<EMAIL_ADDRESS>AkitanKU [KU]Kanazawa University
Kakuma, Kanazawa, 920-1192 Japan

# Measurement and Control of Solenoid Stroke using Its Electrical
Characteristics

###### Abstract

In this paper, we describe the algorithm to measure the stroke of solenoid
using the electric characteristics of the solenoid, without mechanical
attachments. We also describe the experimental results of controlling the
solenoid stroke at intermediate position.

###### keywords:

Solenoid, Inductance, Stroke Measurement, Stroke Control

##  1 Introduction

Solenoid is the actuator composed of the coil and the plunger. Solenoid is
used to push or pull the object, and the stroke is controlled in two states;
ON and OFF, in usual cases. There are also some researches to control the
solenoid stroke at intermediate positions between ON and OFF positions, by
controlling the current of the coil to keep the target position of the
plunger, where plunger position is measured by external mechanical sensor[1].

From the viewpoint of electrical characteristics of the solenoid, its
inductance changes according to the plunger position, and we basically measure
the plunger position with electrical characteristics of the solenoid[2, 3].
Thus, we can measure and control the solenoid’s plunger position without
mechanical attachments. In this paper, we describe the theoretical and
experimental analysis of the solenoid’s electrical characteristics, and
measuring algorithm of the plunger’s position. We also describe the
experimental results of the plunger’s position control without mechanical
attachments.

##  2 Electrical Characteristics of Solenoid and Its Driving Circuit

Figure 1: Solenoid (Takaha’s CBS07300580)

Solenoid is the actuator composed of the coil and the plunger, as shown in
Fig.1. From the viewpoint of electrical characteristics of the solenoid, it is
a simple inductor, whose equivalent electrical circuit is described as shown
in Fig.2.

Figure 2: Equivalent circuit of solenoid Figure 3: Measured induncance and
plunger position

The plunger in the solenoid is a magnetic material, and it affects the
inductance of solenoid, and the position of the plunger also affects the
inductance of the solenoid. Figure 3 shows the measured inductance against the
position of the plunger for the solenoid of Takaha’s CBS07300580[4] at the
frequency of 100[Hz], with LCR meter (????). We can derive the position of the
plunger, $x_{P}$, as follows.

$x_{P}=-0.0843L+9.656$ (1)

Thus, we can measure the position of the plunger by measuring the inductance
of the solenoid.

Figure 4: Driving circuit of solenoid

The typical driving circuit of the solenoid is shown in Fig.4. Here we define
two status of the drive.

  * •

ON: giving a high voltage to G (gate) to turn the nMOSFET on, where the
current flows to make the plunger pulled.

  * •

OFF: giving a low voltage to G to turn the nMOSFET off, where the current
stops to make the plunger released.

The transitional phenomenon occurs between switching OFF-to-ON and ON-to-OFF.

Figure 5: Equivalent Circuit for OFF-to-ON transition

At OFF-to-ON transition, the current from the power source gradually increase
by the back electromotive force of the inductor, who speed is determined by
the time constant of $L_{s}/R_{s}$, as shown in Fig.ref:OFF-to-ON. The current
of OFF-to-ON transition, $I_{1}(t)$, the circuit equations is follows.

$L_{s}\frac{dI_{1}(t)}{dt}+R_{s}I_{1}(t)=V_{s}$

We obtain $I_{1}(t)$ as follows, with the initial current of
$I_{1}(0)=I_{1}^{S}$.

$I_{1}(t)=\frac{V_{s}}{R_{s}}-\left(\frac{V_{s}}{R_{s}}-I_{1}^{S}\right)\exp(-(R_{s}/L_{s})t)$
(2)

Figure 6: Equivalent Circuit for ON-to-OFF transition

At ON-to-OFF transition, the current from the power source stops, and the
current gradually decrease by the closed loop by the flywheel diode, as shown
in Fig.6. The current of ON-to-OFF transition, $I_{0}(t)$, the circuit
equations as follows, with assuming the flywheel diode to be a ideal diode,
whose equivalent resistance is zero.

$L_{s}\frac{dI_{0}(t)}{dt}+R_{s}I_{0}(t)=0$

We obtain $I_{0}(t)$ as follows, with the initial current of
$I_{0}(0)=I_{0}^{S}$.

$I_{0}(t)=I_{1}^{E}\exp(-(R_{s}/L_{s})t)$

##  3 Measurement Method of Solenoid Inductance: ON-to-OFF transition

Figure 7: Simulated waveforms $V_{\rm DS}$ for ON-to-OFF transition Figure 8:
Simulation circuit for ON-to-OFF transition

At ON-to-OFF transition, the voltage at D (drain) of the nMOSFET, $V_{\rm DS}$
changes from almost zero (ON reistance of nMOSFET) to $V_{s}+V_{F}$, where
$V_{D}$ is the forward voltage of the flywheel diode during the charged energy
in the inductor remains. After the charged energy consumed, the $V_{\rm DS}$
goes $V_{s}$. Figure 7 shows the calculated waveform of $V_{\rm DS}$ by
LTspice, for the circuit of Fig.8, with three variations of the inductance.
The time of $V_{\rm DS}$ goes from $V_{s}+V_{F}$ to $V_{s}$ is proportional to
the inductance, hence the position of the plunger. However, this time is
10[ms] at least. It means that we have to make the solenoid OFF at least
10[ms], which makes the plunger at the released state. The mechanical time
constant of the plunger is defined by the mechanical structure of the
solenoid, which is at the order of 10[ms]. It is impossible to keep the
plunger at ON or the intermediate position between ON and OFF with having this
“measurement” period of the ON-to-OFF transition.

##  4 Measurement Method of Solenoid Inductance: OFF-to-ON transition

At OFF-to-ON transition, the current of the nMOSFETf at S (source) or D
changes as $I_{1}(t)$ in Eq.(2). From the viewpoint of controlling the
solenoid stroke, the duty ratio of PWM (pulse width modulation) signal at
nMOSFET’s G is 0[%] to 100[%], and the small duty ratio, such as 5[%] makes no
effect to make the pull operation for the plunger. We can measure the
inductance by the transitional phenomenon at OFF-to-ON transition, with
controlling the position of the plunger by controlling PWM duty ratio.

###  4.1 Theoretical analysis of PWM drive

Figure 9: Current waveform for PWM drive

Under PWM control of the solenoid, OFF state starts at the end status of the
previous ON state, and next ON state starts at the end status of the previous
OFF state, as shown in Fig.9. Here we define $I_{1}^{S}$ and $I_{1}^{E}$ as
the initial and the final current during ON state, respectively, and
$I_{0}^{S}$ and $I_{0}^{E}$ as the initial and the final current during OFF
state, respectively. Since the PWM wave is periodical, the initial current of
each state equals the final current of previous state, which is expressed as
$I_{1}^{S}=I_{0}^{E}$ and $I_{0}^{S}=I_{1}^{E}$. We define the cycle and ON
time of PWM wave as $T$ and $T_{1}$, respectively. We can calculate the
$I_{1}^{S}$ and $I_{0}^{S}$ as follows from Eqs (2) and (2).

$I_{1}^{E}=I_{1}(T_{1})=\frac{V_{s}}{R_{s}}-\left(\frac{V_{s}}{R_{s}}-I_{1}^{S}\right)\exp(-(R_{s}/L_{s})T_{1})$

$I_{1}^{S}=I_{0}(T-T_{1})=I_{1}^{E}\exp(-(R_{s}/L_{s})(T-T_{1}))$

We finally obtain $I_{1}^{E}$ and $I_{1}^{S}$ as follows, as the function of
$R_{s}$, $L_{s}$, $V_{s}$, $T$, and $T_{1}$.

$I_{1}^{E}=\frac{1-\exp(-(R_{s}/L_{s})T_{1})}{1-\exp(-(R_{s}/L_{s})T)}\frac{V_{s}}{R_{s}}$
$I_{1}^{S}=I_{1}^{E}\exp(-(R_{s}/L_{s})(T-T1))$

We can also calculate the current at any point during ON (and OFF) state by
Eqs (2) and (2).

###  4.2 Experimental results and theorical results

Figure 10: Circuit of measurement & control experiment

We carried out the experimental measurement of $I_{1}^{E}$ and $I_{1}^{S}$, to
find the inductance, $L_{s}$ or the position of the plunger, from the current
and PWM ON time. Figure 10 shows the circuit of the experimental setup. The
current of the nMOSFET during ON state is measured as the voltage of $R_{\rm
sense}=0.2[\Omega]$, which is set small so as not to effect the nMOSFET state.
The voltage of $R_{\rm sense}$ is magnified by 101 by the non-inverting
amplifier, where $R_{i}$ and $R_{f}$ are 1[k$\Omega$] and 100[k$\Omega$],
respectively.

We used Arduino UNO [5] for measure and control. PWM signal is generated using
Timer1, and fed to nMOSFET’s gate. $I$ is measured by internal ADC (10bit)
every each PWM cycle at 0.1[ms] and 0.5[ms] after the OFF-to-ON transition, by
using Timer1’s overflow and compare match interrupt. We set $T=10[\rm ms]$
(PWM frequency of 100[Hz]), and measured the currents at $T$ of 0.1[ms] and
0.5[ms], $I_{0.1}(T_{1},L_{s})$ and $I_{0.5}(T_{1},L_{s})$, respectively,
where $T_{1}$ is ON time of PWM waveform and $L_{s}$ is the inductance of the
solenoid.

(a)

(b)

Figure 11: Measured current at 0.1[ms], $I_{0.1}$(a), and its trend against
$L$(b)

(a)

(b)

Figure 12: Measured current at 0.1[ms], $I_{0.5}$(a), and its trend against
$L$(b)

(a)  (b)

Figure 13: Measured current difference, $I_{0.5}-I_{0.1}$(a), and its trend
against $L$(b)

Figure 11, 12 and 13 shows measured and calculated $I_{0.1}(T_{1},L_{s})$,
$I_{0.5}(T_{1},L_{s})$, and $I_{0.5}(T_{1},L_{s})-I_{0.1}(T_{1},L_{s})$,
respectively, for five variations of $L_{s}$, and $T_{1}$ from 1[ms] to 9[ms]
with step of 1[ms].

Since the calculated currents by Eqs (2) and (2) assumes the ideal flywheel
diode, we can see the difference to the measured current, especially for large
$T_{1}$, where the charged energy at the inductor is large.

From Fig.11 and Fig.12, the changes of the current at 0.1[ms] and 0.5[ms] over
$L_{s}$ becomes almost flat for some $T_{1}$. This means that we can’t
determine $L_{s}$ from the measured current at each point.

From Fig.13, the current changes as $L_{s}$ changes. This means that we can
determine $L_{s}$ from the measured current at each point, with the control
value of $T_{1}$.

###  4.3 Interpolating inductance

Figure 14: Table of current $I$ for $T_{\rm ON}$ and inductance $L_{s}$

Since these phenomena are non-linear, we can’t analytically derive the
currents for given $L_{s}$ and $T_{1}$. For the practical applications, we can
generate the table of the measured current, $I=I_{0.5}-I_{0.1}$ for variations
of $L_{s}$ and $T_{1}$ in advance. Here we assume $T_{1}$ and $L_{s}$ changes
independently, and obtain the measured current for each $T_{1}$ and $L_{s}$,
$I(T_{1},L_{s})$, as showin in Fig.14.

We assume that we can set $T_{1}$ as a control parameter. The purpose of this
measurement is to calculate $L_{s}$ from the measured $I$ and the controlled
$T_{1}$ from $I(T_{1},L_{s})$.

Figure 15: Interpolation algorithm

Here, set (controlled) $T_{1}$ exists in the range of $(T_{1}^{0},T_{1}^{1})$,
where $T_{1}^{0}$ and $T_{1}^{1}$ are in the table of $I(T_{1},L_{s})$. We can
also find the pair of $I$ in the table of $I(T_{1},L_{s})$ which covers the
measured value of $I$. Thus, we can define the following four points,
$(T_{1}^{0},I_{00})$, $(T_{1}^{1},I_{10})$, $(T_{1}^{0},I_{01})$ and
$(T_{1}^{1},I_{11})$, which covers the point of $(T_{1},I)$, as shown in
Fig.15. Each point has the value of $L_{s}$ from the table of
$I(T_{1},L_{s})$, as described as $L_{00}$, $L_{10}$, $L_{01}$, and $L_{11}$,
respectively. The problem to solve is to calculate $L_{s}$ from these four
points for measured $I$ and controlled $T_{1}$. By using the bilinear
interpolation, we obtain the interpolation parameter os $t$ and $s$ and the
interpolated $I$ in Fig.15 as follows.

$\displaystyle t$ $\displaystyle=$
$\displaystyle\frac{T_{1}-T_{1}^{0}}{T_{1}^{1}-T_{1}^{0}}$ $\displaystyle
I_{x0}$ $\displaystyle=$ $\displaystyle I_{00}+t(I_{10}-I_{00})$
$\displaystyle I_{x1}$ $\displaystyle=$ $\displaystyle
I_{01}+t(I_{11}-I_{01})$ $\displaystyle L_{x0}$ $\displaystyle=$
$\displaystyle L_{00}+t(L_{10}-L_{00})$ $\displaystyle L_{x1}$
$\displaystyle=$ $\displaystyle L_{01}+t(L_{11}-L_{01})$ $\displaystyle s$
$\displaystyle=$ $\displaystyle\frac{I-I_{x0}}{I_{x1}-I_{x0}}$

Finally, we obtain the interpolated value of the inductance, $\hat{L}$ from
the measured $I$ and the controlled $T_{1}$ as follows.

$\hat{L}=L_{x0}+s(L_{x1}-L_{x0})$

We can calculate the position of the plunger, $x_{P}$, by Eq.(1) as follows.

$x_{P}=-0.0843\hat{L}++9.656$

##  5 Control of Solenoid Stroke using Electrical Characteristics

We carried out the experiment of controlling the solenoid stroke based on the
calculated position of the plunger, $x_{P}$ from the measured $I$ and
controlled $T_{1}$. We used Arduino UNO as in section sec:exp. The $x_{P}$ is
measured at loop() function from the measured $I$, and the PWM duty, next
step’s $T_{1}$, $T_{1}^{\prime}$ is is calculated as follows based on simple
PID control, with the target position of¡

$T_{1}^{\prime}=T_{1}+K_{i}(x_{P}-x_{T})$

Figure 16: Experimental result of solenoid position control

We set the PID gain of $K_{i}$ as 4.0 from some experimental trials. Figure 16
shows the measured (calculated) position of the plunger, with the target
position of the plunger, where $t$ is the number of steps of control loop. We
can find some overshoots at the target position change of around $t=1800$ and
$t=2200$. We can also find an oscillation between around $t=6200$ and
$t=7500$, where the target position is close to the “pulled” state of the
plunger. Solenoid itself has the mechanical characteristics that the plunger
is rapidly ‘pulled” at close position of “pulled” state, and it affects the
PID control gains, and makes the position control more sensitive.

##  6 Conclusion and Future Works

In this paper, we described the algorithm to measure the stroke of solenoid
using the electric characteristics of the solenoid, without mechanical
attachments. We also indicated that this measurement algorithm can be used
with conjuncction of the stroke PWM control, and demonstrated the experimental
results of controlling the solenoid stroke at intermediate position.

The precise measurement of the inductance and the positions the plunger, as
well as the current for each position of the plunger, will be our future works
to realize more accurate and stable mesurement and control of the solenoid
stroke. The precise evaluation of the calculated position of the plunger
against the measured one are also reported in our future works.

The temperature dependency of the inductance and the resistance are also the
parameters to consider, and will be discussed in our future works.

## References

  * [1] P.Mahajan, P.Kalkundri and A.Sultana Shaikh, “Precision Actuator Control for on/off Type Solenoid Valves using Pid Control Loop,” 2019 IEEE 5th International Conference for Convergence in Technology (I2CT), pp.1-4, doi: 10.1109/I2CT45611.2019.9033834, 2019.
  * [2] K.Harmer, G.W.Jewell and D.Howe, “Transient performance of a short-stroke linear solenoid actuator,” IEE Proceedings - Electric Power Applications, Vol.149, No.5, pp.379–384, doi: 10.1049/ip-epa:20020472, 2002.
  * [3] M.Ruderman and A.Gadyuchko, “Phenomenological modeling and measurement of proportional solenoid with stroke-dependent magnetic hysteresis characteristics,” 2013 IEEE International Conference on Mechatronics (ICM), pp.180-185, doi: 10.1109/ICMECH.2013.6518532, 2013.
  * [4] https://www.takaha-japan.com/product/cbs0730/
  * [5] https://arduino.cc/

nJunichi AkitaHe received B.S., M.S. and Ph.D. degrees in electronics
engineering from the University of Tokyo, Japan in 1993, 1995 and 1998
respectively. He joined the Department of Computer and Electrical Engineering,
Kanazawa University as a research associate in 1998. He moved to the
Department of Media Architecture, Future University Hakodate as an assistant
professor in 2000. He moved to the Department of Information and Systems
Engineering, Kanazawa University as an assistant professor in 2004. From 2022,
he is a professor at School of Transdisplenary Science for Innovation,
Kanazawa University. He is also interested in electronics systems including
VLSI systems in the applications of human-machine interaction and human
interface. He is a member of the Institute of Electronics, Information and
Communication Engineers of Japan, Information Processing Society of Japan, and
the Institute of Image Information and Television Engineering.


# Companion Stars of Type Ia Supernovae

Z. Han  National Astronomical Observatories / Yunnan Observatory, the Chinese
Academy of Sciences, Kunming, 650011, China<EMAIL_ADDRESS>
###### Abstract

The WD+MS channel of the single-degenerate scenario is currently favourable
for progenitors of type Ia supernovae (SNe Ia). Incorporating the results of
detailed binary evolution calculations for this channel into the latest
version of a binary population synthesis code, I obtained the distributions of
many properties of the companion stars at the moment of SN explosion. The
properties can be verified by future observations.

binaries: close — stars: evolution — supernovae: general — white dwarfs

††slugcomment: submitted to ApJ Letters

##  1 Introduction

Type Ia supernovae (SNe Ia) have been used as a calibrated candle to probe the
dynamics of the universe, leading to a significant progress in cosmology, i.e.
the determination of $\Lambda$ and $\Omega$ (Riess et al., 1998; Perlmutter et
al., 1999). They are believed to be thermonuclear explosions of carbon-oxygen
(CO) white dwarfs (WDs). However the nature of their progenitors has remained
unclear, and this still raises doubts as to the calibration which is purely
empirical and based on the nearby SN Ia sample. Based on the characteristics
of observed SNe Ia (e.g. light curves, chemical stratification), it seems most
likely that they occur when the accreting CO WDs reach the Chandrasekhar
limit, and sub-Chandrasekhar models appear not to be consistent with the
observations of SNe Ia. Chandrasehar-mass WDs can be created through the
single-degenerate scenario, where the CO WD accretes mass from a non-
degenerate companion (Nomoto, Thielemann & Yokoi, 1984; Hachisu, Kato &
Nomoto, 1999), or the double degenerate scenario, where two CO WDs with a
total mass larger than the Chandrasekhar mass coalesce (Iben & Tutukov, 1984;
Webbink & Iben, 1987)111Note, it is quite likely that the merger product
experiences core collapse rather than a thermonuclear explosion.. Recent
observations indicate that there is a wide spread of delay time between star
formation and SN Ia explosion, and this imply that there exist two populations
of progenitors, a “prompt” one with a delay time less than $\sim 0.1\,{\rm
Gyr}$ and a “tardy” one with a delay time of $\sim 3\,{\rm Gyr}$ (Mannucci,
Della Valle & Panagia, 2006).

Using the archival data prior to explosion from Hubble Space Telescope (HST)
and Chandra, Voss & Nelemans (2008) tried to search for a possible progenitor
of SN2007on (type Ia) in elliptical galaxy NGC 1404. They discovered an object
at the position of SN2007on. The X-ray luminosity of the object and the non-
detection in the optical images are fully consistent with the single-
degenerate scenario, and the the discovery therefore favours the single-
degenerate scenario. However, new Chandra X-ray observations (Roelofs et al.,
2008) and detailed astrometry of the site of SN2007on showed that there
appears to be an offset between the SN and the X-ray source, and the offset
means a small probability ($\sim 1\%$) of the X-ray source being related to
the SN. However, the X-ray source is not unconnected with the SN, as the X-ray
source has dimmed after the explosion and the source before the explosion
showed an excess of soft X-ray photons relative to the other sources in the
field. Kepler’s 1604 supernova is suggested to be of type Ia. Reynolds et al.
(2007) made a deep Chandra observation of Kepler’s supernova remnant and
concluded that Kepler’s SN is a SN Ia with circumstellar medium (CSM)
interaction. This might indicate that the progenitor is a massive (young)
star. Maoz & Mannucci (2008) searched HST pre-explosion images for NGC 1316, a
radio galaxy in the Fornax cluster and a prolific producer of SNe Ia, for
evolved intermediate-mass progenitor stars. The pre-explosion images (3 years
before explosion) of the sites of SN2006dd (a normal SN Ia) and SN2006mr
(likely a subluminous SN Ia) show no potential luminous stellar progenitors.
More effort is still needed in identifying the progenitors of SNe Ia.

Among various possible progenitor models, the WD+MS channel of the single-
degenerate scenario is the most widely accepted one, in which a CO WD accretes
mass from its main-sequence (MS) star or a slightly evolved subgiant in a
close binary system until it reaches a mass of $\sim 1.378M_{\odot}$ and
explodes as a SN Ia (Nomoto, Thielemann & Yokoi, 1984; Li & van den Heuvel,
1997; Hachisu, Kato & Nomoto, 1999; Langer et al., 2000; Han & Podsiadlowski,
2004). The companion star should survive the explosion and show distinguishing
properties, and it is therefore a promising method to test progenitor models
by identifying the surviving companion stars of SNe Ia.

Tycho Brahe’s 1572 supernova is a Galactic SN Ia. Ruiz-Lapuente et al. (2004)
found in the remnant region that Tycho G, a star similar to the Sun but with a
lower gravity, moves at more than three times the mean velocity of the stars
there. They argued that Tycho G could be the surviving companion of the
supernova222However, Fuhrmann (2005) argued that there exists a possibility of
Tycho G being a thick disk star coincidentally passing in the vicinity of the
remnant of SN 1572.. Indeed, a surviving companion would have a high space
velocity and evolve to a WD finally, and the single-degenerate scenario could
potentially explain the properties of halo WDs observed by Oppenheimer et al.
(2001), e.g. their space density and ages (Hansen, 2003; Bergeron, 2003).
Furthermore, Justham et al. (2008) argued that the ultra-cool WDs observed by
Wolf (2005) might have been formed via the single-degenerate scenario, i.e.
they might be the remnants of the non-degenerate donor stars. Note, however,
there have been no conclusive proof yet that any individual object is the
surviving companion of a SN Ia.

Langer et al. (2000) did detailed binary evolution calculations for part of
the WD+MS channel of the single-degenerate scenario, and presented the
properties, e.g. orbital velocities, luminosities, effective temperatures, of
the companion stars at the moment of SN Ia explosion for the sample WD
binaries they studied, in which the Roche lobe overflow (RLOF) starts when the
companion star is in MS. However, the distributions of the properties have not
been obtained. Canal, Méndez & Ruiz-Lapuente (2001) run a Monte Carlo scenario
code to calculate the distributions of masses, luminosities and velocities of
the companion stars of SNe Ia. However, they have not done detailed binary
evolution calculations for the production of SNe Ia, and this results in big
uncertainties (see Han & Podsiadlowski, 2004), e.g. the orbital velocities
obtained for the companion stars from the WD+MS channel are over 450 km/s,
which is far too high.

Han & Podsiadlowski (2004, hereafter HP04) carried out detailed binary
evolution calculations for the WD+MS channel for about 2300 close WD binaries,
in which RLOF starts when the companion star is in MS or in Hertzsprung gap
(i.e. slightly evolved). The study is comprehensive, and various properties of
the companion stars were obtained but not sorted for publishing. In this
Letter, I extract the properties from the data files of the calculations and
incorporate them into the latest version of the binary population synthesis
(BPS) code developed for the study of various binary-related objects (Han,
Podsiadlowski & Eggleton, 1995; Han et al., 1995; Han, 1998; Han et al., 2002,
2003), including the progenitors of SNe Ia (Han & Podsiadlowski, 2004, 2006),
and obtain the distributions of the properties.

##  2 The distributions of properties of the companion stars

In the single-degenerate scenario, the progenitor of a SN Ia is a close WD
binary system, which has most likely emerged from common envelope (CE)
evolution (Paczyński, 1976) of a giant binary system. During the CE evolution,
the envelope engulfs the core (here a CO WD) of the giant and the secondary,
and the orbital energy released in the spiral-in process (i.e. orbital decay)
is used to overcome the binding energy of the CE in order to eject it. For the
CE evolution, I have two parameters: $\alpha_{\rm CE}$ the CE ejection
efficiency, i.e. the fraction of the released orbital energy used to overcome
the binding energy, and $\alpha_{\rm th}$, which defines the fraction of the
thermal energy contributing to the binding energy of the CE. As in previous
studies, I adopted $\alpha_{\rm CE}=\alpha_{\rm th}=1.0$, which gives good
matches between theory and observations for many binary-related objects 333
The prescription adopted here for the CE evolution is different from the
$\lambda$ prescription, but appears to be more physical. See Han,
Podsiadlowski & Eggleton (1995), Dewi & Tauris (2000) and Podsiadlowski,
Rappaport & Han (2003) for details. .

To obtain the distributions of properties of companion stars at the moment of
SN explosion, I have performed a detailed Monte Carlo simulation with the
latest version of the BPS code. The code follows the evolution of binaries
with their properties being recorded at every step. If a binary system evolves
to a WD+MS system, and if the system, at the beginning of the RLOF phase, is
located in the SN Ia production regions in the plane of ($\log P^{\rm i}$,
$M_{2}^{\rm i}$) for its $M_{\rm WD}^{\rm i}$, where $P^{\rm i}$, $M_{2}^{\rm
i}$ and $M_{\rm WD}^{\rm i}$ are, respectively, the orbital period, the
secondary’s mass and the WD’s mass of the WD+MS system at the beginning of the
RLOF (see Fig. 3 of HP04), I assume that a SN Ia is resulted, and the
properties of the WD binary at the moment of SN explosion are obtained by
interpolation in the 3-dimensional grid ($M_{\rm WD}^{\rm i}$, $M_{2}^{\rm
i}$, $\log P^{\rm i}$) of the $\sim 2300$ close WD binaries calculated in
HP04.

In the simulation, I follow the evolution of 100 million sample binaries
according to grids of stellar models of metallicity $Z=0.02$ and the evolution
channels leading to SNe Ia as described in HP04. I adopted the following input
for the simulation (see Han, Podsiadlowski & Eggleton, 1995). (1) The star-
formation rate (SFR) is taken to be constant over the last 15 Gyr. (2) The
initial mass function (IMF) of Miller & Scalo (1979) is adopted. (3) The mass-
ratio distribution is taken to be constant. (4) The distribution of
separations is taken to be constant in $\log a$ for wide binaries, where $a$
is the orbital separation. (5) The orbits are assumed to be circular.

The simulation gives current-epoch-snapshot distributions of many properties
of companion stars at the moment of SN explosion, e.g. the masses, the orbital
periods, the orbital separations, the orbital velocities, the effective
temperatures, the luminosities, the surface gravities, the surface abundances,
the mass transfer rates, the mass loss rates of the optically thick stellar
winds. The simulation also shows the initial parameters of the primordial
binaries and the WD binaries that lead to SNe Ia. Figs 1\- 7 are selected
distributions that may be helpful to identify the progenitors of SNe Ia.

##  3 Discussion

Figs 1 and 2 are the distributions of the masses, the orbital velocities
444The Chandrasekhar-mass WD has an orbital velocity of $\sim 50$ to $\sim
200\,{\rm km/s}$ for a corresponding companion star’s mass of $\sim 0.6$ to
$\sim 2.0M_{\odot}$ at the moment of SN explosion., the effective temperatures
and the surface gravities of companion stars at the moment of SN explosion.
Tycho G was taken as the surviving companion star of Tycho Brahe’s 1572
supernova by Ruiz-Lapuente et al. (2004). It has a space velocity of
$136\,{\rm km/s}$, more than 3 times the mean velocity there. Its surface
gravity is $\log\,(g/{\rm cm}\,{\rm s}^{-2})=3.5\pm 0.5$, while the effective
temperature is $T_{\rm eff}=5750\pm 250{\rm K}$. The parameters are compatible
with Figs 1 and 2. As from our simulation, the recorded properties at each
step show that a primordial binary system with a primary mass $M_{\rm 1i}\sim
4-5.5M_{\odot}$, a secondary mass $M_{\rm 2i}\sim 2-3M_{\odot}$ and an orbital
period $P_{\rm i}\sim 100-250\,{\rm d}$ would evolve to a close WD binary
system with a WD mass $M^{\rm i}_{\rm WD}\sim 0.8-1.2M_{\odot}$, a secondary
mass $M^{\rm i}_{\rm 2}\sim 2-3M_{\odot}$, and an orbital period $P^{\rm
i}\sim 1-4\,{\rm d}$. The WD binary results in SN Ia explosion with companion
parameters ($T_{\rm eff}$ and $\log g$ actually) in the range of Tycho G.

However, Figs 1 and 2 are for that at the moment of SN explosion, the
distributions could be modified due to the explosion. Marietta, Burrows &
Fryxell (2000) presented several high-resolution two-dimensional numerical
simulations of the impacts of SN Ia explosion with companions. The impact make
the companion in the WD+MS channel lose a mass of 0.15-0.17$M_{\odot}$, and
receive a kick of 49 - 86${\rm km/s}$. Meng, Chen & Han (2007) adopted the
simple analytic method of Wheeler, Lecar & McKee (1975), and calculated the
impact to survey the influence of the initial parameters of the progenitor’s
systems. With detailed stellar models and realistic separations that were
obtained from binary evolution, they obtained an even lower ’stripped mass’,
0.03-0.13$M_{\odot}$, but a similar kick velocity 30-90${\rm km/s}$, which is
perpendicular to the orbital velocity. A surviving companion star therefore
has a mass lower by $\sim 0.1M_{\odot}$ and a space velocity larger by $\sim
10\%$ than that in Fig. 1.

The companion stars are out of thermal equilibrium at the moment of SN
explosion. The equilibrium radii are typically larger by $\sim 50\%$ than that
at the moment of SN explosion. Therefore the surface gravity at equilibrium
should be lower than that in Fig. 2. Podsiadlowski (2003) systematically
explored the evolution and appearance of a typical companion star that has
been stripped and heated by the supernova interaction during the post-impact
re-equilibrium phase. Such a star may be significantly overluminous or
underluminous. Fig. 2 could be a starting point for further studies of this
kind.

Fig. 3 is the distribution of orbital periods of the WD+MS systems at the
moment of SN explosion. If I assume that the companion stars co-rotate with
their orbits, I obtain their distributions of equatorial rotational velocities
(see Fig. 4). We see that the surviving companion stars are fast rotators and
their spectral lines should be broadened noticeably.

Fig. 5 shows the distribution of masses lost during optically thick stellar
wind phase. We see that a significant amount of mass is lost in the wind.
Badenes et al. (2007) found that the wind with a velocity above $200\,{\rm
km/s}$, which is believed to be reasonable, would excavate a large low-density
cavity around its progenitor. However, the fundamental properties of seven
young SN Ia remnants (Kepler, Tycho, SN 1006, 0509-67.5, 0519-69.0, N103B and
SN 1885) obtained by Badenes et al. (2007) are incompatible with such large
cavities. A lower wind velocity or the consideration of WD rotation could help
to solve the problem (Badenes et al., 2007).

Fig. 6 presents the distribution of mass transfer rates at the moment of SN
explosion. The mass transfer rates can be converted to X-ray luminosities of
the systems by $L_{\rm X}\sim\epsilon|\dot{M}|$, where $\epsilon=7\times
10^{18}{\rm erg/g}$ gives the approximate amount of energy obtained per gram
of hydrogen burnt into helium or carbon/oxygen. The luminosity of the X-ray
source close to the site of SN 2007on (4 years before the explosion) was
estimated to be $(3.3\pm 1.5)\times 10^{37}\,{\rm erg/s}$ (Voss & Nelemans,
2008), corresponding to a mass accretion rate of $\sim 10^{-7}\,M_{\odot}/{\rm
yr}$, which is consistent with Fig. 6.

QU Carinae, a cataclysmic variable (CV), is suspected to be a SN Ia
progenitor. It has a WD mass of $\sim 1.2M_{\odot}$, a once-reported orbital
period of $0.45\,{\rm d}$, and more importantly, a very high mass transfer
rate of $\sim 10^{-7}\,M_{\odot}/{\rm yr}$ (Kafka, Anderson & Honeycutt,
2008). These properties are consistent with Figs 3 and 6. However, BF Eridani,
another CV with $M_{\rm WD}\sim 1.28M_{\odot}$, $M_{2}\sim 0.52M_{\odot}$ and
$P\sim 0.27\,{\rm d}$ (Neustroev & Zharikov, 2008), appears not to be a SN Ia
progenitor.

Fig. 7 is the distribution of the surface nitrogen mass fraction of companion
stars at the moment of explosion. We see that nitrogen can be significantly
overabundant (with corresponding underabundance of carbon due to the CN-
cycle). However, the surface can be seriously polluted by the ejecta of SN
explosions.

The simulation in this Letter was made with $\alpha_{\rm CE}=\alpha_{\rm
th}=1.0$. If I adopt a lower value for $\alpha_{\rm th}$, say, 0.1, the birth
rate of SNe Ia would be higher (a factor of 1.7) and the delay time from the
star formation to SN explosion is shorter. This is because that binaries
resulted from CE ejections tend to have shorter orbital periods for a small
$\alpha_{\rm th}$ and are more likely to locate in the SN Ia production region
(see Fig.3 of HP04). The companion stars with orbital velocity $V<110\,{\rm
km/s}$ would be absent from Fig. 1, and the ones with $\log(g/{\rm cm\
s^{-2}})<3.1$ would be absent from Fig. 2. This is due to that WD binaries
with long orbital periods are absent due to a small $\alpha_{\rm th}$.

The distributions are snapshots at current epoch for a constant SFR. For a
single star burst, most of the SN explosions occur between 0.1 and 1 Gyr after
the burst (see Fig. 7 of HP04). The evolution of progenitor properties with
time can be understood via Fig. 3 of HP04. A delay time from 0.1 to 1 Gyr
corresponds to $M_{2}^{\rm i}$ of $\sim 3.2M_{\odot}$ to $\sim 1.8M_{\odot}$,
and to $M_{\rm WD}^{\rm i}$ of $\sim 1.2M_{\odot}$ to $\sim 0.67M_{\odot}$ for
the WD+MS system, respectively. As seen from Fig. 3 of HP04, the range of the
orbital periods becomes narrower from a delay time of 0.1 to 1.0 Gyr. Those WD
binaries result in SN Ia explosions via RLOF. Consequently, the range of
progenitor properties at the moment of SN Ia, e.g. the orbital velocities of
companion stars, the surface gravities, the equatorial rotational velocities,
the mass transfer rates, becomes narrower with time. The mass transfer rate
would be smaller with time as $M^{\rm i}_{2}$ becomes smaller.

I thank an anonymous referee for his/her comments which help to improve the
paper. I thank Ph. Podsiadlowski for stimulating discussions. This work was in
part supported by the Natural Science Foundation of China under Grant Nos
10433030, 10521001 and 2007CB815406.

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Figure 1: A snapshot distribution of companion stars in the plane of ($V$,
$M_{2}^{\rm SN}$) at current epoch, where $V$ is the orbital velocity and
$M_{2}^{\rm SN}$ the mass at the moment of SN explosion. The number density
decreases from inner regions to outer regions. Regions, from inside to outside
with corresponding gradational grey or color in the legend (from bottom to
top), together with the regions with higher number densities contain 50.0%,
68.3%, 95.4%, and 99.7% of all the systems, respectively.  Figure 2: Similar
to Fig. 1, but in the plane of ($\log T_{\rm eff}$, $\log g$), where $T_{\rm
eff}$ is the effective temperature of companion stars at the moment of SN
explosion, $\log g$ the surface gravity. The error bars denote the location of
Tycho G (Ruiz-Lapuente et al., 2004).  Figure 3: Similar to Fig. 1, but in the
plane of ($\log P^{\rm SN}$, $M_{2}^{\rm SN}$), where $P^{\rm SN}$ is the
orbital period at the moment of SN explosion.  Figure 4: Similar to Fig. 1,
but in the plane of ($V_{\rm rot}$, $M_{2}^{\rm SN}$), where $V_{\rm rot}$ is
the equatorial rotational velocity of companion stars at the moment of SN
explosion.  Figure 5: Similar to Fig. 1, but in the plane of ($\Delta M_{\rm
wind}$, $M_{2}^{\rm SN}$), where $\Delta M_{\rm wind}$ is the mass lost during
the optically thick stellar wind phase of the WD binaries.  Figure 6: Similar
to Fig. 1, but in the plane of ($\log(-\dot{M}_{2})$, $M_{2}^{\rm SN}$), where
$-\dot{M}_{2}$ is the mass transfer rate at the moment of SN explosion.
Figure 7: Similar to Fig. 1, but in the plane of ($X_{\rm N}$, $M_{2}^{\rm
SN}$), where $X_{\rm N}$ is the nitrogen mass fraction at the surface of
companion stars at the moment of SN explosion.


ISVHECRI 2014

11institutetext: Physics Depart., Rome University 1, Sapienza, Ple. A. Moro 2,
00185, Rome, Italy 22institutetext: INFN, Ple. A. Moro 2, 00185, Rome, Italy
33institutetext: Engin. Depart., Niccolò Cusano University, Via Don Carlo
Gnocchi 3, 00166 Rome, Italy 44institutetext: GUBKIN Uni. of Oil and Gas,
Leninsky prospekt 65, Moscow, Russia.

# The meaning of the UHECR Hot Spots

A Light Nuclei Nearby Astronomy

Daniele Fargion 1122<EMAIL_ADDRESS>Graziano Ucci 11 Pietro
Oliva 33 Pier Giorgio De Sanctis Lucentini 44

###### Abstract

In this paper we review all the up-to-date Ultra High Energy Cosmic Ray
(UHECR) events reported by AUGER, the Telescope Array (TA) and AGASA in common
coordinate maps. We also confirm our earliest (2008-2013) model, where UHECRs
mostly comprise light nuclei (namely He, Be, B), which explains the Virgo
absence and confirms M82 as the main source for the Northern TA Hot Spot. Many
more sources, such as NGC253 and several galactic sources, are possible
candidates for most of the 376 UHECR events. Several correlated maps, already
considered in recent years, are reported to show all the events, with their
statistical correlation values.

##  1 Introduction

In November 2007, AUGER Auger-Nov07  reported, within 27 events, a rare
clustering of UHECR events centered around Cen-A with a spread of $\pm
15^{\circ}$: a first Southern Hot Spot anisotropy. The later 2011 data (69
UHECR events, as well as the additional train of dozens of twin events at 20
EeV Auger-Nov11  Fargion2011nima ) confirmed such a UHECR Hot Spot, thus
strengthening the nuclei-like (not the proton-like) UHECR composition
supposition Fargion2008 . Since 2011, neither the Virgo Cluster nor any Super-
Galactic anisotropy (as had been first considered to be detectable assuming
UHECR proton composition) were in fact detected by AUGER. On the other hand
the Telescope Array (TA) found, in recent months, a comparable remarkable
anisotropy (a Northern Hot Spot, also spread over $\pm 15^{\circ}$) pointing
to an uncorrelated and unexpected region of the sky. Therefore, up to now we
only took care of two Hot Spots in the Northern and Southern Sky. Moreover and
once again unnoticed, the Virgo cluster - better viewed from TA skies - did
not manifest itself at all, even in the TA data, where one would expect it to
show if, as TA claims, UHECRs are protons. To make this race in discovering
UHECR Astronomy more contradictory, we must remember that since 2007 AUGER
favored an iron composition, while TA always supported protons. Eventually,
the most recent TA events ($72+15$ events) and the deeper and final AUGER
records (231 events in the 2004-2014 period) Auger-Nov14  offer a unique
opportunity to combine their maps and test eventual sky correlations though
AUGER disclaimed any possible relevant connection with the Cen-A Hot Spot.

The AUGER and TA maps are often in non-comparable map projections. Here we
combined both of those published (for TA in-the-press) events in a known and
useful coordinate system. We shall discuss and weight the clustering along
these maps overlapping on different ones. It should be remembered that, since
very early 2008 Fargion2008  (see also Fargion2011nima ), we proposed that a
possible solution to the AUGER puzzle (anisotropy size and Virgo absence)
could be if UHECRs were mostly the lightest nuclei, for example helium. Such a
composition would indeed explain the spread angle of UHECR by their random
bending along galactic fields ruling out a unique Hot Spot due to our nearest
AGN: Cen-A. Moreover, He-like nuclei are fragile through photo-nuclear
dissociation by the Cosmic Microwave Background: they cannot cross large GZK
distances as can protons ($50-80$ Mpc), but they can fill a few smaller
Universe size ($3-4$ Mpc). Because of this Cen-A could shine, Virgo could not.
The lightest UHECR nuclei may also explain, as we argued then and now, the
remarkable earliest AUGER and recent TA results, the Virgo absence, by the
lightest fragility and opacity: in the same model the TA Hot Spot in the
Northern Sky must originate from a very nearby source. The Ursa Major Cluster
or Virgo are too far, but a closer source such as the M82 star-burst galaxy
could survive the distance.

Figure 1: An early (2011) UHECR AUGER data above GZK, cut by 69 Auger events
and 20 EeV, clustering on Infrared background: note the Virgo absence and the
Cen-A clustering Fargion2010 . Figure 2: Hammer Projection in Galactic
coordinates for the latest 231 AUGER UHECR (blue) with additional 72+15=87 TA
(72 blue and 15 green) and 58 AGASA (cyan) records, in a total of 376 events.
A few potential sources are labeled.

The so-called TA Hot Spot (about a dozen events) is not centered on M82, but
is coherently bent by ($15-20^{\circ}$) in nearby Northern Galactic fields
(see fig.2-5 and fig.14-15). However, we recognize in the same bending tail a
much nearer, narrower and very recent (this year) a 5 event clustering,
confirming such a probable coherent bending of UHECR light nuclei from M82.
Such a quintuplet cluster within 100 square degrees has a chance probability
of $<10^{-3}$ to occur. Moreover the oldest UHECR AGASA record in the Northern
sky (58 events) showed a unique triplet almost overlapping, making the chance
probability to find such a clustering for 8 events within 150-200 square
degrees, as low as $(1\div 4)\cdot 10^{-4}$. We will reconfirm that Cen-A, M82
and a few galactic sources like Vela, Cygnus X3 and SS433, could eject light
or heavier UHECR nuclei, possibly radioactive ones, bent by large local
magnetic fields. We were inspired by early preliminary UHECR correlations with
TeV anisotropy maps discovered in the last decade by Milagro, ARGO and now
more recently by HAWK and ICECUBE. We again claim that such TeV-UHECR
correlations might be due to UHECR fragment nuclei by radioactive decay in
flight and/or by UHECR lightest nuclei secondaries photo-dissociation in their
travels. We note a new interesting clustering along the South Galactic Pole
pointing to the main nearby star-burst galaxy NGC 253, an object similar to
M82, once again within 3 Mpc distance.

###  1.1 Cen-A, M82 and NGC 253 as the main extragalactic UHECR sources

Figure 3: Mollweide Projection in Celestial coordinates for the latest 231
AUGER UHECR (blue) with additional 72+15=87 latest TA (72 red and 15 green)
records. A few potential sources are labeled.

UHECRs are clustering both within the Southern (AUGER) and Northern (TA) skies
in wide $\pm 15^{\circ}$ Hot Spots. The nearest Galactic Cluster, Virgo,
within the expected GZK opacity distance for protons (related to the
apparently observed GZK cut off observed spectra by Hires, AUGER and TA) is
absent. This absence is remarkable in particular in recent TA data as well as
in the latest 231 AUGER events. The Virgo clustering absence does not fit with
UHECRs as nucleons. The same $\pm 15^{\circ}$ Hot Spot clustering cannot fit
with an extra-galactic heavy nucleus composition (Fe, Ni) because of their
much larger charge and wider deflection angle (above $90^{\circ}$). However,
the lightest UHECR nuclei, namely or mostly He, are fragile enough to be
absorbed and soon hidden by photo-dissociation on cosmic radiation on their 20
Mpc journey from Virgo, thus explaining their absence. On the contrary, AUGER
clustering around the nearest active AGN, Cen-A (3.5 Mpc), may be caused by
random _incoherent_ bending of light He nuclei along the galactic magnetic
fields; the absence of Virgo in the TA data is explained again by the UHECR He
opacity. The TA Hot Spot clustering could be ejected by the star-burst M82
(3.5 Mpc) as the main source, while UHECRs are bent and spread by a _coherent_
magnetic field either galactic at the North Pole and/or extra-galactic. We
want to emphasize here the clustering of 5 UHECR TA events nearer to M82,
since it might be a first UHECR signal around this main source. This very
narrow spot (5 events) almost overlaps an older one: a triplet observed by
AGASA in 1990-2000. The binomial probability to find 4+1 such events inside a
narrow area of $10^{2}$ square degrees, amongst 87 TA signals, is $<8.2\cdot
10^{-4}$, even ignoring the AGASA triplet. Also considering the additional
$58$ AGASA events and a triplet clustering within $150^{\circ}$, the
probability shrinks to $10^{-4}$. These quintuplet signals are additional to
the remaining (more deflected) He-like nuclei found in the wider TA hot spot
(21 events among 87 in nearly $2000$ square degree sky), whose chance
probability to occur is as low as $<2\cdot 10^{-4}$ but their clustering is
more diluted and far from M82. Additional signals might be gamma secondaries
of these UHECR He photo-dissociation in flight (or radioactive decay in flight
as for the He6 isotope or Be7 or the more abundant and deflected Al26) that
might also point and trace, by a boosted Lorentz factor, part of these gamma
anisotropies on TeV maps discovered by Milagro, ARGO, HAWK and ICECUBE. A few
UHECR sources might also be galactic as the very recent multiplet (8 events)
along Vela also shows Cygnus X3 clustering raised as a peculiar narrow
multiplet as well as a much narrower clustering event (around SS433 or Aq1)
and possible spread sources along the Magellanic stream regions (LMC and SMC,
or NGC 253, a second near - 3.5 Mpc - star-burst source and/or Fornax Dwarf
Galaxy source), see Figures 2-5, 12 and 14-15.

Figure 4: Hammer Projection in Celestial coordinate for the latest 231 AUGER
UHECR (blue) with additional 72+15=87 latest TA (72 red and 15 green) records.
A few potential sources are labeled as well as the galactic plane.

###  1.2 Bending for He UHECR and fragments at 20 EeV along Cen-A

Let us remember why we should choose a He-like composition: the old 2011 UHECR
multiplet clustering foreseen in 2009 Fargion2011nima  and observed in 2011
Auger-Nov11  (and forgotten in most reports) by AUGER UHECR at 20 EeV energy
contains just three apparently isolated trains of events which point to
unknown sources (see old 69 events on IR map, see fig.1). However, the
crowding of the two train multiplet tail fixed inside a very narrow disk area
focused about the Cen-A UHECR source is remarkable as it had already been
foreseen Fargion2011c . If UHECRs are composed of protons (as some AUGER and
TA authors believe), they will not naturally explain such a tail structure
because these events do not cluster more than a few degrees, unlike the
observed UHECRs and the associated multiplet. He-like UHECRs fit the AUGER
composition traces as well as the HIRES and TA ones. The He secondaries split
in half (or in fourths) energy fragments along the Cen-A tail, the presence of
was been recently foreseen Fargion2011c . Indeed, the dotted circle around
Cen-A containing two (of three) multiplets in a radius as small as
$7.5^{\circ}$ extends in an area that is as small as $200$ square degrees,
below or near 1% of the AUGER observation sky. The probability that two of
these three sources fall inside this foreseen small area is by the binomial
distribution $\simeq 3\cdot 10^{-4}$. Moreover the same twin tail of the
events is aligned almost exactly $\pm 0.1$ rad along the UHECR train of events
toward Cen-A. Therefore the UHECR multiplet alignment at 20 EeV has a
probability as low as $P(3,2)\simeq 3\cdot 10^{-5}$ of following an _a priori_
foreseen signature (Fargion2011nima , Fargion2011c  and Fargion2010 ).

The incoherent random angle bending along the galactic plane and arms,
$\delta_{rm}$, while crossing along the whole Galactic disk ($L\simeq 20$ kpc)
in different, alternating, spiral arm fields and within a characteristic
coherent length $l_{c}\simeq 2$ kpc for He nuclei is

$\delta_{rm-He}\simeq
16^{\circ}\frac{Z}{Z_{\textrm{He}^{2}}}\cdot\left(\frac{6\cdot
10^{19}\,\textrm{eV}}{E_{CR}}\right)\left(\frac{B}{3\,\mu\textrm{G}}\right)\sqrt{\frac{L}{20\,\textrm{kpc}}}\sqrt{\frac{l_{c}}{2\,\textrm{kpc}}}$

The heavier (but still light) nuclei bounded from Virgo might also be Li and
Be:

$\delta_{rm-
Be}\simeq{32^{\circ}}\left(\frac{Z}{Z_{\textrm{Be}^{4}}}\right)\left(\frac{6\cdot
10^{19}\,\textrm{eV}}{E_{CR}}\right)\left(\frac{B}{3\,\mu\textrm{G}}\right)\sqrt{\frac{L}{20\,\textrm{kpc}}}\sqrt{\frac{l_{c}}{2\,\textrm{kpc}}}$

Figure 5: Mollweide Projection in Galactic coordinates for the latest 231
AUGER UHECR (blue) with additional 72+15=87 latest TA (72 red and 15 green)
records. A few potential sources are labeled. Figure 6: Mollweide Projection
in Celestial coordinates of all oldest and latest UHECR events from AGASA,
AUGER and TA with several candidate sources labeled for a total of 376 UHECR
events, over the Fermi map of MeV-GeV energies. There are clear signals around
Vela and Cygnus and other galactic sources, as well as around Cen-A, M82 and
Magellanic Clouds sources.

It should be noted that the present anisotropy above the GZK energy of
$5.5\cdot 10^{19}$ eV (if extra-galactic) Greisen:1966jv  might leave a tail
of signals: indeed the photo disruption of He into deuterium, tritium, He3 and
protons (and unstable neutrons), arising as clustered events at a half or a
quarter (for the last most stable proton fragment) of the energy: _protons
having a quarter of the energy but a half of the charge of the He parent may
form a tail smeared around Cen-A at a twice larger angle_ (Fargion2011nima ,
Fargion2011c  and Fargion2010 ). We suggested looking for correlated tails of
events, possibly in strings at relatively low energy $\sim(1.5\div 3)\cdot
10^{19}$ eV along the Cen-A train of events. It should be noted that deuterium
fragments have one half of the energy and mass of helium: _therefore D and He
spot are bent in the same way and overlap into UHECR circle clusters_
Fargion2011c . Deuterium is even more bounded in a very local Universe because
of its fragility (explaining the absence of Virgo). In conclusion, He like
UHECRs may be bent by a characteristic angle as large as $\delta_{rm-He}\simeq
16^{\circ}$; its expected lower energy deuterium or proton fragments at half
energy ($30-25$ EeV) are also deflected accordingly at $\delta_{rm-p}\simeq
16^{\circ}$; the last traces of protons at a quarter of the UHECR energy,
around 20 EeV energy, will be bent and spread within $\delta_{rm-p}\simeq
32^{\circ}$, exactly within the observed Cen-A UHECR multiplet Auger-Nov11 .

##  2 TeV Gamma Rays and UHECRs

In recent updated UHECR AUGER-TA maps (fig.2, 3, 4, 5) we have noted the first
hint of a galactic source arising as a UHECR triplet Fargion2010 . The hint of
the Al26 gamma map traced by Comptel somehow overlapping with UHECR events at
1-3 MeV, favors a role of UHECR radioactive elements (Al26). The most prompt
radioactive nuclei are Ni56, Ni57, Co56 and Co60, produced by Supernova (SN)
and possibly by their collimated GRB micro-jet components, ejecta in our own
galaxy. Similar radioactive traces may arise by UHECR scattering on dense gas
clouds. Indeed in all SN Ia models, the decay chain Ni${}^{56}\rightarrow$
Co${}^{56}\rightarrow$ Fe56 provides the primary source of energy that powers
the supernova optical display days and even weeks following the explosion.
Ni56 decays by electron capture and the daughter Co56 emits gamma rays by the
nuclear de-excitation process; the two characteristic gamma lines are at
$E_{\gamma}=158$ keV and $E_{\gamma}=812$ keV respectively.

Figure 7: All oldest and latest UHECR events from AGASA, AUGER and TA, in
Galactic coordinates (Hammer Projection) with several candidate sources with
label for a total 376 UHECR events; the map is overlapped on the Magellanic
Stream in the nearby galactic volume. Figure 8: All oldest and latest UHECR
events from AGASA, AUGER, TA, in galactic Malloweide coordinate with several
candidate sources with label for a total 376 UHECR events, overlap on the
galactic radiation at 408 MHz: it is remarkable that most of the events are
located where there is synchrotron radio emission, possibly reinforcing a
large galactic UHECR origin or a key role of UHECR shining into 408 MHz radio
sky Figure 9: All oldest and latest UHECR events by AGASA, AUGER, TA, in
galactic Hammer coordinate with several candidate sources with label. We
included 390 events = 231 AUGER UHECR, 72+15=87 TA, 58 AGASA and 14 (11
Haverah Park, 1 Yakutsk, 1 Volcano Ranch, 1 Fly’s Eye - represented with black
dots) over the gamma TeV background (2 TeV on the North, 20 TeV on the South),
signals found in the Northern sky by ARGO in Tibet and in the Southern by
ICECUBE at the south pole. Note that the ARGO detector is recording both gamma
and Cosmic Ray at once, keeping partial memory of a small galactic plane
anisotropy toward Cygnus X3.

Their half lifetimes are spread from $35.6$ hours for Ni57 to $6.07$ days for
Ni56. However, there are also more unstable radioactive rates, as happens for
Ni55 nuclei whose half life is just $0.212$s or for Ni67, $21$s. Therefore we
may have an apparent UHECR, boosted by a factor
$\Gamma_{\textrm{Ni}^{56}}\simeq 10^{9}$, lifetime spread from $2.12\cdot
10^{8}$ s or $6.7$ years (for Ni55) up to nearly $670$ years (for Ni67), or
even $4$ million years for Ni57. EeV and PeV radioactive UHECRs or their
fragment may also play a role in gamma and neutrino emission (see UHECR events
as in fig.5, 6, 7 with different Fermi, IR, radio maps, fig.8-9 for gamma TeV-
UHECR correlation and in particular see fig.8, 9, 15 in the TeV gamma
background). This consequent wide range of lifetimes guarantees a long life
activity on UHECR radioactive traces. The arrival tracks of these UHECR
radioactive heavy nuclei may be widely bent by galactic magnetic fields as
shown below. Co${}_{m}^{60}$ whose half life is $10.1$ min and whose decay
gamma line is at $59$ keV is among the excited nuclei to mention for the
UHECR-TeV connection. For a boosted nominal Lorentz factor
$\Gamma_{\textrm{Co}^{60}}=10^{9}$, we obtain $E_{\gamma}\simeq 59$ TeV; note
that a gamma air-shower exhibits a smaller secondary muon abundance with
respect to the equivalent hadronic abundance; therefore a gamma simulates
($10\%$) a hadronic shower ($E_{gamma-hadron}\simeq 6$ TeV) corresponding
closely to the observed ICECUBE-ARGO anisotropy ARGO . The decay boosted
lifetime is $19000$ years, corresponding to 6 kpc distance. Therefore
Co${}_{m}^{60}$ energy decay traces, lifetime and spectra fit well within the
present UHECR-TeV connection for nearby galactic sources such as Vela and -
probably - the Crab. Other radioactive scattering traces, usually at lower
energy may also shine at hundreds or tens of TeV or below by Inverse Compton
and synchrotron radiation. Therefore their UHECR bent parental nuclei may also
shine in TeV Cosmic Ray signals. Electrons and neutrinos are also born in
$\beta$-decay processes providing a new diffused gamma and PeV neutrino
source. Also light nuclei such as He6 might decay in flight playing a
radioactive UHECR-TeV role.

Figure 10: Same as the above Fig. 9. Note that Hawk, like older Milagro
detector, is recording mostly Cosmic Ray (not gamma); therefore they do not
see (clearly like ARGO, figure above) the galactic anisotropy toward Cygnus
X3.

##  3  UHECR galactic bending for Ni57

Cosmic Rays are blurred by magnetic fields. UHECRs also suffer from Lorentz
force deviations. This smearing could be a source of UHECR features, mostly
along the Cen-A direction. There are at least three mechanisms for magnetic
deflection along the galactic plane, giving rise to a sort of galactic
spectroscopy of UHECRs Fargion2008 . Magnetic bending by extra-galactic fields
is in general negligible in comparison with the galactic field. Late nearby
(almost local) bending by a near coherent galactic arm field, random bending
by turbulence and random deflection along the whole plane inside different
arms are:

  1. 1.

The coherent Lorentz bending angle, $\delta_{Coh}$, of a proton UHECR (or
nucleus) (above the GZK energy) within a galactic magnetic field in a final
nearby coherent length of $l_{c}=1$ kpc is

$\delta_{Coh-p}\simeq{2.3^{\circ}}\cdot\frac{Z}{Z_{H}}\left(\frac{6\cdot
10^{19}\,\textrm{eV}}{E_{CR}}\right)\left(\frac{B}{3\,\mu\textrm{G}}\right)\left(\frac{l_{c}}{\textrm{kpc}}\right).$

  2. 2.

Random bending by random turbulent magnetic fields, whose coherent sizes (tens
of parsecs) are short and whose final deflection angle is smaller than others,
are ignored here.

  3. 3.

The ordered multiple UHECR deflection along the galactic plane across and by
alternate arm magnetic field directions whose final random deflection angle is
remarkable and discussed below. The bending angle value is quite different for
a heavy nucleus such as a UHECR from Vela whose distance is only $0.29$ kpc:

$\delta_{Coh-\textrm{Ni}}\simeq
18.7^{\circ}\cdot\frac{Z}{Z_{\textrm{Ni}^{28}}}\left(\frac{6\cdot
10^{19}\,\textrm{eV}}{E_{CR}}\right)\left(\frac{B}{3\,\mu\textrm{G}}\right)\left(\frac{l_{c}}{0.29\,\textrm{kpc}}\right)$

Note that this spread can explain the nearby Vela TeV anisotropy area (because
of the in-flight radioactive emission) around its correlated UHECR triplet.
There is a further extreme possibility: a Crab-like pulsar at a few kpc is
feeding the TeV anisotropy, as shown by overlap clustering of UHECR events,
enclosed in a black oval dashed perimeter in Figs. 14 and 15. For Crab
distances the galactic bending is:

$\delta_{Coh-\textrm{Ni}}^{\prime}\simeq
129^{\circ}\cdot\frac{Z}{Z_{\textrm{Ni}^{28}}}\left(\frac{6\cdot
10^{19}\,\textrm{eV}}{E_{CR}}\right)\left(\frac{B}{3\,\mu\textrm{G}}\right)\left(\frac{l_{c}}{2\,\textrm{kpc}}\right)$

Such a spread is, again, able to explain the localized TeV anisotropy produced
in the Crab (2 kpc), apparently extending around an area near Orion, where the
spread UHECR events also seem to be clustered. Such heavy iron-like (Ni, Co)
UHECRs are mostly bounded inside a Galaxy, as well as in a Virgo cluster
because of the big charge and large angle bending, possibly explaining the
absence of UHECRs in that direction. The possible galactic component of UHECR
is suggested by the correlated dark Hydrogen and dust map with the UHECR
distribution as well as radio 408 MHz emission: see Figures 8-11.

Figure 11: All oldest and latest UHECR events by AGASA, AUGER, TA, in galactic
Hammer coordinates with several candidate sources with label for a total of
376 UHECR events, superposed to the Planck map of infrared due to dust. Again
there is a remarkable signal in the absence of dust where there are also none
or few UHECR events. Figure 12: As above, in Mollweide Projection, Galactic
Coordinate map for 231 AUGER UHECR, 72+15=87 TA, 58 AGASA and 14 (11 Haverah
Park, 1 Yakutsk, 1 Volcano Ranch, 1 Fly’s Eye - represented with black dots)
additional records Nagano  Ave . Few potential sources are labeled. Figure 13:
All oldest UHECR by AGASA, AUGER, TA, in galactic Mollweide coordinate with
several candidate sources with label: blue AUGER, red 72 events by TA, green
last 15 by TA, 58 old AGASA cyan events for a total of 376 UHECR events. Note
the crowding of triplet around the M82 source, the multiplet around Cygnus X3,
M82, ss433, NGC253. The possible correlation between UHECR and ICECUBE UHE
neutrino is still questionable. We note anyway a doublet near Vela and other
marginal correlation discussed elsewhere. Figure 14: All UHECR events
superimposed to the polarized emission in Planck data by Milky Way. Note the
oval contour that defines possible UHECR clustering along candidate source.
Photo Credit: ESA. We added to the 376 events 14 events by Haverah Park, Fly’s
Eye, Yakutsk. Other events by HiRes has not been included. The map is in
galactic Hammer coordinates.

##  4 Conclusions

It is worth remembering that in an (unexpected) future where UHECRs are more
and more homogenous and uncorrelated with nearby GZK sources they will require
a far cosmic UHECR origin (as has been the case for GRB). In this (still not
actual) frame the most reasonable candidates for UHECR are UHE (ZeV) neutrinos
(considered nearly 20 years ago) from far away cosmic source edges (AGN, GRBs
jets), evading the GZK cutoff; they collide with relic neutrinos (with mass)
clustered around our Galaxy’s halo. These scatterings lead to the Z resonance
and its decay to nucleon secondaries observed as UHECRs Fargion1997 . A relic
neutrino mass of 0.4 eV may be ideal for such a resonance, even if a 0.2-0.1
eV neutrino mass may still be (better) compatible with Planck limits and
comparable with atmospheric mass splitting Far . A fourth (now in fashion, but
still speculative) eV sterile neutrino, being thermalized in the big bang and
better clustered, fits better the Z-showering solution. The associated tau
neutrino component (either by Z decay or GZK cut off) and its possible (yet
unobserved) double bang Learned , in ICECUBE or any consequent PeV-EeV Tau
airshowers in TA and AUGER maybe the road map to test any UHECR and the UHE
neutrino astronomy connections (see FarTau , Fargion006 , Fargion1999 ,
Auger-01 , Feng02 , Auger07 , Auger08 ).

Figure 15: As in fig.14, in celestial coordinates (Mollweide), over TeVs gamma
anisotropy by Hawk and IceCube detectors. Note in particular the possible
asymmetric clustering on UHECR nearby Virgo as well as other oval contour for
additional candidates. We added to the 376 events 14 events by Haverah Park,
Fly’s Eye, Yakutsk. Other events by HiRes have not been included.

In conclusion, the two main clusterings in the NORTHERN (HOT SPOT by TA) and
in the SOUTHERN (HOT SPOT by AUGER) are too wide (15-20 degree, as seen in
fig.14, 15) to be due to protons (whose bending extend just a few degree) as
proposed by TA. Such Hot Spots are at the same time too narrow to be produced
by cosmic UHECR heavy (Fe, Ni) nuclei (whose bending may exceed 80 degrees),
as proposed by AUGER. Light or the lightest nuclei may be the best compromise
as the natural extragalactic UHECR carrier (Fargion2011nima , Fargion2008 ,
Fargion2011c , Fargion2010 , Fargion09a ). They fit or coexist with AUGER and
TA composition results. Also a few, very nearby galactic UHECR heavy-light
nuclei may spread over a few tens of degree clustering spots.

We have tried here to present updated maps to correlate these first few
clusterings with their source, offering a name or a preliminary identity. We
combined all known UHECR archives (AUGER-TA-AGASA and a few more UHECR
detections) in best known usable coordinates (see fig. 2-5, 11). We overlap
UHECR on the Fermi gamma sky, on Radio or IR maps, (see fig. 6-10) as well as
with recent Planck magnetic maps and ARGO-ICECUBE TeV maps (see fig 14-15)
tracking the oval clustering mask areas. Analogous recent attempts to
correlate UHECR within any wider (canonical) GZK volumes (with AGN, BL Lac
sources) failed Auger-Nov14 .

Therefore the best clustered source event is near Cen-A, in the SOUTHERN HOT
SPOT; but also M82 might feed the observed TA clustering by light nuclei whose
bending shines the NORTHERN HOT SPOT Fargion2014 . The incoherent random
bending in Cen-A, may set the source in the main clustering center; because of
the horizontal spiral arms fields the spread occurs in a vertical (orthogonal
to the galactic plane) direction. Otherwise a coherent bending in the M82 case
may lead the source at the edge of the clustering Hot Spot; this occurs
because the unique magnetic field coherently bends positive charges in the
same asymmetric way by Lorentz forces. The same coherent asymmetric bending
could be responsable for the Crab location at the oval edge, Fornax and NGC253
clustering, the Vela asymmetric position respect the nearby 8 events (see
fig.14-15). The lightest nuclei provide at the moment a natural bending angle
(and a safe cut off for UHECR) from Virgo, whose distance is too far and whose
central disk sky is nearly empty (see fig 15, in celestial coordinates).
However, as in fig.15, let us note a possible remarkable weak asymmetric
clustering linking bent UHECR events to Virgo in a nearby area (see fig.15).
The probability that such a clustering of 13 events in 159 takes place in the
Northern sky in a thousand square degree oval is less than $7\cdot 10^{-3}$.
This area is coincident with the C anisotropy area found by ARGO (fig.15).

The probability to observe 8 events within the nearby Vela area (fig.14) is
only $2.5\cdot 10^{-2}$; however, the corresponding clustering probability
around the thin Crab oval area of 11 events is near $10^{-4}$ (fig. 15). The
probability to find 7 events around Cygnus X3 is $3.1\cdot 10^{-3}$; note that
two additional HIRES events are in this Cygnus area (but their exact
coordinates have not been published) leading to a remarkable correlation, as
well as the ARGO anisotropy around that area. The probability to find in a
very narrow oval area four UHECR (two of them being the most energetic ones of
TA and AUGER), pointing to SS433 (or AqX1) is about $6.7\cdot 10^{-3}$, see
Fargion2014 , Fargion13 . The eventual clustering around the Small and Large
Magellanic Clouds (SMC.LMC) is still a weak but interesting hint being as rare
as $3.5\cdot 10^{-2}$.

In conclusion the two nearest AGNs, Cen-A and M82, may explain the main strong
statistical presence of two Hot Spots Fargion2014 . The probability for the
by-chance event for Cen-A (wide dashed Hot Spot) is around ($1.5\cdot
10^{-5}$), the probability for its inner smaller clustering is about $5.4\cdot
10^{-4}$, (fig. 14-15). We remember also the tens EeV clustering along the
same oval area (fig. 1). The probability to have a Northern Hot Spot (narrow
area around M82) with 8 events is $2.3\cdot 10^{-3}$ while the probability for
the whole wide Northern Hot Spot (dashed lines in fig.14-15) is $1.3\cdot
10^{-4}$ Fargion2014 , FarO . The lightest UHECR nuclei (He, Li, Be, B) may be
the main natural carriers. Their fragments ($\alpha$, $\gamma$), by their
decay, as being radioactive (or by photo dissociation in flight via infra-red
radiations) may be the cause of the correlated TeV anisotropy. A few heavier
(Ni, Co) UHECR nuclei by nearby galactic sources as Vela, Cygnus and Crab,
Large Magellanic and Small Magellanic Clouds may also play a role.

Additional samples of UHECR events (as well as multiplets at tens EeV
energies), or more precise TeV anisotropy maps, might confirm (or reject) our
present tentative model based on the lightest nuclei partially coherent or
randomly deflected and mostly originating in a nearby Universe.

Indeed, for instance, the very recent results by PAO with more data PAO  is
correlated in most UHECR events composition (see their fig.3) with light or
lightest nuclei (and not with p, Fe ones); moreover above 8 EeV energy AUGER
discovered a remarkable dipolar anisotropy (in the wider Southern Hot Spot) at
4 sigma (see their Fig.6): this UHECR spot encompasses or well correlates with
the higher energy one in our tagged area (see Fig 14), along Cen A, as we
expected, within a nearby Universe.

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