# Local and non-local two-electron tunneling processes in a Cooper pair
splitter

Antti Ranni<EMAIL_ADDRESS>NanoLund and Solid State Physics, Lund
University, Box 118, 22100 Lund, Sweden  Elsa T. Mannila  Pico group, QTF
Centre of Excellence, Department of Applied Physics, Aalto University School
of Science, P.O. Box 13500, 00076 Aalto, Finland  Axel Eriksson  NanoLund and
Solid State Physics, Lund University, Box 118, 22100 Lund, Sweden  Dmitry S.
Golubev  Jukka P. Pekola  Pico group, QTF Centre of Excellence, Department of
Applied Physics, Aalto University School of Science, P.O. Box 13500, 00076
Aalto, Finland  Ville F. Maisi<EMAIL_ADDRESS>NanoLund and Solid
State Physics, Lund University, Box 118, 22100 Lund, Sweden

###### Abstract

We measure the tunneling rates and coupling coefficients for local Andreev,
non-local Andreev and elastic cotunneling processes. The non-local Andreev
process, giving rise to Cooper pair splitting, exhibits the same coupling
coefficient as the elastic co-tunneling whereas the local Andreev process is
more than two orders of magnitude stronger than the corresponding non-local
one. Theory estimates describe the findings and explain the large difference
in the non-local and local coupling arising from competition between electron
diffusion in the superconductor and tunnel junction transparency.

Superconductors give rise to electronic transport via two-electron processes
as Cooper pairs cross for example tunnel junctions Tinkham (2004). The two-
electron transport enables several functionalities used extensively nowadays
in quantum technology to build for example superconducting qubits Makhlin  _et
al._ (1999); Nakamura  _et al._ (1999); Wallraff  _et al._ (2004); Andersson
_et al._ (2019); Arute  _et al._ (2019), Majorana fermions Mourik  _et al._
(2012); Albrecht  _et al._ (2016) and the Cooper pair splitters Recher  _et
al._ (2001); Lesovik  _et al._ (2001); Beckmann  _et al._ (2004); Russo  _et
al._ (2005); Yeyati  _et al._ (2007); Hofstetter  _et al._ (2009); Cadden-
Zimansky  _et al._ (2009); Herrmann  _et al._ (2010) that are in focus in this
study. The two electrons of a Cooper pair, however, yield typically several
alternative transport processes that may happen. Understanding the coupling
coefficients for the different processes is crucial as the coefficients depend
on each other Falci  _et al._ (2001). The coefficients contain information
about the geometry and materials involved in the transport. A common approach
in the experiments is to study the energy dependence of the dominant transport
process Eiles  _et al._ (1993); Greibe  _et al._ (2011); Maisi  _et al._
(2011); Russo  _et al._ (2005); Cadden-Zimansky  _et al._ (2009); Hofstetter
_et al._ (2011); Tan  _et al._ (2015, 2021). The comparison between the
coupling coefficients of different processes has evaded measurements since it
is often experimentally difficult to distinguish them from each other. In this
letter, we use charge readout with two detectors to identify each tunneling
event in a Cooper pair splitter Ranni  _et al._ (2021) and compare the
strength of three two-electron tunneling processes. The Cooper pair splitter
is an ideal device for this purpose as both local Andreev Andreev (1964);
Blonder  _et al._ (1982), non-local Andreev Byers and Flatté (1995); Deutscher
and Feinberg (2000) and elastic cotunneling Averin and Nazarov (1990) transfer
electrons across the two junctions located in the near vicinity of each other.
By measuring the tunneling rates for the three two-electron processes at zero
energy cost and extracting the corresponding coupling coefficients from the
rates, we expand the knowledge of physics behind two-electron tunneling. Our
experimental results, supported by theory predictions, demonstrate that the
elastic cotunneling has the same coupling strength as the non-local Andreev
tunneling and that the local Andreev process is two orders of magnitude
stronger than the non-local one in our structure as a result of limited
electron diffusion in the superconductor.

Figure 1: (a) Scanning electron micrograph of the studied device consisting of
two copper islands (coloured orange) coupled to a superconducting aluminum
electrode (in blue) via tunnel junctions Ranni  _et al._ (2021). The inset on
the right shows a zoom-in of the junctions. The electronic populations on the
islands are controlled by the voltages $V_{\mathrm{GL}}$ and $V_{\mathrm{GR}}$
applied to the gate electrodes. (b) Local Andreev tunneling process where a
Cooper pair tunnels from the central superconductor into the right island. (c)
A Cooper pair splitting where the two electrons forming the pair tunnel into
separate metallic islands in non-local Andreev tunneling event. (d) Elastic
cotunneling process where an electron moves from one island into the other via
a virtual state in the superconductor.

We investigate electron tunneling in a recently realized Cooper pair splitter
device Ranni  _et al._ (2021) where electron tunneling takes place between a
superconductor and two normal metallic islands as depicted in Fig. 1(a). Two
single-electron transistors (SETs) Schoelkopf  _et al._ (1998); Gustavsson
_et al._ (2009); Pekola  _et al._ (2013) act as charge detectors observing the
instantaneous charge state of both islands and thus resolving tunneling events
as they occur. This charge counting technique yields access to the tunneling
rates of the three two-electron processes allowing us to extract the couplings
of these processes.

Figure 2:  (a) The detector signal $I_{\mathrm{DR}}$ as a function of time $t$
revealing three charge states $n_{\mathrm{R}}$ on the right island
corresponding to the energy diagram on the right yielding
$\Gamma_{\mathrm{AR,R}}$. (b) The detector currents $I_{\mathrm{DL}}$ and
$I_{\mathrm{DR}}$ as a function of time, recorded simultaneously. The dashed
lines highlight non-local tunneling events. The islands are tuned to have the
charge states $n_{\alpha}=0,1$ degenerate in energy as presented in the energy
diagrams. $n_{\mathrm{G\alpha}}$ is the normalized offset charge. These data
was recorded at the base temperature of $T=10$ mK in a dilution refrigerator.

Local Andreev tunneling is schematically displayed in the diagram in Fig. 1(b)
where the two electrons forming a Cooper pair tunnel from the superconductor
into either of the islands. To measure the local Andreev tunneling rate
$\Gamma_{\mathrm{AR,R}}$ on the right island, we follow the proceduce of Ref.
Maisi  _et al._ , 2011: One of the charge states denoted with $n_{R}=0$ excess
electrons, is tuned with the gate voltage $V_{\mathrm{GR}}$ to be lowest in
energy as presented in Fig. 2(a). This configuration makes the charge states
$n_{R}=\pm 1$ to be degenerate as shown in the energy diagram and local
Andreev tunneling takes place between these states as seen in the measured
time trace in Fig. 2(a). By determining the number of tunneling events per
time spent in the initial state (Ref. Maisi  _et al._ , 2011), we obtain the
local Andreev tunneling rates $\Gamma_{\mathrm{AR,R}}^{\mathrm{in}}=6.2$ Hz
into and $\Gamma_{\mathrm{AR,R}}^{\mathrm{out}}=6.5$ Hz out from the right
island. Here we used the time window of $4$ ms corresponding to the detector
risetime to determine if two consecutive events are from the same process or
not. Since the rates are essentially the same, the tunneling indeed takes
place without energy cost. Measuring with the other detector and tuning
$V_{\mathrm{GL}}$ instead, we obtain similarly the local Andreev tunneling
rates $\Gamma_{\mathrm{AR,L}}^{\mathrm{in}}=61$ Hz and
$\Gamma_{\mathrm{AR,L}}^{\mathrm{out}}=55$ Hz on the left side. Interestingly,
the left side has an order of magnitude larger rates despite the junctions
have the same area (see inset of Fig. 1(a)) and are made in the same process
round very close to each other. The difference in the rates arise likely from
differences in barrier thicknesses changing the channel transparencies Maisi
_et al._ (2011); Greibe  _et al._ (2011); Aref  _et al._ (2014).

The non-local two-electron processes are illustrated in Figs. 1(c),(d). Panel
(c) presents non-local Andreev tunneling where the electrons forming a Cooper
pair split into separate islands and panel (d) elastic co-tunneling where an
electron moves from one island to the other via the superconductor. To
determine the tunneling rates $\Gamma_{\mathrm{CAR}}$ and
$\Gamma_{\mathrm{EC}}$ for these processes at zero energy cost, the charge
states $n=0$ and $n=1$ are tuned to degeneracy on both islands with the gate
voltages $V_{\mathrm{GL}}$ and $V_{\mathrm{GR}}$. The measured time traces,
shown in Fig. 2(b), have equal occupancy of the charge states and hence are at
equal energy as indicated by the energy diagrams. The non-local processes are
then identified from the transitions as described in Ref. Ranni  _et al._ ,
2021 as transitions within a time window of $1.5$ ms on both detectors. Here
the time resolution is limited by the noise jitter between the two detectors
instead of the detector rise time. At time $t=0.3$ s, the left island loses an
electron and the right one obtains one. Thus we had an elastic cotunneling
from the left island to the right one. Similarly, at $t=4.2$ s both islands
obtain simultaneously an electron resulting in from Cooper pair splitting. We
determine the tunneling rates
$\Gamma_{\mathrm{CAR}}^{\mathrm{in}}=$14\text{\,}\mathrm{m}\mathrm{H}\mathrm{z}$$
for Cooper pair splitting,
$\Gamma_{\mathrm{CAR}}^{\mathrm{out}}=$140\text{\,}\mathrm{m}\mathrm{H}\mathrm{z}$$
for Cooper pair forming,
$\Gamma_{\mathrm{EC}}^{\mathrm{L}\rightarrow\mathrm{R}}=$25\text{\,}\mathrm{m}\mathrm{H}\mathrm{z}$$
and
$\Gamma_{\mathrm{EC}}^{\mathrm{R}\rightarrow\mathrm{L}}=$96\text{\,}\mathrm{m}\mathrm{H}\mathrm{z}$$
similarly as the local Andreev rates as the number of events divided by the
time spent in the initial state. Despite of keeping the charge states $n=0,1$
degenerate, the rates in the two directions, in vs. out, and
$\mathrm{L}\rightarrow\mathrm{R}$ vs $\mathrm{R}\rightarrow\mathrm{L}$, are
not equal. Such a difference arises from a finite energy gain $\delta E$ in
one direction that appears as an energy cost in the opposing direction
decreasing the rate. The rates for a two-electron process at $\delta E=0$ may,
however, be still determined with logarithmic averages of the rates in the two
directions of the process e.g. for non-local Andreev as
$\Gamma_{\mathrm{CAR}}=(\Gamma_{\mathrm{CAR}}^{\mathrm{in}}-\Gamma_{\mathrm{CAR}}^{\mathrm{out}})/(\mathrm{ln}(\Gamma_{\mathrm{CAR}}^{\mathrm{in}})-\mathrm{ln}(\Gamma_{\mathrm{CAR}}^{\mathrm{out}}))$.
Figure 3 summarizes the two-electron tunneling rate measurements where we
repeated the experiment at varying bath temperature $T$.

The second-order perturbation theory Hekking and Nazarov (1994) yields a
general expression for the above three two-electron rates as

$\Gamma_{\mathrm{2e}}(\delta E,T)=\gamma\frac{\delta
E/k_{\mathrm{B}}T}{1-\mathrm{e}^{-\delta E/k_{\mathrm{B}}T}}k_{\mathrm{B}}T,$
(1)

where $\gamma$ is a coupling constant and $k_{\mathrm{B}}$ the Boltzmann
constant. All two-electron processes follow the same functional dependence of
the energy cost $\delta E$ per thermal energy $k_{\mathrm{B}}T$. The energy
cost $\delta E$ itself, and the coupling $\gamma$, are however not the same
for different processes. The charging energy difference between the initial
and final state sets $\delta E$ for the two-electron processes as $\delta
E_{\mathrm{AR,\alpha}}^{\mathrm{in}}=4E_{\mathrm{C}}\;n_{\mathrm{G\alpha}}$
(with $\alpha=\mathrm{L,R}$), $\delta
E_{\mathrm{CAR}}^{\mathrm{in}}=2E_{\mathrm{C}}(n_{\mathrm{GL}}+n_{\mathrm{GR}}-1)$
and $\delta E_{\mathrm{EC}}^{\mathrm{L\rightarrow
R}}=2E_{\mathrm{C}}(n_{\mathrm{GR}}-n_{\mathrm{GL}})$. The costs to opposite
tunneling directions are the same but with opposite signs. Here
$E_{\mathrm{C}}$ is the charging energy of individual identical islands and
$n_{\mathrm{G}\alpha}$ the normalized offset charge controlled by
$V_{\mathrm{G}\alpha}$ Lafarge  _et al._ (1991). The cost vanishes when the
initial and final state of the process are at the same energy as depicted in
Fig. 2. Equation (1) acquires in this case a simple form
$\Gamma_{\mathrm{2e}}(0,T)=\gamma\;k_{\mathrm{B}}T$.

The coupling terms for the three two-electron processes read as

$\begin{split}\gamma_{\mathrm{AR},\alpha}&=\frac{1}{8e^{2}R_{\mathrm{T\alpha}}^{2}}\frac{R_{\mathrm{K}}}{\mathcal{N}_{\alpha}},\\\
\gamma_{\mathrm{CAR}}&=\gamma_{\mathrm{EC}}=\frac{\mathrm{e}^{-l/\xi}}{2e^{2}R_{\mathrm{TL}}R_{\mathrm{TR}}}R_{\mathrm{S}}.\end{split}$
(2)

Here $\mathcal{N}_{\alpha}=A_{\alpha}/A_{\mathrm{ch},\alpha}$ is the effective
number of the conduction channels in a junction $\alpha=\mathrm{L,R}$ with a
junction area $A_{\alpha}$ and effective conduction channel area
$A_{\mathrm{ch},\alpha}$ Maisi  _et al._ (2011). $R_{\mathrm{T}\alpha}$ is the
junction resistance, $R_{\mathrm{K}}\equiv h/e^{2}$ the so-called resistance
quantum, $e$ the elementary charge, $l$ the distance between the two tunnel
junctions, $\xi$ the superconducting coherence length and $R_{\mathrm{S}}$ the
normal-state sheet resistance of the superconducting electrode measured over
the superconducting coherence length. Interestingly, the coupling terms for
non-local Andreev $\gamma_{\mathrm{CAR}}$ and elastic cotunneling
$\gamma_{\mathrm{EC}}$ are identical according to theory. Non-local Andreev
either splits or assembles Cooper pairs whereas elastic cotunneling does not
involve pairing and takes place even in the absence of superconductivity.

On the other hand, the local tunnel coupling $\gamma_{\mathrm{AR}}$ differs
from $\gamma_{\mathrm{CAR}}$ and $\gamma_{\mathrm{EC}}$ Falci  _et al._
(2001); Golubev and Zaikin (2007); Brauer  _et al._ (2010). As seen from Eq.
(2), $\gamma_{\mathrm{AR}}$ depends on the number of conduction channels
$\mathcal{N}_{\alpha}$ in the junction and the junction resistance
$R_{\mathrm{T\alpha}}$ in relation to the resistance quantum $R_{\mathrm{K}}$
Averin and Pekola (2008); Maisi  _et al._ (2011); Aref  _et al._ (2014). The
non-local processes depend instead on the total junction resistances versus
quasiparticle diffusion away from the junction area set by $R_{\mathrm{S}}$
Golubev and Zaikin (2019) but not on $\mathcal{N}_{\alpha}$ nor
$R_{\mathrm{K}}$. In addition, the non-local processes have an exponential
suppression $\mathrm{e}^{-l/\xi}$ for increasing distance $l$ between the two
junctions. Local Andreev is free of this suppression as the process takes
place across a single junction.

Figure 3: (a,b) Local Andreev tunneling rates at the left and the right
junction, respectively. The open red triangles denote tunneling in, open blue
triangles tunneling out of an island and the solid purple diamonds the
logarithmic averages. The solid purple line is a linear fit to the logarithmic
averages above the saturation, $T>$50\text{\,}\mathrm{m}\mathrm{K}$$. (c) Non-
local Andreev tunneling rates in the similar manner. (d) Elastic cotunneling
rates. Here open red and blue triangles denote tunneling from left to right
and vice versa.  Figure 4: (a) Lifetime $t$ distribution of charge states
$n_{\mathrm{R}}=0$ and 1 on the left and right graph, respectively. The black
circles are lifetimes without any condition set for the charge state on the
left island. The blue and red circles show the lifetime distribution on right
island with the condition that the left island is in $n_{\mathrm{L}}=0$ or 1
state respectively during the whole lifetime $t$. The arrows denote the mean
values of the distributions. (b,c) Sequential tunneling rates at the left and
the right junction, respectively at zero energy cost. The open red (blue)
triangles denote an electron tunneling into (out of) an island. The insets
display the rates at four highest temperatures on a logarithmic scale against
inverse temperature. The solid black lines are the theoretical models with
tunnel resistances as free fitting parameters.

We turn now back to the experimental data and determine the couplings
$\gamma$. Two-electron rates in Fig. 3 follow an increasing linear trend for
$T>$50\text{\,}\mathrm{m}\mathrm{K}$$. At lower temperatures the tunnel rates
saturate to a fixed value arising from the saturation of electronic
temperature in our dilution refrigerator at $50\text{\,}\mathrm{m}\mathrm{K}$.
The coupling terms are obtained by a linear fit (purple line) to rates at zero
energy cost above the saturation in Fig. 3. The extracted values are
$\gamma_{\mathrm{AR,L}}=$7.5\text{\,}\mathrm{/}\mathrm{\SIUnitSymbolMicro}\mathrm{e}\mathrm{V}\mathrm{s}$$,
$\gamma_{\mathrm{AR,R}}=$1.1\text{\,}\mathrm{/}\mathrm{\SIUnitSymbolMicro}\mathrm{e}\mathrm{V}\mathrm{s}$$,
$\gamma_{\mathrm{CAR}}=$9.0\text{\times}{10}^{-3}\text{\,}\mathrm{/}\mathrm{\SIUnitSymbolMicro}\mathrm{e}\mathrm{V}\mathrm{s}$$
and
$\gamma_{\mathrm{EC}}=$8.3\text{\times}{10}^{-3}\text{\,}\mathrm{/}\mathrm{\SIUnitSymbolMicro}\mathrm{e}\mathrm{V}\mathrm{s}$$.

Based on the above fits, $\gamma_{\mathrm{CAR}}$ and $\gamma_{\mathrm{EC}}$
are equal within the experimental accuracy, as the theory of Eq. (2) predicts.
The result also implies that there is no significant capacitive coupling
between the islands since with such coupling, the elastic cotunneling rates
would become higher than the non-local Andreev rates as splitting a Cooper
pair to separate islands would require additional energy to charge the two
islands by one electron each Yeyati  _et al._ (2007); Beckmann and v.
Löhneysen (2007). This conclusion is supported by the lifetime distributions
for the charge states $n_{\mathrm{R}}=0,1$ shown in Fig. 4 (a): The lifetime
on the right island is independent of the occupancy on the left island. A
capacitive coupling between the islands would favor energetically to have
dissimilar electron numbers on the islands and hence decrease the lifetime for
same electron numbers and increase it for differing electron numbers.

The above fits also show that the coupling terms for local Andreev tunneling
are two to three orders of magnitude larger than for non-local processes. From
the expressions in Eq. (2) we see that the possible explanations are the
exponential suppression $\mathrm{e}^{-l/\xi}$ and how the terms
$R_{\mathrm{K}}/\mathcal{N}$ and $R_{\mathrm{S}}$ compare to each other. To
assess where the difference arises from, we estimate the parameters
constituting the coupling terms of Eq. (2) in the following manner: The
sequential single-electron tunneling rates, measured also with the protocol
described in Ref. Ranni  _et al._ , 2021, are shown in Figs. 4(b) and (c)
across the left and the right junction. These yield us $R_{\mathrm{T\alpha}}$
since the sequential rates follow an exponential temperature dependence of
$\Gamma_{\mathrm{1e}}(T)=\frac{1}{e^{2}R_{T\alpha}}\sqrt{2\pi\Delta
k_{\mathrm{B}}T}\mathrm{e}^{-\Delta/k_{\mathrm{B}}T}$ without charging energy
cost between $n_{\alpha}=0,1$ Pekola  _et al._ (2013). Similarly to two-
electron tunneling, the sequential rates exhibit saturation at low
temperatures. However, the sequential rates saturate around
$100\text{\,}\mathrm{m}\mathrm{K}$ which is higher than for two-electron
tunneling due to suppression of sequential tunneling by the superconductor
energy gap $\Delta$. Sequential tunneling probes electron distributions in the
superconductor and metallic islands above the gap energies whereas two-
electron tunneling is sensitive to normal-state electrons around the Fermi
energy. Another factor that might play a role in higher saturation temperature
of sequential tunneling is that superconductors do not thermalize as
efficiently as normal-state metals Giazotto  _et al._ (2006). At the highest
temperatures the measured sequential rates grow exponentially as shown in the
insets of Figs. 4(b,c). The superconducting gap for a 20 nm thin film is
$\Delta=210\pm$10\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{e}\mathrm{V}$$
Maisi  _et al._ (2011); Aref  _et al._ (2014); Mannila  _et al._ (2019).
Hence, fitting $\Gamma_{\mathrm{1e}}(T)$ to the high temperature regime, as
shown as the black lines in the inset, yields us the tunnel resistances
$R_{\mathrm{TL}}=$5\text{\,}\mathrm{M}\Omega$$ and
$R_{\mathrm{TR}}=$50\text{\,}\mathrm{M}\Omega$$ as the only free fitting
parameters. Note that due to the strong exponential dependence, the
$\pm$10\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{e}\mathrm{V}$$ uncertainty
in $\Delta$ yields a factor of two uncertainty to the resistance values.

Next, with the experimentally determined $\gamma_{\mathrm{AR,\alpha}}$ and Eq.
(2), we obtain the number of conduction channels as
$\mathcal{N}_{\mathrm{L}}=130$ and $\mathcal{N}_{\mathrm{R}}=7$. With the
junction areas
$A_{\mathrm{L}}=$85\text{\,}\mathrm{n}\mathrm{m}$\times$80\text{\,}\mathrm{n}\mathrm{m}$$
and
$A_{\mathrm{R}}=$80\text{\,}\mathrm{n}\mathrm{m}$\times$70\text{\,}\mathrm{n}\mathrm{m}$$
estimated from the scanning electron micrograph of Fig. 1 (a), the
corresponding effective channel sizes are
$A_{\mathrm{ch,L}}=$50\text{\,}\mathrm{n}\mathrm{m}^{2}$$ and
$A_{\mathrm{ch,R}}=$790\text{\,}\mathrm{n}\mathrm{m}^{2}$$. The values for
$A_{\mathrm{ch,\alpha}}$ are comparable to the earlier work of Refs. Maisi
_et al._ (2011); Aref  _et al._ (2014) where
$A_{\mathrm{ch}}=$30\text{\,}\mathrm{n}\mathrm{m}^{2}$$ was reported for
junctions fabricated with the same process.

Now we turn into the non-local Andreev process. We estimate $R_{S}$ from the
normal-state resistance of a $\xi=$100\text{\,}\mathrm{n}\mathrm{m}$$ Koski
_et al._ (2011) long segment of the superconductor electrode next to the
junctions. The width of the electrode near the junctions is
$W=$210\text{\,}\mathrm{n}\mathrm{m}$$ and the thickness
$d=$20\text{\,}\mathrm{n}\mathrm{m}$$ measured by a crystal monitor during
metal evaporation. With the previously measured normal-state resistance of
e-beam evaporated aluminium films in Ref. Knowles  _et al._ , 2012,
$\rho_{\mathrm{N}}=$31\text{\,}\mathrm{n}\Omega\mathrm{m}$$, we obtain
$R_{\mathrm{S}}=\rho_{\mathrm{N}}\frac{\xi}{Wd}=$0.7\text{\,}\Omega$$. To
determine the exponential suppression factor of $\mathrm{e}^{-l/\xi}$, we
obtain the distance $l$ between the junctions from the scanning electron
micrograph. The shortest distance between the junctions is
$50\text{\,}\mathrm{n}\mathrm{m}$ and the distance between the far edges of
the junctions is $W=$210\text{\,}\mathrm{n}\mathrm{m}$$. We apply the halfway
$l=$130\text{\,}\mathrm{n}\mathrm{m}$$. With the chosen values the exponential
suppression becomes $\mathrm{e}^{-l/\xi}\approx 0.3$. If we instead applied
the minimum or maximum distance in our approximation the value of the
suppression would increase or decrease by a factor of two. With these
independent estimates, we obtain from Eq. (2) the coupling estimate
$\gamma_{\mathrm{CAR}}=$3\text{\times}{10}^{-3}\text{\,}\mathrm{/}\mathrm{\SIUnitSymbolMicro}\mathrm{e}\mathrm{V}\mathrm{s}$$
which is in reasonable agreement with the experimentally determined values,
considering the uncertainties in the parameter estimation. This parameter
estimation allows us to conclude that the two to three orders of magnitude
difference between the local and non-local Andreev process arises
predominantly from the difference in the terms
$R_{\mathrm{K}}/\mathcal{N}_{\alpha}$ and $R_{\mathrm{S}}$ respectively. In
other words, the diffusion away via the superconductor suppresses the non-
local process in the structure.

In conclusion, we used charge counting to determine the coupling coefficients
for three two-electron tunneling processes relevant in Cooper pair splitters.
Our experimental findings validate the theoretical prediction of
$\gamma_{\mathrm{CAR}}=\gamma_{\mathrm{EC}}$. We also determined the coupling
terms for local and non-local Andreev tunneling and found out that the non-
local one is suppressed by more than two orders of magnitude because of
competing diffusion in the superconductor.

We acknowledge Fredrik Brange, Christian Flindt, Martin Leijnse and Claes
Thelander for fruitful discussions and the QuantERA project ”2D hybrid
materials as a platform for topological quantum computing”, Swedish National
Science Foundation (Dnr 2018-00099 and 2019-04111), NanoLund, Academy of
Finland grant 312057 and QTF Centre of Excellence for financial support. We
acknowledge the provision of facilities by Aalto University at OtaNano -
Micronova Nanofabrication Centre.

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# WHTZ 1: A high excitation Planetary Nebula not a gaseous cocoon from runaway
star HD 185806

Quentin A. Parker,1,2 Pascal Le Dû,3,4 Andreas Ritter,1,2 Peter Goodhew,5
Sakib Rasool,6 Stephane Charbonnel,3 Olivier Garde,3 Lionel Mulato,3 and
Thomas Petit3
1Department of Physics, CYM Physics Building, The University of Hong Kong,
Pokfulam, Hong Kong PRC
2The Laboratory for Space Research, The University of Hong Kong, Cyberport 4,
Hong Kong PRC
32SPOT, 38690 Chabons, France
4Kermerrien Observatory, 29840 Porspoder, France
5W4 3EQ, London, UK
6Manchester, UK
E-mail<EMAIL_ADDRESS>(QAP)

(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We present evidence that the nebular cocoon and bow-shock emission nebula
putatively and recently reported as deriving from the 9th magnitude "runaway"
star HD 185806 is the previously discovered but obscure planetary nebula WHTZ
1 (Ra 7). It has a Gaia DR3 G$\sim$16 blue ionizing star at its geometric
centre. We present imagery, spectroscopy, other data and arguments to support
that this emission source is a high excitation Planetary Nebula not a stellar
wind bow shock.

###### keywords:

planetary nebulae: general – techniques: imaging – techniques: spectroscopic –
Astronomical data bases: catalogues

††pubyear: 2022††pagerange: WHTZ 1: A high excitation Planetary Nebula not a
gaseous cocoon from runaway star HD 185806–WHTZ 1: A high excitation Planetary
Nebula not a gaseous cocoon from runaway star HD 185806

##  1 Introduction

Miss-identification, false discoveries and re-assignments of celestial objects
from one class to another are common as new knowledge and data of higher
resolution, sensitivity and wavelength coverage become available. The field of
Planetary Nebula (PN) research, history is littered with many examples of
objects that have been re-discovered and re-identified as PNe only to later be
re-classified as one of the many PN mimics that exist (such as HII regions,
Wolf-Rayet shells, Herbig-Haro nebulae, YSO’s, reflection nebulae, supernova
remnants, nova shells etc). See Frew & Parker (2010) and the recent review by
Parker (2022) for further details. Refer also to Ritter et al. (2021) for a PN
candidate, Pa 30, re-classified recently as a supernova remnant of the Chinese
"guest star" of 1181 AD.

It is much rarer to find examples where a previously reported PN candidate is
later ascribed to another source type but then needs to be moved back to its
original classification.

One recent case concerns the discovery (sic) of a nebula cocoon reported as
deriving from runaway star HD 185806 (Spetsieri et al., 2022). The star is a
long period variable also designated as V 1279 Aql, where the variability is
due to pulsation not binarity (e.g. Smak, 1966). We present on-record
historical context that shows that the adjacent uncovered gaseous emission
region is the previously discovered source WHTZ 1 and observational evidence
to re-assign this source back to its original PN status.

###  1.1 Historical context

The nebulosity was first noticed as a faint emission region on photographic
B-band imagery from the POSS-I survey by Weinberger et al. (1999) and given
the name WHTZ 1. It was found as a serendipitous by-product when looking for
hidden galaxies behind the Milky way. They identified it as a PN candidate
with a morphology "typical" of many PNe and with a blue central star (CSPN).
The source was never incorporated into the SIMBAD astronomical database
(Wenger et al., 2000) at CDS, Strasbourg.

The object was independently "re-found" by French PN amateur astronomer
Thierry Raffaelli in 2014 and called "Ra 7" where it was added to the
dedicated on-line database created to record and present their work111
http://planetarynebulae.net/EN/page_np.php?id=237 and see Le Dû et al. (in
press). The object appears as "Ra 7" in SIMBAD. It was also re-discovered by
the Deep Sky Hunters team led by Matthias Kronberger and Dana Patchick (e.g.
Kronberger et al., 2016), based in part on assessments of its WISE MIR imagery
(Wright et al., 2010). It was ingested into the "HASH"
database222http://hashpn.space/ as a likely PN in 2015, with unique HASH ID
4418. HASH is the current "gold standard" consolidated on-line catalogue of
all known PN in our Galaxy and Magellanic clouds (Parker et al., 2016) having
evolved from the previous "MASH" surveys, Parker et al. (2006), Miszalski et
al. (2008).

It has also been reported in several editions of the French popular
"L’Astronomie" magazine in February 2015, vol. 129, No. 80,
p.42333https://ui.adsabs.harvard.edu/abs/2015LAstr.129b..42A/; February 2016,
vol. 130, No. 91,
p.26444https://ui.adsabs.harvard.edu/abs/2016LAstr.130b..26A/ and finally Le
Dû (2017).

The source has now re-appeared in the literature as a bow-shock cocoon nebula
of star HD 185806 in Spetsieri et al. (2022).

##  2 Methods and Observations

We provide accumulated multi-wavelength imagery, new optical spectroscopy,
identification of the actual ionising star, associated data, salient
characteristics and other evidence to confirm the source as a "True" high
excitation PN following the precepts outlined in Frew & Parker (2010) and
Parker (2022). The star HD 185806 is merely a chance, closely projected
neighbour that is unrelated to the actual emission observed.

###  2.1 More recent deep amateur narrow-band imagery

Deep, narrow-band, optical imagery of the candidate PN was taken with the
Chart32 "Chilean advanced robotic 32inch telescope" in 2017. The resultant
10$\times$8 arcmin RGB composite narrow-band image is shown in Fig 1, taken
directly from the Chart32 open-access website: www.chart32.de. This colour
image can be directly compared to Figs. 1,2 & 3 in Spetsieri et al. (2022).

The Chart32 RGB colour image was formed from co-adding narrow-band H$\alpha$
images (bandpass 30Å) of 280 minutes total duration (red channel), [OIII]
images of 360 minutes total duration (green channel) and then 3 broad-band
Astrodon Gen2 RGB filter images (blue channel) for a total of 100 min each
respectively. This gave a total on-source exposure time of 15.7 hours. The
typical seeing was reported as 0.8-1.2 arcseconds and the data were acquired
with an 81cm f/7 Astrooptik Keller Cassegrain telescope with the images
processed by Johannes Schedler of the Chart32 team.

In Fig 2 we also show the 5$\times$5 arcmin Chart32 H$\alpha$ image to show
H$\alpha$ emission is present. The overall form of the stronger signal seen in
[OIII] is there but is somewhat less distinct in character.

The main body of the WHTZ 1 nebula is oval in shape with a major axis
$\sim$193 arcseconds across and a minor axis of $\sim$134 arcseconds. The
opposing edges across the minor axes have enhanced intensity and there are
internal striations approximately perpendicular to these edges. There is a
CSPN located almost exactly at the geometric centre of the nebula, like many
typical PNe of elliptical morphology.

Figure 1: Combined 10$\times$8 arcmin narrow-band (30Å) image of WHTZ 1
comprising combined H$\alpha$ images of 280 minutes (red-channel), combined
[OIII] images of 360 minutes (green channel) and then 3 broad-band Astrodon
Gen2 RGB filter images for 100 min each respectively (blue channel). This gave
a total on-source exposure time of 15.7 hours. In the figure North is up and
East to the left. The typical seeing was reported as 0.8-1.2 arcseconds. The
blue CSPN is clear at the nebula’s geometric centre. Figure 2: Chart32
H$\alpha$ 5$\times$5 arcmin image for WHTZ 1 showing that the H$\alpha$
closely follows that of the [OIII] but is fainter and less distinct in
character for the equivalent exposure time. North is up and East to the left.

We have supplemented these data with very deep narrow-band H$\alpha$
imaging555see https://www.imagingdeepspace.com/observatories.html). A combined
total of 40 hours and 25 mins H$\alpha$ imaging were combined from
observations on August 17th and September 8,9,10,13,15,16th 2022 using two
separate automated telescopes in the UK (Celestron C14 EdgeHD telescope with
ZWO ADI6200MM Pro camera and a Chroma H$\alpha$ 3 nm bandpass filter for 13
hours and 10 mins observations) and Spain (Twin APM LZOS 152/1200 telescopes
with QSI6120 cameras and an Astrodon H$\alpha$ 3 nm bandpass filter for 27
hours and 15mins of observations). In Fig 3 we present the resultant contrast
enhanced 20$\times$16 arcmin H$\alpha$ image of WHTZ1 (stars removed for
clarity) obtained over these $\sim$40 hours of combined imagery. A faint outer
halo can be discerned which is $\sim$10 arcmins across the major axis. Such an
extensive, faint halo is difficult to reconcile with any bow-shock scenario.

Deep amateur narrow-band exposures of PN and PN candidates are now providing
highly competitive imagery, matching, and in many cases exceeding, the best
professional efforts previously available (Parker, 2022).

Figure 3: Large area, contrast enhanced, deep H$\alpha$ 20$\times$16 arcmin
image for WHTZ 1, with stars removed for clarity. Clear evidence of a faint
$\sim$10$\times$7 arcmin H$\alpha$ halo is seen surrounding the main nebula.
North is up and East to the left. The image derives from 40 hours and 25 mins
of combined narrow-band exposures.

###  2.2 Mid Infrared Imagery

In Fig. 4 we show a 9$\times$9 arcmin WISE W4 22$\mu$m (Wright et al., 2010)
image for WHTZ 1 and HD 185806. The well defined emission region is prominent
and has two thick, opposing arc-like structures that follow the enhanced
[OIII] edges seen in the optical. The interior is of much lower intensity
suggesting a cavity. The Northern MIR emission arc is more prominent. The
nebula can also be seen in the W3 12$\mu$m image, contrary to what was
reported by Spetsieri et al. (2022). Annotation indicates the faint MIR
emission of the outer oval nebula to the SE and NW reflecting what is also
seen in the optical. This compact 3$\times$2 arcmin MIR emission region is
isolated. The proper motion vector for HD 185806 (see later) is added, taken
from Gaia DR3 data for this star, e.g. Gaia Collaboration et al. (2016). The
prominence of HD 185806 in the MIR is also clear.

Figure 4: A 9$\times$9 arcmin WISE W4 22$\mu$m image for WHTZ 1 and HD 185806.
It shows the main opposing arc like structures and hollow interior. Annotation
indicates the faint MIR emission of the outer oval nebula to the SE and NW
reflecting what is also seen in the optical. The green arrow marks the almost
directly Southern direction of the Gaia proper motion vector for HD 185806.

###  2.3 Optical Spectroscopy

No low resolution spectroscopy of the nebula was presented by Spetsieri et al.
(2022) who obtained high resolution echelle spectroscopy that covered the
H$\alpha$ \+ [NII] lines and [OIII] in two separate spectral windows. These
were taken in Mexico with the 2.1 m San Pedro Martir Telescope and Manchester
Echelle spectrograph in November 2014. This was supplemented by high
dispersion spectra of HD 185806 on the 1.2 m Mercator telescope on La Palma,
Canary Islands in July 2021 using the HERMES instrument, confirming it as an M
4 late type star.

Figure 5: Low resolution 1-D optical spectra of WHTZ 1 taken with the
dedicated 2SPOT System in Chile. The [OIII] and high excitation He II 4686Å
emission lines are seen in the blue, indicating it is a high excitation PN.
Weaker H$\alpha$ is evident in the red. The not fully cancelled bright
Sodium-D night sky emission line is also indicated.

We present in Fig. 5 new, low-resolution, optical spectra of the nebula taken
with the 2SPOT666for details on the 2SPOT amateur spectroscopy consortium see:
https://2spot.org/EN/ Ritchey-Chrétien RC12 12-inch telescope in Chile
equipped with the very stable Alpy 600 spectrograph from Shelyak Instruments
(resolution 600). The final 1-D spectrum was obtained after combining
5$\times$1200 second exposures from the 12th and 10$\times$1200 second
exposures from 15th September 2022. Not only are the [OIII] optical emission
lines visible but clearly so is the high excitation He II line at 4686Å . In
the red the H$\alpha$ can be seen but is not strong compared to [OIII]. The
residual Sodium D (Na D) line is from the night sky. The 2-D spectral images
were reduced following the standard pipeline describe in Le Dû et al. (in
press). The presence of He II indicates a high excitation nebula. This would
be an unprecedented detection for any optical bow-shock, e.g. see Hartigan
(1999) for attempts at such detection.

###  2.4 Proper motion arguments

Gaia (Gaia Collaboration et al., 2016) DR3 data have now provided reliable
proper motion and parallax data for both HD 185806 and the CSPN. This provides
the opportunity to examine the proper motion vectors of these stars with
respect to the nebula. As has been shown by Peri et al. (2012) with a MIR
selected sample of bow-shock candidates, the earlier Hipparchus proper motion
vectors of the stars are well aligned with their bow-shocks, i.e. they
generally point in the direction of the bow-shock. For HD 185806 no Gaia
proper motion vector data were provided by Spetsieri et al. (2022), nor
overlaid on their figures. The proper motion vector is added in Fig 4 which
points almost directly South and is not aligned with the major symmetry axis
of the nebula but is offset by $\sim$50 degrees.

##  3 Broader Geometric considerations

Visual inspection of the available, deep, narrow band imagery indicates the
proposed blue CSPN is the actual ionising source for the nebula. It is located
within 5 arcseconds of the intersection of the major and minor axis best fit
by eye to the nebula’s overall oval shape as would be expected for any true
CSPN. This is also the case for the WISE MIR imagery where the optical
enhancements on the NE and SW sides are reflected in a two component but
uneven MIR intensity arc structure and hollow interior in the 22$\mu$m band-4
WISE data where the CSPN resides. The 9$\times$9 arcmin band-4 WISE image in
Fig 4 is dominated by HD 185806. This makes it difficult to assess the MIR
emission component from the nebula as it is so close to the bright star, at
least in a projected sense. Apart from the compact WISE nebula there is no
other obvious MIR emission across the 9$\times$9 arcmin field shown. Contour
fits (as also done by Spetsieri et al., 2022) can give a false impression of
the actual nebula emission close to such a bright star so examination of the
MIR imagery itself is needed. There is a hint of W4 WISE emission beyond the
star to the SE. We believe this shows the faint nebula extension expected
here, assuming it reflects the faint outer envelope of the oval nebula seen to
the NW in the optical and MIR imagery.

A further piece of contrary evidence to a bow-shock interpretation can be seen
in Fig. 3 of Spetsieri et al. (2022) where, at the extreme Northern corner of
the [OIII] emission mosaic, there appears to be a faint emission arc parallel
to the enhanced Northern edge of the main nebula but 3 arcminutes away from
the CSPN. This could be [OIII] emission associated with a possible AGB halo of
the PN given its geometry and alignment. In Fig 3 we show that indeed there is
a faint outer 10 arcmin dimension halo visible, in this case in H$\alpha$.

###  3.1 The bow-shock interpretation

Bow-shocks can form both around hot, young stars where strong stellar winds
slam into the surrounding interstellar medium or more commonly where runaway
typically O/B stars are ploughing into a dense ISM. Examination of the best
extant image examples of bow-shocks around mostly runaway stars have little in
common with the observed nebular features seen here. See the compilations,
discoveries and imagery reported by Peri et al. (2012) and later by Kobulnicky
et al. (2016) and Kobulnicky et al. (2017). These show major, new samples of
Galactic candidate stellar bow shocks found on Spitzer and WISE MIR data for
runaway stars. All 244 examples listed by Peri et al. (2012) were from O and B
type stars and no M-type stars, like HD 185806, were found in their entire
sample. However, Cox et al. (2012) provide a catalogue of “wind-ISM” bow
shocks and “wind-wind” interactions detected around AGB stars but only as seen
in the far infrared with Herschel/PACSs imagery (Pilbratt, 2001) and not at
these shorter wavelengths.

Most bow-shocks exhibit very open angles on the forward curve and are well
separated and in front of the associated star. The only example found that
even remotely resembles the case here is associated with the binary star BZ
Cam but the prominent striations seen are lacking in that case and there is a
prominent, if faint, more forward bow-shock too.

The 3 main arguments to support a bow-shock interpretation made by Spetsieri
et al. (2022) while seemingly plausible, lack firm observational evidence and
are more descriptive than numerical. The claim of a bow-shock structure being
"clearly depicted" in the WISE imagery is based on contour fits to the WISE w4
22$\mu$m data that are affected by the intensity and close proximity of HD
185806 in the MIR. Close examination of the actual MIR imagery does not bear
this out while they themselves admit to no evidence of a bow shock in the
optical band as might be expected. They multiply claim that HD 185806 is
"surrounded" by the nebula when there is clearly almost no projected overlap
between the star and the main body of the nebula region.

The star HD 185806 is not aligned with the major axis of the fitted ellipse
that best describes the nebula but is $\sim$15 degrees off, while the star
itself is also located $\sim$1.5 arcmin to the SE of the nebula centre. The
expected faint SE extension of the nebula to match that seen to the NW is
largely obscured by the brightness of HD 185806 but can just be discerned at
the edges. The Gaia proper motion vector is poorly aligned with the major axis
of the nebula.

##  4 Distance estimates and Kinematic age for the nebula

PN WHTZ 1 was included in the calculated Surface Brightness radius (SB-r)
relation PN distances paper of Frew et al. (2016) as entry 307. The published
distance from this robust PN statistical distance indicator is 2.49$\pm$0.71
kpc. This compares with a Gaia DR3 parallax based distance for the assumed
CSPN of 1.83 kpc (Bailer-Jones et al., 2021). This just agrees to within the
admittedly large 20-30% errors typically reported for the SB-r technique so
the PN and CSPN distances are compatible. The robust Gaia distance for HD
185806 is 910 pc (Bailer-Jones et al., 2021).

The expansion velocity of the gas inferred from the data reported by Spetsieri
et al. (2022) is taken as $\sim 57\pm 10$ km $\mathrm{s^{-1}}$ based on an
average of the positive and negative velocity components reported at multiple
points across the nebula and from the H$\alpha$, [NII] and [OIII] emission
lines sampled. This is in the accepted range for a PN. Assuming this has been
effectively constant since the envelope ejection from the progenitor star that
created the PN and taking the physical size of the PN to be 1.7$\times$1.2 pc,
as estimated by taking the PN angular size in radians and the Gaia DR3
distance for the assumed CSPN of 1.8 kpc, yields a kinematic age of the nebula
of $\sim$25,000 years (see Tab. 1). This is within the range of PN kinematic
ages, if at the higher end, but certainly not without precedent for such a
faint and evolved PN (Fragkou et al., 2022).

##  5 Dust and extinction in the local environment

The WISE data shows there is no further MIR emission in a large 9$\times$9
arcmin area around WHTZ 1 - it is an isolated 3$\times$2 arcmin MIR emission
region. Even on one degree scales there is very little MIR emission at this
Galactic location and what there is is extremely faint and very diffuse.
Likewise, the Schelgel, Finkbeiner and Davis dust maps (Schlegel et al., 1998)
show little dust in this zone while the large-scale SHASSA (Gaustad et al.,
2001) H$\alpha$ gaseous emission maps show no significant ionised regions in
the vicinity. This is not surprising given the nebula is 10 degrees latitude
above the Galactic mid-plane. The ISM is not significant here and the
extinction is assumed modest.

The 3D dust map by Green et al. (2019) gives a low E(B-V) value of 0.33,
quantitively confirming the impressions of a relatively low extinction
environment. This explains why the [OIII] narrow-band images and spectroscopic
emission lines are strong as these data are not significantly extincted. In
low extinction environments the [OIII] lines can be much stronger than
H$\alpha$ emission in PNe. This is seen in many higher Galactic latitude
examples such as Abell 78 and as is the case for this emission object.

##  6 Corollaries with other known PNe

The morphological structure of the nebula is typical of many elliptical shaped
PNe. There are a many known PN corollaries, including a recently discovered PN
found by the French Amateur group, StDr 47 (HASH ID 32596), LTNF 1 (HASH ID
677) reported by Liebert et al. (1995), Kn 121 (HASH ID 23344) and Abell 36
(HASH ID 988) where all their positions, sizes, imagery etc can be located.
Deep, narrow band amateur imagery of all of these PNe corollaries can also be
found here: https://www.imagingdeepspace.com/peter-goodhew-planetary-nebulae-
images.html.

These PNe share many of the features of WHTZ 1. They have an elliptical
morphology, enhanced opposing edges, similar internal structure, a faint blue
CSPN at the geometric centre and even, in the cases of StDr 47 and Kn 121,
unrelated nearby bright stars. Two examples are shown for comparison purposes
in Fig 6 and are extracted from deep narrow-band H$\alpha$ and [OIII] amateur
images777see http://planetarynebulae.net/EN/page_np.php?id=845 for StDr 47 and
https://www.imagingdeepspace.com/ltnf1.html for LTNF 1). There are many
examples of PNe being in close projected proximity to unrelated bright stars
as might be expected given the majority of PNe are located in the Galactic
plane. Perhaps the best known example is Abell 12 the so-called "hidden
planetary", a small PN in the constellation of Orion heavily obscured by the
glare of 4th magnitude star Mu Orionis in the optical but nicely seen in the
WISE MIR imagery.

Figure 6: Deep, narrow-band H$\alpha$ and [OIII] amateur images of PN StDr 47
(HASH ID 32596, top with PN major axis 270 arcsec) and LTNF 1 (HASH ID 677,
bottom - with PN major axis 230 arcsec) as examples of excellent morphological
PNe corollaries to WHTZ 1. This includes the presence of faint blue CSPNe at
their geometric centres and even, in the case of StDr 47, a bright, unrelated
star nearby.

##  7 Summary of observed properties and assessment

We provide below the main accumulated arguments against the bow-shock
interpretation and supporting the PN nature of the observed nebula emission.

###  7.1 Arguments against the bow-shock scenario

A brief summary of points concerning the bow-shock interpretation are as
follows:

  * •

The morphology of the nebula is unlike other extant examples in the literature
of bow-shock nebulae in the optical

  * •

The host star is not an O or B type star as found for most other examples in
the optical and MIR as reported by Peri et al. (2012) but is an M 4 late type
star. This would be very unusual at these wavelengths, although some are found
around AGB stars in the far infrared with Herschel

  * •

The presence of an faint outer nebular halo fits a PN AGB halo interpretation
but not a bow-shock

  * •

The star’s location is not aligned with the major axis of the elliptical
nebula with a $\sim$15 degree offset

  * •

The strength of [OIII] relative to H$\alpha$ can be explained by shocks but
can also easily be explained in a PN interpretation and by the Galactic
location out of the mid-plane so the blue emission lines are not heavily
extincted

  * •

The low extinction and lack of gas and dust in the general area means the ISM
does not provide a dense medium for bow shocks to develop easily

  * •

The stellar and nebula systemic velocities do not agree

  * •

The Gaia proper motion vector of the star is not aligned with the supposedly
trailing nebula (see Fig. 4) but is off by $\sim$50 degrees

###  7.2 Factors supporting a PN identification

A brief summary of points supporting a PN classification is as follows:

  * •

The morphology is PN like with many corollaries with known PNe (see Fig. 6)

  * •

There is a plausible blue, ionising star at almost the exact geometric centre
of the nebula. This is a compelling argument for a PN origin for the nebula
emission

  * •

the optical spectrum is also compelling given the spectrum has a clear
detection of He II 4686Å emission which requires a CSPN with a Teff of at
least 50,000 K, implying a high excitation PN identification

  * •

The SB-r distance to the nebula and the CSPN parallax distance from Gaia are
compatible within the errors

  * •

The expansion velocity, kinematic age and physical size are all within
accepted ranges for PNe

  * •

The presence of a faint 10 arcmin outer halo - shown in our deep H$\alpha$
image (Fig 3), is a feature also seen in many PNe

Based on all these combined observed characteristics and also applying the
decision tree for PNe to the key observations provided in Fig.11 of Parker
(2022) leads us to a straightforward identification of WHTZ 1 as a high
excitation PN.

In Tab. 1 we present the combined summary of all the observed and estimated
parameters for the PN, proposed CSPN and for HD 185806.

Table 1: Summary Table of all observed and determined PN, CSPN and star HD 185806 parameters from this work and from the literature. Parameter | PN | CSPN | HD 185806
---|---|---|---
RA (J2000) | 19:40:43.84 | 19:40:$43.840^{\bigtriangledown}$ | 19:40:$47.56^{\bigtriangledown}$
DEC (J2000) | 02:30:31.80 | 02:30:$31.928^{\bigtriangledown}$ | 02:29:$28.64^{\bigtriangledown}$
Galactic longitude | 40.875 | 40.87508 | 40.86675
Galactic latitude | -9.7764 | -9.77643 | -9.79839
Gaia stellar ID: 428968+ | - | 4146940013184 | 3322306283904
Gaia G-band (mag) | - | 16.887 | 7.606
$B_{j}$ (mag)⋄ | - |  $\sim$16.94 |  $\sim$10.37
R-band (mag)⋄ | - | 17.42 | 8.00
$E(B-V)^{\bigtriangleup}$ | 0.33 | - | -
$\mu_{\delta}$ $(\mathrm{masyr^{-1}})^{\bigtriangledown}$ | - | $-7.78\pm 0.06$ | $-10.28\pm 0.03$
$\mu_{\alpha}\mathrm{cos}\delta$ $(\mathrm{masyr^{-1}})^{\bigtriangledown}$ | - | $-5.03\pm 0.08$ | $-0.36\pm 0.04$
Distance (kpc) | $2.49\pm 0.71^{*}$ | $1.83^{+0.27^{\bullet}}_{-0.21}$ | $0.91^{+0.04^{\bullet}}_{-0.02}$
Velocity (km $\mathrm{s}^{-1}$) |  $-34\pm 13$ (systemic)# | - |  $13.76\pm 0.37$ (heliocentric)▽
|  $57\pm 10$ (expansion)# | - | -
Physical size major axis (pc) | $1.72^{+0.24}_{-0.21}$ | - | -
Physical size minor axis (pc) | $1.19^{+0.17}_{-0.12}$ | - | -
Nebula outer H$\alpha$ halo (arcmin) |  $\sim$10 | - | -
Kinematic age (yr) | $25000^{+15000}_{-10000}$ | - | -
▽from Gaia DR3 (Gaia Collaboration et al., 2022)
∗from SB-r relation of Frew et al. (2016)
# estimated from data in Spetsieri et al. (2022)
⋄ taken from SuperCOSMOS photometry, see Hambly et al. (2001)
△ taken from Green et al. (2019)
∙ taken from Bailer-Jones et al. (2021)

##  8 Conclusions

We have shown that the recently reported cocoon "bow-shock" nebula, supposedly
trailing the bright, 9.4th magnitude star HD 185806 is actually a previously
identified, faint, evolved, high excitation PN WHTZ 1 (Ra 7). This is
confirmed by new, low resolution optical spectroscopy and multiple other
pieces of evidence. The blue, ionizing CSPN, detected in Gaia DR3 (Gaia
Collaboration et al., 2022) as star 4289684146940013184, has a reported
parallax of 0.5548 mas from which Bailer-Jones et al. (2021) infer a distance
of $\sim$1.8 kpc. This gives the PN a physical extent across the major axis of
$\sim$1.7 pc, well within the range of known PNe. The expansion velocity and
kinematic age are also compatible with a PN origin. The elliptical morphology
is also typical of many evolved PNe with LTNF 1, KN 121, Abell 36 and the
recent discovery of PN StDr 47 being particularly apt corollaries. They all
have faint blue CSPNe with very similar morphological structures and, in the
case of StDr 47 and KN 1212, bright, unrelated close stellar projected
neighbours. The bright star HD 185806 is merely a chance line-of-site
projected neighbour situated in the foreground at 910 pc.

## Acknowledgements

We would like to thank the anonymous referee who helped us improve the paper.
QAP thanks the Hong Kong Research Grants Council for GRF research support
under grants 17326116 and 17300417. AR thanks HKU for the provision of a
postdoctoral fellowship. This work has made use of data from the European
Space Agency (ESA) mission Gaia  (https://www.cosmos.esa.int/gaia), processed
by the Gaia Data Processing and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium. Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. We also thank Johannes
Schedler of the Chart32 team for the excellent Chart32 processed images used
in this paper.

## Data Availability

The data underlying this article are available in the article itself and in
its associated online material freely accessible from the HASH database found
here: http://hashpn.space by simply entering the unique HASH ID number for
each source as provided.

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