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# Gadolinium concentration measurement with an atomic absorption
spectrophotometer

Ll. Marti<EMAIL_ADDRESS>Department of Physics, Yokohama
National University, Yokohama, Kanagawa, 240-8501, Japan  L. Labarga
Department of Theoretical Physics, University Autonoma Madrid, 28049 Madrid,
Spain

###### Abstract

Because gadolinium (Gd) has the highest thermal neutron capture cross section,
resulting in an 8 MeV gamma cascade upon capture, it has been proposed for
dissolution in water Cherenkov detectors to achieve efficient neutron tagging
capabilities. While metallic Gd is insoluble in water, several compounds are
very easy to dissolve. Gadolinium sulfate, Gd2(SO4)3, has been thoroughly
tested and proposed as the best candidate. Accurate measurement of its
concentration, free of doubt from impurities in water, is crucial. An atomic
absorption spectrophotometer (AAS) is a device that suits this purpose and is
widely used to measure the concentration of many elements. In this study, we
describe three different approaches to measure Gd sulfate concentrations in
water using an AAS: doping samples with potassium and lanthanum, and employing
tantalum and tungsten platforms.

xxxx, xxx

##  1 Introduction and Motivation

Water Cherenkov (WC) detectors are very massive and can reconstruct charged
particle tracks over a wide energy range. However, their efficiency in
detecting neutrons is relatively very low. When neutrons are produced in a WC
detector, they first undergo thermalization and are then mostly captured on
protons due to the larger thermal neutron capture cross section of protons
compared to oxygen nuclei: 0.3 barns and 0.19 millibarns, respectively.
Neutron capture on protons results in the production of a single 2.2 MeV gamma
within approximately 200 $\mu$s, which is difficult to detect due to its
relatively low energy. This single gamma produces few Cherenkov photons to be
detected in a WC detector such as Super-Kamiokande Zhang:2013tua .

In 2003, GADZOOKS! was proposed as an approach to achieve efficient neutron
tagging in WC detectors Beacom:2003nk . The method involves introducing a
gadolinium (Gd) solute into the pure water of WC detectors. The thermal
neutron capture cross section of naturally occurring Gd ($\sim$49,000 barns)
is about 5 orders of magnitude larger than that of hydrogen. The capture on Gd
yields an 8 MeV gamma cascade, which is usually shared among three or four
gammas. This technique has been shown to be feasible by diluting Gd sulfate
octahydrate, ${Gd}_{2}(SO_{4})_{3}\cdot 8H_{2}O$, as demonstrated at EGADS
MARTI . Gd sulfate octahydrate is easy to dissolve, essentially transparent to
Cherenkov light, and can be produced to the required radio-purity levels for
WC detectors hosokawa2022development .

The concentration of Gd sulfate octahydrate in water, herafter Gd sulfate if
not stated otherwise, becomes a critical parameter to measure, as the neutron
capture detection efficiency depends on the fraction of neutron captures on
Gd. Figure 1a shows this relationship. At a concentration of only 0.02$\%$
(200 ppm) of Gd sulfate, about 50$\%$ of neutron captures are on Gd. At a
concentration of 0.2$\%$ (2000 ppm), the fraction of captures on Gd rises to
about 90$\%$ while reducing the capture time from 200 $\mu$s to about 30
$\mu$s.

Figure 1: Left (a) fraction of neutrons captured on Gd as a function of the Gd
concentration in water by mass. Right (b) uncertainty on Gd captures for a 3.5
$\%$ uncertainty in the measurement on the Gd concentration.

Indirect methods such as measuring water resistivity or light absorption in
Gd-loaded water can be employed to determine the concentration of Gd sulfate
in WC detectors. However, whenever it is necessary to ensure that other
elements do not interfere with these measurements, a more reliable method is
required, as was the case for the EGADS R$\&$D studies MARTI  and later at
Super-Kamiokande Abe_2022  for its SKGd phases. An atomic absorption
spectrophotometer (AAS) is a commonly used device for concentration
measurements of a wide range of elements in liquids.

Figure 2 shows the schematic view of an AAS. A sample of about 15 $\mu$L is
inserted into a cuvette, which is typically a container with a cylindrical
shape. In some cases a dopant to enhance signal is added as well, see Section
2.3. Cuvettes are made of pyrolytic carbon and they are sometimes modified to
improve the atomization of the sample by adding a L’vov platform inside them
LVOV1978153  or variations of this idea, for example in liang1991determination
, see Section 2.4. The sample is then heated to high temperatures to achieve
its atomization. During this atomization the sample is illuminated by a
hollow-cathode lamp made of the same chemical element of study (in our case
Gd) and the absorbance measured with a photo-multiplier as main detector
element. The absorbance is a measure of the concentration of the chemical
element in the sample. The advantages are evident: by using a Gd hollow-
cathode lamp to illuminate an atomized sample, the Gd concentration of a
sample can be unequivocally determined. In addition, these measurements
require only small sample sizes.

As shown in Figure 1a the slope of neutron captures on Gd is highest around
0.02$\%$. At this concentration, and considering an uncertainty of 3.5$\%$ in
a single Gd sulfate concentration measurement (see Section 3 for typical
values), the uncertainty in neutron captures on Gd is about 0.87$\%$. One of
our goals is to improve the uncertainty.

Figure 2: Schematic view of an AAS: light source, sample, dopant (optional),
atomizer, optics and detector. In our case, the light source is a hollow-
cathode lamp made of Gd. To atomize the sample, it is inserted into a cuvette,
which may sometimes include a dopant or be a modified cuvette, see text for
more details. The detector is a photo-multiplier.

Three main drawbacks were identified for the measurements with an AAS :

  * •

Limited measurement range. The optimal measurement range for Gd is around 5-30
ppm. However, both the lower and upper bounds of the measurement range are
limited by imperfect atomization, as previously described. To measure higher
concentrations, precise dilution is necessary, which further increases an
already long measurement time and complexity.

  * •

Memory effects. The AAS atomizes samples at 2700 - 2800 ∘C in a pyrolytic
carbon cuvette. While this is sufficient for many elements, similarly to other
rare earth metals, Gd requires a higher temperature Johansson_1975 . This
means that Gd is not fully atomized at these temperatures, reducing the
sensitivity of the measurement and leaving some Gd in the cuvette after
atomization. Additionally, Gd may react with the carbon of the cuvette and
become temporarily fixed, this not only reducing the efficiency of the current
atomization but also leading to inaccurate results in subsequent measurements.

Standard AAS measurement methods are susceptible to these atomization
inefficiencies - also known as memory effects - which negatively impact the
accuracy and precision of Gd concentration measurements using an AAS.

  * •

Cuvette aging. The sample is injected into the cuvette, and atomization is
achieved through high temperatures. Although cuvettes are designed to
withstand the high temperatures needed for atomization, they undergo aging,
which can significantly affect the atomization efficiency. The rate of aging
is dependent not only on the cuvette type but also exhibits variations among
cuvettes of the same type.

While AAS is commonly used to measure the concentration of a wide range of
elements, these limitations highlight the necessity of a careful
reconsideration when using this technique for Gd measurements.

In this paper we present and discuss the different methods developed for the
use of an AAS as the technique for the measurement of Gd sulfate
concentrations for GADZOOKS! in EGADS and SKGd. Section 2 will describe our
measurement methods, including some of the key elements of our apparatus.
Section 3 will present the characterization of the AAS cuvette types and the
measurement errors will be derived. The paper will be concluded with a summary
of the methods and the main results in Section 4.

##  2 Measurement Methods

In the following subsection, the general settings common to the different
methods will be described, while specific details for each method will be
provided in the subsequent subsections.

###  2.1 Instrumentation and General Settings

For this study, a Hitachi polarized Zeeman AAS of the ZA3000 series was
utilized (property of the Institute for Cosmic Ray Research University of
Tokyo). Two types of cuvettes were employed: Pyro Tube C HR (used for
comparison purposes as its production has been discontinued) and Pyro Tube HR.
Hereafter, they will be referred as C HR and HR, respectively. A negative
feature shared by both types of cuvettes is that the high temperatures
required for sample atomization or cuvette cleaning gradually degrade their
quality, although, as it will be shown, to varying degrees. Henceforth, these
two processes will be referred to as furnace processes. There is a limited
number of times these processes can be repeated before their effectiveness
significantly diminishes, thereby determining their effective lifetime. Based
on our experience, C HR cuvettes could be used for almost 100 furnace
processes, whereas HR cuvettes can be used for only about 70.

Gd hollow-cathode lamps were operated with a current of 10 mA. The analysis
wavelength was set to 422.6 nm, and the slit width was adjusted to 1.3 nm to
maximize sensitivity for the AAS photo-multiplier and other relevant
conditions. Concentrations were determined based on the measured
absorption111Strictly speaking, it measures absorbance. peak height (ABS).
Argon (Ar) gas was supplied to aid in sample drying and to protect the sample
from being contaminated and the cuvette from aging at high temperatures. After
turning on the Gd hollow-cathode lamp, about 5 minutes are needed to warm it
up and ensure light intensity stability well within 1$\%$.

###  2.2 Measurement General Settings

This paper focuses on two types of measurements: doping with lanthanum (La)
and potassium (K), and using platforms made of either tantalum (Ta) or
tungsten (W). As it will be shown, doping with La and K (La+K) requires more
furnace processes compared to using Ta/W platforms. Consequently, doping
becomes increasingly impractical with HR cuvettes due to the limited number of
furnace processes this cuvette type can perform. As a result, when the
production of C HR cuvettes was discontinued, we were compelled to search for
a better solution. The measurement methods and cuvettes used are summarized in
Table 1.

| Doping with | Ta and W
---|---|---
| La+K | platforms
Pyro Tube C HR | ✓ | ✗
Pyro Tube HR | ✓ | ✓
Table 1: Table with the different methods and cuvette types employed.

Once the AAS has been prepared, see Section 2.1, the basic sequence begins.
Their common settings (dry stages and ash) are shown in Table 2. The settings
for the subsequent stages (atomize, heating and cool) differ depending on the
cuvettes and method. Specifically, the settings for C HR cuvettes and doping
with La+K are shown in Table 3, while the settings for HR cuvettes are shown
in Tables 4 and 5, corresponding to the La+K doping and Ta/W platform methods,
respectively.

Program | Start | End | Ramp | Hold | Ar
---|---|---|---|---|---
stage | temperature | temperature | time | time | flow
Dry-1 | 50 | 130 | 70 | - | 200
Dry-2 | 130 | 500 | 30 | - | 200
Ash | 1800 | 1800 | 20 | - | 200
Table 2: The three first stages: dry-1, dry-2 and ash of the basic sequence. They are common to all methods and cuvettes. See text for details. Temperature units in ∘C, time intervals in seconds and flow in mL/min. Program | Start | End | Ramp | Hold | Ar
---|---|---|---|---|---
stage | temperature | temperature | time | time | flow
Atomize | 2800 | 2800 | - | 10 | 10
Heating | 3000 | 3000 | - | 10 | 200
Cool | - | - | - | 20 | 200
Table 3: Settings for measurements with C HR cuvettes and doping with La+K. The photo-multiplier voltage was set to 260 V. Sample injection volume: 15 $\mu$L. After the cooling stage, 25 $\mu$L of pure water are injected in the cuvette and the stages of heating and cooling are repeated twice. See text for details. Temperature units in ∘C, time intervals in seconds and flow in mL/min. Program | Start | End | Ramp | Hold | Ar
---|---|---|---|---|---
stage | temperature | temperature | time | time | flow
Atomize | 2800 | 2800 | - | 10 | 10
Heating | 2800 | 2800 | - | 10 | 200
Cool | - | - | - | 20 | 200
Table 4: Settings for measurements with HR cuvettes and doping with La+K. The photo-multiplier voltage was set to 400 V. Sample injection volume: 15 $\mu$L. After the cooling stage, 25 $\mu$L of pure water are injected in the cuvette and the stages of heating and cooling are repeated twice. See text for details. Temperature units in ∘C, time intervals in seconds and flow in mL/min. Program | Start | End | Ramp | Hold | Ar
---|---|---|---|---|---
stage | temperature | temperature | time | time | flow
Atomize | 2700 | 2700 | - | 10 | 10
Heating | 2800 | 2800 | - | 10 | 200
Cool | - | - | - | 20 | 200
Table 5: Settings for measurements with HR cuvettes and Ta/W platforms. The
photo-multiplier voltage was set to 400 V. Sample injection volume: 13 $\mu$L.
After the cooling stage, a heating stage of 5 seconds followed by a cooling
stage of 20 seconds is enough to ensure no memory effects. See text for
details. Temperature units in ∘C, time intervals in seconds and flow in
mL/min.

The total duration of the basic sequence is about 160 seconds (excluding
sample injection time). The ramp time of both drying processes were set to be
long enough to ensure a slow and smooth drying process, preventing sample
bubbling or spillage within the cuvette. Suppressing bubbling and spillage
ensures an efficient and homogeneous atomization resulting in enhanced signal
quality and improved repeatability. Despite the absence of organic materials
in our samples, the ashing step was included to broaden the applicability of
our results and make them relevant for other purposes. Note the higher
temperatures the C HR cuvettes can achieve as compared to those with HR
cuvettes222Cuvette maximum temperatures are provided by the manufacturer,
Hitachi, Ltd.. This allows the former to achieve a better atomization of the
sample.

The heating stage following atomization serves as a cleaning process to
eliminate any residual impurities in the cuvette. However, this is not
achieved when doping with La+K and a cleaning process is repeated twice,
independently of cuvette type. This cleaning process consists in the injection
of 25 $\mu$L of pure water into the cuvette followed by the heating and
cooling stages, similar to those shown in Tables 3 and 4. Sometimes this
procedure may not be sufficient, and a blank measurement, i.e. including all
stages, is needed to completely remove all impurities. For the measurements
with platforms, a heating stage of 5 seconds followed by a cooling stage of 20
seconds is enough to ensure no memory effects. The difference in the cleaning
procedures needed after atomization translates to a much longer measurement
time for the doping with La+K method compared to the Ta and W platforms
method. Including samples and doping injection time, the measurement time for
the Ta and W platforms method is only 25$\%$ of that required by the La+K
doping method.

###  2.3 Doping with Potassium and Lanthanum

To increase the signal and reduce memory effects two dopants were found to be
useful: lanthanum (La) and potassium (K) personal_communication .

AAS measurements rely on the absorption of light from the hollow-cathode lamp
by the ground state atoms of an element, in our case Gd. Ionized Gd atoms do
not absorb radiation like neutral ground states do. It has been shown that,
under similar conditions, adding K, which has a low ionization potential,
increases the signal, i.e. the ABS of light by the measured element
SANUI1968330 .

When analysing sulfates it has been found the presence of chemical
interference that can distort the measurement results. It has been reported
that La can suppress this interference under similar conditions AN9608500495 ;
WILLIS1960259 ; YOFE1958166 . The formation of carbides, compounds of carbon
and a metal, hinders atomization liang1991determination , making it an
important effect to avoid. Applying a coating of lanthanum (La) is known to
reduce this effect ebdon1991introduction .

Approximately 15 $\mu L$ of the sample are injected into the cuvette for the
measurement using this method. The La+K doping is injected separately. The
best results were obtained when injecting 10 $\mu L$ of a mixture containing K
and La in a proportion of 100:5 from 1000 ppm solutions.

###  2.4 Tantalum and Tungsten Platforms

Because the production of C HR cuvettes was discontinued and the serious
limitations of the HR cuvettes (lower number of furnace processes during its
lifetime and maximum temperature), a new method was required to reduce memory
effects. We drew inspiration from L’vov platforms and a previous study that
utilized Ta foils liang1991determination , although we arrived at somewhat
different results. Ta is a transition metal that exhibits excellent heat
conductivity, low thermal expansion, and high melting point (3017∘C) and
density (16.7 g/cm3). Ta is a rather ductile metal that is relatively easy to
work with. We searched for similar or even better candidates than Ta and found
that W was a suitable candidate due to its higher melting point (3422∘C) and
density (19.25 g/cm3), which are comparable to those of uranium and gold.
Considering that these platforms are inserted into the cuvette, the low
expansion coefficient of W, which is the lowest among all pure metals,
contributes to achieving mechanical stability inside the cuvette.

These platforms were made by machining foils of Ta and W of 20 cm x 20 cm.
Foil thicknesses of 0.1 mm, 0.2 mm and 0.3 mm were evaluated. While platforms
of 0.1 mm did not work reliably for more than a few measurements, platforms of
0.2 mm would last for at least one cuvette lifetime. However, platforms with a
thickness of 0.3 mm were more reliable and could typically last through the
lifetimes of at least two cuvettes333If the platform showed a crack or any
other damage, it would not be used again.

Various platform sizes were evaluated as well. The best results were obtained
with pieces measuring 4.37 mm in width and 7.50 mm in length. Usual machining
tools tend to damage the edges of the platforms. Therefore, a company was
commissioned to machine these pieces using electrical discharge machining
(EDM). Although other techniques such as water jet machining may also be
viable. EDM has proved to be an effective, precise and quite economical way of
machining Ta and W pieces out of larger foils.

Several shapes, from just flat to curved with different curvatures, were
tested. The best results were achieved when the pieces were molded into a pipe
with a diameter of 4.35 mm. However, while Ta was easy to work with in the
molding process, the brittleness of W posed more challenges. To mold the W
pieces they had to be heated to approximately 450∘C KRSJAK201481 . A Hakko
FR-810B hot air rework station was utilized to heat the W piece within the
mold itself before giving it the final shape.

The sample injection volume was reduced from 15 $\mu L$ to 13 $\mu L$ to
prevent it from spilling outside the Ta/W platforms onto the cuvette floor,
which would lead to repeatability issues.

##  3 Results

As stated in the Introduction 1, the Gd concentration is a critical parameter
to measure, and our main goal is to improve the uncertainty of our
measurements. Before we assess the uncertainties of our methods, we
investigate how the average ABS of a sample changes as a function of the
number of furnace processes a cuvette has undergone. Additionally, we study
the differences from one cuvette to another. This will lead to the
determination of a correction factor that is estimated for each cuvette and
method, see 3.1. Using this correction, we then estimate the uncertainties for
each cuvette type and method in 3.2.

###  3.1 ABS dependence on number of furnace processes

As shown in Tables 3, 4 and 5, the cuvettes reach temperatures up to about
2800-3000∘C. Such temperatures are necessary to achieve an efficient sample
atomization and cleaning to remove any impurity left in the cuvette. Prolonged
exposure to high temperatures gradually degrades the cuvettes, requiring their
replacement at a certain point: approximately 100 atomizations for C HR and
about 70 for HR cuvettes.

Measuring the ABS of a sample requires to go through the basic sequence that
was detailed in Section 2.2. The ABS of a sample varies after a certain number
of furnace processes. This variation depends not only on the total number of
furnace processes that the current cuvette has undergone but also on the
efficiency of the preceding furnace processes as well. While cuvette aging
leads to a decrease in ABS values, atomization inefficiencies or memory
effects potentially have the opposite effect, artificially increasing the ABS
value. Consequently, in the ideal scenario of perfect sample atomization, we
would observe solely the degradation of the cuvette, indicated by decreasing
ABS values after several furnace processes.

The ABS variation of a sample typically follows a linear trend for all cuvette
types and analysis methods. The slope of the ABS variation depends on the
cuvette aging rate and the accumulated memory effects. Measuring the slope
allows for the correction of these effects and enhances the precision and
accuracy of our measurements. Although the rate of quality degradation and the
extent of memory effects vary between individual cuvettes, it is interesting
to asses the quality traits of the two cuvette types and assess differences
among measurement methods in this context. Each line in Figure 3 represents
the average slope during the lifetime of C HR and HR cuvette types, and for
the methods of La+K doping and using Ta and W platforms. The colored area in
each figure represents the observed slope variability for a particular cuvette
type and method.

The C HR cuvettes with the La+K doping method (upper left) exhibit an average
positive slope. This means that when comparing from one cuvette to another,
the difference in memory effects are the most important factor in the behavior
observed for this cuvette type and method combination. The memory effects
could have been reduced by adopting a more aggressive cleaning method. We
could have tried this if the C HR cuvettes production would not have been
discontinued. However, the associated costs in measurement time and increase
(decrease) of furnace processes (cuvette lifetime) would have made this
undesirable.

An average negative slope is observed for the HR cuvette type with the method
of La+K doping (upper right), although the slope variability is large and in
many instances, it is positive. This indicates that cuvette aging is more
important for this cuvette type than for the C HR type. The slope variability
among individual cuvettes is also larger compared to the C HR cuvettes.

The HR cuvette type with the Ta platforms method (bottom left) also exhibits
an average negative slope, which is more pronounced compared to the previous
case. As the cuvette types are the same in these two cases, this suggests that
the memory effects have been significantly diminished. The slope variability
for this method is lower compared to the case of La+K doping with the same
cuvette type. However, we still observe a larger slope variability for this
cuvette type and method compared to the C HR cuvette type with La+K doping.

The HR cuvette type with the W platforms method (bottom right) exhibits a
similar average slope and variability to that of Ta platforms. Because both
the Ta and W platforms typically outlast the lifetime of a single HR cuvette,
and their performance is restored when inserted into a second cuvette, this
suggests that most of the observed aging can be attributed to the cuvette
itself.

Figure 3: Quality traits of cuvettes and analizing methods: average ABS slope
of a sample as a function of furnace processes for Pyro Tube C HR cuvettes
with La+K doping method (upper left), Pyro Tube HR cuvette with La+K doping
method (upper right), Pyro Tube HR cuvette with the Ta platform method (bottom
left) and Pyro Tube HR cuvette with W platform method (bottom right). The
colored areas show the observed slope variability for a given cuvette type and
method.

In summary, Figure 3 shows how in general the ABS of one sample would change
during the lifetime of a cuvette for a given method and cuvette type. C HR
cuvettes last longer, the ABS of a sample does not change much during a
cuvette’s lifetime and a slight memory effect is seen. For the HR cuvette
type, we observe greater variations from one cuvette to another. With Ta/W
platforms the memory effects basically disappear and we are left with the
cuvette aging effects. Note that this figure does not reflect the measured ABS
variations of one sample within the lifetime of a cuvette, which we will study
next.

###  3.2 Measurement Uncertainty

After applying a linear correction for aging and memory effects to a series of
samples with known concentration for each cuvette type and measurement method
combination, the dispersion of ABS measurements was studied. Figures 4, 5, 6
and 7 show the distribution of the measured ABS as percentage from the true
value. These represent the resolution of our different approaches: C HR
cuvettes with La+K doping method, HR cuvettes with La+K doping method, HR
cuvettes with the Ta and W platforms method, respectively. In Figure 4, a
standard deviation of about 5$\%$ is observed for the C HR cuvettes with La+K
doping method. This is very similar to the HR cuvettes with La+K doping method
in Figure 5 (also 5$\%$). The ABS dispersion is significantly reduced when
using the Ta and W platform methods, see Figures 6 and 7, with both methods
yielding a similar standard deviation of about 3$\%$.

Figure 4: Distribution of measured ABS as percentage from the true value for
samples of known concentration with the Pyro Tube C HR cuvettes and La+K
doping method after applying a correction for the aging and memory effects.
Figure 5: Distribution of measured ABS as percentage from the true value for
samples of known concentration with the Pyro Tube HR cuvettes and La+K doping
method after applying a correction for the aging and memory effects. Figure 6:
Distribution of measured ABS as percentage from the true value for samples of
known concentration with the Pyro Tube HR cuvettes and the method of Ta
platforms after applying a correction for the aging and memory effects. Figure
7: Distribution of measured ABS as percentage from the true value for samples
of known concentration with the Pyro Tube HR cuvettes and the method of W
platforms after applying a correction for the aging and memory effects.

Note that after correcting for aging and memory effects, the variance of the
distribution of measured ABS is significantly smaller for Ta/W platforms than
for La+K doping, the later being mostly independent of cuvette type. These
results are consistent with a very significant reduction of memory effects
when using the Ta/W platforms method even though smaller variations were seen
from one C HR cuvette to another.

For our Gd sulfate measurements at EGADS and Super-Kamiokande, two consecutive
ABS measurements are performed and combined into an average. This is what we
commonly call a sample measurement. Based on the evaluated standard errors
mentioned above, the errors for each cuvette type and method can be
calculated. These errors are summarized in Table 6. Since the primary
contribution to the errors is of a statistical nature, further reduction in
errors can be achieved through subsequent measurements.

Measurement | Doping with | Ta and W
---|---|---
resolution | La+K | platforms
Pyro Tube C HR | 3.5$\%$ | ✗
Pyro Tube HR | 3.5$\%$ | 2$\%$
Table 6: Resolution of the procedure of average measurement as used at EGADS
and Super-Kamiokande for the different methods and cuvette types.

Before concentration measurements of Gd sulfate samples can be done, a
calibration of the AAS is needed to translate from the sample ABS to Gd
sulfate concentration. For that, the ABS of 3 samples are measured: blank
(pure water), 10 ppm Gd sulfate and 20 ppm Gd sulfate. For each sample the ABS
is measured twice and the average is used in a linear fit ABS vs
concentration. An example of such a calibration is shown in Figure 8a. After
that, the ABS of samples of unknown concentration are measured.

As mentioned in Section 1, the AAS measurement range is between 5-30 ppm.
However, the samples are usually above this range and they must be carefully
diluted, their diluted concentration measured and the original concentration
calculated from the dilution factor. With these setup and settings, samples
from the EGADS and Super-Kamiokande detectors were taken at different depths
and measured MARTI ; Abe_2022 . An example of the Gd sulfate concentration for
the three sampling positions in the EGADS detector, top, centre and bottom, is
shown in Figure 8b from MARTI .

Figure 8: Left a) example of calibration data at three Gd sulfate
concentrations pure water (0 ppm), 10 ppm and 20 ppm including the linear fit.
Right b) Gd sulfate concentration for the three sampling positions in the
EGADS detector.

##  4 Conclusion

Two methods for measurements of Gd sulfate with an Atomic Absorption
Spectrometer have been presented and compared: doping with La+K and using Ta/W
platforms. Additionally, a comparison between the discontinued C HR cuvette
and the HR cuvette types when doping with La+K was also shown.

Cuvette type C HR were more stable and showed a smaller variability among
cuvettes in the measurements. Moreover, they lasted a larger number of furnace
processes which made measurements easier. Despite the discontinued production,
we found a good alternative by utilizing Ta and W platforms with the HR
cuvettes. Ta and W are two metals that are very suitable for our purposes
since they provide mechanical stability and a slow rate of aging compared to
the HR cuvette. Furthermore, they improve atomization of Gd and minimize
memory effects.

The reduced memory effects have another positive effect: less cuvette cleaning
is needed and therefore a more efficient usage of the cuvette lifetime can be
done. Another positive consequence is the reduction in measurement time to
only 25$\%$ of that required by the La+K doping method.

The uncertainty error of a single sample measurement for the La+K doping
method has been reduced from 3.5$\%$ to 2$\%$ with the Ta/W platform method.

Both the La+K doping and Ta/W platform methods have been successfully used in
assessing the concentration and homogeneity of Gd sulfate in the EGADS and
Super-Kamiokande detectors, as well as in monitoring concentration changes.

## Acknowledgments

We would like to thank the Super-Kamiokande collaboration and very specially
to the EGADS group for their help in conducting this study. We also would like
to thank the technicians of Kavli-IPMU Nakagawa Hitoshi and Kanazawa Motoichi
for their help and support. We gratefully acknowledge the cooperation of the
Kamioka Mining and Smelting Company. Ll. Marti have been partially supported
by funds from the Ministry of Education, Culture, Sports, Science and
Technology (Grant-in-Aid for Young Scientists No. 15K17638). L. Labarga
acknowledges the support from the Spanish Ministry of Science, Universities
and Innovation (grant PID2021-124050NB-C31) and the European Union’s Horizon
2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant
agreement no. 872549 H2020-MSCA-RISE-2019 SK2HK.

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#  Compact and variable radio emission from an active galaxy with supersoft
X-ray emission

Lei Yang  Department of Physics, Anhui Normal University, Wuhu, Anhui, 241002,
China  Xinwen Shu Department of Physics, Anhui Normal University, Wuhu, Anhui,
241002, China  Fabao Zhang  Department of Physics, Anhui Normal University,
Wuhu, Anhui, 241002, China  Yogesh Chandola  Purple Mountain Observatory,
Chinese Academy of Sciences, No.10 Yuanhua Road, Qixia District, Nanjing
210023, China  Daizhong Liu  Max-Planck-Institut für Extraterrestrische Physik
(MPE), Giessenbachstr. 1, D-85748 Garching, Germany  Yi Liu  Purple Mountain
Observatory, Chinese Academy of Sciences, No.10 Yuanhua Road, Qixia District,
Nanjing 210023, China  Minfeng Gu  Key Laboratory for Research in Galaxies and
Cosmology, Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80
Nandan Road, Shanghai 200030, China  Margherita Giustini  Centro de
Astrobiologia (CAB), CSIC-INTA, Camino Bajo del Castillo s/n, Villanueva de la
Cañada, E-28692 Madrid, Spain  Ning Jiang  Department of Astronomy, University
of Science and Technology of China, Hefei, Anhui 230026, China  Ya-Ping Li
Key Laboratory for Research in Galaxies and Cosmology, Shanghai Astronomical
Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030,
China  Di Li  National Astronomical Observatories, Chinese Academy of
Sciences, Beijing 100012, China  David Elbaz  Laboratoire AIM-Paris-Saclay,
CEA/DRF/Irfu - CNRS - Université Paris Diderot, CEA-Saclay, 91191 Gif-sur-
Yvette, France  Stephanie Juneau  NSF’s National Optical-Infrared Astronomy
Research Laboratory, 950 North Cherry Ave, Tucson, AZ 85719, USA  Maurilio
Pannella  Università di Trieste, Dipartimento di Fisica, Sezione di
Astronomia, via Tiepolo 11, 34143 Trieste, Italy  Luming Sun  Department of
Physics, Anhui Normal University, Wuhu, Anhui, 241002, China  Ningyu Tang
Department of Physics, Anhui Normal University, Wuhu, Anhui, 241002, China
Tinggui Wang  Department of Astronomy, University of Science and Technology of
China, Hefei, Anhui 230026, China  Hongyan Zhou  Polar Research Institute of
China, 451 Jinqiao Road, Shanghai, China  Department of Astronomy, University
of Science and Technology of China, Hefei, Anhui 230026, China

###### Abstract

RX J1301.9+2747 is a unique active galaxy with supersoft X-ray spectrum that
lacks significant emission at energies above 2 keV. In addition, it is one of
few galaxies displaying quasi-periodic X-ray eruptions that recur on a
timescale of 13-20 ks. We present multi-epoch radio observations of RX
J1301.9+2747 using GMRT, VLA and VLBA. The VLBA imaging at 1.6 GHz reveals a
compact radio emission unresolved at a scale of $<$0.7 pc, with a brightness
temperature of $T_{\rm b}$$>$$5\times 10^{7}$ K. The radio emission is
variable by more than a factor of 2.5 over a few days, based on the data taken
from VLA monitoring campaigns. The short-term radio variability suggests that
the radio emitting region has a size as small as $8\times 10^{-4}$ pc,
resulting in an even higher brightness temperature of $T_{\rm
b}$$\sim$$10^{12}$ K. A similar limit on the source size can be obtained if
the observed flux variability is not intrinsic and caused by the interstellar
scintillation effect. The overall radio spectrum is steep with a time-averaged
spectral index $\alpha=-0.78\pm 0.03$ between 0.89 GHz and 14 GHz. These
observational properties rule out a thermal or star-formation origin of the
radio emission, and appear to be consistent with the scenario of episodic jet
ejections driven by magnetohydrodynamic process. Simultaneous radio and X-ray
monitoring observations down to a cadence of hours are required to test
whether the compact and variable radio emission is correlated with the quasi-
periodic X-ray eruptions.

Active galactic nuclei (16); Accretion (14); Radio jets (1347)

††software: CASA (v5.3.0 and v5.6.1; McMullin et al., 2007), AIPS (Greisen,
2003), DiFX software correlator (Deller et al., 2011), DIFMAP (Shepherd,
1997), GILDAS777https://www.iram.fr/IRAMFR/GILDAS

##  1 Introduction

Active galactic nuclei (AGNs) are powered by accretion of gas onto
supermassive black holes (SMBHs) with $M_{\rm BH}\sim 10^{6}-10^{9}$ M⊙. They
are considered to be scaled-up versions of Galactic black hole X-ray binaries
(XRBs, $M_{\rm BH}$ $\sim$10 M⊙), because of the similarities seen from the
accretion flow, such as rapid X-ray variability (Markowitz & Uttley, 2005;
McHardy et al., 2006), the relation between the X-ray and radio emission
(Merloni et al., 2003; King et al., 2013), and the correlation between the
X-ray spectral index and Eddington ratio (Yang et al., 2015; Ruan et al.,
2019; Ai et al., 2020). X-ray observations of XRBs have revealed the existence
of two characteristic accretion states, namely soft and hard states (Done et
al., 2007). The soft state is dominated by the thermal emission from an inner
accretion disk. As accretion rate drops, the Comptonized coronal emission at
higher energies comes to dominate the X-ray spectrum (hard state). It is well
established that a flat-spectrum, compact jet is commonly observed during the
hard state, which is however significantly quenched in the soft state (Fender
et al., 2004). When sources transition from the hard to the soft accretion
state, the radio emission begins to vary more dramatically, showing episodic
jet ejection events (Miller-Jones et al., 2012; Bright et al., 2020). Such
spectral state transitions and the relationships between jet ejections and
accretion disk emission are still poorly understood in AGNs.

AGNs can be divided into radio-loud and radio-quiet populations according to
the radio loudness parameter, which is defined as the ratio of the flux
densities between 6 cm and optical 4400Å ($R\equiv f_{\rm
6~{}cm}/f_{4400\AA}$). Radio-loud AGNs are conventionally classified as those
with $R\lower 2.15277pt\hbox{$\;\buildrel>\over{\sim}\;$}10$ (Kellermann et
al., 1989). It has been found that the radio loudness is anti-correlated with
the Eddington ratios (Ho, 2002; Greene et al., 2006), albeit with a larger
scatter, implying that the jet radiation may be dependent on the accretion
process. This seems supported by the low radio-loud fraction ($\sim$7%,
Stepanian et al., 2003; Zhou et al., 2006) observed in narrow-line Seyfert 1
galaxies (NLSy1s), a population of AGNs characterized by high accretion rates
(Collin & Kawaguchi, 2004; Komossa et al., 2008). However, there are a few
radio-loud NLSy1s exhibiting blazar properties (Zhou et al., 2007; Yuan et
al., 2008; Abdo et al., 2009; Foschini, 2020), indicating that a relativistic
jet can be formed at high accretion rate. This challenges canonical theories
of jet formation that have been established in XRBs. Strictly speaking, the
accretion states in NLSy1s are not analogous to the high-soft states seen in
XRBs, as their X-ray spectra are still dominated by power-law emission
originating from the corona.

The discovery of AGNs with supersoft X-ray emission in the past decade has
drawn a considerable attention, including 2XMM J123103.2+110648 (Terashima et
al., 2012), GSN 069 (Miniutti et al., 2013), and RX J1301.9+2747 (hereafter
J1302, Sun et al., 2013). Their X-ray spectra have weak or no hard X-ray
emission at energies above $\sim$2 keV, and can be described by a dominant
blackbody component with a temperature of $kT\sim 0.05-0.1$ keV. This appears
to be a close analog to the disk-dominated spectrum that is typically seen in
the high and soft states of XRBs (Shu et al., 2017). While such an extreme
soft emission is unprecedented among AGNs or NLSy1s, they are more commonly
seen in stellar tidal disruption event (TDE; Komossa, 2015; Saxton et al.,
2020). Indeed, two out of three known supersoft AGNs, 2XMM J123103.2+110648
and GSN 069, could be associated with TDEs (Lin et al., 2017; Shu et al.,
2018; Sheng et al., 2021). Of particular interest, all supersoft AGNs are
found to show regular X-ray variability in the form of quasi-periodic
oscillations (QPOs, Lin et al., 2013; Song et al., 2020) or quasi-periodic
eruptions (QPEs, Miniutti et al., 2019; Giustini et al., 2020). The latter are
characterized by short-lived flares of supersoft X-ray emission over a stable
(quiescent) flux level, and recur on time scales of hours, representing a new
cosmic phenomenon associated with extreme variability close to SMBHs, e.g.,
the radiation pressure instability in the accretion disk (Pan et al., 2022).
This suggests a possible link on the part of the extreme variability
phenomenon to the supersoft X-ray component.

J1302 is the only supersoft AGN in which both QPOs and QPEs are detected (Song
et al., 2020; Giustini et al., 2020). The QPO frequency is stable over almost
two decades, suggesting that it may correspond to the high-frequency QPOs
found in XRBs, adding further evidence of the similarity of J1302 to the XRBs.
In this paper, we report the detection of a compact, variable radio emission
in J1302, possibly originating from optically-thin jet ejections. We adopt a
cosmology of $\Omega_{M}$ = 0.3, $\Omega_{\lambda}$ = 0.7, and $H_{0}$ = 70 km
s-1 Mpc-1 when computing luminosity distance.

Table 1: Summary of the radio observations of RX J1301.9+2747

Project | Date | Array |  $\nu$obs | Sint. | Speak | rms | Beam Size (PA)
---|---|---|---|---|---|---|---
|  |  | GHz |  $\mu$Jy |  $\mu$Jy/Beam |  $\mu$Jy/Beam | arcsec × arcsec(deg)
15A-349 | 05 July 2015 | VLA | 9.0 | 119.2 | 115.1 | 10.1 | 0.23 $\times$ 0.18 (84.21)
| 07 Aug 2015 | VLA | 9.0 | 154.7 | 154.4 | 10.4 | 0.18 $\times$ 0.17 (-22.89)
| 07 Aug 2015 | VLA | 9.0 | 123.3 | 126.4 | 10.3 | 0.18 $\times$ 0.17 (-62.03)
| 07 Aug 2015 | VLA | 9.0 | 141.6 | 143.4 | 9.8 | 0.19 $\times$ 0.18 (-87.24)
| 08 Aug 2015 | VLA | 9.0 | 78.4 | 57.9 | 11.1 | 0.39 $\times$ 0.17 (68.58)
| 09 Aug 2015 | VLA | 9.0 | 89.0 | 84.6 | 10.7 | 0.18 $\times$ 0.17 (-23.63)
| 10 Aug 2015 | VLA | 9.0 | 90.4 | 98.2 | 10.0 | 0.18 $\times$ 0.18 (-65.56)
| 10 Aug 2015 | VLA | 9.0 | 144.5 | 131.2 | 10.4 | 0.20 $\times$ 0.18 (88.07)
17B-027 | 04 Sep 2017 | VLA | 6.0 | 295 | 304 | 10.2 | 2.43 $\times$ 0.84 (-63.19)
18B-115 | 05 Jan 2019 | VLA | 14.0 | 183.7 | 174.8 | 9.2 | 2.12 $\times$ 1.19 (-69.92)
| 06 Jan 2019 | VLA | 14.0 | 162.6 | 173.6 | 11.5 | 2.09 $\times$ 1.19 (-67.75)
| 07 Jan 2019 | VLA | 14.0 | 188.5 | 154.8 | 9.0 | 2.16 $\times$ 1.22 (-68.15)
| 08 Jan 2019 | VLA | 14.0 | 176.5 | 180.6 | 9.3 | 2.33 $\times$ 1.21 (-65.13)
| 09 Jan 2019 | VLA | 14.0 | 183.4 | 158.9 | 8.4 | 2.00 $\times$ 1.24 (-69.84)
| 10 Jan 2019 | VLA | 14.0 | 147.7 | 116.7 | 8.7 | 2.14 $\times$ 1.25 (-67.12)
| 12 Jan 2019 | VLA | 14.0 | 179 | 139.8 | 9.2 | 2.08 $\times$ 1.24 (-67.62)
28$\\_$039 | 31 May 2015 | GMRT | 1.4 | 764 | 735 | 23.2 | 2.40 $\times$ 1.97 (92.7)
BS255 | 14 Feb 2017 | VLBA | 1.6 | 670 | 559 | 32.5 | 0.012 $\times$ 0.0066 (25.22)
AM868 | 18 June 2006 | VLA | 1.4 | 866 | 779 | 117.2 |  $\sbond$†
VLASS‡ | 25 Nov 2017 | VLA | 3.0 | 894 | 513 | 107 | 2.60 $\times$ 2.16 (-54.25)
AS110 | 17 Oct 2020 | ASKAP | 0.89 | 1880 | 1896 | 348.2 | 25.0 $\times$ 25.0 (0.00)

Note. — †Due to the poor imaging quality, the beam size cannot be measured
using CASA. ‡VLA Sky Survey (VLASS) consists of three-epoch observations, each
separated by approximately a period of 32 months (Lacy et al., 2020). Only the
epoch I data are used in this paper. The last three rows represent the
archival VLA and Australian Square Kilometre Array Pathfinder (ASKAP) data
(Section 3.3).

##  2 OBSERVATION AND DATA REDUCTION

###  2.1 VLA

J1302 was not detected by Faint Images of the Radio Sky at Twenty cm (FIRST)
using Karl G. Jansky Very Large Array (VLA), with a 5$\sigma$ upper limit on
the peak flux of 0.95 mJy/beam. It was serendipitously detected in the deeper
VLA 1.4 GHz imaging of Coma cluster, with a peak flux density of $0.78\pm
0.11$ mJy (Miller et al., 2009). To further study the origin of the radio
emission, we observed J1302 with the VLA in three different bands, C, X, and
Ku, centered at 6.0 GHz, 9.0 GHz, and 14.0 GHz, respectively. The C-band
observation was performed in the B configuration on 2017 Sep 4 (project code:
17B-027), and the data were divided into 16 spectral windows with a total
bandwidth of 2 GHz. The X-band observations were carried out eight times in
the A configuration between 2015 July 5 and Aug 10 (project code: 15A-349). At
the Ku-band, monitoring observations with a daily cadence were carried out in
the C configuration between 2019 Jan 5 and Jan 12 (project code: 18B-115). All
the observations were phase-calibrated using the calibrator J1310+3220, and 3C
286 was used for bandpass and flux density calibration. The total integration
time is 30-35 min per band, with on-source time of 20 min at C-band, 10 min at
X-band, and 12 min at Ku-band, respectively.

The data were reduced using the Common Astronomy Software Applications (CASA,
version 5.3.0) and the standard VLA data reduction pipeline (version 5.3.1).
For the reduced data product, we inspected each spectral window and manually
flagged channels affected by radio frequency interference (RFI). The
calibrated data were imaged using the CLEAN algorithm with Briggs weighting
and ROBUST parameter of 0, which helps to reduce side-lobes and achieve a good
sensitivity. The final cleaned maps have a typical synthesized beam of
2$\farcs$4$\times$0$\farcs$8, 0$\farcs$2$\times$0$\farcs$2,
2$\farcs$1$\times$1$\farcs$2 and an rms noise of 10, $\sim$10-11, $\sim$8-12
$\mu$Jy/beam at C, X, and Ku-band, respectively. J1302 was clearly detected in
all observations. We used the IMFIT task in CASA to fit the radio emission
component with a two-dimensional elliptical Gaussian model to determine the
position, integrated and peak flux density. The radio emission at the three
bands is unresolved and no extended emission is detected. The compactness of
the radio emission is confirmed by the ratios of integrated and peak flux
density, which are in the range 0.92–1.35, with a median of 1.09. For
consistency, only peak flux densities are used in our following analysis. The
VLA observation log and flux density measurements are presented in Table 1.

###  2.2 GMRT

J1302 was observed with the Giant Metrewave Radio Telescope (GMRT) at band 5
(central frequency of 1.37 GHz) on 2015 May 31 (project code: 28$\\_$039). The
GMRT band 5 data were divided into 512 channels across a bandwidth of 33.3
MHz. Flux calibration was conducted using 3C 147 and 3C 286, whereas the
nearby source 3C 286 was also used to determine the complex gain solutions. 3C
147 was observed for $\sim$30 minutes in the beginning while 3C 286 was
observed for 4 minutes after every 55 minutes of the J1302 scan and $\sim$30
minutes at the end of observation. 3C 147, 3C 286, and J1302 were observed for
$\sim$30 min, $\sim$65 min and $\sim$ 9.2 h, respectively. The data from the
GMRT observations were reduced using CASA (version 5.6.1) following standard
procedures and by using a pipeline adapted from the CAsa Pipeline-cum-Toolkit
for Upgraded Giant Metrewave Radio Telescope data REduction (CAPTURE; Kale &
Ishwara-Chandra, 2021). We began our reduction by flagging known bad channels,
and the remaining RFI was flagged with the flagdata task using the clip and
tfcrop modes. In total, we flagged $\sim$20$\%$ of the data. We ran the task
tclean with the options of the MS-MFS (multi-scale multi-frequency synthesis,
Rau & Cornwell, 2011) deconvolver, two Taylor terms (nterms=2), and
W-Projection (Cornwell et al., 2008) to accurately model the wide bandwidth
and the non-coplanar field of view of GMRT. We also used a robust parameter of
0, imsize of 2500 pixels and cellsize of 0.5$\arcsec$ in task tclean. In
addition, we performed a few rounds of phase-only self-calibration to improve
the fidelity of imaging. The final image has a synthesized beam of
2$\farcs$4$\times$2$\farcs$0\. The GMRT flux density measurements are shown in
Table 1.

Figure 1: Left panel: The normalized VLA peak flux densities relative to the
mean flux at 9.0 GHz ($\left\langle S_{\rm 9GHz}\right\rangle$). The lower
panel shows the same normalized peak flux densities but for the phase
calibrator J1310+3220. Right panel: The same as left, but for the radio light
curve observed at 14 GHz.

###  2.3 VLBA

We observed J1302 on 2017 Feb 14 using the Very Long Baseline Array (VLBA)
with its 10 antennas (project code: BS255). The observing frequency was
centered at 1.576 GHz in the L band. The observation was performed in the
phase-referencing mode to a nearby strong compact radio source (J1300+28).
Phase-reference cycle times were 4.5 minutes, with 3 minutes on-source and 1.5
minutes for the phase calibrator. We also inserted several scans of the bright
radio source 3C 273 for fringe and bandpass calibration with an integration
time of 2 minutes for each scan. The resulting total on-source time was 6
hours. To achieve sufficiently high imaging sensitivity, we adopted the
observational mode RDBE/DDC to use the largest recording rate of 2 Gbps,
corresponding to a recording bandwidth of 256 MHz in each of the dual circular
polarizations. The data from the VLBA experiment were correlated with the DiFX
software correlator (Deller et al., 2011). We used the NRAO AIPS software to
calibrate the amplitudes and phases of the visibility data, following the
standard procedure from the AIPS
Cookbook111http://www.aips.nrao.edu/cook.html. The calibrated data were
imported into the Caltech DIFMAP package (Shepherd, 1997) for imaging and
model-fitting. The results are given in Table 1.

##  3 Results

###  3.1 Radio variability analysis

Using the flux density between 6 cm and optical 4400 ${\AA}$ (Shu et al.,
2017), we derived the radio-loudness parameter R $\sim$ 3.3. This suggests
that J1302 is formally radio quiet, because a radio-loud object is usually
defined to have R $>$ 10 (Kellermann et al., 1989). We investigated the radio
variability based on the radio flux measurements from the VLA monitoring
observations at X and Ku-band. As shown in Table 1, the radio emission of
J1302 is variable on timescales of days to month (as short as a few hours
within one day). Specifically, the maximum flux density is higher than minimum
one by a factor of 2.6 at X-band, and the variability amplitude is a factor of
1.5 at Ku-band. To further inspect the radio variability in individual
observations, we plot in Figure 1 the radio flux densities normalized to their
time-average value for X-band (left) and Ku-band (right), respectively. We
note that the error on the peak flux density given by IMFIT task in CASA is
likely underestimated, as it is smaller than the image off-source root-mean-
square (rms). To be conservative, the flux errors shown in Figure 1 were
calculated as the sum in quadrature of map rms and calibration uncertainty
that is assumed to be of 5% of the flux density (e.g., Panessa et al., 2022).
It can be seen that the variability amplitude in the percent change in flux
relative to the averaged one can be as high as $\sim$50% at X-band, while it
is $\sim$30% at Ku-band. In the lower panel, we also show the percent flux
changes for the phase calibrator (J1310+3220), which are at a level of only
$\;\buildrel<\over{\sim}\;$10%. This flux variability does not significantly
correlated with that of J1302, indicating that the observed variability can
not be dominated by the variability of phase or flux calibrators.

To quantify the radio variability pattern of J1302 we calculated the debiased
variability index $V_{\rm rms}$ (e.g., Barvainis et al., 2005). $V_{\rm rms}$
is similar to the fractional variability $F_{\rm var}$ that is commonly used
in analyzing X-ray light curves (e.g., Vaughan et al., 2003). $V_{\rm rms}$
quantifies the variability amplitude in excess of uncertainties as a
percentage of the mean flux,

$V_{\rm
rms}=\sqrt{\frac{S^{2}-\left\langle\sigma^{2}\right\rangle}{\left\langle
F_{\nu}\right\rangle^{2}}}$ (1)

where $S^{2}$ is the variance of the light curve,
$\left\langle\sigma^{2}\right\rangle$ is the mean squared flux errors which
are the sum in quadrature of map rms and 5% flux calibration uncertainty, and
$\left\langle F_{\nu}\right\rangle$ is the mean flux density. A source is
considered to be variable when $V_{\rm rms}>0$ by a significant amount. For
J1302 we measured $V_{\rm rms}\rm(9GHz)=26\pm$4 per cent and $V_{\rm
rms}\rm(14GHz)=12\pm$3 per cent, respectively (Table 2).

In addition, we performed $\chi^{2}$ analysis to test the significance of
variability in the light curve differing from a constant. For a non-variable
source, the value of reduced $\chi^{2}$ (i.e., $\chi^{2}$/d.o.f) is expected
to be 1. For a given $\chi^{2}$ value, we can derive the variability
significance $P_{\rm var}=1-$P($>$$\chi^{2};\rm d.o.f)$, where
$P$($>$$\chi^{2};\rm d.o.f)$ is the probability to observe a $\chi^{2}$ larger
than expected under the null hypothesis of no variability. According to the
$\chi^{2}$ test, the X-band and Ku-band light curves shown in Figure 1 are
variable at a confidence level of $>$99.99% and $>$99.94%, respectively,
providing further evidence for the variability of J1302. Note that J1302 was
observed three times on 2015 Aug 7 at 9 GHz, separated by $\sim$1-2 hours, but
the intraday variability amplitude was marginal with $V_{\rm rms}$(9 GHz)=
4.8$\pm$8.4 per cent. However, a larger intraday variability amplitude of
$V_{\rm rms}$(9 GHz)= 20$\pm$7 per cent was found for the observations
performed between 2015 Aug 9 and 2015 Aug 10, indicating that the radio
emission can vary on a timescale as short as a few hours.

Table 2: Variability analysis of the radio light curves.

Peak flux | Mean | Std. dev. |  $\chi^{2}$/d.o.f | $P_{\rm var}$ |  $V_{\rm rms}$ ($\%$)
---|---|---|---|---|---
J1302 $S_{\rm 9GHz}$ ($\mu$Jy) | 113.9 | 32 | 51/7 |  $>99.99$% | 26$\pm$4
J1302 $S_{\rm 14GHz}$ ($\mu$Jy) | 157 | 23 | 24/6 |  $>99.94$% | 12$\pm$3
Calibrator $S_{\rm 9GHz}$ (Jy) | 1.6 | 0.08 | 7/7 | 0.57 | 1.6$\pm$4.3
Calibrator $S_{\rm 14GHz}$(Jy) | 1.38 | 0.03 | 0.9/6 | 0.01 | $\sbond$

Note. — Calibrator refers to J1310+3220.

Figure 2: VLBA 1.6 GHz image of J1302 and uv-plane source fitting result.
Panel (a) and (c) shows the dirty source and beam images, respectively. The
shape of the beam is shown in the left corner (gray filled ellipse) in panel
(a). Panel (b) shows the residual map which was imaged from visibilities
(subtracted a two-dimensional Gaussian model in the uv-plane). There are no
additional emission components in the residual map shown. Panel (d) is the
modeled intrinsic source image. All panels have the same color scale. The
radio source position (cyan plus sign) detected by VLBA is centered at
RA(J2000) = $13^{\rm h}02^{\rm m}00\fs 13804$ $(\pm 0\fs 00025)$ and
DEC(J2000) = +27$\arcdeg$46$\arcmin$57$\farcs$8489 ($\pm 0\farcs 00032$). The
black cross marks the optical centroid obtained from Gaia DR3. The circle
denotes the Gaia 1$\sigma$ positional error, which is the sum in quadrature of
the astrometric error and the uncertainty from astrometric excess noise.

###  3.2 Parsec-scale radio morphology

In Figure 2 (a), we show the VLBA image of J1302 at 1.6 GHz. The source
appears to be unresolved which is very similar to the beam shape in size.
Other than the central peak, no extended emission was seen above the image
sensitivity of 0.098 mJy beam-1 ($3\sigma$). To measure the source size more
accurately, we performed source fitting in the uv-plane to the total
polarization intensity data using the UV_FIT task in the GILDAS software
package. We found no additional components in the residual map (Figure 2 (b)).
The integrated flux density for the source in the uv-plane is $\sim$ 655
$\mu$Jy, in good agreement with the flux density measured in the image plane
using the DIFMAP package (Table 1). As shown in Figure 2 (d), the VLBA source
has a deconvolved size of 5.61 mas $\times$ 1.43 mas, indicating the extreme
compactness of radio emission ($<$0.7 pc at the redshift of J1302,
$z=0.0237$). This is also consistent with the size measured using DIFMAP. The
optical centroid reported by the Gaia DR3 (Gaia Collaboration et al., 2021) is
marked as a black cross in Figure 2, which is RA(J2000)$=13^{\rm h}02^{\rm
m}00\fs 13806$, Dec(J2000)$=27\arcdeg 46\arcmin 57\farcs 8496$, with
$\sigma_{\rm ra}=0.18$ mas, $\sigma_{\rm dec}=0.14$ mas, and the astrometric
excess noise of 1.35 mas222Since J1302 is an extragalactic galaxy, we used the
Gaia position without taking into account proper motions.. Considering the
positional uncertainties of Gaia, the radio peak does not show any positional
offset with respect to the optical centroid, indicating that the emission
components at the two bands arises probably from the same region very close to
SMBH.

The brightness temperature of compact radio emission can be estimated as
(e.g., Ulvestad et al., 2005)

$T_{b}=\rm{1.8\times
10^{9}(1+z)\left(\frac{S_{\nu}}{1\,mJy}\right)\left(\frac{\nu}{1\,GHz}\right)^{-2}\left(\frac{{\theta_{1}}{\theta_{2}}}{1\,mas^{2}}\right)^{-1}K.}$
(2)

where $S_{\nu}$ is the peak flux density in mJy at the observing frequency
$\nu$ in GHz, with $\theta_{1}$ and $\theta_{2}$ are the fitted FWHM of the
major and minor axes of the Gaussian component in units of mas. Using the
deconvolved size ($\theta$) derived from the VLBA image, we obtained a
brightness temperature of $\sim$ 5.0 $\times$ $10^{7}$ K. Note that the pc-
scale structure of J1302 is very compact and not resolved with the VLBA, only
the upper limit on the source size can be constrained. Hence, the brightness
temperature should be considered as a lower limit. Such a high brightness
temperature allows us to exclude the star-formation origin for the radio
emission since $T_{b}$ is typically lower than $10^{6}$ K as expected from
star-forming processes (Pérez-Torres et al., 2021). The emission from young
supernova remnants can also be ruled out, as the 1.4 GHz radio luminosity of
J1302 ($L_{\nu}=7.3\times 10^{20}$ W Hz-1) is higher than the majority of the
radio supernova remnants, such as those studied in the starburst galaxy Arp
220 (Varenius et al., 2019). In fact, despite different resolutions, the radio
flux densities measured with the VLBA and GMRT are comparable to that obtained
with the VLA about a decade ago at the similar band (Miller et al., 2009),
disfavoring the scenario of transients as the origin of the radio emission,
such as a supernova explosion, gamma-ray burst or TDE.

###  3.3 Radio spectrum

Figure 3 shows all the radio measurements available for J1302 based on our
GMRT, VLA and VLBA projects. We also included the publicly available data from
archival radio surveys such as Rapid ASKAP Continuum Survey (RACS, McConnell
et al., 2020), VLA-Coma (Miller et al., 2009), and VLASS (Lacy et al., 2020).
We retrieved the public radio maps and then measured the integrated and peak
flux density with CASA, following the same procedures described in Section
2.1. The results are shown in Table 1. Although most observations were taken
at different epochs and various resolutions, the radio flux density appear to
decrease with frequency, indicating a steep radio spectrum between 0.89 GHz
and 14 GHz. By fitting a power law spectrum ($S_{\nu}\propto\nu^{\alpha}$) to
the data points, we obtained a spectral index $\alpha=-0.78\pm$ 0.03 (red line
in Figure 3). This value is consistent with the typical radio spectral index
of $\alpha=-0.6$ for the Palomar Seyfert galaxies (Ho & Ulvestad, 2001). Note
that using the data obtained from the quasi-simultaneous observations only,
i.e., the GMRT and VLA observations performed on 2015 May-Aug, the radio
spectrum of J1302 can still be described by a steep power law with slope
$\alpha=-1.03\pm$ 0.04. Therefore, the emission from J1302 has a steep radio
spectrum, even considering the time variability, suggesting that it may be
related to optically thin synchrotron emission. We will discuss the
implications of the steep radio spectrum in Section 4.

Figure 3: The broad-band radio spectrum of J1302. The flux density errors are
calculated as the sum in quadrature of map rms and calibration uncertainty
that is assumed to be 5% of the flux density (Section 3.1). The red line shows
the best-fit power-law spectrum using the data from all observations. The
resulting radio spectral index is $\alpha=-0.78\pm$ 0.03. The error bars for
the radio spectral index are estimated using Monte Carlo simulations (gray
shaded region), assuming that the error on each flux density measurement
follows a Gaussian distribution.

##  4 Discussion

We report radio variability on daily to month timescales in the supersoft AGN
J1302 through VLA monitoring campaigns in 15 epochs on 2015 July-Aug and 2019
Jan. In addition, we detect an unresolved radio emission at a mas-scale with
the VLBA, corresponding to $<$0.7 pc at the redshift of J1302. J1302 is one of
few AGNs with X-ray QPEs, and has a low black hole mass ($M_{\rm BH}\lower
2.15277pt\hbox{$\;\buildrel<\over{\sim}\;$}10^{6}$ M⊙) accreting at a high
rate ($L_{\rm bol}/L_{\rm Edd}\lower
2.15277pt\hbox{$\;\buildrel>\over{\sim}\;$}$0.1, Shu et al., 2017). The radio
light curve is variable with a rms amplitude of 26 $\pm$ 4 per cent and 12
$\pm$ 3 per cent with respect to the mean flux density at X-band (9 GHz) and
Ku-band (14 GHz), respectively. Daily flux variation up to a factor of
$\sim$2.6 is also observed at X-band. Such highly variable radio emission is
an unusual property for J1302 as a radio-quiet AGN (Section 3.1). Radio
emission from radio-quiet AGNs could arise from different physical processes
(Panessa et al., 2019), including star-formation, outflow, jet and accretion-
disk corona. We will discuss these scenarios in detail according to the radio
flux variability, morphology, size, brightness temperature, and time-averaged
spectral index.

###  4.1  Extrinsic variability caused by interstellar scintillation?

The radio flux variability, if it is intrinsic to the AGN, would be useful to
distinguish the sources of radio emission. We first consider whether the
observed variability might be induced by the effect of refractive interstellar
scintillation (ISS). This process occurs when radio waves propagate through an
inhomogeneous plasma of our Galaxy, which could cause intraday variability in
some AGNs with compact radio emission (Lovell et al., 2003; Rickett, 2007).
The amount and timescale of radio variation caused by ISS depend on the
Galactic electron column density along the line of sight and the observing
frequency. Using the NE2001 free electron density model developed by Cordes &
Lazio (2002)333https://pypi.org/project/pyne2001/, and the Galactic dispersion
measure (DM)444 J1302 has a galactic coordinate of
$(l,b=49.138781^{\circ},87.566837^{\circ})$. We used the DM of 9.25 cm-3 pc
for J1302, which was derived from the pulsar J1239+2453 ($b>86^{\circ}$) in
the ATNF Pulsar Catalogue. along the line of sight to J1302, we find that, at
the position of J1302, the transition frequency between strong and weak
scattering regime is $\nu_{0}$$\sim$4.9 GHz. Hence J1302 is in the weak-
scattering regime at 9 GHz and 14 GHz. In this case, we computed the
fractional modulation index due to ISS (Walker, 1998)555In Walker (1998), the
modulation index $m$ is used to calculate the variability amplitude caused by
ISS, which is defined as the ratio of the rms deviation to the mean value of
the observed flux densities, $m=\sqrt{\frac{S^{2}}{\left\langle
F_{\nu}\right\rangle^{2}}}$.  which is $m=0.42$ at 9 GHz and $m=0.23$ at 14
GHz, respectively, comparable to that observed in J1302. This amount of
modulation is expected to occur on a time-scale of $t_{\rm F}\sim
2(\nu_{0}/\nu)^{1/2}$ h $\sim$1-2 h. While J1302 is found to vary at 9 GHz on
a timescale as short as a few hours, the variability amplitude can be as low
as $V_{\rm rms}=4.8\pm 8.4$ per cent, which seems inconsistent with the
prediction of the ISS effect. On the other hand, if ISS is the main mechanism
responsible for the flux density variation, the angular size of the radio
source should be similar to the first Fresnel zone, $\theta_{\rm F}\sim
8/\sqrt{D\nu}\sim$ 2.4-3.0 $\mu$as, where $D$ (in kpc) is taken as the NE2001
model distance for DM$=9.25$ cm-3 pc, and $\nu$ is the observed frequency.

###  4.2  Sub-kpc outflow

Although the radio emission is variable and observed at different epochs and
resolutions, we can obtain a time-averaged radio spectral index of
$\alpha=-0.78\pm$ 0.03 between 0.89 GHz and 14 GHz (Figure 3), suggestive of
an optically-thin steep spectrum. Note that if using the data from GMRT 1.4
GHz, VLA 3 GHz, 6 GHz, and 14 GHz observations which have similar resolutions
(i.e., $\sim$2″), a consistent radio steep spectrum can be obtained
($\alpha=-0.70\pm$ 0.03). Laor et al. (2019) suggested that a sub-kpc outflow
interaction with the ambient interstellar medium could cause the optically-
thin radio emission in radio-quiet AGNs. However, if such a nuclear outflow
interaction were present, it would be resolved by our high-resolution VLBA
observation into a number of clumpy structures or extended diffused emission
(e.g., Yang et al., 2021; Yao et al., 2021). It is obviously incompatible with
the VLBA imaging of J1302. On the other hand, there are no blue-shifted
absorption or emission lines in the X-ray and optical spectra suggestive of
outflows. Hence the outflow interpretation for the radio emission seems
disfavored.

###  4.3  Steady and continuous jet

Based on the high-resolution VLBA observation, J1302 has a high brightness
temperature of $\;\buildrel>\over{\sim}\;$5$\times$ $10^{7}$ K, which rules
out the origin of radio emission from star-forming region or thermal processes
(Section 3.2). Such a brightness temperature can place J1302 at the high end
of the $T_{\rm b}$ range for the radio cores detected in local Seyfert
galaxies ($D\lower 2.15277pt\hbox{$\;\buildrel<\over{\sim}\;$}22$ Mpc, Panessa
& Giroletti, 2013). If the flux variations in the radio light curve (Figure 1)
are intrinsic to the AGN, the minimum variability on a timescale of one day
can place a constraint on the source size of less than $8\times 10^{-4}$ pc
using the light-crossing time. Such a small source size suggests that the
radio variability might originate from the innermost region of the AGN.
Adopting the mean flux density at 9 GHz, this implies that the brightness
temperature of the variable radio emission is $\;\buildrel>\over{\sim}\;$9.4
$\times$ $10^{11}$ K. Therefore, the brightness temperature is comparable to
the inverse Compton catastrophe limit of $\sim$ $10^{12}$ K (Kellermann &
Pauliny-Toth, 1969), at which an emission region will radiate away most of its
energy in X-rays via inverse Compton scattering in a timescale of days. The
brightness temperature is however an order of magnitude higher than the
equipartition temperature of 5$\times$ $10^{10}$ K (Readhead, 1994), which is
also usually used to indicate the intrinsic brightness temperature of the
radio core in AGNs. The value was estimated by assuming that there is
equipartition of energy between the radiating particles and the magnetic
field, which is derived from a spectral cutoff due to synchrotron self-
absorption (see details in Readhead, 1994). Note that if the radio variability
is extrinsic and caused by ISS, a similar limit on source size ($r_{\rm
src}\sim 1.2-1.4\times 10^{-4}$ pc constrained by the first Fresnel zone)
hence the brightness temperature can be obtained. This implies that the radio
emission could be associated with a jet. In this case, the jet could have a
Doppler factor of $\sim$1–10, depending on which intrinsic brightness
temperature is taken. Hence, the beaming effect is not significant.

If the radio emission is from a steady and continuous jet, standard
presumptions (by analog with XRBs) would be that J1302 is in the low-hard
state which is dominated by a hard X-ray power-law component at energies above
2 keV (Fender et al., 2004). However, X-ray emissions from J1302 have been
supersoft, with more than 90 per cent of photons having energies below 1 keV
(Sun et al., 2013; Shu et al., 2017; Giustini et al., 2020), resembling the
high/soft state observed in XRBs. High-resolution VLBI observations have found
evidence of the presence of a jet feature in many local Seyfert galaxies
(Panessa & Giroletti, 2013) as well as radio quiet NLSy1s with high accretion
rates (e.g., Doi et al., 2013; Yao et al., 2021), either extending up to kpc
scales or being confined to the inner pc regions due to the jet interaction
with the circumnuclear gas medium. We do not find any extended structures in
J1302 predicated by steady jets with the high-resolution VLBA observation.
This suggests that the steady-jet model cannot account for the radio emission.

###  4.4 Episodic jet ejections

Given its high accretion rate ($L_{\rm bol}/L_{\rm Edd}\lower
2.15277pt\hbox{$\;\buildrel>\over{\sim}\;$}$0.1) and steep radio spectrum, one
possible identity for J1302 is transitioning from the hard to soft state
accompanied by an isolated radio ejection event, as observed in some XRBs
(Corbel et al., 2001; Fender et al., 2004; Bright et al., 2020). It should be
noted that J1302 is one of the few AGNs with X-ray QPEs detected, which are
characterized by repetitive short-lived eruptions in the light curves.
Strictly speaking, the X-ray eruptions in J1302 seem to be irregularly spaced
in time rather than quasi-periodic (Giustini et al., 2020), which may be
linked to the evolving corona as well as jet launching process (Wilkins &
Gallo, 2015; Gallo et al., 2019). Although no hard X-ray detected in J1302,
the ratio of 5 GHz to X-ray (0.3-2 keV) luminosity in the flare state is
$3.4\times 10^{-5}$, consistent with the relation for stars with active
coronae (Laor & Behar, 2008). In the quiescent state, the luminosity ratio is
an order of magnitude higher ($L_{\rm 5GHz}/L_{\rm 0.3-2keV}=7.7\times
10^{-4}$), but still much lower than for radio-loud AGNs. This analog suggests
that a magnetically heated corona may be responsible for the radio emission of
J1302. However, theoretical studies suggest that a flat synchrotron radio
spectrum (between $\sim 1-300$ GHz) would be expected from an X-ray corona
(Raginski & Laor, 2016), which seems inconsistent with the steep spectrum
observed in J1302 (Section 3.3). It should be noted that steep radio cores at
mas scales have also detected in other Seyfert galaxies, though not being
prevalent (e.g., Panessa & Giroletti, 2013; Congiu et al., 2020), which
usually indicate the presence of optically thin synchrotron emission.

On the other hand, episodic ejections of magnetized plasmoids in the innermost
region of the AGN could be invoked to explain the radio emission. By analogy
with the coronal mass ejection in solar physics (Lin & Forbes, 2000), Yuan et
al. (2009) proposed a magnetohydrodynamical model for episodic ejection of
plasmoids from black holes associated with the closed magnetic fields in an
accretion flow. In the model, magnetic field loops are twisted to form flux
ropes because of the turbulence of the accretion flow. With the magnetic
energy gradually accumulated to reach a threshold, the flux rope loses its
equilibrium and is thrust outwards in a catastrophic way, leading to magnetic
reconnection. The magnetic energy is released in this process and converted
into the energy of thermal electrons in plasmoids associated with the ejection
of the flux rope, which then emit strong synchrotron radiation. Since the
plasmoid ejecta can be considered as single blobs, they expand almost
adiabatically after leaving the accretion disk and can quickly become
optically thin in the radio band (Yuan et al., 2009), explaining the steep
spectrum. If this is the case, the episodic X-ray eruptions in J1302 may be
regulated by magnetohydrodynamic process as well (Li et al., 2017). A high
degree of polarization and polarization angle change would also be expected
during the multi-band flares. Simultaneous radio and X-ray monitoring
observations, particularly in the X-ray eruption state, are required to search
for any correlated variability between the two bands, which is a hallmark of
the coronal ejections as the origin of short-lived X-ray flares and will be
presented elsewhere.

###  4.5  Comparison to other supersoft AGNs

In addition to J1302, two other AGNs having supersoft X-ray spectra666Note
that while two more galaxies are found to show QPEs with similar supersoft
X-ray spectra (Arcodia et al., 2021), they are possibly not be associated with
AGNs. are 2XMM J123103.2+110648 and GSN069. The latter two sources were also
observed with the VLA on 2017 Nov, in the same program as J1302 (17B-027). GSN
069 has weak radio emission, with a flux density of $S_{\rm 6GHz}=61\pm 25$
$\mu$Jy, while J1231+1106 was not detected with a 5$\sigma$ upper limit of
38.6 $\mu$Jy. Following the X-ray QPEs detected in GSN 069, an X-ray/radio
campaign has been carried out, and no significant radio variability during
QPEs is found (Miniutti et al., 2019). The inferred radio spectral index is
steep ($\alpha=-$0.7), consistent with that measured in J1302, suggesting a
radio origin from optically thin synchrotron emission. However, the ratio of 5
GHz to X-ray (0.3-2 keV) luminosity in the QPE state is $4.5\times 10^{-7}$,
about two orders of magnitude lower than that for J1302, indicating either the
radio emission or the flaring X-ray emission has different origins between the
two objects. Owing to its faint radio flux density ($<$100 $\mu$Jy), using the
VLBA to image the pc-scale structure of radio emission in GSN 069 is
challenging.

##  5 Conclusion

We present GMRT, VLA, and VLBA observations of the supersoft AGN J1302, which
revealed compact radio emission with a size of $<$0.7 pc. The radio emission
is variable on a daily timescale at both 9 GHz and 14 GHz, implying that the
radio emitting region can have a size as small as $8\times 10^{-4}$ pc, with a
high brightness temperature of $T_{\rm b}$$\sim$$10^{12}$ K. If the observed
flux variability is not intrinsic and caused by the interstellar scintillation
effect, a similar limit on the source size can also be obtained ($\sim
1.2-1.4\times 10^{-4}$ pc). The radio spectrum is steep with a time-averaged
spectral index $\alpha=-0.78\pm 0.03$ between 0.89 and 14 GHz, suggesting that
it may be related to optically thin synchrotron emission. These observational
properties rule out the radio origin from star-formation activities, sub-kpc
outflows, or AGN corona. Optically thin jet ejection driven by
magnetohydrodynamic process seems to be the most favored scenario. The
magnetohydrodynamic model can be tested with future more sensitive
polarimetric observations, which predicts a high degree of polarization in the
radio emission.

We thank the anonymous referee for his/her helpful comments that improve the
work. The data presented in this paper are based on observations made with the
Karl G. Jansky Very Large Array from the program VLA/15A-349, VLA/17B-027, and
VLA/18B-115, the Very Long Baseline Array from the project VLBA/BS255, and the
Giant Metrewave Radio Telescope from the project 28_039. We thank the staff of
the VLA, VLBA, and GMRT that made these observations possible. The National
Radio Astronomy Observatory is a facility of the National Science Foundation
operated under cooperative agreement by Associated Universities, Inc. GMRT is
run by the National Centre for Radio Astrophysics of the Tata Institute of
Fundamental Research. The work is supported by National Science Foundation of
China (NSFC) through grant No. 11822301, 12192220, 12192221, and 11833007.
M.F.G acknowledges support from the NSCS (grant No. 11873073), Shanghai Pilot
Program for Basic Research Chinese Academy of Science, Shanghai Branch (JCYJ-
SHFY-2021-013), and the science research grants from the China Manned Space
Project with NO. CMSCSST-2021-A06. Y.C. acknowledges the support from the NSFC
under grant No. 12050410259, and Center for Astronomical Mega-Science, Chinese
Academy of Sciences, for the FAST distinguished young researcher fellowship
(19-FAST-02), and MOST through grant no. QNJ2021061003L. Y.L. acknowledges the
support from Major Science and Technology Project of Qinghai Province
(2019-ZJ-A10). M.G. is supported by the “Programa de Atracción de Talento” of
the Comunidad de Madrid, grant number 2018-T1/TIC-11733.

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