling synchrotron radiation from BeHe pairs and 3)
a cutoff between $50$--$100$ MeV corresponding to the injection limit of BeHe pairs. Furthermore,
analysis of panel c) and d) in Figure 2 of \citet{CPB20} shows that the ratio between the low
and the high peak frequency is about $100$, in rough agreement with Equation \eqref{eq:ratio_peak_energy}.

In our analysis, there are additional emission processes not dealt with that might modify the spectrum. We briefly discuss some of them here. First, we neglected the modification of the high energy peak by $\gamma\gamma$ absorption. Indeed, Equation \eqref{eq:ratio_peak_energy} shows that the synchrotron peak of the pairs is marginally below the energy threshold for pair creation. Therefore, only the spectrum at energies larger than the peak can be affected by this process. Pair recombination could produce an observable characteristic around observed frequency $\nu_{{\rm obs},\gamma \gamma} \sim 2\Gamma \, m_e c^2 /h = 2.4 \times 10^{22} ~{\rm Hz} ~ \Gamma_2$. Yet, the time for pair recombination approximated by  $t_{e^\pm \rightarrow \gamma\gamma} = 2 /(\sigma_{\rm T} n_\pm \langle v \rangle)$ is such that
\begin{align}
    \frac{t_{e^\pm \rightarrow \gamma\gamma}}{t_{\rm dyn}} = 2.0 \times 10^2 ~ \Gamma_2^{\frac{10}{3}} r_{14}^{\frac{22}{9}} \kappa_{\rm e, -4} \nu_{\rm MeV}^{\frac{20}{9}} L_{52}^{-2},
\end{align}
where we have approximated the density of pairs as $n_\pm  = \dot n_\pm t_{\rm dyn}$ using the upper branch of Equation \eqref{eq:n_pm_dot} and use for the average electron velocity $\langle v \rangle = c$. Thus, pairs do not substantially recombine for our fiducial parameters. However, we note the large dependence on the parameters, therefore, such a signature could in some parameter space regions be present.

Furthermore, we did not treat the radiation from the initial population of electrons. This was discussed in
\citet{GGO19}, who argued that under the assumption that the same number of protons and electrons are
accelerated, the electrons would not be seen if they achieve the same injection spectrum as the protons since
their luminosity would be a factor $m_e/m_p$ lower. If instead of similar injection spectrum, both electrons
and protons carry the same energy, electrons would radiate their energy in the TeV band, which should trigger
a leptonic cascade. In addition, thermalization of the background electrons via synchrotron self-absorption
could also change the low energy spectrum.  We expect this process to change the spectrum mostly in the optical
band, therefore our conclusions would be largely unaffected as we have focused on the keV to GeV band.

We assumed that photo-pion interaction is inefficient in our model since the threshold for this process is not reached for the fiducial parameters, see Equation \eqref{eq:prod_gps_nup}. However, it was argued by \cite{FPM21} that cooling by photo-pion dominates cooling by the BeHe process. We show in Appendix \ref{app:photopioncooling} the additional conditions that the parameters should satisfy for BeHe cooling to dominate. We find that this holds true for a large set of parameters. Yet, if a substantial amount of energy is transferred from protons to charged pions by photo-hadronic interaction, the spectrum above the peak would be modified.

In a future work, we will compute a table model with \textit{SOPRANO}, a code designed to simulate
lepto-hadronic processes in optically thin environment \citep{GBS21}. There, we perform direct fits
of a proton synchrotron model with BeHe pair production to GRB 190114C, in order to understand if the
additional power-law and its cutoff are in agreement with the model presented here. The sample of
bursts in \cite{BBB19} will also be studied, in order to constrain the parameters and further test the model.

To conclude, proton synchrotron models have a clear smoking-gun signature: the synchrotron radiation
produced by the BeHe pairs. The emerging spectrum is composed of a main synchrotron peak produced by protons,
and a power-law with index $\alpha = -1.5$ extending from sub-keV energies to few tens or hundreds of MeV. The peak
frequency of this component is linearly linked to the frequency of the MeV peak frequency. Identification of this
extra power-law in spectra will help to constrain the emission mechanism of GRB jets and their parameters.

\vspace{1cm}

\begin{acknowledgments}
DB and AP acknowledge support from the European Research Council via the ERC consolidating grant $\sharp$773062 (acronym O.M.J.).
F.S. acknowledges support from the G\"oran Gustafsson Foundation for Research in Natural Sciences and Medicine.
\end{acknowledgments}

\clearpage

redpajama_set_name: RedPajamaArXiv


Stress kills. If we're going to be friends then I figured I'd go ahead and introduce you to this blunt, but loving side of me. At the end of the day I want what's best for you. Stress is not it. That's not to say that stress is not a normal part of life that we all deal with. It's the "deal with" part that I want to help you with. I believe that we should always have a go to toolbox of skills to rely on to help us cope effectively with the stress we may encounter when following our dreams. Wanting to be an entrepreneur is one thing, but properly preparing for the journey is another. That's why today I want to help you beat stress before you even experience it. Check out your very own toolkit below.
Be aware of what you are feeling and why you are feeling it. By the time we realize we are stressed it is often after we have hit the point of being overwhelmed. The key is to know what triggers stress for you and to cope with immediately instead of letting build up.
Clarity often comes from simplifying. If you need clarity it's good to get the problem out and then break the problem down. Start by writing the problem down and then breaking it into small parts. Solve each part until you've solved your problem and found clarity.
When things get tough remind yourself of why you started. Your goal should always be in the front of your mind. Your why should be so strong that you refuse to quit until you've accomplished what you set out to do. Remember to always work from a creative mind and not a competitive mind. When we are competitive we compare ourselves to others and have a limited mindset. When we are creative we do not compare ourselves because we know we are unlimited and that there is more than enough for all.
Instead of thinking of the barriers visualize your desired outcome. Take a few minutes to see yourself having already achieved your goal or dream. Visualize how you will feel, act, and think. When we visualize we not only relieve stress, but we also keep ourselves motivated.
We often face the most problems and stress when we are about to break through. It is up to us to realize this and pass the test. I like to think of it as leveling up. When you're facing a problem or stress, remind yourself of your dream and that this will not make or break your dream. Face the problem or stress you are dealing with head on.
What is causing you the most stress on your entrepreneurship journey?
Hi Kelly. I can relate to number 2 on the list so much. As soon as I began to simplify my life, my vision and goals started to become more clear. As an entrepreneur, it's beyond important to have clarity. Your vision is the basic foundation for everything you do. Great post!


text:
Nuclear site shutdown marks 'good start' but 'complete denuclearization' still far off
Ha Yoon Ah
On May 24, North Korea voluntarily shut down its nuclear site at Punggye-ri, Kilju, North Hamgyong Province, the site of six nuclear tests conducted from 2006 to 2017. Although some observers have claimed that the gesture demonstrates North Korea's intention to denuclearize, others remain doubtful of the regime's real intentions.
So how do experts view the alleged nuclear site shutdown conducted by North Korea?
Lee Chun Geun, a senior researcher and nuclear weapons expert at South Korea's Science and Technology Policy Institute, believes that the shutdown of the nuclear site is meaningful because "North Korea has promised not to conduct further technological development of nuclear weapons." He believes the shutdown of the facility is a "good start."
Lee added that while the underground tunnels Number 3 and Number 4 have never been used for nuclear weapons testing, North Korea could repair them to full working order if desired. Moreover, he points out that nuclear experts did not attend the event on May 24 to fully verify what North Korea did or did not do. Nevertheless, he argues that North Korea's actions to shut down the site are significant in the broader perspective of taking steps toward denuclearization.
He adds, however, that there is "still a long road to go" before North Korea achieves "complete denuclearization."
Lee says that North Korea's nuclear program has become so utterly complicated that the country will not complete denuclearization while Trump is president. He says that the Trump administration must now focus on how to bring it about if it wants to see progress on denuclearization in the near future.
Lee believes the most important issue is for North Korea's nuclear material and warheads to be removed and for nuclear weapons-related equipment to be destroyed. He also states that the issue of trust is always in play, which means North Korea must make a sincere effort to report on its progress toward denuclearization. Accordingly, Lee says that the US and the rest of the international community must have sufficient capabilities, data and methods to verify North Korea's reports.
The following is an edited script of an interview with Lee conducted by Daily NK.
Q. North Korea blew up [parts of] its nuclear site in Punggye-ri on May 24, calling it a "shutdown" of the nuclear site, but can we view it that way?
Broadly, yes, it is a shutdown. There are, however, some issues concerning underground tunnels Number 3 and Number 4 that are unaddressed.
Q. What issues are those, for example?
They didn't destroy the inside of the detonation room and just blew up underground tunnels. They could rebuild them if they wanted to. Underground tunnel Number 2's detonation room had already collapsed during a past nuclear test so they just needed to blow up the tunnel. But Number 3 and Number 4 both should have had their detonation rooms destroyed for it to be deemed a complete shutdown.
Q. Do you believe North Korea could rebuild Number 3 and Number 4 and use them for nuclear testing again?
If North Korea has the will to do it, they can do it.
Q. Are there any areas of the recent demolishing of the underground tunnels that caught your eye in particular?
Yes. Particularly how the deputy head of North Korea's Nuclear Weapons Research Center explained the process North Korea went through to shutdown the site. The Punggye-ri site has long received a lot of attention. North Korea officially decided to shut down the site through a decision by the Party – without any pressure from outside forces. They did it of their own volition. They called the foreign press to witness the shutdown and showed they were completely done with the site by blowing up the living residences and support facilities near the site. Given all that, it can definitely be called a shutdown.
Q. As a nuclear weapons expert, there must have been some things you wish had happened.
They didn't allow experts to witness the shutdown. It would have been good to go inside the tunnels, but they didn't allow that. There were some areas of the shutdown process that were unsatisfactory as a result.
Q. Can you glean any insight into whether North Korea's technological development of nuclear weapons will end with the shutdown of the Punggye-ri site?
Nuclear testing ultimately refers to both the development and testing of nuclear weapons – the whole process. I think it's significant that North Korea said [in light of the shutdown of the nuclear site] they won't conduct further technological development in the future.
Q. Do you think that means they won't conduct any more nuclear weapons development?
It means that they have ruled out a major way of doing it. Why did they dig the Number 3 and Number 4 underground tunnels? Number 4 was rebuilt after conducting a nuclear test there. They did have the intention of modernizing their stockpile through further testing, but they've now abandoned those plans.
Q. Some believe that North Korea can conduct nuclear test simulations [without the need for the nuclear site] following their sixth nuclear test last year.
I don't see it that way. Simulations are hard. They require a lot of nuclear testing and I don't believe just six tests would allow them to conduct proper simulations. North Korea conducted a sprawling range of tests using plutonium, uranium, regular nuclear weapons and hydrogen bombs. I don't think that gave them enough data. Simulations require supercomputers, really fast ones, and I don't think they have them. Simulations, moreover, are just practice runs – you have to run simulations a couple of times and then see if they work out. Verifying the results of a simulation ultimately means you have to conduct a nuclear test. I don't think North Korea has conducted those kinds of tests yet. They just haven't done enough tests to make simulations a real possibility.
Q. Is there a symbolic significance to North Korea's shutdown of the site, i.e. that they have shown the will to denuclearize?
Yes, I think it's a good start, despite some unsatisfactory areas.
Q. The US talks about "complete denuclearization." What is the basis of deciding whether "complete denuclearization" has been achieved?
Complete denuclearization doesn't just refer to nuclear sites. Complete denuclearization means that North Korea goes through a set of procedures to report all aspects of its nuclear program (nuclear material and warheads), pass verification on all of that, and then shut down or ship out all of its nuclear material and warheads while shutting down its nuclear-related facilities. Ultimately, North Korea would get to a stage where it couldn't develop nuclear weapons again.
Q. It's uncertain whether North Korea would transparently report all of those things to the international community, don't you think?
That's where the "trust issue" comes in. It's always been there. That's why North Korea must be sincere in its efforts to report on its program, and the US and other countries must have the capability, data and methods to sufficiently verify it.
Q. Do you think it's really possible for North Korea to completely denuclearize?
It's hard to predict such a thing. There's no reason to talk to North Korea if it's all impossible.
Q. The central focus of denuclearization is the reprocessing of plutonium and enrichment of uranium. Can targeting these two methods lead to a satisfactory agreement between the US and DPRK?
Those two methods lead to nuclear weapons in the nuclear energy cycle. South Korea abandoned these two methods as it declared denuclearization on the Korean Peninsula, so that's why we are talking about it. However, North Korea is not at the stage of development; rather, it has already developed nuclear material and warheads. It's not enough just to block North Korea from acquiring those methods. It's important that the nuclear material and warheads are shipped out of the country.
Also important is the shutdown of nuclear weapons-related facilities. North Korea also conducted hydrogen bomb tests. They don't just have plutonium and uranium; they have a factory enriching lithium and fusionable material along with a factory making heavy water and tritiate. Those facilities must also be shutdown.
Q. So denuclearization includes having North Korea dismantle all those nuclear weapons-related facilities and shipping nuclear material out of the country?
Yes. Nuclear material and nuclear warheads must be shipped out and the nuclear facilities must be dismantled or destroyed.
Q. Then it seems like the path to complete denuclearization still has a long way to go.
Yes, a very long way. The program now doesn't compare at all with the program at the time the September 19, 2005 agreement was reached (when North Korea agreed to halt all nuclear weapons development). North Korea's program has become so immensely complicated since then that I don't think it will be completely dismantled during Trump's term, or Moon Jae-in's. Dr. Siegfried Hecker (a nuclear scientist) estimates it will take 15 years. That's why the classification of "periods" and "stages" is very important. Trump will need to know what to focus on and how best to do it.
I think that the most important thing, ultimately, is the shipping out of nuclear materials and warheads and destroying the nuclear facilities. It will take a lot of time to completely get rid of any suspicions through special surveillance and verification. Generally the procedure for denuclearization is to first report, verify and conduct surveillance before shipping out materials or warheads or shutting down facilities. That's going to take too long, however, so that's why there's talk about first shipping out all the nuclear-related materials in regards to the US and North Korea talks. That's why setting periods of completion and stages are important. Complete denuclearization will come about first by focusing on things that are possible before using surveillance to fix all of the incomplete areas later.
The shutdown of the nuclear site is the same thing. It's not perfect because no surveillance or verification was done. However, if at this stage North Korea has halted and frozen its nuclear weapons development, the shutdown of the nuclear site is significant. They've made it very difficult to start it up again.
Q. Is that because it takes a lot of time and effort to rebuild it?
Yes. Recovery is only possible with a lot of time. The shutdown of the nuclear site was done voluntarily by North Korea. You could say its "incomplete," "they fooled us" or "they're hiding something from us," but from the broader perspective of a staged approach to denuclearization, it's a very significant step forward.

redpajama_set_name: RedPajamaCommonCrawl


Least-squares refinement has traditionally been a strong research field in Chem. Cryst., with developments in this area being programmed into CRYSTALS.
The laboratory has long been recognised as having expertise in dealing with difficult refinement as well as developing and implementing new and novel techniques. Some examples of these include twinning; geometry restraints; weighting schemes; pseudosymmetry, atomic displacement parameters, absolute configuration; hydrogen atom location, etc.


#9 Regular Envelopes (3-7/8" x 8-7/8") are one of the most popular commercial-sized envelopes available, commonly used as a reply envelope for invoice and business mailings, sent to recipients inside #10 Envelopes in order to mail something back to the sender. Our 60lb. Natural white is a light, cream colored off-white. It's a classy, natural alternative to everday white, and the paper weight says quality. Available both plain or custom printed for branding, address printing services are also available. These envelopes are sealed by a moistenable glue on the back flap.
One of our most popular collections, Our 60lb. Natural is a light, cream colored off-white. It's a classy, natural alternative to everday white, and the paper weight says quality.
These worked for gift certificate envelopes. They were nice and thick and classy looking. Thank you envelopes.com! Met Expectations? Exceeds Expectation - Thicker than expected Usage? Gift Certificate Envelopes Recommended: Yes, I would recommend this product.
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Former Island Lake Police Chief Anthony Sciarrone.
Write-in candidate Chris Carlsen has beat out former Island Lake Police Chief Anthony Sciarrone for a spot on the Island Lake Village Board, according to unofficial results.
Recently released write-in candidate results showed the owner of Chi-Town Dogs in Island Lake maintained the necessary votes to win a spot on the board.
Although results do not include provisional votes or late mail-ins, Carlsen received 195 votes in McHenry County and 21 more in Lake County, giving him a total of 216 votes.
Sciarrone had a combined vote total of 190. He was fired amid an investigation led by the mayor's office in November.
Three seats on the board were up for grabs in Tuesday's consolidated election and William Ziegler, Richard McLaughlin Jr. and Sciarrone ran.
McLaughlin took in the most votes – 542 – and incumbent Ziegler received 510 votes, according to unofficial voting totals in Lake and McHenry counties.


text:
Torquato Conti, född 1591, död i juni 1636, var en italiensk markis och militär, senare hertig av Guadagnolo.

Conti blev 1619 överstelöjtnant och regementsbefälhavare vid ett av Albrecht von Wallenstein värvat kyrassiärregemente i kejserlig tjänst. 1624 blev han överste och innehavare av samma regemente, och deltid även fortsättningsvis i trettioåriga kriget ända till 1630, och avancerade under tiden till fältmarskalk. Som sådan förde han 1630 befälet mot Gustav II Adolf i Pommern, men kunde på grund av sin armés dåliga skick inte uträtta mycket mot den svenska armén. På hösten 1630 lade han ned sitt befäl och återvände till Italien, där han blev chef för påven Urban VIII:s garden.

Källor
 Svensk uppslagsbok. Malmö 1931.

Födda 1591
Avlidna 1636
Män
Italienska fältmarskalkar

redpajama_set_name: RedPajamaWikipedia


text:
New study suggests supermassive black holes could form from dark matter
Artist's impression of a spiral galaxy embedded in a larger distribution of invisible dark matter, known as a dark matter halo (coloured in blue). Studies looking at the formation of dark matter haloes have suggested that each halo could harbour a very dense nucleus of dark matter, which may potentially mimic the effects of a central black hole, or eventually collapse to form one.
ESO / L. Calçada
A new theoretical study has proposed a novel mechanism for the creation of supermassive black holes from dark matter. The international team find that rather than the conventional formation scenarios involving 'normal' matter, supermassive black holes could instead form directly from dark matter in high density regions in the centres of galaxies. The result has key implications for cosmology in the early Universe, and is published in Monthly Notices of the Royal Astronomical Society.
Exactly how supermassive black holes initially formed is one of the biggest problems in the study of galaxy evolution today. Supermassive black holes have been observed as early as 800 million years after the Big Bang, and how they could grow so quickly remains unexplained.
Standard formation models involve normal baryonic matter – the atoms and elements that that make up stars, planets, and all visible objects – collapsing under gravity to form black holes, which then grow over time. However the new work investigates the potential existence of stable galactic cores made of dark matter, and surrounded by a diluted dark matter halo, finding that the centres of these structures could become so concentrated that they could also collapse into supermassive black holes once a critical threshold is reached.
According to the model this could have happened much more quickly than other proposed formation mechanisms, and would have allowed supermassive black holes in the early Universe to form before the galaxies they inhabit, contrary to current understanding.
Carlos R. Argüelles, the researcher at Universidad Nacional de La Plata and ICRANet who led the investigation comments: "This new formation scenario may offer a natural explanation for how supermassive black holes formed in the early Universe, without requiring prior star formation or needing to invoke seed black holes with unrealistic accretion rates."
Another intriguing consequence of the new model is that the critical mass for collapse into a black hole might not be reached for smaller dark matter halos, for example those surrounding some dwarf galaxies. The authors suggest that this then might leave smaller dwarf galaxies with a central dark matter nucleus rather than the expected black hole. Such a dark matter core could still mimic the gravitational signatures of a conventional central black hole, whilst the dark matter outer halo could also explain the observed galaxy rotation curves.
"This model shows how dark matter haloes could harbour dense concentrations at their centres, which may play a crucial role in helping to understand the formation of supermassive black holes," added Carlos.
"Here we've proven for the first time that such core–halo dark matter distributions can indeed form in a cosmological framework, and remain stable for the lifetime of the Universe."
The authors hope that further studies will shed more light on supermassive black hole formation in the very earliest days of our Universe, as well as investigating whether the centres of non-active galaxies, including our own Milky Way, may play host to these dense dark matter cores.
Dr Morgan Hollis
Mob: +44 (0)7802 877 700
Science contacts
Dr Carlos R. Argüelles
Facultad de Ciencias Astronómicas y Geofísicas
carguelles@fcaglp.fcaglp.unlp.edu.ar
Images and captions
The new work appears in, "On the formation and stability of fermionic dark matter haloes in a cosmological framework", Carlos R Argüelles, Manuel I Díaz, Andreas Krut, and Rafael Yunis, Monthly Notices of the Royal Astronomical Society (2020), in press (DOI: 10.1093/mnras/staa3986).
A copy of the paper is available from: https://doi.org/10.1093/mnras/staa3986
The institutions participating in the research were Universidad Nacional de La Plata, the National Research Council of Science and Technology, the International Center for Relativistic Astrophysics Network, and Buenos Aires National University.
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High School Football – Plays For Scholarships
American expert football has its beginnings in school football. It remains incredibly mainstream today among understudies, graduated class, and different devotees of the game. Numerous understudies who partake in secondary school football end of the season games later join tryouts in football enrolling. Some extraordinary understudies have sufficient ability to draw in the consideration of selecting mentors in the wake of making outstanding plays in secondary school football end of the season games.
There are numerous plays in football, one of them being the forward pass. There were numerous groups that endeavored the forward pass in different plays for a very long time before it was really made lawful. Obviously it had been played viably yet in an illicit way. E. B. Cochems, a mentor utilized by Saint Louis University from 1906 through 1908, was quick to use a legitimate, lawful forward pass. On September 5, 1906, player Bradbury Robinson passed the ball to his partner Jack Schneider in a game held at Carroll College, Wisconsin. St. Louis in the long run dominated the match, scoring 22-0.
The starting a forward pass being played is essential to a football match-up. As the passer's arm begins to push ahead, the forward pass is checked and authoritatively put into play. In the event that the player fails before this, the play is known as a bobble, bringing about a free ball. เว็บบาคาร่า In the present circumstance anyone from the two groups can acquire ownership of the ball previously or after it interacts with the ground. In Canadian football, if the hostile player fails as his arm is pushing ahead, it is considered as a deficient pass. In the event that another player gets the ball before it hits the ground, it's anything but a finished pass or an interference. In American football, when the quarterback endeavors to take the ball back to his body once a passing movement has been made, a lost ball might be viewed as a deficient pass despite the fact that the quarterback's arm is as yet going in reverse at that point. This in known as the fold rule.
With every one of the capable understudies associated with seeking after a higher education, football enlisting stays a huge movement for understudies and universities the same. Some remarkable understudies have sufficient ability to draw in the consideration of football enlisting mentors while still in secondary school. Others, in any case, need to put forth additional attempt to excel all the while. Getting public openness is a vital factor in prevailing in the enrollment cycle.


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Q: how can i set the Tag value For multiple buttons in a single Cell in tableView in ios in my project i have 5 row in a TableView each cell having four button totally i have 20 buttons for this my requirement is i want set tag value for Each buttons like
in First Cell -- 1 for btn1, 2 for btn2, 3 for btn3, 4 for btn4
   Second Cell-- 5 for btn5, 6 for btn6, 7 for btn7, 8 for btn8

like all Five Cells i need set a tag Value like this
Note: When i scroll the TableView it not changing the tag Value
i have set the tag value like this inside the cellForRowAtIndexPath Delegate Method
UIButton *btnLeftW,*btnLeft,*btnRight,*btnRightW;

btnLeftW=(UIButton*)[cell viewWithTag:90];
btnLeft=(UIButton*)[cell viewWithTag:91];
btnRight=(UIButton*)[cell viewWithTag:92];
btnRightW=(UIButton*)[cell viewWithTag:93];

 btnLeftW.tag=indexPath.row;
 btnLeft.tag=indexPath.row;
 btnRight.tag=indexPath.row;
    btnRightW.tag=indexPath.row;

it gives only
0,0,0,0
 1,1,1,1
 2,2,2,2
 3,3,3,3
 4,4,4,4

A: try this
btnLeftW.tag  = indexPath.row*4 + 1;
btnLeft.tag   = indexPath.row*4 + 2;
btnRight.tag  = indexPath.row*4 + 3;
btnRightW.tag = indexPath.row*4 + 4;

redpajama_set_name: RedPajamaStackExchange


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As Our Past Wars Are Glorified This Memorial Day Weekend, Give Some Thought To Our Prospects Against The Russians And Chinese In World War IIIby Dr. The Saker reports that Russia is preparing for World War III, not because Russia intends to initiate aggression but because Russia is alarmed by the hubris and arrogance of the West, by the demonization of Russia, by provocative military actions by the West, by American interference in the Russian province of Chechnya and in former Russian provinces of Ukraine and Georgia, and by the absence of any restraint from Western Europe on Washington's ability to foment war. Like Steven Starr, Stephen Cohen, myself, and a small number of others, the Saker understands the reckless irresponsibility of convincing Russia that the United States intends to attack her.
We at the Mises Institute wish all a happy Memorial Weekend, hopefully free from the horrors of the TSA. Memorial Day marks the unofficial beginning of summer, but baseball and barbecues may have to take a back seat to Fed watching for a while longer for investors who remain preoccupied with the timing of the Federal Reserve's next rate increase. The nonfarm payrolls report, a closely watched barometer of growth, is likely to provide an important clue given the increasingly hawkish tone of Fed officials with even Chairwoman Janet Yellen embracing the possibility of higher rates. I could here the roar of the Canoe River and its tributaries as they made their descent hundreds of feet below me.
In 2004, Rick Waugh, then Bank of Nova Scotia's chief executive, proudly posed with a gold bar for a photo to tout the Canadian bank's new leadership position among the world's top bullion dealers. With the price of gold and silver pulling back and consolidating recent gains, today legendary Pierre Lassonde spoke with King World News and predicted that the price of gold will skyrocket because as China's Gold Exchange becomes like a casino. Indianapolis -- There isn't going to be much change on the Packers' roster this off-season, especially on offense.
Many a-list celebs have tones of fame but their fortunes are small potatoes compared to these folks, the billionaires.
The story of millionaire Simon Cowell, who dropped out of school at 15, worked for Sony BMG and EMI Music. Our roundtable guests talk about their roles as agents and being acknowledged by their clients.
The world knows Valeria Lukyanova as the girl who turned herself into a real-life Barbie doll.
Though we must admit, we're not really sure what sustainable transport is…or why the world's transition to it should be accelerated. In fact, the twelve billion dollar man is so sure of merits of the endeavor, he keeps upping the ante. Regrettably, as Jeff Deist notes, the holiday is often used by politicians as an opportunity to "materialize at parades, picnics, and churches to give speeches about 'freedom,'" unaware of how their own actions are a greater threat to it than any foreign entity in the world. I couldn't see them from the logging road we were on but their flight was so steep and so rapid that it filled the valley with mist and noise as the various creeks and the river itself made the first leg of their inevitable journey south and west to the Pacific. He is past president of Newmont Mining, former chairman of the World Gold Council and current chairman of Franco Nevada. But , there is a reasonable chance Green Bay loses its all-time receiving leader, Donald Driver.
According to the Tesla Motors website, the company's mission is: to accelerate the world's transition to sustainable transport. The company is now on the hook to expand production of its electric vehicles to 500,000 a year by 2018.
Tom discusses how the late Murray Rothbard convinced him that peace and liberty cannot be severed, that empire abroad leads to socialism at home, and that foreign policy should be front and center in a libertarian worldview.
Below, you'll learn why Saudi Arabia has a lot to do with that…and more importantly, why this is presenting investors with a huge opportunity. The road and surrounding vegetation were damp as the mist from the creek filled the air, climbing upwards with the tips of giant spruce and pine towards the ridges that birthed the torrent below while simultaneously mingling with the sun and creating hues of yellow, blue and purple in the spaces between the trees and the sky. Lassonde is one of the wealthiest, most respected individuals in the gold world, and as always King World News would like to thank him for sharing his wisdom with our global readers during this critical period in these markets. NO MATERIAL HERE CONSTITUTES "INVESTMENT ADVICE" NOR IS IT A RECOMMENDATION TO BUY OR SELL ANY FINANCIAL INSTRUMENT, INCLUDING BUT NOT LIMITED TO STOCKS, COMMODITIES, OPTIONS, BONDS, OR FUTURES. And as Jeff Deist notes, Memorial Day should be free of political grandstanding — especially by those who don't understand what liberty really means. Standing on the road I rubbed the sleep from my eyes as the moisture slipped past my nostrils, filled my lungs and cooled my skin. ACTIONS YOU UNDERTAKE AS A CONSEQUENCE OF ANY ANALYSIS, OPINION OR ADVERTISEMENT ON THIS SITE ARE YOUR SOLE RESPONSIBILITY. Buzzard sat next to the truck and camper in a lawn chair glassing white dots on the upper ridges of the valley that surrounded it all.
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CSU group condemns university, Board of Governors statements on misconduct investigations
A week after the CSU Faculty Council grilled the administration on its handling of sexual misconduct and other issues, another university organization came forward to condemn what it called the school's and Board of Governors' "repeated and unnecessary efforts to minimize and discredit students who are sharing their experiences."
In recent weeks, a growing number of student-athletes, faculty and university offices have expressed their concerns publicly about the way sexual misconduct, COVID-19 and racial insensitivity issues have been handled by President Joyce McConnell; Diana Prieto, vice president for equity, equal opportunity and Title IX; athletic director Joe Parker and other athletic administrators.
On Tuesday, the university's Women and Gender Advocacy Center sent a letter to the campus community stating it unequivocally supports survivors and the unprecedented number of people speaking out on the issues, even at the risk of retaliation to the center that serves CSU students.
Center director Monica Rivera said in an email response to the Coloradoan that the fear of retaliation for anyone who speaks out about interpersonal violence is significant and real.
"Most survivors and their supporters have almost nothing to gain by going public," Rivera said. "We felt compelled to write a letter because we were hearing from students that they felt abandoned by our silence. Our role is to make sure survivors, many of whom are too scared to come forward, know that we are here to support them."
The Women and Gender Advocacy Center's letter was in response to the BOG statement supporting administration, CSU administration's responses to issues during last week's faculty council virtual meeting and an opinion piece by McConnell and Prieto that appeared in the Coloradoan.
The letter said its response was not based on opinion but "our truth about things that have been well documented."
Confidentiality often prevents the center from sharing specific incidents and concerns, the center wrote, but it was prompted to respond broadly now that the issues have been made public.
"Some of (the university's and Board of Governors' statements) have come from folks who have never had a single conversation with students who are speaking out," the letter reads. "As an institution, we cannot ask survivors of violence to come forward with their experiences and then turn around and publicly discredit them or frame their experiences as anomalies.' "
CSU turmoil: Student-athletes call for AD's firing
The Coloradoan in a Wednesday email requested an interview with Board of Governors members. The email was acknowledged, but a response had not been received by the Coloradoan as of late Thursday afternoon.
The center's letter acknowledged McConnell's elevation of the office that oversees Title IX to cabinet level and expanded budgets for such resources as a "good thing." McConnell also has recently created an action plan to address recommendations, prompted by an external investigation of the university's athletic department regarding allegations of a COVID-19 cover-up, racial insensitivity and verbal abuse.
The letter also stated that CSU, like other universities, is not immune to issues involving sexual misconduct and racial insensitivity.
"We have witnessed the university conduct investigations which indicate no existence of 'systemic abnormalities' while also losing survivors who transfer, drop out and/or die by homicide or suicide every year," the letter says. "To suggest that CSU is somehow exempt from dynamics which are present on every single college campus in the country would be naive at best and dangerous at worst."
The letter pointed out a Board of Governors statement that said CSU had no history of major NCAA infractions but did not mention the 62 Title IX cases involving student- athletes over the past four years at CSU.
Rivera said reaction to the letter has been mixed, with some believing it is disloyal to CSU. However, she said mostly the responses from students, alumni, former and current staff and faculty have been "overwhelmingly validating" and some have called the center "brave."
"I don't believe that supporting students should ever be considered disloyal or brave," Rivera said.
Barry Braun, professor and head of CSU's Department of Health and Exercise Science, said he wants to believe McConnelI and the administration are sincere in fixing the problems, some of which he said predate McConnell, who was selected as the university's first female president in July 2019.
However, he said the Board of Governor's statement last week in support of the administration's handling of the issues and discounting concerns repeatedly raised by student-athletes and staff was counterproductive.
"The letter the Board of Governors sent didn't make me feel like the issues were being taken seriously, and that has been a source of frustration for those who have come forward and put themselves on the line," Braun said. "I see this as an opportunity to right historical wrongs and for the university to commit to being accountable for that which we all aspire."
CSU's Asian Pacific American Cultural Center and Native American Cultural Center expressed support of Women and Gender Advocacy Center's letter on Instagram.
Emma Corwin is a CSU tennis player and leadership member of Rambition, a group that supports leadership development of female student-athletes. She said university and Board of Governors statements indicating they have a better grasp of the facts experienced by student-athletes and students is essentially calling them liars.
"Their statements are attempts to discredit and silence us," Corwin said. "But WGAC, faculty and many others within CSU recognizing the current culture and voicing support for change should let them know that we will not be pushed aside."
CSU inclusion: Mary Onitveros lived it
Reporter Miles Blumhardt looks for stories that impact your life. Be it news, outdoors, sports — you name it, he wants to report it. Have a story idea? Contact him at milesblumhardt@coloradoan.com or on Twitter @MilesBlumhardt. Support his work and that of other Coloradoan journalists by purchasing a digital subscription today.
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A week had passed, and Mrs. Charmond had left Hintock House. Middleton Abbey, the place of her sojourn, was about twenty miles distant by road, eighteen by bridle-paths and footways.
Grace observed, for the first time, that her husband was restless, that at moments he even was disposed to avoid her. The scrupulous civility of mere acquaintanceship crept into his manner; yet, when sitting at meals, he seemed hardly to hear her remarks. Her little doings interested him no longer, while towards her father his bearing was not far from supercilious. It was plain that his mind was entirely outside her life, whereabouts outside it she could not tell; in some region of science, possibly, or of psychological literature. But her hope that he was again immersing himself in those lucubrations which before her marriage had made his light a landmark in Hintock, was founded simply on the slender fact that he often sat up late.
One evening she discovered him leaning over a gate on Rub-Down Hill, the gate at which Winterborne had once been standing, and which opened on the brink of a steep, slanting down directly into Blackmoor Vale, or the Vale of the White Hart, extending beneath the eye at this point to a distance of many miles. His attention was fixed on the landscape far away, and Grace's approach was so noiseless that he did not hear her. When she came close she could see his lips moving unconsciously, as to some impassioned visionary theme.
She spoke, and Fitzpiers started. "What are you looking at?" she asked.
"Oh! I was contemplating our old place of Buckbury, in my idle way," he said.
It had seemed to her that he was looking much to the right of that cradle and tomb of his ancestral dignity; but she made no further observation, and taking his arm walked home beside him almost in silence. She did not know that Middleton Abbey lay in the direction of his gaze. "Are you going to have out Darling this afternoon?" she asked, presently. Darling being the light-gray mare which Winterborne had bought for Grace, and which Fitzpiers now constantly used, the animal having turned out a wonderful bargain, in combining a perfect docility with an almost human intelligence; moreover, she was not too young. Fitzpiers was unfamiliar with horses, and he valued these qualities.
"Yes," he replied, "but not to drive. I am riding her. I practise crossing a horse as often as I can now, for I find that I can take much shorter cuts on horseback."
He had, in fact, taken these riding exercises for about a week, only since Mrs. Charmond's absence, his universal practice hitherto having been to drive.
Some few days later, Fitzpiers started on the back of this horse to see a patient in the aforesaid Vale. It was about five o'clock in the evening when he went away, and at bedtime he had not reached home. There was nothing very singular in this, though she was not aware that he had any patient more than five or six miles distant in that direction. The clock had struck one before Fitzpiers entered the house, and he came to his room softly, as if anxious not to disturb her.
The next morning she was stirring considerably earlier than he.
In the yard there was a conversation going on about the mare; the man who attended to the horses, Darling included, insisted that the latter was "hag-rid;" for when he had arrived at the stable that morning she was in such a state as no horse could be in by honest riding. It was true that the doctor had stabled her himself when he got home, so that she was not looked after as she would have been if he had groomed and fed her; but that did not account for the appearance she presented, if Mr. Fitzpiers's journey had been only where he had stated. The phenomenal exhaustion of Darling, as thus related, was sufficient to develop a whole series of tales about riding witches and demons, the narration of which occupied a considerable time.
Grace returned in-doors. In passing through the outer room she picked up her husband's overcoat which he had carelessly flung down across a chair. A turnpike ticket fell out of the breast- pocket, and she saw that it had been issued at Middleton Gate. He had therefore visited Middleton the previous night, a distance of at least five-and-thirty miles on horseback, there and back.
During the day she made some inquiries, and learned for the first time that Mrs. Charmond was staying at Middleton Abbey. She could not resist an inference--strange as that inference was.
A few days later he prepared to start again, at the same time and in the same direction. She knew that the state of the cottager who lived that way was a mere pretext; she was quite sure he was going to Mrs. Charmond. Grace was amazed at the mildness of the passion which the suspicion engendered in her. She was but little excited, and her jealousy was languid even to death. It told tales of the nature of her affection for him. In truth, her antenuptial regard for Fitzpiers had been rather of the quality of awe towards a superior being than of tender solicitude for a lover. It had been based upon mystery and strangeness--the mystery of his past, of his knowledge, of his professional skill, of his beliefs. When this structure of ideals was demolished by the intimacy of common life, and she found him as merely human as the Hintock people themselves, a new foundation was in demand for an enduring and stanch affection--a sympathetic interdependence, wherein mutual weaknesses were made the grounds of a defensive alliance. Fitzpiers had furnished none of that single-minded confidence and truth out of which alone such a second union could spring; hence it was with a controllable emotion that she now watched the mare brought round.
"I'll walk with you to the hill if you are not in a great hurry," she said, rather loath, after all, to let him go.
"Do; there's plenty of time," replied her husband. Accordingly he led along the horse, and walked beside her, impatient enough nevertheless. Thus they proceeded to the turnpike road, and ascended Rub-Down Hill to the gate he had been leaning over when she surprised him ten days before. This was the end of her excursion. Fitzpiers bade her adieu with affection, even with tenderness, and she observed that he looked weary-eyed.
"Why do you go to-night?" she said. "You have been called up two nights in succession already."
"I must go," he answered, almost gloomily. "Don't wait up for me." With these words he mounted his horse, passed through the gate which Grace held open for him, and ambled down the steep bridle-track to the valley.
She closed the gate and watched his descent, and then his journey onward. His way was east, the evening sun which stood behind her back beaming full upon him as soon as he got out from the shade of the hill. Notwithstanding this untoward proceeding she was determined to be loyal if he proved true; and the determination to love one's best will carry a heart a long way towards making that best an ever-growing thing. The conspicuous coat of the active though blanching mare made horse and rider easy objects for the vision. Though Darling had been chosen with such pains by Winterborne for Grace, she had never ridden the sleek creature; but her husband had found the animal exceedingly convenient, particularly now that he had taken to the saddle, plenty of staying power being left in Darling yet. Fitzpiers, like others of his character, while despising Melbury and his station, did not at all disdain to spend Melbury's money, or appropriate to his own use the horse which belonged to Melbury's daughter.
And so the infatuated young surgeon went along through the gorgeous autumn landscape of White Hart Vale, surrounded by orchards lustrous with the reds of apple-crops, berries, and foliage, the whole intensified by the gilding of the declining sun. The earth this year had been prodigally bountiful, and now was the supreme moment of her bounty. In the poorest spots the hedges were bowed with haws and blackberries; acorns cracked underfoot, and the burst husks of chestnuts lay exposing their auburn contents as if arranged by anxious sellers in a fruit- market. In all this proud show some kernels were unsound as her own situation, and she wondered if there were one world in the universe where the fruit had no worm, and marriage no sorrow.
I flitted, even as a dizzy moth in the owlet light."
But he was a silent spectacle to her now. Soon he rose out of the valley, and skirted a high plateau of the chalk formation on his right, which rested abruptly upon the fruity district of loamy clay, the character and herbage of the two formations being so distinct that the calcareous upland appeared but as a deposit of a few years' antiquity upon the level vale. He kept along the edge of this high, unenclosed country, and the sky behind him being deep violet, she could still see white Darling in relief upon it-- a mere speck now--a Wouvermans eccentricity reduced to microscopic dimensions. Upon this high ground he gradually disappeared.
Thus she had beheld the pet animal purchased for her own use, in pure love of her, by one who had always been true, impressed to convey her husband away from her to the side of a new-found idol. While she was musing on the vicissitudes of horses and wives, she discerned shapes moving up the valley towards her, quite near at hand, though till now hidden by the hedges. Surely they were Giles Winterborne, with his two horses and cider-apparatus, conducted by Robert Creedle. Up, upward they crept, a stray beam of the sun alighting every now and then like a star on the blades of the pomace-shovels, which had been converted to steel mirrors by the action of the malic acid. She opened the gate when he came close, and the panting horses rested as they achieved the ascent.
"How do you do, Giles?" said she, under a sudden impulse to be familiar with him.
He replied with much more reserve. "You are going for a walk, Mrs. Fitzpiers?" he added. "It is pleasant just now."
"No, I am returning," said she.
The vehicles passed through, the gate slammed, and Winterborne walked by her side in the rear of the apple-mill.
He looked and smelt like Autumn's very brother, his face being sunburnt to wheat-color, his eyes blue as corn-flowers, his boots and leggings dyed with fruit-stains, his hands clammy with the sweet juice of apples, his hat sprinkled with pips, and everywhere about him that atmosphere of cider which at its first return each season has such an indescribable fascination for those who have been born and bred among the orchards. Her heart rose from its late sadness like a released spring; her senses revelled in the sudden lapse back to nature unadorned. The consciousness of having to be genteel because of her husband's profession, the veneer of artificiality which she had acquired at the fashionable schools, were thrown off, and she became the crude, country girl of her latent, earliest instincts.
Nature was bountiful, she thought. No sooner had she been starved off by Edgar Fitzpiers than another being, impersonating bare and undiluted manliness, had arisen out of the earth, ready to hand. This was an excursion of the imagination which she did not encourage, and she said suddenly, to disguise the confused regard which had followed her thoughts, "Did you meet my husband?"
Winterborne, with some hesitation, "Yes."
"At Calfhay Cross. I come from Middleton Abbey; I have been making there for the last week."
"Haven't they a mill of their own?"
"Yes, but it's out of repair."
"I think--I heard that Mrs. Charmond had gone there to stay?"
"Yes. I have seen her at the windows once or twice."
Grace waited an interval before she went on: "Did Mr. Fitzpiers take the way to Middleton?"
"Yes...I met him on Darling." As she did not reply, he added, with a gentler inflection, "You know why the mare was called that?"
"Oh yes--of course," she answered, quickly.
They had risen so far over the crest of the hill that the whole west sky was revealed. Between the broken clouds they could see far into the recesses of heaven, the eye journeying on under a species of golden arcades, and past fiery obstructions, fancied cairns, logan-stones, stalactites and stalagmite of topaz. Deeper than this their gaze passed thin flakes of incandescence, till it plunged into a bottomless medium of soft green fire.
Her abandonment to the luscious time after her sense of ill-usage, her revolt for the nonce against social law, her passionate desire for primitive life, may have showed in her face. Winterborne was looking at her, his eyes lingering on a flower that she wore in her bosom. Almost with the abstraction of a somnambulist he stretched out his hand and gently caressed the flower.
She drew back. "What are you doing, Giles Winterborne!" she exclaimed, with a look of severe surprise. The evident absence of all premeditation from the act, however, speedily led her to think that it was not necessary to stand upon her dignity here and now. "You must bear in mind, Giles," she said, kindly, "that we are not as we were; and some people might have said that what you did was taking a liberty."
It was more than she need have told him; his action of forgetfulness had made him so angry with himself that he flushed through his tan. "I don't know what I am coming to!" he exclaimed, savagely. "Ah--I was not once like this!" Tears of vexation were in his eyes.
"No, now--it was nothing. I was too reproachful."
"It would not have occurred to me if I had not seen something like it done elsewhere--at Middleton lately," he said, thoughtfully, after a while.
She scanned him narrowly. "I know quite well enough," she returned, indifferently. "It was by my husband, and the woman was Mrs. Charmond. Association of ideas reminded you when you saw me....Giles--tell me all you know about that--please do, Giles! But no--I won't hear it. Let the subject cease. And as you are my friend, say nothing to my father."
They reached a place where their ways divided. Winterborne continued along the highway which kept outside the copse, and Grace opened a gate that entered it.


How about a lesson in cell phone etiquette… Cell phone clutching parents, its time for YOU to go to the corner and take a time out!
Daycare centers must enforce many rules to ensure the safety of the children as well as the maintenance of a smooth, predictable routine on which children thrive. Employees must follow specific rules as well as the children attending daycare.
There are also rules that parents must follow such as being responsible for sending their child(ren) with certain meals or being prompt for drop-off and pick-up. One daycare chose to make an additional rule for parents specifically regarding pick-up that has received attention from around the world.
This particular daycare center in Texas was alarmed by the number of parents coming in to pick up their children while glued to their cell phones. They decided that a "rule" needed to be created so that the children being picked up would receive their parents' full attention.
The rule was simple: "Get off your phone!" When Juliana Farris Mazurkewicz was picking up her children at this daycare, she was informed of this new "rule" via a sign posted on the door.
The sign shouted "Get off your phone!!" The message is underlined, in a bold font, and repeated for emphasis. The sign explained the daycare's reasoning for posting such a strongly worded sign.
We all know how difficult it can be to put the phone down even in the presence of loved ones. Yet, some have found the sign itself to be appalling.
Almost everyone can get on board with the message behind the rather aggressive sign. Who has not found themselves regretting the amount of time spent on the phone at least once in their lives?
Other parents have said that getting off of their phones is easier said than done as their jobs do not automatically end the moment they get out of the office. Yet, many have applauded the sign and will be more conscious of their cell phone usage not only at pick up, but any time they are with their children.
This should be a no brainer, unfortunately parents are in high demand with their jobs, their careers often over ride important decisions when it comes to their children. Parents please put the cell phone down and put things in perspective. A cell phone and a job can always be replaced, your child can not! Please make your children a priority before and after work. Employers please cut your employees some slack! Understanding and respecting the delicate balance between job and family is crucial for everyone's bottom line!
Who cares how the sign is worded! Pass on an important message to all parents, employers and cell phone users!