text:
\section{Introduction}

The flux of cosmic rays is described by a smooth
single power-law spectrum which extends up to the so-called
`knee'  around $10^{15} \, \rm eV$.  This can
be interpreted as an evidence that the bulk of
galactic cosmic rays is produced by a single source population.
Since the early 60's the supernova remnants (SNRs) are believed to
be the most probable sites of acceleration of galactic cosmic rays
(see e.g.  Ginzburg \& Syrovatskii \ \cite{GS64}),  the basic
argument being that the galactic Supernovae (SNe), and
the resulting supernova remnants (SNRs) are almost the only
known potential sources with available (kinetic) energy needed  to provide
the observed luminosity of the Galaxy in cosmic rays,
$L_{\rm CR} \geq 10^{40} \, \rm erg/s$. Moreover, it has been shown
(see e.g.  Drury  \cite{Drury83}, Blandford \& Eichler\ \cite{BlEich87},
Berezhko \& Krymski\ \cite{BerKrm88}, Jones \& Ellison\ \cite{JonEl91})
that a viable mechanism -- diffusive shock
acceleration --  can effectively operate
in relatively young SNRs accelerating particles to 100 TeV
(Lagage \& Cesarsky \cite{LagCes83}) or perhaps to  higher energies
(V\"olk \& Biermann \cite{VlkBi}).
The strong shocks in SNRs
provide not only very effective, 10 per cent or more,  conversion of
the total SN explosion energy  into
the accelerated particles   but also can naturally explain hard
($\propto E^{-\Gamma}$ with $\Gamma \sim 2.0-2.1$)  source spectrum
which follows from   the standard `leaky box' propagation
model of  galactic  cosmic rays (see e.g. Gaisser \cite{Gaisser1}).

The nonthermal (synchrotron) radio emission observed from shell-type
SNRs is an unambiguous indicator of acceleration  of GeV electrons there.
Possible association of some of the $\gamma$-ray
`hot spots' detected by COS B  (Bhat et al. \ \cite{Bhat};
Pollock \cite{Pollock};  Wolfendale \& Zhang \cite{Wolf})
and EGRET (Sturner \& Dermer \cite{StrDer};  Esposito et al. \cite{Esposito})
with galactic SNRs could be another  evidence for acceleration
of  electrons and  possibly also protons in SNRs
(Blandford \& Cowie \cite{Bland}, Sturner et al. \cite{Sturner}; Gaisser et al.
\cite{Gaisser2};
Baring et al. \cite{baring}). However these observations concern only
the low energy, typically $E \leq 10 \, \rm GeV$ particles, therefore
they cannot yet conclusively  argue in favor of SNRs as suppliers
of the whole spectrum of galactic cosmic rays.  An unbiased proof
of this hypothesis  can be provided only by  detection of  TeV
$\gamma$-radiation produced at interactions of
accelerated protons and nuclei with ambient gas through production
and subsequent decay of $\pi^0$-mesons
(Drury et al. \cite{DAV}; Naito \& Takahara \cite{NT})
and/or by accelerated   electrons upscattering  the 2.7 K MBR
(Mastichiadis \cite{masti0}).
Therefore it is difficult to overestimate the significance
of the discovery  of TeV radiation from
the historical supernova  SN 1006 reported by the CANGAROO
collaboration  (Tanimori et al. \cite{tani}).

Actually the first, although rather  circumstantial evidence
for the presence of ultrarelativistic particles in SN 1006
was  found  two decades ago by means of X-ray observations.
It was suggested that the power-law  X-ray spectrum  of SN 1006
observed by the Einstein
(Becker et al. \cite{Xeinst}) and EXOSAT (Jones \& Pye \cite{Xexosat})
satellites could be explained by synchrotron radiation of
electrons accelerated in the  SNR shell (Reynolds \& Chevalier \cite{Chevalier},
Amosov et al. \cite{Amosov}). The recent detection
of a spatially resolved power-law component of hard X-radiation
from the edges of the remnant of SN 1006
by ASCA (Koyama et al. \cite{Koyama}) and ROSAT (Willingale et al.  \cite{ROSAT})
strongly supports the synchrotron origin of the radiation that implies
acceleration of electrons to energies  $\sim 100 \, \rm TeV$.
It should be noted that  a featureless, power-law spectrum of X-radiation
could be produced by a plasma with
multi-temperature structure (Hamilton et al. \cite{Hamilton}), or
by a  heavy-element-dominated plasma with possible deviation of
the electron distribution from the standard   Maxwellian
spectrum (Laming \cite{Laming}).
Therefore the very fact of detection of a power-law component of X-radiation
does not yet  automatically  imply a nonthermal  origin of the radiation. However
in the case of SN 1006 the thermal interpretation of
the continuous X-radiation faces serious difficulties, and the
preference therefore is given to the nonthermal synchrotron hypothesis
(Koyama et al. \cite{Koyama};  Laming \cite{Laming}).

Motivated by this fact,  several  theorists
(Pohl \cite{pohl}; Mastichiadis \&
de Jager \cite{masti}; Yoshida \& Yanagita \cite{yoshida})  predicted
detectable fluxes of  inverse Compton (IC) TeV emission.
Remarkably, very soon this object has been detected  as a
TeV emitter  (Tanimori et al. \cite{tani}). Both the  reported
flux  and the  spatial position of the TeV
source centered on the NE rim
are close  to the predictions. This circumstance
strengthened the belief in the electronic   origin of TeV radiation.
The  $\pi^0$-decay  contribution  to the observed
flux is widely considered as less important.

However,  given the fact that  SN~1006 is the only shell-type
SNR reported as TeV  $\gamma$-ray source, a  careful examination
of different scenarios of $\gamma$-ray production
is obviously needed prior to exclude the  nucleonic origin of the
observed TeV radiation (Aharonian \cite{vertalk}).
In particular, the contribution of the
$\pi^0$-decay $\gamma$-rays could be enhanced to the level
of the observed fluxes if we assume a relatively small distance
to the source of about  $\simeq 1\, \rm kpc$
(Willingale et al. \cite{ROSAT}), as well as
take  into account a significant compression of gas
in the NE  rim by the shock. It is important that
this scenario does not limit the  magnetic field in the
acceleration region  to values comparable with the interstellar
B-field as required by the IC  models of the observed
TeV radiation.  The magnetic field in the rim could be then as high as
$B \sim 100 \mu \rm G$ which is favorable  for acceleration
of particles up to $\gg  10 \, \rm  TeV$,  taking into account
the young  age of SN~1006.  Obviously in both scenarios the nonthermal
X-ray emission observed from the NE rim is
explained by synchrotron radiation of directly accelerated electrons.

The current data do not allow us to give preference to the electronic
or nucleonic origin of the observed TeV radiation.
In  this paper we study in detail the spectral and spatial
characteristics of the IC
and  $\pi^0$-decay $\gamma$-rays.
In particular we show that while the size of $\pi^0$-decay
$\gamma$-ray emission is  expected to be
of the size of the  rim,  the size of the inverse Compton
TeV source should be significantly larger because of
inevitable escape of very high energy electrons from the
acceleration region,   and their subsequent upscattering
of the 2.7 K  MBR outside of the rim.

\section{Inverse Compton versus $\pi^0$-decay $\gamma$-rays}

For a ``standard'' injection spectrum  of shock-accelerated particles
(protons and electrons) in a SNR,
\begin{equation}
Q(E)  \propto E^{-\Gamma} \, \exp{(-E/E_0)} \, ,
\label{standard}
\end{equation}
with $\Gamma \approx 2$ and $E_0 \approx 100 \, \rm  TeV$,
the flux of  $\pi^0$-decay $\gamma$-rays at
$E \leq 0.05 E_0$,
\begin{equation}
F(> E) \approx 10^{-11} \, A \rm (E/1 \,
{\rm TeV})^{-1}  \, \rm ph/cm^2 s \, ,
\label{intflux}
\end{equation}
is determined by a simple scaling parameter,
\begin{equation}
A=(W_{\rm CR}/10^{50} \, {\rm erg}) \, (n/1 \,
{\rm cm^{-3})} \, (d/1 \, {\rm kpc})^{-2} \, .
\label{A}
\end{equation}
Here $W_{\rm CR}$ is the total energy in relativistic  protons, $n$
is the ambient gas density, and $d$ is the  distance to the source.

The peak luminosity of $\gamma$-rays is reached   at
the early Sedov phase (Berezhko \& V\"olk \cite{BVLK}), i.e.
typically $10{^3}-10^{4}$ years after  the SN
explosion. At this stage the  radius of the shell exceeds
several parsecs. This results in  a typical angular size of
relatively close ($d \leq 1 \, \rm kpc$) SNRs of about $1^{\circ}$.
The apparent conflict, from the point of view of source
detectability, between the angular size
($\phi \propto 1/d$) and the $\gamma$-ray flux
($F_\gamma \propto 1/d^2$) significantly limits the
number of SNRs   which could be detected by the current
most sensitive imaging atmospheric Cherenkov telescopes (IACT),
to the range of  $A \geq 0.1$. Future large stereoscopic IACT arrays
will extend this limit down to $A \sim 0.01$
(Aharonian \& Akerlof \cite{AhAk}).

\begin{figure}[htbp]
\resizebox{8cm}{!}{\includegraphics{MS8595.f1.epsi}}
\caption
{The integral fluxes of $\pi^0$-decay (heavy solid line)
and IC  (thin lines) $\gamma$-rays
from a $10^3 \, \rm year$ old SNR. The $\pi^0$ decay
$\gamma$-rays are calculated for the scaling parameter $A=1$.
The IC $\gamma$-ray fluxes are calculated for 3 different values  of
the magnetic field $B=3$ (solid curve), 10 (dashed curve),  and
$30 \, \rm \mu G$ (dot-dashed curve),  assuming the electrons
produce the same flux of synchrotron radiation $S_\nu=10 \, \mu \rm Jy$.
For both the protons and electrons we assume the same injection
spectrum given in the form of Eq.(1) with $\Gamma=2$ and
$E_0=100 \, \rm TeV$.}
\label{f1}
\end{figure}

When extracting information about the accelerated protons one has to
subtract  a possible non-negligible ``contamination'' caused  by
parallelly accelerated electrons that upscatter the photons of
2.7 K  MBR (which is the dominant target photon field for production
of TeV photons in most of SNRs; see e.g. Gaisser et al. \cite{Gaisser2})
up to $\gamma$-ray energies.
For production of IC
$\gamma$-rays of TeV energies multi-TeV  electrons are needed.
The same electrons produce also synchrotron UV/X-ray
radiation. The typical energies  $E_\gamma$ and $E_{\rm X }$
of the IC and synchrotron photons produced by an electron are
related as (see e.g. Aharonian et al. \cite{AAK})
\footnote{Note that this  relation neglects the
Klein-Nishina effect which becomes important at energies
$E_\gamma  \geq 10 \, \rm TeV$.}
\begin{equation}
E_\gamma \simeq 1.5 (E_{\rm X}/0.1 \, \rm keV) \, (B/10 \,
\mu \rm G)^{-1}  \, \rm TeV \, .
\end{equation}
The ratio of the synchrotron and IC fluxes $f_{\rm E} \equiv E^2 F(E)=\nu S_\nu$
at these energies does not practically depend on the shape of the spectrum
of parent relativistic electrons, but strongly depends on
the magnetic field:
\begin{equation}
\frac{f_{\rm IC} (E_\gamma)}{f_{\rm sy} (E_{\rm X})}
\simeq 0.1 \,  (B/10 \, \mu \rm G)^{-2}
\end{equation}

For the X-ray spectrum with photon index
$\alpha_{\rm X} \sim 2$ the energy flux $f_{\rm X}$
is almost energy-independent. Therefore
$f_{\rm X}$  at  a  typical  energy  of 1 keV
could serve as a good indicator for the IC $\gamma$-ray
fluxes expected at TeV
energies, although for magnetic fields $B \leq 100 \, \mu \rm G$
the energy of synchrotron photons relevant
(produced by the same parent electrons)
to $\sim 1 \, \rm TeV$
$\gamma$-rays is in the soft X-ray domain (see Eq. 4).

The contribution of $\pi^0$-decay $\gamma$-rays dominates over
the  contribution of the  IC  component  when
\begin{equation}
A \geq  0.1 \, (S_{1 \rm keV}/{10 \mu \rm Jy}) \,
(B/10 \, \mu \rm G)^{-2}~,
\end{equation}
where $S_{1 \rm keV}$ is the flux of nonthermal synchrotron radiation
at 1 keV normalized to  $10 \, \mu \rm Jy$ (the corresponding energy flux
$f_{\rm X} \approx  2.4 \times 10^{-11} \, \rm erg/cm^2 s$). Note that
$S_{\rm 1keV}=10 \, \mu \rm Jy$ is a typical level of nonthermal X-ray fluxes
reported recently from four  shell-type SNRs --
SN 1006 (Koyama et al. \cite{Koyama}),  Cas A (Allen et al. \cite{Cas}),
IC 443  (Keohane et al. \cite {IC443}) and  RXJ1713.7-3946
(Koyama et al. \cite{Koyama2}).

In Fig.~\ref{f1} we present integral fluxes of
$\pi^0$-decay and inverse Compton $\gamma$-rays from a  SNR
of age $10^{3} \, \rm yr$.
The $\pi^0$-decay $\gamma$-ray flux
corresponds to the scaling factor $A=1$. The IC fluxes are calculated by
normalizing the  synchrotron X-ray fluxes  to $S_{\rm 1 keV}=10 \mu \rm Jy$
for ambient B-fields $3 \mu \rm G$, $10 \mu \rm G$, and $30 \mu \rm G$. For
both electrons and protons we assume continuous acceleration during
$10^{3} \, \rm years$ with a time-independent source spectrum taken in
the form of Eq.(1) with $\Gamma=2$ and
$E_0=100 \, \rm TeV$.  Note that for the normalizations used,
the results presented in Fig.~\ref{f1}   only slightly depend on the source age,
unless it is larger than the radiative cooling time of multi-TeV electrons,
$t_ {\rm rad} \approx 10^4 \, (B/10 \, \mu \rm G)^{-2} \,
(E_{\rm e}/10 \, \rm TeV)^{-1} \, \rm yr$.

\section{Synchrotron and IC components  of
nonthermal radiation of SN 1006}

The   bulk ($\simeq 75 \%$) of the nonthermal X-ray component  of SN 1006
is contributed by the northeast (NE)  and the southwest (SW) rims
(Koyama et al. \cite{Koyama},  Willingale  et al. \cite{ROSAT}).
The observations of SN 1006 by the CANGAROO
collaboration (Tanimori et al. \cite{tani}) have revealed TeV radiation
from the  NE rim, but only an upper limit from the SW rim was reported.
Therefore in this paper the nonthermal radiation of only NE rim is
discussed.

For the spectral characteristics of the nonthermal X-ray emission of
NE rim we follow the procedure used by Mastichiadis \& de Jager  (\cite{masti}).
Namely we assume that the X-ray spectrum below 1.5 keV is described by a  power-law
with mean photon index $\alpha_{\rm x} \simeq 2.2$ as it follows from the
combined Einstein/EXOSAT/ROSAT data. At higher energies up to
8 keV the spectrum reported by ASCA from NE+SW rims is significantly
steeper,  with a power-law photon index $\alpha_{\rm x} \simeq 3$.
For the estimate of the absolute X-ray flux from NE rim we
take into account that  $\simeq 60 \%$ of the
total emission of NE and SW rims  is contributed by NE rim,
as it  follows from the respective count rates of ROSAT
(see Willingale et al. \cite{ROSAT}).
The resulting range of the X-ray fluxes observed from the NE rim
in the range from 0.1 keV to 8 keV  is shown in Fig.~\ref{f2}.

The radio emission of SN 1006   has a power-law spectrum with
an index $\alpha_{\rm r} \simeq 0.57$ and intensity 30.8 Jy at 408 MHz
(Stephenson  et al. \cite{radio}). In Fig.~\ref{f2} one half  of this flux is
taken because the observed total radio flux is equally
contributed from the northeast and southwest directions
(see e.g. Reynolds \& Gilmore \cite{ReGil86}).

In Fig.~\ref{f2}  we show also the range of TeV $\gamma$-ray fluxes observed
by CANGAROO from the direction of  NE rim of SN 1006 at energies above 1.7 TeV
(Tanimori et al. \cite{tani}), as well as  the EGRET  flux upper
limit   from  SN 1006 (Mori \cite{Mori}).

\subsection{One zone model}

In this section we assume that
synchrotron and IC $\gamma$-rays are produced
by relativistic electrons confined
in a spatially homogeneous rim. In this simplified
case the IC fluxes shown in Fig~1 could serve as  first
approximation estimates for the expected TeV $\gamma$-radiation.
However, more reliable predictions of $\gamma$-ray
fluxes require a careful derivation  of the spectrum of
$\geq 10 \, \rm TeV$ electrons which is controlled by
the spectrum of synchrotron X-rays.

\begin{figure}[htbp]
\resizebox{8.cm}{!}{\includegraphics{MS8595.f2.epsi}}
\caption
{The synchrotron (heavy lines) and IC (thin lines)
fluxes calculated for the  homogeneous source without escape of
accelerated particles (one-zone model).  Power-law
injection spectrum of electrons with $\Gamma_{\rm e}=2.15$
is assumed in order to fit the radio data.
The maximum energy $E_0$ is determined from the condition
given by Eq.(9) for 3 different values of the magnetic field:
$B=3 \, \rm \mu G$ (dashed line), $5 \, \rm \mu G$
(solid line), and $8 \, \rm \mu G$ (dot-dashed line).}
\label{f2}
\end{figure}

In the synchrotron-inverse Compton models
the spectral fit to the  X-ray flux is crucial
because the fluxes  are produced  by electrons
in the region of the exponential cutoff $E_0$
between 10 and 100 TeV.
The spectral index $\Gamma$ of accelerated electrons
is derived  from the radio data,
$\Gamma=1+2 \, \alpha_{\rm r} \simeq 2.15$. Information about $E_0$
in Eq.~(1) is contained in the  X-ray spectrum .
In particular case of negligible energy losses, the spectrum of
electrons  $N(E_{\rm e})$ repeats the injection spectrum,
$N(E_{\rm e}) \propto Q(E_{\rm e})$,
therefore in the $\delta$-functional approximation for
the synchrotron emissivity, the X-ray spectrum can be
presented in a  simple form (see e.g.
Yoshida \& Yanagita \cite{yoshida}, Reynolds \cite{Reyn})
\begin{equation}
F(E) \propto E^{-(\Gamma +1)/2} \, \exp[-(E/E_{\rm m})^{1/2}] \, ,
\end{equation}
where
\begin{equation}
E_{\rm m} \simeq 0.29 h \nu_{\rm c} \simeq 0.02 \, (B/10 \mu {\rm G}) \,
(E_0/10 \, \rm TeV)^2 \, \rm keV
\label{emax}
\end{equation}
is the mean energy of synchrotron photons
produced by an electron of energy $E_0$
($\nu_{\rm c}$ is the characteristic synchrotron frequency ).

From Eq.~\ref{emax} follows that the spectrum of synchrotron radiation
depends only on the product $E_0 \, B^{1/2}$.
Numerical calculations using the accurate expression for synchrotron
radiation  generally confirm that approximation in the form
of Eq.(7) holds at least until $E \sim10  E_{\rm m}$ (Reynolds \cite{Reyn}).

In Fig.~2. we show 3 spectra of synchrotron radiation
calculated for the same product
\begin{equation}
\Pi=E \, B^{1/2}=61.5 \, \rm TeV \, \mu G^{1/2} \, ,
\end{equation}
but for 3 different combinations of $E_0$ and $B$:
(1)  $B=3 \mu \rm G$, $E_0=35.5 \, \rm TeV$;
(2)  $B=5 \mu \rm G$, $E_0=27.5 \, \rm TeV$;
(3)  $B=8 \mu \rm G$, $E_0=21.3 \, \rm TeV$
\footnote{
Note that our best fit value for the product
$\Pi=E \, B^{1/2}=61.5 \rm TeV \, \mu G^{1/2}$
is by a factor of two less than
obtained by Yoshida \& Yanagita \cite{yoshida}. The reason presumably is
connected with different fluxes of X-rays used in calculations.}.
In all calculations  we use the same normalization to
the radio fluxes. Therefore different
magnetic fields require different total energy
in relativistic electrons.
At the same time, because the target photon field (2.7 K MBR)
for the IC scattering is fixed, there is a strong dependence
of the IC $\gamma$-ray fluxes on the magnetic field. In particular,
in the case of small magnetic fields $B \leq 10 {\mu \rm G}$,
when the radiative cooling time
\begin{equation}
t_{\rm sy}\approx 1.2 \cdot 10^{4}
\, (E/10 \, {\rm TeV})^{-1} (B/10 \, {\mu \rm G})^{-2} \, \rm yr
\end{equation}
of 10 to  100 TeV electrons  responsible for the
observed X-rays and TeV $\gamma$-rays
exceeds the age  of the source,  we have
$ F_\gamma \propto B^{-(\alpha_{\rm r}+1)}$.
Note that for $B \leq 3  {\mu \rm G}$ the radiative losses
on 2.7 K MBR become dominant.

Fig.~\ref{f2} shows that the interpretation of the observed TeV radiation
by IC mechanism in the framework of a simplified  spatially
homogeneous (one-zone) model is possible only for an
ambient magnetic field in a very narrow range
around  $5 \mu \rm G$.  Magnetic fields $\geq 7 \mu \rm G$
result in a strong  reduction of the IC flux,
while the assumption of low magnetic fields, $B \leq 4 \, \mu \rm G$,
leads to overproduction of $\gamma$-rays.

For such small magnetic fields a question arises whether the
acceleration of electrons could be efficient enough in order
to boost  particles up to energies
$E_0=\Pi /B^{1/2} \sim 25-30 \, \rm TeV$
during the time of acceleration $t_0$ limited
by the  age $10^3$ yr of SN 1006.
Indeed, in the model of diffusive shock acceleration the
characteristic maximum energy $E_0$
that a particle could achieve during the time $t_0$
is determined (see e.g. Lagage and Cesarsky \cite{ LagCes83})
by the shock velocity
$v_{\rm s}$, the magnetic field $B$, and the so-called gyrofactor
$\eta$ (the ratio of the particle mean free path to the gyroradius):
\begin{eqnarray}
E_{\rm 0} & \simeq & 20 \, \left( \frac{B}{10 \, \rm \mu G} \right) \, \left(
\frac{t_0}{10^3 \, \rm yr} \right) \times  \nonumber \\
& & \left( \frac{v_{\rm s}}{2000 \, \rm km/s} \right)^2 \, \eta^{-1} \, \rm TeV \, .
\end{eqnarray}
This estimate would be not  significantly  changed even
if we take into account that in the past the shock speed was much
higher than the present value $v_{\rm s}$ in Eq.(11). Indeed, even
assuming that the Sedov phase in SN 1006 has started at $t_\ast \ll 1000 \, \rm yr$
and applying the Sedov solution for the shock speed in the past,
$v(t)=v_{\rm s} (t/t_0)^{-3/5}$ for $t \geq t_\ast$, the maximum energy
of accelerated particles which is reached at $t \sim t_\ast$ could be
higher than it  is given by Eq.(11) only  by a factor of  $(t_0/t_\ast)^{1/5}$.
Therefore, even for $t_\ast \sim 0.1 t_0 \sim 100 \, \rm yr$, the maximum energy
of the particles in the past  could be only by a factor of 1.5 higher
than it follows from Eq.(11).  On the other hand  Eq.(11) does not include
possible dissipative effects, such as  the wave damping and the  synchrotron
losses of  the electrons,  therefore it can be considered as a good  estimate for
the maximum possible energy of accelerated particles.

Eqs.(9) and (11) result in a lower limit on the
strength of the magnetic field
\begin{equation}
B \geq 12 \,  \left( \frac{t_0}{10^3 \, \rm yr} \right)^{-2/3} \,
\left( \frac{v_{\rm s}}{2000 \, \rm km/s} \right)^{-4/3} \,
\eta^{2/3} \, \rm \mu G
\end{equation}

The  Sedov solution for the shock speed in SN 1006 gives
(Willingale et al. \cite{ROSAT})
\begin{equation}
v_{\rm s} \simeq 2000 (d/1 \, {\rm kpc})^2 \, \rm km/s .
\end{equation}

The shock speed  $1400 \pm 200 \, \rm km/c$
estimated  by Willingale et al. (\cite{ROSAT}) from the ROSAT
X-ray data implies a rather small distance to the source,
$d=0.7 \pm 0.1 \, \rm kpc$.
Winkler \&  Long  (\cite{winkler}) argued that the
distance to the source should be larger,  $d=1.8 \pm 0.3 \, \rm kpc$.
At the same time, the shock speed  $v_{\rm s}=2600 \, \pm 300 \rm km/c$
preferred by Winkler \&  Long  (\cite{winkler}) is significantly lower than
$\simeq 3600\,\rm  km/c$ following from Eq.(12) at $d=1.8\,\rm kpc$.
Given the current controversy both in the estimated shock speed and the distance,
below we will discuss distances in the range from 0.7 to 1.8 kpc, but using
for all distances  Eq.(13).

Thus,  if the shock speed does not significantly exceed 2000 km/s
which implies a distance $\simeq 1 \, \rm kpc$, even in the
Bohm limit ($\eta=1$) the strength of the  magnetic field should
not  be less than $10 \, \rm \mu G$ even if we assume that
the effective particle acceleration has started at early stages of this SNR.
This limitation could be softened by a factor of 2  for larger
distances to the source  (see below).

Another way to soften the
conflict between the sestimate of the B-field
given by Eq.(12) and the value of $B \leq 7\, \rm \mu G$ needed for
explanation of TeV fluxes  is possible if we assume
that the bulk of the observed $\gamma$-ray flux is  produced outside of the shell.
The  highest energy electrons produced in the shell
can effectively escape  the  acceleration region. This will give rise to an
enhanced IC  emission outside of the rim, namely in the interior regions of the
remnant  where the
magnetic field could be as low as the typical interstellar B-field.
Such a leakage of electrons from the rim is unavoidable
because of diffusive and convective  propagation of particles.
This effect should be taken into account
not only for correct derivation of the electron spectrum inside the rim,
but also for calculations of the IC  radiation
outside of the rim.  Below we show that in fact the contribution of this
component (missed in previous studies)  is comparable or even can
exceed  TeV flux produced in the rim.

\subsection{Inverse Compton  TeV emission outside of the rim}

The radio and X-ray images of SN 1006
indicate that the most probable  site of particle acceleration
is the  thin shell of the remnant, in particular the NE rim.
The width $\Delta r$ of the NE rim in X-rays  as measured by ROSAT
does not exceed $20 \%$ of the angular radius of the remnant
of about 17 arcminutes  (Willingale et al. \cite{ROSAT})
which corresponds to
$r_{\rm s}=4.9 \, d_{\rm kpc} \, \rm pc$  at a distance to the source
$d=1 \, d_{\rm kpc} \, \rm kpc$.
In calculations we assume a constant  $\Delta r/r_{\rm s}=0.2$
ratio throughout the  evolution of the remnant.

Due to two principal mechanisms of propagation -- diffusion and convection --
the relativistic particles cannot be completely confined in the rim.
The characteristic escape time  is $\tau_{\rm esc}=(\tau_{\rm con}^{-1}+
\tau_{\rm dif}^{-1})^{-1}$. The convective escape time is
\begin{equation}
\tau_{\rm con}(t)=\Delta  r/u_2 \, ,
\end{equation}
where $u_2$ is the fluid speed
downstream of the shock (in it's rest frame), thus
at present $ u_2=v_{\rm s}/\rho \sim 500 \, \rm km/s$
for the compression ratio $\rho \sim 4$.
The  width of the shell $\Delta r \simeq 0.2 r_{\rm s} \propto t^{2/5}$
assuming a  Sedov-type solution for the shock radius $r_{\rm s}$.
Note that strictly speaking this solution is valid only at stages after
the onset of the Sedov phase,  i.e.  for $t_\ast \le  t \leq t_0$.
However the energy distribution of electrons formed in the shell
at present should be  dominated by particles accelerated
recently, $t \geq 0.3 t_0$ or so, unless one would assume
that most of particles have been injected at very early stages.
Therefore possible deviation
of $\Delta r(t)$ from the law $\propto t^{2/5}$ at times
$t \ll t_0$  does not significantly affect the spectrum of electrons at
present.

The diffusive escape time is
\begin{equation}
\tau_{\rm diff} (t) \simeq \frac{(\Delta r)^2}{2 \, D(E)} \, ,
\end{equation}
where $D(E)$ is the diffusion coefficient in the shocked region (the rim).
In the theory of shock acceleration
the diffusion coefficient is generally taken in the form
\begin{equation}
D(E)=\eta \frac{r_{\rm g}\, c}{3} \, ,
\end{equation}
where $r_{\rm g} = 3.3 \cdot 10^{15}
(E/10 \, \rm TeV)  (B/10 \, \mu \rm G)^{-1} \, \rm cm$
is the particle gyroradius, and $\eta \geq 1$ is the
gyrofactor. The maximum confinement (and therefore the maximum energy)
of  particles is achieved in the Bohm diffusion
regime corresponding to  $\eta=1$.

The kinetic equation for energy distribution
of relativistic electrons $N(E)$ in a source reads
(see e.g. Ginzburg \& Syrovatskii \cite{GS64}):
\begin{equation}
\frac{\partial N}{\partial t} = \frac{\partial}{\partial E_{\rm e}}
 \left[ P\, N \right] - \frac{N}{\tau_{\rm esc}} + Q \, ,
\end{equation}
where $Q\equiv Q(E_{\rm e}, t)$ is the electron injection rate,
and   $P = -{\rm d} E_{\rm e}/{\rm d}t$
is the electron energy loss rate.
The solution to this equation, including the {\em time} and {\it energy}
dependent escape losses is
(Atoyan \& Aharonian \cite{aa99}):

\begin{eqnarray}
N(E_{\rm e},t) & = & \frac{1}{P(E_{\rm e})} \int_{-\infty}^{t}
P(\zeta_t) Q(\zeta_t,t_1) \times \nonumber \\
& & \exp \left( -\int_{t_1}^{t}\frac{{\rm d} x}
{\tau_{\rm esc}(\zeta_x,x)}\right)
{\rm d} t_1\, .
\end{eqnarray}
The  variable $\zeta_t$ corresponds to the initial energy of an electron at
instant $t_1$ which is cooled down to given energy $E_{\rm e}$ by the
instant $t$, and is determined from the equation
\begin{equation}
t-t_1 =\int_{E_{\rm e}}^{\zeta_t}{\frac{{\rm d}E}{P(E)}} \, .
\end{equation}

In this paper we
consider only  overall  (i.e. integrated over the volumes)
fluxes from the NE rim (zone 1) and outside (zone 2).
The electron distribution in the rim $N_1(E_{\rm e},t)$ is found
assuming injection of electrons
at a constant rate during the age of SN~1006,  with the spectrum
 $Q_1(E_{\rm e})$ in the form of Eq.(1).  Although  the injection rate of
accelerated electrons is actually time-dependent,  the
main contribution to the total
amount of particles  in the rim comes from the acceleration
at  epochs from $t \sim t_\ast$ to
several times $t_\ast$ ($t_\ast$ corresponding  to the
onset of the Sedov phase) when the injection rate $Q_1(t)$ is almost
time-independent   (see Berezhko \& V\"olk \cite{BVLK}).
Since SN 1006  most probably has already reached the Sedov phase
(V\"olk \cite{KPVLK})  an assumption of  time-independent
$Q_1(E,t)$ is an adequate approximation (see below).  At the same time
we assume time-dependent escape, as described above (see Eq.~14 and 15),
which have a stronger impact on the results
than the weak time dependence of the injection rate.

Outside the rim the energy distribution
$N_2(E_{\rm e},t)$ is found
from the same Eq.(18) where the injection function is given
by the rate of escape of electrons from the rim,
$Q_2(E_{\rm e},t)=N_1/\tau_{\rm esc}$.
The region outside of the rim corresponds to the
interior of  the remnant close to NE rim.  Therefore  in this region
we ignore the losses due to escape.

\begin{figure}[htbp]
\resizebox{8.cm}{!}{\includegraphics{MS8595.f3.epsi}}
\caption
{The synchrotron  and IC  fluxes produced
inside (heavy lines) and outside (thin lines) of the rim
calculated within 2-zone model for two values of the gyrofactor:
$\eta=1$ (solid), and 10 (dashed).
The magnetic fields inside and outside
of the rim are taken   as $B_1=8 \, \rm \mu G$
and   $B_2=3 \, \rm \mu G$, respectively. The distance to the source is assumed
1 kpc.}
\label{f3}
\end{figure}

In Fig.~\ref{f3}  we show the synchrotron and IC fluxes from the NE rim
and from the inner part of the remnant  for the magnetic field in the rim $B_1=8  \, \mu
\rm G$ and $B_2=3  \, \mu \rm G$ in the remnant. In order to show the
impact of diffusive escape on the resulting radiation spectra, we
considered 2 values for the parameter $\eta$.
The case of maximum confinement of particles in the rim,
$\eta=1$,  is shown  by solid lines, while the dashed lines correspond
to the case of $\eta=10$. The heavy and thin lines
correspond to the  emission produced inside and outside of the rim,
respectively.

For the parameters described above
the observed X-ray spectrum of the rim is best explained for
the exponential cutoff energy  $E_0 = 30 \, \rm TeV$.
The increase  in the value of $E_0$ compared with the best-fit value
of 21.3 TeV used in Fig.~2 for the same magnetic field 8 $\mu \, \rm G$
in the simple single-zone approach, is
explained by diffusive escape of the electrons from the rim.
For the magnetic
field used,  even in the Bohm limit  the diffusive escape time of
electrons  at present is $\tau_{\rm dif}\simeq 3500 \,\rm yr /(E/10 \,\rm TeV)$,
therefore for electrons with energy $E\sim (30-100) \,\rm TeV$
which are responsible for the X-ray fluxes, the diffusive escape time
becomes comparable or even less than the age of the source.
This results in a  modification (steepening) of the spectral
shape at high energies.  In order to compensate this effect,
a higher $E_0$ is to be assumed. Note that
the convective escape time at present,
$\tau_{\rm con} =2000 \,\rm yr$,
is also comparable with the
age of the source.  However the convective escape does not
modify the energy spectrum of electrons.
This is true, to some extent,  also for radiative losses in the case
of small magnetic fields   $B\sim 10\,\rm \mu G$,
since the synchrotron cooling time then equals the
source age only at $E_{\rm e}\geq 100\,\rm TeV$.

The electron escape from the rim leads to nonthermal X-ray
production in  a broader region (zone 2). Note that for the case
of diffusion in Bohm limit ($\eta=1$) and the assumed magnetic field
$B_2=3 \, \rm \mu G$, the
X-ray flux outside of the NE rim makes
$\simeq 10 \%$ of the flux produced in the rim.
This implies that the magnetic field $B_2$ cannot be larger than
$5 \, \rm \mu G$, otherwise the ratio of the fluxes
produced outside and inside of the rim would
exceed the value of about 1/3 as observed by ASCA (Koyama et al. \cite{Koyama})
and ROSAT  (Willingale et al. \cite{ROSAT}).

While the synchrotron radiation outside of the rim can be suppressed
assuming low magnetic field $B_2$,  the formation of an extended
IC radiation is unavoidable due to the uniform distribution of
the principal target photon field for the Compton scattering -
2.7 K  MBR.  In particular even for $\eta=1$
the contribution of $\gamma$-ray fluxes at $\geq 1 \, \rm TeV$
from the region outside of the rim becomes comparable with the flux from
the rim.  In the case of fast diffusion corresponding to  $\eta=10$,
the contribution from the extended region
outside  of the rim,  i.e. inside the remnant at $r \leq 0.8  r_{\rm s}$,
well dominates the overall TeV flux of SN~1006 (see Fig.~\ref{f3}).

The value of $E_0=30 \, \rm TeV$ in Fig.~3
is by a factor 1.5 larger than the estimate of the
characteristic maximum energy of electrons
following from Eq.~(11) for the shock speed
2000 km/s corresponding to a distance to the source
$d=1 \, \rm kpc$  (see Eq.~13).
This conflict could be overcome assuming a higher speed of the shock, i.e.
lager $d$. It is important to note that the assumed distance to the source
has a significant impact also on the timescale of the diffusive
(but not the convective)  escape of the electrons from  the shell as
$\tau_{\rm dif} \propto \Delta r^2 \propto d^2$ (see Eq.~15).
Therefore the relative contribution of the TeV emission produced in the
interior of the remnant depends on the assumed distance to the source.
This effect is seen in Fig.~4 where we show the results of calculations
for two different distances currently discussed in the literature,
$d=0.7 \, \rm kpc$ (Willingale et al. \cite{ROSAT}) and
$d=1.8 \, \rm kpc$ (Winkler \& Long  \cite{winkler}).
For  the distance $d=0.7 \, \rm kpc$ we used
$E_0=18 \, \rm TeV$ which is 2 times larger than it follows from
the estimate of the maximum energy by  Eq.~(11).
However, even under such an extreme assumption the calculated synchrotron fluxes
roll over  too early, failing to reach the observed X-ray fluxes.
Meanwhile for the distance $d=1.8 \rm kpc$ the chosen value
of $E_0=35 \, \rm TeV$ is in agreement with Eq~(11) even for $\eta=2$.
We note that the contribution of the TeV flux produced outside of the rim
is still very significant even for this  large distance.

\begin{figure}[htbp]
\resizebox{8.cm}{!}{\includegraphics{MS8595.f4.epsi}}
\caption
{The synchrotron  and IC  fluxes produced
inside (heavy lines) and outside (thin lines) of the rim
calculated within 2-zone model for two distances to the source:
$d=1.8 \, \rm kpc$, and  $d=0.7 \, \rm kpc$.
The gyrofactor and maximum energy are:
$\eta=2$ and $E_0=35 \, \rm TeV$  for $d=1.8 \, \rm kpc$
(solid lines),
and $\eta=1$ and $E_0=18 \, \rm TeV$  for $d=0.7 \, \rm kpc$
(dashed  lines).
The magnetic fields inside and outside
of the rim are taken   as $B_1=6 \, \rm \mu G$
and   $B_2=1.5 \, \rm \mu G$, respectively. }
\label{f4}
\end{figure}

The existence of the external  IC  component due to the
escape of electrons from the rim results in a significant increase
of the overall TeV radiation, and thus allows a larger  magnetic
field as compared with  the  value $B_1 = 5 \pm 1 \, \rm \mu G$ derived
within the one-zone model (Section 3.1). In order to investigate
the impact of this effect we have calculated the synchrotron and IC
fluxes   for two different combinations of $B_1$  and $\eta$
shown in  In Fig.~5. In both cases we assume for the distance to the source
$d=1.8 \, \rm kpc$.  The maximum electron energy
$E_0=32 \, \rm TeV$ is calculated from Eq.(11).
We also assume low  magnetic field
outside of the rim,  $B_2=B_1/4$,  in order to avoid overproduction of
X-radiation in this region.

\begin{figure}[htbp]
\resizebox{8.cm}{!}{\includegraphics{MS8595.f5.epsi}}
\caption
{The synchrotron (top panel) and IC  $\gamma$-ray (bottom panel)
fluxes calculated in the framework of 2-zone model for two values
of the magnetic field in the rim: $B_1=5 \, \rm \mu G$ (solid lines) and
$B_1=10 \, \rm \mu G$ (dashed lines). The magnetic field outside of the rim
is taken as $B_2 =B_1/4$. The heavy lines show the
fluxes from  the NE rim, and thin lines  correspond to
the total fluxes. The distance to the source is assumed 1.8 kpc.
The maximum electron energy $E_0$ is calculated from Eq. (11)
for the gyrofactor $\eta=1$ for $B_1=5 \, \rm \mu G$, and
$\eta=2$ for $B_1=10 \, \rm \mu G$.}
\label{f5}
\end{figure}

The combination $B_{\rm rim} \equiv B_1=5 \, \mu \rm G$,
$\eta=1$ provides a good fit to the X-ray data,  but it
leads to an overproduction of the total TeV
emission compared with the CANGAROO measurements by a factor of
two. Given a possibility that the TeV emission from extended region
of the remnant (outside of the rim), which contributes half of the total
flux,  could be difficult to extract   by the CANGAROO,  this combination
of parameters seems still  acceptable.  The assumption of
$B_1=10 \, \rm \mu G$ and $\eta=2$ results in overproduction
of X-rays by $50 \%$. At the same time the predicted fluxes of TeV
$\gamma$-rays from the rim are below the reported fluxes by
a factor of 3.

From Fig.~5 we may draw a  conclusion  that the magnetic field
in the rim should be within the limits $5 \le B_1 \le 10  \, \rm \mu G$
(preferably   $B_1 \simeq 6-8  \, \rm \mu G$), and $\eta$ close to
1,  e.g. the diffusion in the rim should take place essentially  in the Bohm limit.
In order to provide maximum electron energy $E_0$ of order of 30 TeV, the
shock speed  should exceed 3000 km/s which implies a large
distance to the source,  $d \geq 1.5 \, \rm kpc$. For this set of
parameters, approximately half of the total TeV emission is contributed
from the inner parts of the remnant,
$r \leq 0.8 r_{\rm s}$. The narrow range of the required
magnetic field in the rim allows rather accurate estimate of the total energy
of relativistic electrons in SN 1006. For example for the distance
$d=1.8 \, \rm kpc$ in Fig.~4 the total electron energy in the rim is
$W_{\rm e}\simeq 2.9 \times 10^{48}  \rm erg$, whereas
the energy in the electrons escaped the rim is
$W_{\rm e}\simeq 1.9 \times 10^{48}  \rm erg$. It should be noted that the spectrum
of electrons outside of the rim is enriched  by multi-TeV particles
due to the effect of energy dependent ($\propto E$) diffusive escape.
The total energy in electrons required to explain the X-ray and
TeV $\gamma$-ray fluxes is about $5 \times 10^{48}$ erg.
Since the total energy of electrons depends on the
B-field as $W_{\rm e} \propto B^{-(1+\alpha_{\rm r})}$ the total electron energy could
be reduced only by a factor of $(8/6)^{1.6} \simeq 1.6$ for the magnetic
field $B=8 \, \mu \rm G$. Therefore
the inverse Compton origin of the detected
TeV radiation requires about 1 percent of the total explosion energy of SN 1006
in relativistic electrons.

The total energy of the magnetic field in the remnant with
$B_2= B_1/4 \simeq  2 \, \mu \rm G$ for the distance 1.8 kpc is
about $10^{46} \, \rm erg$.  A similar  amount of magnetic field
energy is expected also in the rim since  the amplification of the
B-field there is compensated by a smaller volume of the rim.
Thus,  the inverse Compton origin of TeV $\gamma$-radiation
implies that the conditions in SN 1006 are far from the equipartition
between relativistic electrons and the magnetic field.

In all calculations above we have assumed a stationary injection rate of
relativistic electrons which is a good approximation as far as
the source is in an early Sedov phase. In order to demonstrate that,
in Fig.~6 we show the spectra of synchrotron and IC fluxes calculated
for two different assumptions: (i) a time-independent injection rate
$Q(t)=\rm const$, (ii) injection rate in the form $Q(t) \propto (1+t/t _\ast)^{-1}$
with a  characteristic time (onset of the Sedov phase) $t _\ast=100 \, \rm yr$.
In both cases we have assumed  acceleration spectrum given by Eq.~(1)
with  $E_0=30 \, \rm TeV$.  For the assumed  magnetic field
in the rim   $B_1=7 \, \mu \rm G$  and the current shock speed
$v_{\rm s}=3600 \, \rm km/s$  this value of $E_0$ implies  a
gyrofactor $\eta=1.5$  (see Eq.~11).
As it is seen from Fig.~6 the higher injection rate in the past does not affect
significantly the fluxes of nonthermal radiation even for a very small
values of $t_\ast=100 \, \rm yr$. The main difference between the stationary
and the time-dependent injection cases is reduced to somewhat
higher IC $\gamma$-ray fluxes outside of the rim. For more realistic
values of $t_\ast \geq  300 \, \rm yr$ the effect of time-dependent  injection
becomes practically  negligible.

\begin{figure}[htbp]
\resizebox{8.cm}{!}{\includegraphics{MS8595.f6.epsi}}
\caption
{The synchrotron (top panel) and IC  $\gamma$-ray (bottom panel)
fluxes calculated in the framework of 2-zone model for two
assumptions about the injection rate of electrons:
$Q(t)=\rm const$ (solid lines), and  $Q(t) \propto (1+t/t _\ast)^{-1}$ with
$t_\ast=100 \, \rm yr$. In both cases $B=7 \, \mu \rm G$
and $E_0=30 \, \rm TeV$.
The distance to the source is 1.8 kpc.}
\label{f6}
\end{figure}

The above calculations show that the electronic origin
of the observed TeV $\gamma$-ray emission meets  difficulties
for small distances to the source, $d \simeq  1 \, \rm kpc$ or less,
since the latter implies a small shock speed, and therefore insufficient
acceleration rate in order to accelerate  electrons  to  energies of about
30 TeV and beyond.   In case of confirmation of the recent claims
about small distance to the source (Willingale et al. \cite{ROSAT}),
a possible solution to this difficulty could be an
assumption of a more effective
acceleration mechanism compared with the
conventional diffusive shock acceleration,
e.g. by invoking the mechanism of perpendicular
diffusion proposed by Jokipii \cite{Jok}.
Another principal possibility to increase the  accelerate rate  is connected
with an assumption of a   large magnetic field in the rim,
$B_1 \gg 10 \, \rm \mu G$. Obviously in this scenario
the TeV radiation principally cannot be explained
by the IC mechanism. The only reasonable alternative
could be the  nucleonic origin of TeV radiation.

\section{TeV gamma rays of nucleonic origin}

Currently,  the nucleonic origin of the observed TeV emission
is treated by the community as an inadequate  alternative
to the IC mechanism,
the main argument being the low ambient density of the
gas in SN 1006, $n \simeq 0.4 \, \rm cm^{-3}$ (Willingale et al. \cite{ROSAT})
as well as the supposed large distance to the source of
about 2 kpc  (Winkler and Long \cite{winkler}).
Hower these arguments are not sufficiently robust in order to dismiss
such an important possibility with far going conclusions
concerning the origin of the nucleonic component
of galactic cosmic rays (Aharonian \cite{vertalk}).

Indeed, the very fact of the existence of
$\gg 10 \, \rm TeV$  electrons as it follows from the X-ray data
is an evidence for a strong shock in SN 1006, and
implies a large compression  factor, $\rho \simeq 4$
or even more, up to 10,  as it follows from
non-linear studies of shock acceleration in
SNRs (Malkov \cite{misha}, Berezhko \cite{berezh96},
Berezhko \& V\"olk \cite{BVLK}, V\"olk \cite{KPVLK},
Baring et al. \cite{baring}).
Therefore it is not unrealistic if one
assumes a significantly higher density of the gas in the
rim region, e.g.  $n \simeq 2 \, \rm cm^{-3}$.
The current estimates of the distance to the source also contain
large uncertainties, and do not exclude a distance of about 1 kpc or even less.
In particular, one of the recent studies
of SN 1006 based on the ROSAT observations suggests  a
distance $d=0.7 \pm 0.1 \, \rm kpc$
(Willingale et al. \cite{ROSAT}).
To explain  the observed flux of TeV emission,
for $\Gamma_{\rm p}=2$ the scaling factor
$A \simeq 0.83$ is needed (Fig.~\ref{f7}). This requires
for the total energy in accelerated protons
\begin{equation}
W_{\rm p} \simeq 4  \times 10^{49} \,  (n/2 \,
{\rm cm^{-3}})^{-1} \, d_{\rm kpc}^2 \, \rm erg \, .
\end{equation}
This is only $\sim 10$ per cent   of the  total kinetic energy
of explosion estimated for SN 1006 as
$5 \times 10^{50} \, \rm erg$.  The numerical calculations
within the kinetic theory of  shock acceleration
show  (Berezhko \cite{berezh99})
that even for a large
distance to  SN~1006, the energy budget in
accelerated protons can be sufficient to explain the TeV $\gamma$-ray emission
from SN~1006 by hadronic interactions.

\begin{figure}[htbp]
\resizebox{8.cm}{!}{\includegraphics{MS8595.f7.epsi}}
\caption
{The fluxes of $\pi^0$-decay $\gamma$-rays calculated for the
proton spectrum in  Eq.(1)  with $E =200  \, \rm TeV$,
and 3 different power-law indices: $\Gamma_{\rm p}=1.8$
(dashed), 2 (solid),  and 2.1 (dot-dashed).  The fluxes
are normalized to the observed flux  at
3 TeV. This results in the values of scaling parameter  $A=0.44$, 0.83, and 1.35,
respectively.}
\label{f7}
\end{figure}

In fact this estimate of the scaling factor A derived
from the comparison of calculated and observed TeV fluxes
depends significantly on the  spectrum of protons.
In Fig.~7 we show  the $\pi^0$-decay
$\gamma$-ray fluxes calculated for 3 spectra of
protons taken in the form of Eq. (1)  with spectral
index $\Gamma_{\rm p}=$1.8, 2, and 2.1.
The fluxes are normalized to the observed flux  at 3 TeV.
The corresponding values of the scaling factor
are A=0.44, 0.83, and 1.35, respectively.
Even in the case of relatively soft spectrum of protons
with $\Gamma_{\rm p}=2.1$, the required scaling factor is
still acceptable taking into account that
more than  $20 \%$ of the energy of the supernova
explosion can be transformed into  accelerated protons
(Berezhko \& V\"olk  \cite{BVLK}). Steeper spectra of protons
with a slope $\Gamma_{\rm p} \ge 2.1$ do not match
the energy budget of the source.
Such spectra are excluded also by the EGRET flux upper
limit, $F_\gamma \leq 1.7 \cdot 10^{-7}
\, \rm ph/cm^2 s$ at $E \geq 100 \, \rm MeV$ (Mori \cite{Mori}).

\begin{figure}[htbp]
\resizebox{8.cm}{!}{\includegraphics{MS8595.f8.epsi}}
\caption
{The nonthermal radiation of SN 1006
calculated for large magnetic field in the NE rim $B=70 \, \rm \mu G$.
Solid curves correspond to the synchrotron radiation of directly
accelerated electrons, while the dotted curve
corresponds to the synchrotron radiation produced  by secondary
($\pi^{\pm}$-decay) electrons.   The dashed curve shows the
flux of $\pi^0$-decay $\gamma$-rays calculated for
proton spectrum with $\Gamma_{\rm p}=2$, $E_0=200 \, \rm TeV$,
and  scaling parameter $A=0.83$.  The dot-dashed line shows the
flux of IC $\gamma$-rays contributed mostly by directly
accelerated electrons.  All fluxes  shown are well dominated by the
emission produced in the rim.}
\label{f8}
\end{figure}

The $\gamma$-ray spectra shown in Fig.~7 are calculated
assuming  for the maximum
energy of protons $E_0=200 \, \rm TeV$.
Although the exact value of $E_0 $
do not noticeably change the requirements to the
scaling factor $A$,   it has a noticeable impact on the
spectral form of $\gamma$-rays above 10 TeV.
Therefore only future precise spectroscopic measurements
in this energy region could provide an important information
about $E_0$. At the same time the existing sub-10 TeV data
already tell us that within the framework of nucleonic
model of TeV radiation of SN 1006 the cutoff energy
$E_0$ could not be significantly less than 100 TeV.

Although in this paper we do not attempt to
discuss the aspects related to the theory of
diffusive shock acceleration in SNRs, it
is clear that such large values of $E_0$ could be achieved
only under the assumption of a large magnetic field in the
shock region, $B \sim 10^{-4} \, \rm G$ or even more
(see Eq.~11). Obviously this assumption does not leave any
chance for the IC mechanism to give  a noticeable
contribution into the observed TeV emission.
On the other hand the featureless X-ray radiation could
be naturally explained by the synchrotron radiation
of accelerated electrons. In such strong magnetic fields
the maximum energy of accelerated electrons is determined
by the balance between the acceleration rate and the
synchrotron energy loss rate:
\begin{equation}
E_0 \simeq 45  \, \eta^{-1/2}    \left(\frac{
B}{10 \, \rm {\mu G}}\right)^{-1/2}
\left(\frac{v_{\rm s}}{2000 \, \rm km/s}\right )
\; \rm TeV \, ,
\end{equation}
and therefore,  as it follows  from Eq.(8)  the energy of exponential cutoff in the
synchrotron spectrum,
\begin{equation}
E_{\rm m}  \simeq 0.5 (v_{\rm s}/2000 \, \rm km/s)^2
\eta^{-1} \, \rm  keV \, .
\end{equation}
does not depend on neither the magnetic field nor the age of
a SNR. The very fact of detection of nonthermal X-rays
above 1 keV testifies that the particle acceleration
takes place  in the limit of Bohm diffusion ($\eta \sim 1$).

Therefore an observation of flat X-ray spectrum
in the region 1-10 keV from any SNR would imply, for
a reasonable  shock speed in the Sedov phase
$v_{\rm s} \leq 4000 \, \rm km/s$,  a more effective
acceleration than it follows from the
prediction of conventional parallel shock acceleration model.

In the regime of non-negligible synchrotron losses
we should expect, in addition to the exponential cutoff at
$E_{\rm m}$, another spectral feature -- a spectral
break (increase of the power-law index by 0.5)
at the  energy $E_{\rm b}$ which is determined from the
condition $t_{\rm sy}=t_0$:
\begin{equation}
E_{\rm b} \simeq 2.9  (B/10 \, {\rm \mu G})^{-3}
\, (t_0/10^3 \, {\rm yr})^{-2} \, \rm keV.
\end{equation}

In Fig.~\ref{f8}  we show the spectrum of synchrotron radiation calculated for
the following parameters: $B = 70 \, \rm \mu G$,
$t_0 = 700 \, \rm yr$, $v_{\rm s} = 2900 \, \rm km/s$,
and $\eta=1$. For these parameters the spectral break
is  at $E_{\rm b} \simeq 0.02 \, \rm keV$, while
the exponential cutoff $E_{\rm m} \simeq 1 \, \rm keV$.
Although there is a gap by a factor of 20 between  these two
characteristic photon energies, the additional gradual steepening
due to the exponential cutoff in the electron spectrum
becomes noticeable already at energies $E_{\rm x} \geq 0.1 E_{\rm m}$.

\section{Conclusions}

In the previous theoretical studies of the IC $\gamma$-radiation of SN 1006
a  homogeneous one-zone model  has been implied (Mastichiadis \& de Jager  \cite{masti},
Pohl \cite{pohl},  Yoshida \& Yanagita \cite{yoshida})
which assumes that  all accelerated electrons are confined in the NE rim.
The magnetic field in the rim derived from these studies which would  not contradict
the observed X-ray to TeV $\gamma$-ray flux ratio should not exceed
$7 \, \rm \mu G$.

Our study of the  $\gamma$-ray production in SN 1006
which includes the effect of convective and diffusive escape of
electrons,  allows  some increase of the magnetic field
up to  10 $\rm \mu G$, with preferable values being in a
rather narrow   range between 6 and 8 $\rm \mu G$.
Given the short time of particle acceleration
available, $t_0 \le t_{\rm SN 1006} \simeq 10^3 \,\rm yr$,
the assumption of such a small magnetic field
requires a very  high shock speed in SN 1006, $v_{\rm s} \geq 3000 \, \rm km/s$,
in order to provide acceleration of electrons to energies $E_0\sim  30 \,\rm TeV$
needed for explanation of X-ray and TeV observations. This implies a {\it large}
distance to the source, $d \geq 1.5 \, \rm kpc$.

This model allows definite predictions which could be tested by future observations.
A significant, if not dominant, fraction of the IC TeV emission is to be produced
outside of the NE rim.  Namely,  a $\gamma$-ray flux comparable with the flux from
NE rim, should be then expected from the extended inner region  of the remnant
adjacent to the rim. The size  of this region depends on the character of propagation
of electrons in the rim.  Indeed, even in the case of
diffusion of electrons in the Bohm limit in the remnant with magnetic field
$B_2 \sim 2 \, \rm \mu \rm G$,  the characteristic distance of penetration of electrons
towards the central region of the remnant
could be estimated as
\begin{equation}
l(E_{\rm e}) \simeq \sqrt{2 \, D(E_{\rm e}) t_0} \simeq 0.75 \,
(E_{\rm e}/10 \, \rm TeV)^{1/2} \, \rm pc .
\end{equation}

Since the  IC production of TeV $\gamma$-rays (on 2.7 K MBR)
with energies  less than several TeV takes place in the Thompson regime,
and therefore their characteristic energy
scales as $E \simeq 1 \, (E_{\rm e}/20 \, \rm TeV)^2 \, \rm TeV$,
the size of the emission region of TeV gamma rays should be as large as the
width  of the rim, and  increases  linearly with energy of $\gamma$-rays.
Moreover,  if the propagation of electrons in the remnant is  much faster
than in the Bohm limit ($\eta \gg 1$),  the electrons could fill up practically
the entire  remnant.  In that case the energy dependence of the
size of the $\gamma$-ray emission will be significantly weakened.

Another distinctive feature of the IC origin of TeV radiation is the spectral
shape of the radiation: very hard, with the photon index
$\alpha_\gamma\sim 1.5$ below 1 TeV, a flat spectrum with
$\alpha_\gamma\sim 2$ between 1 and 10 TeV, and very steep above  10 TeV.

The alternative to the IC interpretation  is the nucleonic origin of the observed
TeV radiation. This interpretation becomes energetically comfortable,  which
implies no more than $10^{50}\,\rm erg$ in accelerated protons and nuclei,
if we assume (i) a {\it small} distance to the source of about 1 kpc or less,
and (ii)  a significant enhancement of the gas density in the rim due
to strong shock compression. This predicts a compact size of the TeV emission
comparable with that of the X-ray rim. In the region below 1 TeV
the spectrum of $\gamma$-rays of nucleonic origin,  with a power-law
index $\alpha_{\gamma}\simeq \Gamma\sim 2$  is expected
steeper than the spectrum of IC $\gamma$-rays.
However  a flatter spectrum of $\pi^0$-decay  $\gamma$-rays
cannot be excluded if the protons would  have an acceleration spectrum
as hard as  $E^{-1.5}$ (see Malkov \cite{misha}).

The shape of the
spectrum of $\pi^0$-decay $\gamma$-rays above 1 TeV depends
on the characteristic  maximum energy of accelerated protons.
Since the flux of TeV $\gamma$-rays
is no more connected with  the X-ray fluxes,
the value of the magnetic field in the acceleration region (NE rim) could be adopted
as high as $\sim 100\,\rm \mu G$. Correspondingly, the energies
$E_0\geq 100\,\rm TeV $ could be achieved. On the other hand if $E_0$
would be significantly less than 100 TeV, one may expect a
turnover in the spectrum of $\gamma$-rays above several TeV.

Thus, it is quite possible that both in the low
(sub-TeV)  and in the high (multi-TeV) energy regions
the IC and $\pi^0$-decay $\gamma$-rays may
have similar spectra.
Therefore the spatial rather than spectroscopic measurements
of $\gamma$-radiation above 100 GeV with future IACT arrays could provide
decisive information about the origin  of very high energy radiation of  SN 1006.
The IC models predict significant $\gamma$-ray fluxes not only
from the rim, but also from the inner parts of the remnant.
Meanwhile, the $\pi^0$-decay $\gamma$-rays trace the density
profile of the gas in the production region,  therefore one should expect
a rather compact $\gamma$-ray source
essentially coinciding with the rim.

We emphasize that both the electronic and the nucleonic models of
the observed TeV radiation of SN 1006 require a very effective acceleration
of particles in the regime close to the Bohm limit. Also,  the both models
predict a very high conversion efficiency of the total kinetic energy of
the explosion available ($\sim 5 \times 10^{50} \, \rm erg$)
into relativistic particles. The energy required for relativistic electrons
within  the framework of the IC model is predicted with a
good accuracy,  given the small range of allowed B-field:
$W_{\rm e} \simeq 5 \times 10^{48} \, \rm erg$.  This is by two orders of magnitude
larger than the energy contained in the magnetic field;
this suggests that the  conditions in SN 1006  are far from the equipartition regime.

The nucleonic model of TeV emission requires total energy in accelerated
protons from  $2 \times 10^{50} \, \rm erg$ down to  $10^{49} \, \rm erg$,
depending on the enhancement factor for the gas density in the rim,
the spectral index of the accelerated protons, and the distance to the source.
In particular for moderate assumption for the spectral index
$\Gamma_{\rm p}=2$,  and the gas compression ratio $\rho=4$
(i.e. $n=1.6 \, \rm cm^{-3}$),  the energy in  protons
is estimated $\approx 5 \times 10^{49} (d/1 \, \rm kpc)^2 \, \rm erg$.
Note that since the magnetic field in the rim for the nucleonic  model could be
as high as $100 \, \mu \rm G$, this model predicts a situation
close to the equipartition.

High magnetic fields in the rim can equally well explain the current X-ray data.
The synchrotron X-radiation in this case is produced in the regime of saturated
energy losses of electrons, which results in a somewhat different spectral shape
of the synchrotron fluxes. In both large and small  magnetic field limits,
the spectrum would be best fitted in the form $F(E)\propto E^{-\alpha_{\rm x}}
\exp[-(E/E_\ast)^{-1/2}]$, where $\alpha_{\rm x}\simeq 2.1$
and $\alpha_{\rm x}\simeq 1.6$ for  the cases of large and small magnetic fields,
respectively.

\begin{acknowledgements}  We express our thanks to  H. J. V\"{o}lk, M. Malkov,  E. Berezhko,
T. Kifune and T. Tanimori  for very fruitful discussions. The work of AMA was
supported through the Verbundforschung
Astronomie/Astrophysik of the German BMBF under grant No. 05-2HD66A(7).
\end{acknowledgements}

redpajama_set_name: RedPajamaArXiv


In a small bowl, whisk together yeast, sugar and warm water. Let sit about 10 minutes until foamy.
Heat cup of water, molasses, vinegar, butter and chocolate in a small saucepan until the butter and chocolate are melted. Set aside.
Whisk together whole wheat, rye and all-purpose flours in a separate large bowl. Set aside.
In the bowl of a stand mixer fitted with paddle attachment, combine 2 cups flours, bran, caraway seeds, fennel seeds, salt, espresso and shallots (or red onion). Mixing on low speed, add yeast and chocolate mixtures. Mix at medium speed until smooth, about 3 minutes.
At low speed, add 1/2 cup remaining flours at a time, using a spatula to scrape excess flour from the sides of the bowl. Add just enough flour until the dough comes away from the sides of the bowl. Switch to dough hook and knead about 5-8 minutes on medium speed — adding 1 tsp all-purpose flour at a time if needed for dough to pull away from the sides of the bowl — until smooth and elastic (or knead by hand on floured countertop for about 10 minutes until smooth and elastic).
Shape dough into a ball and place in a lightly greased bowl, turning once to coat. Cover with plastic wrap and let rise until doubled, about 1-2 hours.
Turn out risen dough onto a lightly floured surface. Shape into round or sandwich loaf and place either on a parchment paper-lined baking sheet (for round) or in a lightly greased loaf pan (for sandwich loaf). Cover lightly and let rise until doubled, about 45 minutes to 1 hour. Slash an X in the top of the round before baking (this is not needed for the sandwich loaf).
Preheat oven to 350°F. Bake bread until deeply browned and 200-210°F when an instant-read thermometer is inserted in the bottom center, about 45 to 50 minutes. Allow bread to cool completely on cooling rack before slicing.
I've been trying to build myself a bucket list for years. Sometimes, along with "write a book" and "go to Greece," I think "write bucket list" should go on my bucket list! One thing that is on my rather paltry bucket list is "bake pumpernickel bread." Pumpernickel – light or dark – is one of my absolute favorite types of bread, and I knew that making it at home would be a real treat. Of course, this Russian Black Bread isn't quite pumpernickel. The bread does taste strikingly similar to my beloved pumpernickel, and the ingredients — rye flour, molasses, cocoa powder — seem to fit the bill. But it just wasn't quite the same. So I'm on the fence as to whether or not I've actually "baked pumpernickel bread." Regardless, it was still the treat I'd hoped it would be. I can't say I'm disappointed in my slightly off-track endeavor — this bread renders a flavor so rich and dense that it is, dare I say it, better than pumpernickel! I only say this because I've eaten pumpernickel so often that this bread offers a new dynamic of flavors – a refreshing change. I know the list of ingredients is rather intimidating, but I don't recommend cutting corners with this bread – each ingredient significantly serves a purpose in creating that unique black bread flavor. The result is delicious on its own, with butter or with mayo and fresh, sliced tomatoes as a simple, late summer sandwich. It's bread worthy of putting on a bucket list and crossing off as soon as possible.


text:
International Women's Day 2021: Women Who #ChooseToChallenge
8 March 21 words: LeftLion
In celebration of International Women's Day 2021, we've complied a list of articles showcasing times in which Nottingham Women have actively chosen to challenge the norm...
Zoo Indigo Are Taking Us To No Woman's Land
Far from the generals and politicians who instigate conflict, the ordinary people who suffer in wars are often forgotten. In their production No Woman's Land, local theatre duo Zoo Indigo – made up of Rosie Garton and Ildikó Rippel – shine a spotlight on the extraordinary women who struggled under threat of violence and rape to find a safer place for their families after the end of the Second World War. We caught up with Ildiko to find out more...
International Women's Day: #Choosetochallenge in Music
Whether it's the gender disparity on festival line ups, or reports of women being assaulted in the sector, conversation is building towards creating a safer music industry, as diverse as the huge amount of talent that exists within it. A large portion of this talent lies here in Nottingham, with numerous women working as artists, presenters, promoters, label owners and more. We wanted to celebrate them and share their voice...
The Carousel Launches International Womxn's Day Exhibition
The project showcases artists from all over the UK and is created by womxn, about womxn, to celebrate womxn...
SHEAfriq: The New Creative Collective in Nottingham Town
SHEAfriq is a brand new collective of creative women of black heritage. We sat down with members Aïcha – DJ, artist and business owner – and Saziso – freelance creative producer and founder of The Anti Gallery – to talk about the collective's aims, challenging stereotypes, and bringing the goods to the Nottingham populace...
7 Organisations Combatting Misogyny in Nottingham
Nottinghamshire Police are the first police force in the country to rule misogyny as a hate crime. That includes physical or verbal harassment directed at women, because they are a woman, via any means. So, if you're walking home and a group of guys decide to shout inappropriate, sexual comments at you, or someone grabs your arse on a night out, you're well within your rights to report the behaviour to the authorities. All you have to do is ring 101, and if the assault is particularly severe, call 999. This doesn't necessarily mean that the perpetrator will be punished, but it does mean the police can collect information regarding these types of incidents – where, when and how often they happen – and work on making the streets of Notts safer for all. It also means that they can direct you to any support and guidance you may need following the event. There are some incredible local organisations who'll go out of their way to help you...
The Party Somewhere Else Festival Line Up
The women-led theatre festival is doing bits in March...
A History of Women and Feminism in Nottingham 1903-2014
In Celebration of International Women's Day 2014, WoLAN take us through the history of women's rights in the 20th and 21st century and Nottingham's part in the movement...
Women Say Stuff 5
We chat to Leanne Moden to find out about Women Say Stuff, which is getting ready to celebrate it's fifth year on International Women's Day this Sunday...
10 Nottingham Women in Literature
Mention Nottingham's literary heritage and people often cite Byron, Lawrence or Sillitoe. But our female writers are equally as rebellious and ground-breaking. Margaret Cavendish was one of the earliest science fiction writers; Lucy Hutchinson was the first female writer of an epic English poem; Ada Lovelace is credited as the first computer programmer; suffragist, Alice Zimmerman, worked as a writer and translator; and Alma Reville was an influential screenwriter. In more recent times, Nottingham has been home to one of Britain's funniest authors, Mhairi McFarlane; Pippa Hennessy played a key role in our successful bid to become UNESCO City of Literature; and Sandeep Mahal took up her position as its first director last year. Up the women. Here's ten more who've contributed to Nottingham's incredible literary landscape...

redpajama_set_name: RedPajamaCommonCrawl


text:
Virtual Town Hall York Region Transit & TTC 5 Year Fare Policy Review
Feb 2, 2022 - 06:30pm to Feb 2, 2022 - 08:30pm
Public Information Centre
The TTC and YRT are working together to develop a new 5-Year Fare Policy and 10-Year Fare Collection Outlook. The TTC and YRT are hosting a Virtual Town Hall to cover the following topics:
Overview of policy goals, such as equity, affordability, revenue and ridership
Fare policy options based on feedback from the first two phases of the consultation process
Limits and opportunities in the current fare structure affecting fare policy decision-making
The virtual Town Hall is taking place on Wednesday, February 2, 2022 from 6:30 p.m. to 8:30 p.m. via Zoom. Project information and access on the day of event are available at yrt.ca/FareReview.
Pre-registration for the event is not required but recommended through this link.
Input collected during the Virtual Town Hall will be incorporated into a final 5-Year Fare Policy recommendation report, which will be presented to York Regional Council in Spring 2022.


text:
Lester Lee (November 7, 1903 – June 19, 1956) was an American composer. He was nominated for an Academy Award in the category Best Original Song for the film Miss Sadie Thompson. Lee was also the co-writer of "Pennsylvania Polka". Lee died in June 1956 of a heart attack in Los Angeles, California, at the age of 52.

Selected filmography
 Miss Sadie Thompson (1953; co-nominated with Ned Washington)

References

External links

1903 births
1956 deaths
People from New York (state)
American film score composers
American male film score composers
20th-century American composers

redpajama_set_name: RedPajamaWikipedia


Peter Dreier: Hey, Paul Ryan—We All Depend on Government—Even You (and Your Mom)!
Wisconsin Rep. Paul Ryan is driving a hard bargain over the Republican Party's plans to make him the next House speaker. But that's not surprising. He's also continually played tough with the middle class and the most vulnerable in our society. In his constant assault on 'big government', he's called for slashing public education, roads, and public services like food stamps, the core public goods that lift people out of poverty and strengthen our economy.
With Ryan in the national news again, we should all take a moment to remember his vision for the role of government. Peter Dreier sums it up in this piece from 2013, when Ryan had food stamp recipients in his crosshairs.
Hey, Paul Ryan—We All Depend on Government—Even You (and Your Mom)!
Rep. Paul Ryan is back to his old tricks, demonizing people who rely on government to improve their lives. This week, his target was food stamp recipients.
He's already come out in favor of $20 billion in cuts that will throw an estimated two million children, elderly, and disabled Americans off food stamps. But now Ryan—the millionaire Wisconsin Congressman who was Mitt Romney's VP running mate last year—is pushing an amendment to eliminate food stamps for people who have $2,000 in savings, or a car worth more than $5,000.
This is the Paul Ryan whose budget plan would have slashed funding for public education, roads, and public services that are the investments we need to lift people out of poverty and strengthen our economy. Now he's taking aim at the most vulnerable people in society—food stamp recipients.
Public education, roads, and public services like food stamps are the core public goods that lift people out of poverty and strengthen our economy.
Ryan worships at the altar of novelist Ayn Rand, the philosopher of you're-on-your-own selfishness, whose books were required reading for his Congressional staffers.
This post originally appeared on HuffPost on 06/21/2013.


text:
Plant mothers talk to their embryos via the hormone auxin
Scientists solve long-standing question about signal that regulates embryo development – Study in Nature Plants
Arabidopsis developing seed: Auxin (here visualized in green) is produced and accumulates in the maternal tissue close to the young embryo. © Chulmin Park
While pregnancy in humans and seed development in plants look very different, parallels exist – not least that the embryo develops in close connection with the mother. In animals, a whole network of signals from the mother is known to influence embryo development. In plants, it has been clear for a while that maternal signals regulate embryo development. However, the signal itself was unknown – until now. Plant scientists at the Institute of Science and Technology Austria (IST Austria), Central European Institute of Technology (CEITEC) and the University of Freiburg have now found that a plant hormone, called auxin, from the mother is one of the signals that pattern the plant embryo. Their study is published today in Nature Plants.
"Plant scientists have been trying to figure out the nature of the signal between mother and embryo for decades", explains Jiri Friml, Professor at IST Austria and one of the corresponding authors. "We show that the mother is the source of auxin which regulates early embryo development." Auxin is a hormone that plays many roles in the development of plants, and has been known to regulate embryo development. By visualizing the biosynthesis of and the response to auxin, the researchers show that the maternal tissue which surrounds the embryo in the seed starts to produce more auxin after fertilization.
The authors then go on to show that this increased maternal auxin production is crucial for the embryo: when auxin production is interrupted, the embryo does not develop correctly. And it is specifically maternal auxin that plays this important role. When the researchers set up a cross between plants so that the mother does not produce auxin but the embryo does, the same defects in embryo development are seen – proving that auxin from the mother is the key developmental signal.
However, auxin is not the only maternal signal influencing the embryo, Friml explains: "When we stop the supply of auxin from the mother to the embryo, the embryo grows abnormally, but it still manages to develop somehow. This means that there must be another, auxin-independent, signal." The paper is a collaboration between Jiri Friml and his group, notably Helene S. Robert, a previous Post-doc of Friml and now group leader at CEITEC in Brno, and the group of Thomas Laux at the University of Freiburg.
Helene S. Robert et al. 2018. Maternal auxin supply contributes to early embryo patterning in Arabidopsis. Nature Plants. DOI: 10.1038/s41477-018-0204-z
Jiri FrimlLife SciencesPlant BiologyPublication


text:
Kanye West rapped on phone to fan battling with cancer
Ye reached out days before the fan passed away
By Luke Morgan Britton
Kanye West reached out to a fan battling cancer to rap down the phone for her a few days before she passed away.
A Twitter user first tweeted about the story last week (January 3), writing that "This girl in my town had cancer and Kanye called her a couple days ago to rap for her".
"I think Kim was there too," the person added. "Wasn't even blasted on social media or anything. She passed yesterday. I have so much respect for him tho. Making her happy in her last moments."
West's wife Kim Kardashian then appeared to confirm the reports earlier today (January 8), responding to the original by saying: "We are praying for her family". See below.
This girl in my town had cancer and Kanye called her a couple days ago to rap for her. I think Kim was there too. Wasn't even blasted on social media or anything. She passed yesterday. I have so much respect for him tho. Making her happy in her last moments.
— debbie (@stalkdebbie) January 3, 2018
We are praying for her family. ?? https://t.co/pjEUhPboFb
— Kim Kardashian West (@KimKardashian) January 8, 2018
Meanwhile, West and Kardashian's young son Saint was recently hospitalised with a "bad case" of pneumonia.
TMZ reported that the two-year-old son of the rapper and reality TV star was taken to a hospital in the Los Angeles area over the festive period. His parents remained with him to "share overnight duties", before he was eventually released a few days later. Saint is now said to be back at home with his family and "doing well".
Kardashian later tweeted about the health scare, writing: "My precious baby boy is so strong! After spending three nights in the hospital & seeing my baby get multiple IV's and hooked up to oxygen machines, our end of year was challenging. Pneumonia is so scary."
Kanye and Kim are currently expecting their third child after hiring a surrogate last year.
Truth, trauma and Tommy Lee: 7 key revelations from Pamela Anderson's new doc


text:
NewsGreat Falls News
NorthWestern Energy restores power after fire damaged Great Falls utility lines
Residents affected in Sun Prairie, Vaughn, and Power
By: David Sherman & Elizabeth Transue
A large wildland fire just north-northwest of Great Falls on Monday afternoon damaged or destroyed several buildings, and also knocked out power to about 1,380 customers of NorthWestern Energy.
The power outage affected people in the area (along Stuckey/Vinyard roads and Golden Valley Loop), and affected hundreds more in Sun Prairie, Vaughn, and Power. The affected customers were without power from about 5 p.m. to 6:30 p.m.
A spokeswoman with NorthWestern Energy says the fire damaged several distribution and transmission poles and lines.
Engineers were on site overnight and into Tuesday fixing about a dozen connected power lines on Stuckey Road.
The fire was contained late Monday evening ; the cause and size of the fire has not yet been determined.
We are working to get more information about the people affected by the fire.
(MONDAY, 5:30 pm) More than 1,300 customers are without electricity in and around Great Falls.
According to NorthWestern Energy, about 1,253 customers in and around Vaughn are without power; the company estimates that power will be restored by 7:30 p.m. on Monday.
In addition, nearly 100 customers in and around Power are without power. The utility company estimates that power will be restored to those customers by 7 p.m. on Monday.
Another outage affecting up to 50 customers has been reported in Great Falls, centered near 15th Street North and 8th Avenue North.
We have also received one unconfirmed report that some people in Sun Prairie are without power.
There is no word yet on the cause of the power outages, although there is speculation that the wildland fire just north of Great Falls may be a factor.
You can monitor power outages on the NorthWestern Energy website .


text:
Photo: BryantBaseballAcademy.com
Exclusive: Kris Bryant's Dad, Mike, Talks to CI About Crafting an MVP Swing and How His Son Can Get Even Better (Part 3)
Brendan MillerFebruary 20, 2017
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If you find yourself reading this and haven't seen Part 1 and Part 2, please remedy that posthaste and make your way back when you're done. In addition to providing context, there's some great stuff in there for Cubs fans or just baseball fans in general.
We've already learned about how Kris Bryant adjusted his swing between his rookie and sophomore seasons and how Mike thinks the ceiling for his son is a better version of Miguel Cabrera. In this installment, we'll get into baserunning, and what the MVP is looking to improve upon this season. As always, the audio version of this portion of the interview is available at the conclusion of the text.
Cubs Insider: Kris was one of the league's best baserunners last year. There's a stat called BSR. They take into account stolen bases and other baserunning plays. He was second, I believe, in the league. I think he was first in the National League but I have to double check. That's remarkable. You don't see power hitters run the bases that well. [Ed. note: Bryant was 5th in MLB and 2nd in NL with 7.3 BSR]
Mike Bryant: Do you know how that comes about being? I've always said you don't have to have speed. And speed is great in the game, don't get me wrong. I'm not going to build the team around speed, ever. I'm going to build the team around power. Power arms, power bats.
CI: 100 percent, yeah.
MB: Theo's onto something. Kris's BSR rating becomes about because of instinct and how he was taught and how to have that internal time clock going on in your head every minute you're on the field. Knowing you can get an extra two steps, which for him is 12 feet…or more when he gets those legs moving. He's hit strides, and I've measured them — I've measured them — when he gets going underway it's 12 feet. He covers 24 feet [in four strides].
CI: That's crazy.
MB: That's the high end of it. It's like 19 to 24 feet when he gets going underway. Because it's like he's a long jumper. If you get a guy that can move his legs pretty fast, he's going to be a good base runner.
CI: I mean, we saw it in the world series, too, in that one Rizzo double down the right field line. He's going on a pitch. That's an underrated part of that game right there. He scores on first base on a line drive basically to right field. That was crazy.
MB: So the swing changes were really minuscule. I don't like the word "level." I was taught to have a level swing all my life and it's wrong. The way the ball's coming in, coming down, at a six to a 10-degree angle and with break — horizontal and vertical break on it — the depth of the pitches adds 12 or 13 degrees to the angle. So if you want to meet the ball squarely on most of the pitches, you've got to have at least a 10-degree angle up.
I was taught to have a level swing all my life and it's wrong. So if you want to meet the ball squarely on most of the pitches, you've got to have at least a 10 degree angle up. And that's only going to produce a line drive that can get caught in the infield…And then you notice most of the home runs are hit between 25 and 30…
And that's only going to produce a line drive that can get caught in the infield if it's anywhere near the fielders. You have to have a 15- to 20-degree upward angle on the ball. And then you notice most of the home runs are hit between 25 and 30, so think about that.
CI: Right and then you saw the one post, he reduced his batted-ball angle. The total amount of batted balls hit above 36 degrees his rookie year was, I believe, 26 or 27 percent. And then he brought that down last year, those same 36-degree batted balls. He brought that down to I think it was 16 percent, so that's a huge dropoff to hit more of those more sweet-spot 20- to 25-degree batted balls. So there you go.
It's funny because it sounds like a goal of last season was to decrease the whiffs. Mission accomplished. But what's even more remarkable is that in doing so, in reducing the whiffs, he actually hit better balls. He hit better pitches. I think there's this thought process where people want to, and correct me if I'm wrong, they want to just decrease strikeouts because strikeouts are bad. But sometimes when people decrease strikeouts, they compensate and they lose power and they hit more weak batted balls and they don't really maximize their value.
It's pretty remarkable that you're able to increase your contact but you increase your better contact. I think that's a goal that should be taught. Don't just increase your contact for the hell of it. Don't just go opposite field to go opposite field. Do it with purpose. Do it to hit better contact, right?
MB: Right, so it comes back to your process on what you're trying to accomplish. You're not changing your thinking pattern. You still get the same swing thoughts. You're just changing your process by which you get there, which includes the thought process but not the thinking pattern, meaning just being a defensive hitter and trying to put the ball in play or swinging at bad pitches early in the count just so you don't strike out. The pitcher fears you more than you fear him, okay?
The pitcher fears you more than you fear him, okay…pitchers are way more high maintenance than hitters.
They just do. You know what's funny, you take it even a step deeper. The insecurity of athletes, the need to have their ego stroked all the time, pitchers are way more high maintenance than hitters. They just are. And they succeed way more. Because they get you out and you bat .180 against Max Scherzer. Why is a pitcher insecure then? You just go up, they give me the ball, I'll get the guy out. So much damage is done on those two out of 10 times that they're always thinking about that. I love it. You got to use the psychology to your advantage. It's hard. It's not easy. It's easier said than done.
CI: This past offseason, has there been any more work with this Zepp analytics stuff or is it pretty much status quo, just keep doing what you're doing? Has there any been any other conscious efforts to change?
MB: No, not with the analytics. It was very ingrained now in his thought process and plus, with my eye I've been able to see. So what we did this year was more or less get prepared for how we think that the pitchers are going to pitch and pay more attention to the actual locational type of hit, meaning outer third, inner third.
If the pitchers are going to be stupid enough to try to change the way they pitch to him because he's got a .429 batting average on pulled balls or whatever, we're already a step ahead of them. [W]e prepared together what the technique's going to be to drive the ball hard into the right-center field gap which, at Wrigley, is a smart thing to do…
If the pitchers are going to be stupid enough to try to change the way they pitch to him because he's got a .429 batting average on pulled balls or whatever, we're already a step ahead of them. So if you're going to pitch him on the outer half of the plate this year, we prepared together what the technique's going to be to drive the ball hard into the right-center field gap which, at Wrigley, is a smart thing to do because the wind blows across and trying to hit to right field is a graveyard.
And Wrigley is not a hitter-friendly park, I don't care what anybody says, man. That ball (off Cole Hamels in the no-hitter) would've left any stadium in the continental United States.
And Wrigley is not a hitter-friendly park, I don't care what anybody says, man. This 368 to the gaps, give me a break. It plays like 400 in the gaps and it plays 420 to center. Two words: Cole Hamels. You remember the no-hitter he threw that Odubel Herrera dove in to make that catch off him? That ball would've left any stadium in the continental United States.
CI: That wind, it's crazy there.
MB: It was more a process of preparing location, inner half versus outer half and to look away early in the count. Look away early in the count and adjust in, as opposed to looking in and adjusting away. You have to respect the speed of the game. Guys are throwing 95 all the time, so if you look away and try to adjust in you better have really fast hands to be able to do it that way.
Look away early in the count and adjust in, as opposed to looking in and adjusting away. Guys are throwing 95 all the time, so if you look away and try to adjust in you better have really fast hands to be able to do it that way.
Ted Williams used to be a big guess hitter. He called it anticipation but he said 13-letter words aren't his forte so he just called it guess. He says, "I don't like using college level words. I didn't go to college so I use just blue collar words." So "guess." Which was really anticipating locational type of pitch and they settle into patterns, locational patterns and sequencing patterns and they do. You can see it.
CI: On that note, do you and Kris, or do Kris and John Mallee, do they go over before maybe a series or a game, the actual pitch locations of these guys? Let's say you're facing Lance Lynn on the Cardinals and he's predominantly a fastball/sinker guy, he's going to attack most players the outside portion of the plate. Is that knowledge that Kris likes? I forgot who it was, but one player mentioned that he doesn't even want to know where the pitcher is pitching. He wants to just react. He doesn't want to put bad thoughts in his mind. Is it the opposite for Kris? Does he want to know that type of knowledge beforehand?
MB: He's still, again, he's in the trust-but-verify stage on that. He doesn't go and pore over it intensely. He'll brief himself on the scouting report that's there of the pitcher every day, what he likes to throw in certain counts and stuff like that. But he doesn't like a lot of details and he doesn't like to guess and he's not comfortable doing that yet.
Thome was talking about it on MLB last night, he would sit on the pitch. He goes, "What does 'sit on a pitch' mean?"
Adrian Gonzalez nowadays, being in his mid 30's, he sits on pitches. Big Papi was sitting on pitches. If a pitcher up there knows he's sitting on a pitch, which is what they did with Bonds, that's why he walked 225 times.
Will Kris get that respect? Maybe. And if you start to see that, then Kris will start walking a lot more. We get into the hundreds of walks a year, 150 walks a year, which'll be amazing because he'll start sitting on pitches. But he won't sit on pitches now because he doesn't trust his thinking yet. Eventually he will, as he gains experience.
We get into the hundreds of walks a year, which'll be amazing because he'll start sitting on pitches. But he won't sit on pitches now because he doesn't trust his thinking yet. Eventually he will, as he gains experience.
It's the big leagues and these pitchers, they're just not going to give into you. They're not going to say, "Here, here's my fastball. Hit it." They're just not going to do it. He does look at some reports and he'll look at video. If he's had a bad game or a good game and he'll see what he's doing good and what he's doing bad or wrong, or if there's anything different and he just needs to be a little bit more patient up there and wait for the game to come to him. You're going to have your 2-for-15 series and you're going to have your 3-for-25 before you break out again.
He's going to have five, six months straight of hitting .300 and having a hot month, two hot months, where he hits .400. Then he'll hit .340 and it'll happen.
It just happens. It just happens. Daniel Murphy didn't have a run like that. That's why he hit .340, you know? That's going to happen to Kris. He's going to have five, six months straight of hitting .300 and having a hot month, two hot months, where he hits .400. Then he'll hit .340 and it'll happen.
Be sure to come back for the conclusion of our series as we wrap up our conversation with Mike Bryant.
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Tombstone Review: Neon Maniacs (1986)
Judge Redd
Location : Ireland
Subject: Tombstone Review: Neon Maniacs (1986) Sat May 04, 2019 2:35 pm
Greetings folks
Tombstone is back from a long hiatus due to a large back log of films I have to review of varying genres and eras. This includes a film series or two that I am currently trying to finish up, and a certain superhero film I will be writing up about soon enough. However, we are not here to talk about the reviews that are coming, we are here to talk about one(of two) of director Joseph Mangine's films, specifically 1986's "Neon Maniacs" and yes its as cheesy and corny as the trailer makes it out to be.
Movie Run Time: 1hr 31mins
About this movie: What I am about to tell you about this movie will make you believe one of three things-
1.I am clearly making this whole review up, as this movie sounds very silly to actually be real.
2.Someone was VERY HIGH while making this movie.
3.This movie sounds like its gonna be so bad its good!
And you would be right two out of three there, with the third being entirely possible due to the fact it was made in the 80s. But this movie has garnered a cult following over the years since its release, despite its almost unknown status among more casual horror fans. Before we get into the plot I want to state that this film is absolutely bonkers with some of its plot. This not only grants for an interesting viewing, but also a rather cheesy film you could watch if you wanted to shut your brain off and watch a movie that just runs with its bizarre premise. The make up is done by Douglas J.White who worked on movies like Desperado and The Return of the living Dead and Allan A. Apone who worked on movies like Captain America: The Winter soldier, and Westworld, as a result you can see some pretty good make-up for the time in regards to the monsters (while technically they are the Maniacs, I will be referring to them as monsters in this review, because thats how good the make-up is). Honestly the make-up is possibly one of the best parts of this film, as the dialogue and some of the scenes come off as outright silly. There is also a lot of confusion in the movie, because as some speculate, there was a lot of movie cut out due to budget restrictions leaving the film unfinished in a matter of speaking. The original script is nowhere to be found, and those who worked on it either don't talk about it or have since passed away. This movie is pretty much every B movie Horror film of the 80s at its worst, and in a weird way thats what makes this movie kind of enjoyable.
Basic Plot: Something strange and dangerous is happening in San Francisco, as in the cities heart a group of monsters lay wait under the Golden gate bridge until nightfall. As the sun sets and the moon rise they are unleashed upon the city, on the hunt for new victims they can slaughter before sunrise. Usually they, nor their victims are ever discovered, but tonight is different. Tonight after watching her friends get slaughtered by the maniacs, Natalie escapes the slaughter but is unable to convince anyone else of the true monsters responsible for her friends death. Now as she is hunted down by the monsters, she must also deal with the hard time shes having at highschool and haunted by the memories of the slaughter. Can she survive against these neon maniacs? And just who else will fall victim to them in the process?
Kills: Honestly the Kills in this movie get creative here and there, however they are nothing extremely special compared to modern kills. We have seen a lot of these kills before, but what makes them somewhat special is that each kill is unique because it is part of the monsters identity. Hangman hangs people, Biker uses chains or his bike to kill people, and Doc rips out a mans heart. Its not really about how cool the kills are, since some of the kills are clearly half assed or just stupid looking, but a the fact that there are specialized kills and a more than just three maniacs (I counted 10, but there might be some that I am missing).
Best Kill in the Movie: I think my favorite kill in the movie, has to be when our young sidekick Paula discovers the monsters weakness and when she is cornered by one, she not only uses said weakness but turns it up to a level to make sure that sucker is dead. Honestly its so refreshing to watch somone actually capitalize on a monsters weakness.
Just for those who want to be surprised at this:
The monsters weakness for some damn reason is water. Its never elaborated on, and brings up more questions as to why they live under a bridge, but its one of those points in the movie where you have to just laugh and be like OKAY!
Worst Kill of the movie: In my personal opinion I think the worst kill of the movie goes to Ray, who runs right into a noose and is then proceeded to be hung by the neck by the monster hangman. Its just been done before and better by so many different killers that it just seemed a little lazy, especially considering that there is another victim in a van, and another one running way at time time. Its just very time consuming for a kill, that isnt even done very well. If this was an isolated area, and the victims had a worse understanding of the place then the killers, then sure go ahead and hang them high. But they don't, and the other monsters have to apparently pick up the slack that rope boy leaves by indulging in this act.
Upsides in this film: This movie can be all over the place at the time, and honestly that is where some of the fun comes into it. The first thing I want to praise though is the make-up, which despite not being fantastic for the time, is still very impressive. Add to the fact that each maniac had its own look and you have to admire just how much work was put into creating each of the maniacs looks and personas. Besides that, we have some genuinely 80s cheesy moments, such as a battle of the bands , where our male hero is participating, and horny teens unable to keep their hands off each other.
Downsides in this film: *Cracks knuckles* where do I begin? So, first off a lot of the dialogue in this movie is cringey as fuck, with only one or two bits actually being either funny or make sense. One example of that I would like to point out is when our hero and heroine are cornered by the monsters and they decide to say this to each other.
"I wont let anything happen to you. I just met you."
"I know you wont…that's why I like you."
This exchange of dialogue alone should make you cringe, but thats not even the worst of it. The movie has a lot of scenes where you literally respond with what the fuck?! An example of this being a young girl returning to her bike to find a fully grown police officer playing on it. While funny at first, it still makes you question what the fuck the purpose of this scene was. This movie can be infuriating with some of these scenes, and I think I enjoyed giving out about some of these scenes more so than actually enjoying them.
Personal Verdict: Personally I found this movie rather enjoyable, if not infuriating at times. With some of the nonsensical scenes taking you out of the movie now and again, it only added to the enjoyment when you see just how stupid some of the scenes could be. From the cheesy dialogue and scenes, to the great make-up, if this movie had a better script or a second chance, maybe more people would know the film. However, it might not be as enjoyable as it is in its current muddled state. Its a movie that is all over the place and whose characters seem to quickly forget they witnessed murders in record time. I found the movie stupid at times, but it fell under the category of this is so bad its good to me. Its a movie that I would recommend to those who enjoy a silly cheesy romp that they don't need to think too much about while watching.
This movie isn't for everyone, and I realize. I think this will only satisfy those who enjoy really cheesy 80s films, those who like movies that are so bad they are good, and those who like to admire practical make up. Its a decent enough story if it doesn't get too infuriating now and again for you, but depending on your temperament you will either love it or hate it.
Last edited by Judge Redd on Sun May 05, 2019 1:21 pm; edited 1 time in total
Tribal Raven
Location : The New World
Name: Jack
Faction: No Gods, No Masters
Subject: Re: Tombstone Review: Neon Maniacs (1986) Sun May 05, 2019 12:09 am
I read that the movie was released under the title: Evil Dead Warriors (Thank God this wasn't an Evil Dead sequel)
I watched a few scenes from the film after reading your review and man... As cheesy of a low-budget 80's film can get.
There's 80s horror movies that need to be on their 5th sequel to get as cheesy as this one, so I guess they at least got that out of the way early
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