2021 June 29 2021 September 22 $\langle$publication date$\rangle$

33affiliationtext: SKA Organization, Jodrell Bank, Lower Withington,
Macclesfield, SK11 9DL, UK1111affiliationtext: Astronomical Institute, Tohoku
University, Sendai 980-8578, Japan1212affiliationtext: Department of Physical
Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan

pulsars: general — stars: magnetars — pulsars: individual (XTE J1810-197)

# Multi-frequency radio observations of the radio-loud magnetar XTE J1810-197

Sujin Eie11affiliation: Department of Astronomy, Graduate School of Science,
The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
22affiliation: Mizusawa VLBI Observatory, National Astronomical Observatory of
Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan<EMAIL_ADDRESS>Toshio Terasawa22affiliationmark:  Takuya Akahori22affiliationmark:  3
3affiliationmark:  Tomoaki Oyama22affiliationmark:  Tomoya
Hirota22affiliationmark:  44affiliation: Department of Astronomical Science,
The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka,
Tokyo 181-8588, Japan Yoshinori Yonekura55affiliation: Center for Astronomy,
Ibaraki University, 2-1-1 Bunkyo, Mito, Ibaraki 310-8512, Japan Teruaki
Enoto66affiliation: Extreme Natural Phenomena RIKEN Hakubi Research Team,
RIKEN Cluster for Pioneering Research, 2-1 Hirosawa, Wako, Saitama 351-0198,
Japan Mamoru Sekido77affiliation: Kashima Space Technology Center, National
Institute of Information and Communications Technology, Kashima, Ibaraki
314-8501, Japan Kazuhiro Takefuji77affiliationmark:  88affiliation: Japan
Aerospace Exploration Agency, Usuda Deep Space Center, 1831-6 Oomagari,
Kamiodagiri, Saku, Nagano 384-0306, Japan Hiroaki Misawa99affiliation:
Planetary Plasma and Atmospheric Research Center, Tohoku University, 6-3 Aoba,
Aramaki, Aoba-ku, Sendai, Miyagi 980-8578, Japan Fuminori
Tsuchiya99affiliationmark:  Shota Kisaka1010affiliation: Frontier Research
Institute for Interdisciplinary Sciences, Tohoku University, Sendai 980-8578,
Japan 11 11affiliationmark:  12 12affiliationmark:  Takahiro
Aoki1313affiliation: The Research Institute for Time Studies, Yamaguchi
University, 1677-1 Yoshida, Yamaguchi 753-8511, Japan Mareki
Honma11affiliationmark:  22affiliationmark:  44affiliationmark:

###### Abstract

We report on the multi-frequency multi-epoch radio observations of the
magnetar, XTE J1810-197, which exhibited a radio outburst from December 2018
after its 10-year quiescent period. We performed quasi-simultaneous
observations with VERA (22 GHz), Hitachi (6.9 GHz and 8.4 GHz), Kashima (2.3
GHz), and Iitate (0.3 GHz) radio telescopes located in Japan to trace the
variability of the magnetar radio pulsations during the observing period from
13 December 2018 to 12 June 2019. The pulse width goes narrower as the
observing frequency goes higher, analogous to the general profile narrowing
behavior of ordinary pulsars. When assuming a simple power law in the range of
2.3 GHz and 8.7 GHz, the radio spectrum of the magnetar goes steeper with the
average spectral index $\langle\alpha\rangle\approx-0.85$ for the first four
months. The wide-band radio spectra inferred from our observations and the
literature suggest that XTE J1810-197 would have a double-peaked spectrum with
a valley point in 22 – 150 GHz, where the first spectral peak infers a
gigahertz-peaked spectrum (GPS) feature with a peak at a few GHz. The GPS and
the high-frequency peak have been identified in the spectra of other radio-
loud magnetars, thus they may be intrinsic features that can give a new
insight to understand various emission mechanisms and surrounding environments
of radio magnetars. Our study emphasizes the importance of simultaneous long-
term broad-band observations toward radio-loud magnetars to capture the
puzzling spectral features and establish a link to other types of neutron
stars.

##  1 Introduction

Magnetars, which are a subset of pulsars with strong X-ray/$\gamma$-ray
outbursts, have long rotation periods ( $>1$ s) and large spin-down rates,
inferring that they are young ($\lesssim 10^{4}$ yrs) neutron stars with
extremely strong magnetic fields ( $\geq 10^{14}$ G) (Thompson & Duncan,
1993). While radio pulsation is a common nature of ordinary pulsars, only 6
out of $\sim$ 30 confirmed magnetars have shown detectable radio pulses as of
November 2020 (Olausen & Kaspi 2014111McGill Online Magnetar Catalog:
http://www.physics.mcgill.ca/~pulsar/magnetar/main.html). The radio pulses
from magnetars have some different properties from those of ordinary pulsars.

One different property is the radio frequency spectrum; the spectral index,
$\alpha$, defined with the total intensity $I$ and the frequency $\nu$ as
$I\propto\nu^{\alpha}$, is close to zero (e.g. Torne et al. 2015) and a
gradual spectral steepening has been seen in some cases (e.g., Lazaridis et
al. 2008), while ordinary pulsars show much steeper spectra with the average
spectral index $\langle\alpha\rangle=-1.8\pm 0.2$ (Maron et al., 2000). The
flatter spectra of radio-loud magnetars lead to relatively stronger radio
emission at high frequencies. It allows us to explore the new type of neutron
star emission in much wider radio band.

Another different property is the strong time-variability of flux density,
spectrum, pulse shape, and polarization (e.g., Camilo et al. 2008; Lazaridis
et al. 2008; Levin et al. 2010). The variation trend is poorly understood,
nevertheless the fluctuations are known to be extreme both in the short- and
long-terms. Even, their radio emissions are transient phenomena; the
appearance is possibly associated with X-ray outbursts (e.g., Anderson et al.
2012). The flatter spectra and erratic variations of magnetar radio pulsations
have been thought to be intrinsic to magnetars themselves, suggesting a
possibility that there are some different radio-emission mechanisms in neutron
star magnetospheres.

The triggers for their extraordinary features are not yet figured out despite
numerous hypotheses on the origins of magnetars. Meanwhile, Camilo et al.
(2016) suggested that the spectrum of XTE J1810-197 became steeper down to
$\alpha\approx-3$ before it entered the radio quiescent period. Such a steep
spectrum at a late phase of outburst looks like, or even steeper than, that of
ordinary pulsars, which can infer a possible similarity in emission mechanism
except that the magnetar pulsations faded out by unknown reasons. Very
recently, in addition, the discovery of the fifth radio-loud source showed
that the magnetar Swift J1818.0-1607 has a steep spectrum with
$\alpha\simeq-2.26$ (Lower et al., 2020) even soon after the radio outburst
emerged. It opened a new paradigm that a magnetar can also emit radio pulses
akin to those from ordinary pulsars. Its spectrum later flattened (Majid et
al., 2020), implying the variety of magnetar spectral changes. Because such
behavior is known in only one example to date, it is important to examine
spectral indices and time variability for other magnetar radio outbursts.

XTE J1810-197 is known as the first radio-loud magnetar (Halpern et al., 2005)
as well as the first transient magnetar detected with a significant increase
of its X-ray luminosity (Ibrahim et al., 2004). The rotational period,
$P=5.541~{}\rm s$, and the spin-down rate, $\dot{P}=2.83\times 10^{-11}~{}\rm
s\;s^{-1}$ (Pintore et al., 2016), imply the strength of the dipole magnetic
field, $B_{\rm d}=3.2\times 10^{19}\sqrt{P\dot{P}}\approx 1.3\times
10^{14}\,\rm G$, and the characteristic age, $\tau_{\rm c}=P/2\dot{P}\approx
31000$ yr, both of which are typical values for magnetars. Radio pulsations of
XTE J1810-197 were detected in 2006 with the very same period of its X-ray
pulsations (Camilo et al., 2006). After that, the radio flux density
dramatically decreased. Then, it turned out to be in a quiescent state from
November 2008 (Camilo et al., 2016). Hereafter, we call the radio-bright
period in 2005 – 2008 “the previous outburst” in this paper.

After the long radio-silent phase of about 10 years, intense radio pulses from
XTE J1810-197 were again observed on MJD 58460 (2018-12-08) (Lyne et al.,
2018). Gotthelf et al. (2019) reported an earlier increase of its X-ray flux
between MJDs 58442 and 58448, and confirmed X-ray outburst has preceded the
radio burst. Many radio follow-up observations have reported the broad
frequency range of its radio activity during this outburst, from 300 MHz (Maan
et al., 2019) to a few GHz (Levin et al., 2019; Dai et al., 2019; Johnston et
al., 2020), to 32 GHz (Pearlman et al., 2019) and even up to 150 GHz and 260
GHz (Torne et al., 2020).

These extensive studies of XTE J1810-197 at multiple radio frequencies during
the second outburst, though, mostly cover time spans shorter than two months
and are less overlapped in the observing periods. This could restrict the
comprehensive understanding of highly variable magnetar emission in frequency
and time domains. Simultaneous broad radio-band observations of radio
magnetars in a wide time span that can capture from the very first moment of
an outburst would enable to trace their long-term emission evolution and put
together low and high frequency characteristics, providing important aspects
to understand the behavior of one of the early phases of neutron stars.

In this paper, we analyze our radio data of $\sim\,$monthly observations of
XTE J1810-197 during its second outburst and investigate the temporal and
frequency evolutions of its pulsed emission for six months. This paper is
organized as follows. In Section 2, we describe our observations and data
reduction. We show the variations in spin parameters, pulse profile, flux, and
spectrum in Section 3. In Section 4, we discuss our results of the spectra and
pulse widths and underline the significance of simultaneous long-term broad-
band observations of radio magnetars.

##  2 Observation and Data Reduction

We have conducted roughly-monthly, quasi-simultaneous, single-dish
observations using radio telescopes in Japan. The observations started on MJD
58465 (2018-12-13), five days after the first report of the strong radio
flares of XTE J1810-197 in late 2018 (Lyne et al., 2018). Our observations
were organized at 0.3 GHz, 2.3 GHz, 6.9 GHz, 8.4 GHz, and 22 GHz and they are
summarized in Table 1. If the time difference between observations is shorter
than $\sim$a day, we classified them in the same session assuming that
averaged pulse shape would not change significantly within 24 hours.

###  2.1 Observations

VERA: VLBI Exploration of Radio Astrometry (VERA) is a very long baseline
interferometry (VLBI) array operated by the National Astronomical Observatory
of Japan (NAOJ) (VERA Collaboration et al., 2020). VERA consists of four 20-m
diameter antennas located at Mizusawa, Iriki, Ishigaki, and Ogasawara in
Japan. The director’s discretionary time observations of XTE J1810-197 with
VERA were conducted for four sessions, and the total amount of observing time
per session is $\sim$ 4.2 hours including overhead. We note that VLBI was not
achieved owing to a lack of a bright calibrator. In this study, therefore, we
utilized the four VERA stations as separate four single-dish telescopes. Among
them, Ishigaki station did not capture any pulsed signals which were observed
at the other three VERA stations. It is likely due to bad weather at this
station, therefore we exclude the data of Ishigaki station from our data
reduction for this study. K-band (21.5 – 23.5 GHz) receiver was used and the
left-hand circular polarized (LCP) waves were recorded. The 22 GHz data of
VERA was recorded after divided into four sub-bands (bandwidth of 512 MHz
each) with the data recording rate of 2048 Mbps. Due to the weak intensity of
the magnetar, we integrated the four sub-bands into one broad-band in order to
increase the continuum sensitivity by a factor of 2. We then combined the
three VERA stations into one dataset to earn an additional increase of the
sensitivity (a factor of $\sqrt{3}$) after the phase is aligned by the
barycentric dynamical time (TDB).

Hitachi: Hitachi 32-m telescope is located at Hitachi in Japan (Yonekura et
al., 2016). Operated by Ibaraki University, Hitachi observations were
performed for nine sessions. The C-band (6.6 – 7.1 GHz) and X-band (8.1 – 8.7
GHz) receivers recorded LCP and right-hand circular polarized (RCP) waves,
respectively. Each band has the bandwidth of 512 MHz and the data recordings
rate of 2048 Mbps.

Figure 1:  Left panels: The probability distributions of the S/N of single
pulses on MJD 58490 (2019-01-07) after RFI cleaning. The vertical dashed line
indicates the S/N value of 5, the plotting threshold for the right panels.
Right panels: Single pulses detected during our observations on the same date
after RFI-cleaning in time-phase domain. The optimal period and period
derivatives on this observing epoch are deduced by the timing solution
reported by Levin et al. (2019) (see Section 3.1 for details), and the phase
of the main peak is adjusted to be 0.5 based on the integrated profile at 6.9
GHz. Only signals with S/N $\rm>$ 5 are plotted and S/N values are indicated
with the size and color scale shown by the color bar on the panels. The gray-
shaded areas indicate the time before and after the observations at each band.
Kashima observation at 2.3 GHz was contaminated by strong RFIs $\sim$ 106 s
after the observation started.  Table 1: Summary of observations. (1)
Observing sessions. If observation dates are within a day for datasets, we
consider them as the same session. (2) UTC-based date and MJD. (3) Center
frequency and effective bandwidth. (4) Polarization information: XY (Cartesian
orthogonal), R (RCP), L (LCP) (5) System equivalent flux density (SEFD). (6)
Start time of the observation in UT. (7) Total observation time. (8) Detection
(Y) or non-detection (N) of the pulsed emission.

|  Date (MJD) |  $\nu_{\rm center}$ (BW) [MHz] | Pol. |  SEFD [Jy] |  $t_{\rm start}$ [hh:mm] |  $t_{\rm obs}$ [hr] |
---|---|---|---|---|---|---|---
(1) |  (2) |  (3) |  (4) |  (5) |  (6) |  (7) |  (8)
1 | 2018-12-13 | 6856 (512) | L | 157.8 | 23:30 | 1.5 | Y
| (58465) | 8448 (512) | R | 137.4 | 23:30 | 1.5 | Y
| 2018-12-14 | 325.1 (4) | XY | 846.0 | 00:11 | 2.8 | N
| (58466) | 2258 (96) | R | 532.0 | 00:10 | 4.0 | Y
2 | 2018-12-18 | 6856 (512) | L | 139.1 | 02:00 | 4.0 | Y
| (58470) | 8448 (512) | R | 122.3 | 02:00 | 4.0 | Y
|  | 22483 (2048) | L | 2944.4 | 02:44 | 4.2 | Y
3 | 2019-01-07 | 325.1 (4) | XY | 846.0 | 01:00 | 2.0 | N
| (58490) | 2258 (96) | R | 532.0 | 00:00 | 0.5 | Y
|  | 6856 (512) | L | 136.8 | 01:00 | 4.2 | Y
|  | 8448 (512) | R | 123.8 | 01:00 | 4.2 | Y
|  | 22483 (2048) | L | 2820.5 | 01:24 | 4.2 | Y
4 | 2019-01-09 | 6856 (512) | L | 137.8 | 22:40 | 0.6 | Y
| (58492) | 8448 (512) | R | 129.0 | 22:40 | 1.3 | Y
5 | 2019-01-21 | 22483 (2048) | L | 2510.0 | 00:24 | 4.2 | N
| (58504) |  |  |  |  |  |
6 | 2019-02-15 | 6856 (512) | L | 133.4 | 21:00 | 3.0 | Y
| (58529) | 8448 (512) | R | 144.9 | 21:00 | 3.0 | Y
|  | 22483 (2048) | L | 4413.4 | 21:29 | 4.2 |  Y∗
7 | 2019-03-04 | 2258 (96) | R | 532.0 | 22:00 | 1.0 | Y
| (58546) | 6856 (512) | L | 136.4 | 20:00 | 4.0 | Y
|  | 8448 (512) | R | 129.2 | 19:00 | 5.0 | Y
8 | 2019-03-31 | 6856 (512) | L | 133.2 | 18:00 | 4.0 | Y
| (58573) | 8448 (512) | R | 131.1 | 18:00 | 4.0 | Y
9 | 2019-04-23 | 6856 (512) | L | 139.2 | 16:00 | 4.0 | Y
| (58596) | 8448 (512) | R | 131.1 | 16:00 | 4.0 | Y
| 2019-04-24 | 325.1 (4) | XY | 846.0 | 16:00 | 3.6 | N
| (58597) | 2258 (96) | R | 532.0 | 16:00 | 4.0 | Y
10 | 2019-06-12 | 325.1 (4) | XY | 846.0 | 13:00 | 2.0 | N
| (58646) | 2258 (96) | R | 532.0 | 13:30 | 4.0 | N
|  | 6856 (512) | L | 139.2 | 13:00 | 4.0 | Y
|  | 8448 (512) | R | 131.1 | 13:00 | 4.0 | Y

∗ Only six single pulses were detected and an integrated profile was not
obtained (see Section 3.3 for details).

Kashima: Kashima 34-m telescope had been operated by the National Institute of
Information and Communications Technology (NICT) of Japan. The telescope was
located at Kashima, Japan. We used the S-band (2210 – 2350 MHz) receiver and
recorded RCP waves. It is found that the second sub-band among four-divided
frequency bands (bandwidth of 32 MHz each) of Kashima data is highly
contaminated by radio frequency interferences (RFIs), hence 96 MHz in the
recorded bandwidth was chosen for our analysis.

IPRT: Iitate Planetary Radio Telescope (IPRT) is a dual symmetric offset
parabolic antenna with an aperture size of 31-m $\times$ 16.5-m in 2 sets
(aperture area of 1023 $\rm m^{2}$ in total; Iwai et al. 2012). The telescope
is located at Iitate, Japan, and operated by Tohoku University, primarily for
investigating the dynamic behavior of Jupiter’s synchrotron radiation
(Tsuchiya et al., 2010) and solar radio emission at low frequencies. It has
been used as well for the study of giant pulses from the Crab pulsar (Mikami
et al., 2016). We conducted IPRT observations of XTE J1810-197 at P-band
(323.1 – 327.1 MHz) and recorded two orthogonal polarized waves.

###  2.2 Data Reduction

The data obtained at the frequency lower than 6.9 GHz were coherently de-
dispersed (Hankins & Rickett, 1975; Lorimer & Kramer, 2012) with the known
dispersion measure (DM) of $178\rm\ pc\ cm^{-3}$ (Camilo et al., 2006) to
correct the dispersion delay caused by free electrons in the interstellar
medium. Later, each data was averaged in each 2-ms. The frequencies of 8.4 GHz
and 22 GHz are high enough to be free from dispersion effect (see also Torne
et al. 2015); with the known DM and the given bandwidth, the dispersion delays
are 1.3 ms and 0.2 ms at 8.4 GHz and 22 GHz, respectively, which are smaller
than the averaging time. Hence, we did not carry out a de-dispersion process
to the data at the two frequencies and averaged data for each 2-ms.

Non-periodical RFIs were manually removed from the data in frequency and time
domains to prevent any artifacts from being recognized as strong pulses. A
general trend caused by atmospheric changes and/or receiver characteristics is
as well examined and calibrated. A pulsar-timing package TEMPO2 (Hobbs et al.,
2006) is used for transforming the reference frame from each geographic
location to the solar system barycenter, i.e., from the coordinated universal
time (UTC) to TDB.

##  3 Analysis and Results

We detected strong pulsed emission from XTE J1810-197 including a number of
single pulses in most of our observing sessions in 2.3 – 22 GHz bands. We
could not detect any pulsed emission at 0.3 GHz over $5\,\sigma$. The
$3\,\sigma$ upper limit on the mean flux density at 0.3 GHz is $\sim\,$13 mJy
when assuming a duty cycle of 5 % (see Section 3.2 for the assumed duty
cycle). We show one sample of the dataset on MJD 58490 in Figure 1. No
presence of interpulse is observed during our observations (see also Dai et
al. 2019), whereas during the previous outburst highly variable interpulse
components were intermittently detected in 2006 at 0.72 pulse phase later than
the main pulse phase, some of which were brighter than the main pulses (Kramer
et al., 2007; Lazaridis et al., 2008).

###  3.1 Spin parameters

Table 2:  Spin parameters of XTE J1810-197 estimated by Levin et al. (2019) and this work. Numbers in parenthesis represent $1\,\sigma$ errors in unit of the last significant digits.  Work |  Date range [MJD] |  Epoch [MJD] |  $\nu_{0}$ [$\rm Hz$] |  $\dot{\nu}_{0}$ [$\rm Hz\ s^{-1}$] |  $\ddot{\nu}_{0}$ [$\rm Hz\ s^{-2}$] |  ${\nu}^{\ldots}_{0}$ [$\rm Hz\ s^{-3}$] |  ${\nu}^{....}_{0}$ [$\rm Hz\ s^{-4}$] |  RMSE [period]
---|---|---|---|---|---|---|---|---
Levin et al. (2019) | 58460 – 58507 | 58484.0 | 0.180 458 147(2) | $-2.575(4)\times 10^{-13}$ | $-5.5(4)\times 10^{-20}$ | $-1.7(2)\>\,\,\times 10^{-26}$ | $4.2(10)\times 10^{-32}$ | 0.0007
This work | 58465 – 58597 | 58484.0 | 0.180 458 142(1) | $-2.52(1)~{}~{}\times 10^{-13}$ | $-4.1(2)\times 10^{-20}$ | $~{}~{}~{}4.1(11)\times 10^{-27}$ |  - | 0.15
Figure 2:  Top panel: Spin frequencies ($\nu$) of XTE J1810-197 during our
observations. The arrow at the bottom left corner indicates the duration of 48
days when pulsar timing solutions were achieved by Levin et al. (2019), i.e.
MJDs 58470 – 58507. Open circles are spin frequencies on our observing
sessions 1 – 4, which are derived by eq. (1) with the spin parameters of Levin
et al. (2019). Filled circles are the values estimated from our data (see
Section 3.1 for the method). The curved line is a fitted variation of the
rotation frequency (solid line: interpolation for MJDs 58507 – 58596, dashed
line: extrapolation of our fit to MJD 58646), and the shaded region
encompasses $3\,\sigma$ confidence interval. Bottom panel: Changes of the spin
frequency derivative ($\dot{\nu}$) during our observing period. The solid line
indicates $\dot{\nu}$ estimated from the upper panel, and the dashed line is
an extrapolation of our fit to MJD 58646 which is excluded from the iteration
process (see text for details). The shaded region encompasses $3\,\sigma$
confidence interval. The triangles are data taken from Fig. 6 in Levin et al.
(2019), while black dots indicate the estimated $\dot{\nu}$ on our observing
sessions 6–9.

Levin et al. (2019) determined spin parameters from their nearly-daily
observations of XTE J1810-197 in the interval between MJDs 58460 and 58507,
which includes our observing sessions 1 – 5. Single pulses obtained in these
sessions are well aligned in phase with their timing results (Figure 1). To
follow up the timing parameters covering the whole observation period in this
work, we determine spin parameters using arrival times of single pulse
components at 8.4 GHz obtained by Hitachi telescope, except for session 5 when
the Hitachi observation was not conducted. The determination process of spin
frequency $\nu(t_{i})$ (i = 1 – 9) for session i is in four steps. (i) We
roughly find the optimal spin frequency, $\nu(t_{i})$, that derives the
maximum signal-to-noise ratio (S/N) in an integrated profile. (ii) Grounded on
the $\nu(t_{i})$ estimated in the previous step, we search the frequency on
closer inspection by conducting weighted least squares fitting to best align
all single pulse components with $\rm S/N>6$ at the same pulse phase
throughout an observation, as is in Figure 1. It gives the consistent results
with Levin et al. (2019) for the first four sessions. (iii) We fit a Taylor
polynomial (making use of polynomial package NumPy)

$\nu(t_{i})=\nu_{0}+\dot{\nu}_{0}(t_{i}-t_{0})+\frac{1}{2}\ddot{\nu}_{0}(t_{i}-t_{0})^{2}+\frac{1}{6}{\nu^{\ldots}_{0}}(t_{i}-t_{0})^{3}$
(1)

to $\nu(t_{i})$ (i = 1 – 9), and estimate derivatives of spin frequency for
sessions 6 – 9. Here we remark that $\nu(t_{i})$ (i = 1 – 4; session 5 has
non-detection) is obtained from Table 1 by Levin et al. (2019) which are
derived from observations with a much higher cadence than ours. (iv) Applying
the derivatives, we perform step (ii) again by aligning single pulses
components in phase domain. Repeating steps (iii) and (iv) iteratively, we
obtain $\nu(t_{i})$ (i = 6 – 9) and its derivatives. The last Hitachi
observation on session 10 (MJD 58646; 2019-06-12) detected only a few weak
single pulses at $>5\,\sigma$, therefore it is excluded from the above
iteration process; i.e., only step (i) was conducted, resulting in a large
uncertainty of $\nu(t_{10})$. The upper panel of Figure 2 shows the resultant
$\nu(t_{i})$ (i = 6 – 10). The coefficients of the Taylor expansion (Eq. 1)
are listed in the second row of Table 2.

We confirmed the spin parameters obtained with the data at 8.4 GHz by applying
them to align the single pulse components at 6.9 GHz which was simultaneously
recorded with 8.4 GHz. Later we additionally verified that timing with TEMPO2
gives consistent parameters with our method stated above.

By differentiating the Eq. (1) with respect to $t_{i}$, we obtain the spin
frequency derivative, $\dot{\nu}$, of the magnetar (Figure 2, lower panel).
Its absolute value $|\dot{\nu}|$ increased continuously, but the change became
more gradual over time by MJD 58596, as was the case during the early 48-days
as reported by Levin et al. (2019). The similar trend in the X-ray band was
also recently reported by Borghese et al. (2021).

Figure 3:  Four examples of single pulses detected simultaneously at 6.9
(LCP), 8.4 (RCP), and 22 GHz (LCP) on MJD 58490 (2019-01-07). They are listed
in order of complexity from left to right panels. The horizontal axes are
aligned in TDB and set to zero at the peak phase of the average profile at 6.9
GHz, as is also in Figure 1. The vertical dashed lines indicate the central
phase of 0.5. The peak flux density of each single pulse profile is marked in
Jy level, where its $1\,\sigma$ error in the last digit is shown in
parentheses. The average profiles at the same frequency on MJD 58490 are shown
as the solid gray lines, and scaled to the peak S/N in each panel.

###  3.2 Pulse profiles

Figure 3 shows some examples of single-pulse profiles (solid black lines)
simultaneously observed at three different frequencies (6.9 GHz, 8.4 GHz, and
22 GHz). We note again that 6.9 GHz and 22 GHz indicate LCP waves, while 8.4
GHz does RCP waves. The shapes of the profiles are highly variable depending
on time and polarization. Single pulses are approximately normally distributed
within the pulse width, centered at the peak of the average profiles. We
confirm that there is no periodicity in their occurrence in time and phase
domains. We find that the profiles at 6.9 GHz and 8.4 GHz consist of more
multiple components than those at 22 GHz. However, it is possible that the
corresponding microstructures at a higher frequency have smaller relative
strength so that are easily shrouded in strong noise. Some distinct examples
of the multiplicity are shown in panels (c) and (d) of Figure 3. In addition,
strong pulse-to-pulse profile variations are prominently seen in Figure 3 when
considering a direction of circular polarization. We could not differentiate
that the variations are due to whether the change of the intensity of circular
polarization or the real change of total intensity.

Table 3: Profile widths at each direction of circular polarization (Pol.). For each observing frequency and MJD, pulse widths $W50_{\,\rm MJD}$ and $W10_{\,\rm MJD}$ are given in percentage of the duty cycle. The hyphen ‘–’ indicates that an observation was conducted but the width is less than $3\,\sigma$ confidence. Pol. |  Observing frequency |  $W10_{58465}$ [%] |  $W10_{58470}$ [%] |  $W10_{58490}$ [%] |  $W10_{58492}$ [%] |  $W10_{58529}$ [%] |  $W10_{58546}$ [%] |  $W10_{58573}$ [%] |  $W10_{58596}$ [%] |  $W10_{58646}$ [%]
---|---|---|---|---|---|---|---|---|---|---
RCP | 2.3 GHz | 5.7 |  | – |  |  | – |  | – | –
8.4 GHz | 3.8 | 4.3 | 4.9 | 4.6 | – | 4.6 | 3.2 | – | –
LCP | 6.9 GHz | 5.7 | 4.7 | 4.9 | 4.1 | 5.4 | 4.7 | – | – | –
22 GHz |  | 4.2 | 2.4 |  | – |  |  |  |
|  |  $W50_{58465}$ [%] |  $W50_{58470}$ [%] |  $W50_{58490}$ [%] |  $W50_{58492}$ [%] |  $W50_{58529}$ [%] |  $W50_{58546}$ [%] |  $W50_{58573}$ [%] |  $W50_{58596}$ [%] |  $W50_{58646}$ [%]
RCP | 2.3 GHz | 3.0 |  | 2.4 |  |  | 2.5 |  | 1.1 | –
8.4 GHz | 1.8 | 1.6 | 2.1 | 2.2 | 2.1 | 2.3 | 2.0 | 2.5 | 2.7
LCP | 6.9 GHz | 3.7 | 3.0 | 1.9 | 2.1 | 2.3 | 1.9 | 2.2 | 2.7 |
22 GHz |  | 1.4 | 0.9 |  | – |  |  |  |

The average profiles are overlaid in Figure 3 with solid gray lines. It is
clear that single pulses have much narrower widths compared to the
corresponding average profile. The pulse width is measured as the width at 10
% of the maximum intensity ($W_{10}$) of an integrated profile when the 10 %
of the intensity is over $3\,\sigma$ (Table 3). It derives a duty cycle of
$\sim$5 % at 2.3 – 8.4 GHz range which is comparable to the duty cycle during
the previous outburst of XTE J1810-197 (Camilo et al., 2016) as well as to the
typical duty cycle of ordinary pulsars (Maciesiak et al., 2011). Since the 10
% of the maximum intensity of the profiles at 22 GHz are less than
$3\,\sigma$, we measure the widths at 50 % of the peak intensity ($W_{50}$)
and compare with $W_{50}$ at other frequencies in the same session. For each
direction of the circular polarization, the pulse width $W_{50}$ (duty cycle
likewise) goes slightly narrower as the observing frequency goes higher.

The average profile at 8.4 GHz is delayed when compared to those at 6.9 GHz
and 22 GHz (see the phases at the peaks of solid gray profiles in Figure 3).
The degree of the phase delay is different at different observing epoch, but
larger at earlier sessions. We presumed that the phase shift is caused by the
time variations of the polarization degree, then we compared it with the
polarization profiles of XTE J1810-197 in the literature. Taking into account
a polarization study during MJDs 58463 – 58470 at 0.7 – 4 GHz (Dai et al.,
2019), we derived LCP and RCP profiles from the total intensity ($I$) and
circular polarization ($V$) profiles by $I{\rm(LCP)}=(I+V)/2$ and
$I{\rm(RCP)}=(I-V)/2$. The degree of the phase shift between our profiles at
6.9 and 22 GHz (LCP) and 8.4 GHz (RCP) on MJD 58470 (2018-12-18) is comparable
with that between the two profiles at different circular polarization
handedness taken from Dai et al. (2019) on MJD 58470. We, therefore, suggest
the phase delay of averaged profiles inferred by Figure 3 would be on account
of the different polarization degrees on each session.

###  3.3 Flux variations

To discuss the flux variations of XTE J1810-197, we estimate the total
intensity, $I$, from single circular polarizations, LCP and RCP as follows. In
the case of the data simultaneously taken with Hitachi (LCP at 6.9 GHz and RCP
at 8.4 GHz), we simply combine them in each time bin (TDB) as $I$ =
$I{\rm(LCP)}+I\rm(RCP)$ at $7.6\pm 1.1$ GHz. For the other data (Kashima 2.3
GHz and VERA 22 GHz), we measure conversion factors for converting the
intensity at one circular handedness to total intensity. From the RCP and LCP
profiles derived from the data obtained by Dai et al. (2019), as described in
Section 3.2, we calculate the ratio of mean flux densities of RCP or LCP
profiles to the total flux density. Reciprocals of the ratios, $I$/LCP or
$I$/RCP, are shown in Table 4. We employ these conversion factors to derive
the total intensities at 2.3 GHz and 22 GHz. Although the conversion factors
can depend on the frequency, there is no significant change in the
polarization profiles between 1920.0 MHz and 3712.0 MHz (Dai et al., 2019).
Therefore, we assume the polarization property at 3712.0 MHz would be stable
up to 22 GHz, and apply the conversion factors obtained at 3712 MHz on MJD
58470 (2018-12-18) to our data at 22 GHz obtained on the same date.
Additionally, the integrated profiles at 7.6 GHz do not appear to undergo
significant temporal evolution during our observing period, we suppose that
the averaged polarization pulse profiles and the averaged polarization angle
are both relatively stable during this outburst. Therefore, we assume that the
conversion factors do not significantly change during our observing period,
and apply the mean conversion factors ($2.07\pm 0.08$ and $2.01\pm 0.09$ for
LCP and RCP, respectively) to the other data except on MJD 58470.

Table 4: Conversion factors from the intensity at single polarizations to the total intensity. The values are estimated from the profiles by Dai et al. (2019) (see text for details). $\nu_{\rm center}$ [MHz] | MJD 58463 | MJD 58467 |  MJD 58470
---|---|---|---
(2018-12-11) | (2018-12-15) | (2018-12-18)
I/L | I/R | I/L | I/R | I/L |  I/R
1024 | 1.97 | 2.03 | 2.29 | 1.77 | 2.06 |  1.94
1920 | 1.55 | 2.81 | 2.16 | 1.86 | 2.45 |  1.69
2816 | 1.69 | 2.44 | 2.03 | 1.97 | 2.25 |  1.80
3712 | 1.79 | 2.27 | 2.07 | 1.93 | 2.54 |  1.65

As a result, Figure 4 shows time variations of total intensity at 2.3 GHz, 7.6
GHz, and 22 GHz. To compare and understand the variations with that at a lower
frequency, daily flux densities at 1.52 GHz (data from Levin et al. 2019) are
marked in the top panel of Figure 4.

Mean flux density at 2.3 GHz was higher on MJD 58490 (2019-01-07) than that on
MJD 58466 (2018-12-14). We note that it does not necessarily mean the
intensity has gradually increased for a month; Levin et al. (2019) showed two
drastic decreases in daily flux at 1.52 GHz within a month during this
outburst and MJD 58466 is when the flux was in the first trough. Meanwhile,
MJD 58490 is after the 1.52 GHz intensity recovered from the second trough
(see vertical dashed lines in Figure 4). Therefore, we remark that the early
change at 2.3 GHz reflects erratic daily changes which is seen at the lower
frequency. The last 2.3 GHz observation on MJD 58646 (2019-06-12) did not
capture any pulsed emission and gives only an upper limit, as marked with a
triangle in Figure 4.

On the other hand, the flux density at 7.6 GHz does not seem to fully follow
the low-frequency behavior on the same dates. On session 3 (MJD 58490;
2019-01-09), the intensity at 7.6 GHz is not brighter than the previous unlike
the similar flux changes between 1.52 GHz and 2.3 GHz. The time-variable
spectral indices are rather common for radio magnetars (e.g., Anderson et al.,
2012; Pennucci et al., 2015; Champion et al., 2020), thus this would reflect a
typical behavior of magnetar radio emission. Otherwise, it may suggest that
there is a time lag in daily variations between low and high frequencies or
that the flux variation includes narrow-band behaviors, which are not easy to
be studied due to the strong variability.

Among four 22 GHz observations, we obtained integrated profiles only at the
first and second sessions. We found the third session is when the luminosity
at 1.52 GHz is two times fainter than at the second session (Levin et al.,
2019), which may imply the general flux variations would be the wide-band
feature. On MJD 58529 (2019-02-15) at 22 GHz, we found only six single pulses
at $>6\,\sigma$ significance due to the relatively low sensitivity. We thus
marginally obtained the integrated pulse profile, hence no confident mean flux
density is measured. The detection of a few reoccurred strong single pulses
manifests the huge variability in flux density up to high frequency.

While the long-term variation of flux density might have been affected by
daily variations, we see the radio intensity generally gets fainter over time.
This result is in agreement with previous studies (e.g. Camilo et al. 2007a).
During its previous radio outburst in 2005 – 2008, Camilo et al. (2016)
reported that XTE J1810-197 has shown a significant decrease in the mean flux
density at 1.4 – 3 GHz to a factor of 20 fainter than the first measured
pulsed intensity during the first ten months, followed by a stable period for
a twice longer period until it paused the radio emission. From our higher
frequency observations, though, the intensity became $\sim$ ten times fainter
at 7.6 GHz in six months after the outburst, therefore may not suggest a clear
manifestation of radio cessation but infer a continuously decreasing phase in
June 2019. Considering that the first radio detection in 2005 of XTE J1810-197
was a half year later than its X-ray outburst and an additional year has
passed until the first detection of radio pulses, we estimate the time range
of the observable decreasing phase in intensity would be longer for this
outburst if the radio turn-off mechanism is analogous to its previous radio
outburst. Further monitoring observations until this radio outburst come to
the end, therefore, are needed to compare the radio behaviors and physical
properties of XTE J1810-197 between the two outbursts.

Figure 4:  Top panel: Daily flux density variations at 1.52 GHz ($S_{1.52}$).
Data are from Levin et al. (2019). Lower panels: Variations of total intensity
of XTE J1810-197 at 2.3 GHz, 7.6 GHz, and 22 GHz ($S_{2.3}$, $S_{7.6}$ and
$S_{22}$, respectively). Dashed vertical lines are for indicating the first
session at 2.3 GHz is when the 1.52 GHz brightness has drastically decreased
(first local minimum), whereas the second session is when the brightness is
recovered from the next local minimum. Downwards pointing triangles indicate
upper limits.

###  3.4 Spectral variations

Figure 5:  Spectral variations of XTE J1810-197. Measured mean flux densities
(converted to total intensity) at 2.3, 7.6, and 22 GHz are presented. For
comparison, we added the flux densities obtained by [1] Dai et al. (2019), [2]
Maan et al. (2019), [3] Pearlman et al. (2019), [4] Pearlman et al. (2020),
and [5] Torne et al. (2020) with connected gray dots. Downwards pointing
triangles indicate upper limits at 0.3 GHz.

We present the spectra of XTE J1810-197 between 2.3 GHz and 22 GHz obtained
(quasi-) simultaneously. The time gaps between observations are smaller than
24 hours if not simultaneous. Figure 5 shows five spectra between December
2018 and April 2019, with early results of precedent studies (Maan et al.
2019; Dai et al. 2019; Pearlman et al. 2019, 2020; Torne et al. 2020). Our
upper limit at 0.3 GHz is marked as well.

Even though each data point could be affected by short-term (shorter than a
day) variations in flux density, our results suggest clear negative spectral
indices in cm-wavelengths. The daily variations inferred by Figure 4 lead to
the high variability in spectral indices, though we found the spectrum in 2.3
– 8.7 GHz becomes steeper during the period when assuming a power law;
$\alpha=-0.57\pm 0.04$ on MJD 58465 to $-0.85\pm 0.10$ on MJD 58596. During
the previous outburst in 2006, the spectral index of the main pulse as well
went steeper from $0.05\pm 1.12$ (MJD 53873) to $-0.90\pm 0.38$ (MJD 53983) in
the frequency range of 1.4 – 4.9 GHz during the first $\sim$4 months (Camilo
et al., 2007b). Therefore, XTE J1810-197 shows a faster decline in its
intensity toward higher frequency, both in the previous and this outburst.

The mean power-law spectral index in 2.3 – 8.7 GHz during the 4.5 months of
our observations is $\langle\alpha\rangle=-0.85\pm 0.14$. With regard to the
spectrum up to 8 GHz, the previously measured index on MJD 53862 (2006-05-07)
is $-0.30\pm 0.04$ between 1.4 and 8.5 GHz (Camilo et al., 2007b), implying
that the decreasing trends of the flux density at the radio frequency higher
than 4 GHz are both observed in the previous and this radio outbursts.

##  4 Discussion

###  4.1 Double-peaked spectrum?

In Figure 5, we overlay the flux densities obtained by Dai et al., 2019 (0.7 –
4 GHz), Maan et al., 2019 (0.3 – 0.7 GHz), Pearlman et al., 2019 (8.4 and 32
GHz), Pearlman et al., 2020 (8.3 and 31.9 GHz), and Torne et al., 2020 (150
and 260 GHz). In contrast to that Maan et al. (2019) showed a monotonous
positive spectral index at a broad low-frequency band of 0.3 – 4 GHz by
combining their results with the results of Dai et al. (2019), the negative
spectra at higher frequencies from our observations indicate that it is very
difficult to explain the broad-band spectrum with a single power law,
especially when we pay attention to the spectrum on MJD 58470 (2018-12-18).

In the frequency range up to $\sim$10 GHz, XTE J1810-197 shows a
characteristic feature of gigahertz-peaked spectrum (GPS). To verify the GPS
appearance even with the daily variations, we estimate a degree of flux
variation from the daily observations at 1.52 GHz by Levin et al. (2019) (see
the top panel of Figure 4). The flux density has drastically decreased during
the two local minima on MJDs 58466 and 58478; down to $\sim\\!-35$ % in 2 days
for both troughs. Even though assuming at most 50 % of daily flux changes
randomly without a frequency-dependence, the flux density at 7.6 GHz is lower
than the flux densities at 1.5 – 3 GHz. Hence, XTE J1810-197 would still
possess the GPS feature with a peak frequency between 1.5 GHz and 7.6 GHz.
Moreover, the flux densities at adjacent frequencies would change similarly as
inferred from Figure 4, thus the overall shape of the spectra is expected to
be relatively stable.

Such a GPS feature has already been discussed for radio pulsars and other
radio-bright magnetars. Among known radio pulsars, eleven or more GPS pulsars
have been identified (Jankowski et al., 2018) and they may account for up to
10 % of the pulsar population (Bates et al., 2013). They typically have peak
frequencies around 1 GHz or smaller (Kijak et al., 2017). Two radio magnetars,
1E 1547.1-5408 and PSR J1622-4950, have shown apparent GPS shapes with peak
frequencies of 5 GHz and 8.3 GHz, respectively (Kijak et al., 2013). The turn-
over features can be attributed to the thermal free-free absorption of the
pulsar radio emission in peculiar environments, such as supernova remnants,
pulsar wind nebulae, or dense H II regions (Sieber, 1973; Kijak et al., 2011).
A radio magnetar located in the Galactic center, SGR J1745-2900, has been also
suggested to be a candidate of GPS pulsar, while no apparent increase in flux
density at low frequency was detected (Lewandowski et al., 2015). Lewandowski
et al. (2015) suggest the free-free absorption in the electron material
ejected during a magnetar outburst could be responsible for the GPS and the
spectral evolution with peak frequency shifting toward lower frequency. As for
XTE J1810-197, we could imply a long-term shift of the GPS peak to the lower
frequency from two results; i) the decrease of the peak frequency in 5-days in
the early spectra at 0.7 – 4 GHz (Dai et al., 2019) and ii) the steepening
spectra at 2.3 – 7.6 GHz from our observations. To further discuss the free-
free absorption model by materials from the magnetar outburst to explain the
spectral variations of XTE J1810-197, short-cadence observations around peak
frequencies are needed for coming outbursts.

XTE J1810-197 has a more complicated spectral transition at higher radio
frequencies over 20 GHz; the negative spectrum extending to 22 GHz is expected
to face a spectral turn-up. Indeed, as marked in Figure 5, Torne et al. (2020)
has detected the magnetar emission on MJD 58567 (2019-03-25) at 150 and 260
GHz whose mean flux densities (11.7(7) mJy and 6.4(10) mJy, respectively) are
higher than our upper limit at 22 GHz on MJD 58529 (2019-02-15; 2.6 mJy). The
higher frequency intensities are even stronger than the intensity at 7.6 GHz
obtained before and after their observation; the closest observation on MJD
58573 (2019-03-31) presents $0.90\pm 0.01$ mJy at 7.6 GHz, suggesting that the
spectrum would be inverted at over 22 GHz and has a second spectral peak
between 22 – 150 GHz. Here we remark the high-frequency peak is plausible even
allowing daily flux fluctuations up to 50 %, as is confirmed for GPS. Thus we
suggest XTE J1810-197 would have a bimodal spectrum in the frequency range of
300 MHz to 250 GHz.

Double-peaked spectral features are recently discussed for two other radio
magnetars as well, SGR J1745-2900 and PSR J1622-4950, indicating that the
emission mechanism could be different at low and high frequency ranges (Chu et
al., 2021). However, including for XTE J1810-197, it is necessary to note that
only simultaneous wide-band observations would confirm their extraordinary
spectral shapes. But if true, they would be the first group with multiple
spectral peaks in the radio band in the whole neutron star population.
Although not all magnetar radio spectra have double-peaked features, this
spectral hallmark could be intrinsic to radio magnetars, giving a new insight
to study the radio emissions from neutron stars in wide frequency domain. For
better constraints for magnetar emission models at different frequency ranges,
tracing the timely variations of the double peaks would be highly required.
Further multi-epoch broad-band observations toward radio-loud magnetars,
therefore, would be necessary to investigate the origin and behavior of the
double-peaked spectra.

###  4.2 Pulse width narrowing behavior

We showed the pulse width variations in Section 3.2. XTE J1810-197 during the
second outburst shows the narrower average profile toward high frequency in
the range of 2.3 – 22 GHz. This inverse frequency-dependency of pulse width is
one of the general features of plenty of ordinary pulsars (Pilia et al.,
2016). A radius-to-frequency mapping (RFM; Cordes 1978) is usually used to
describe the narrowing of pulse profiles. The RFM model postulates that higher
radio frequency emission originates from lower altitude of the neutron star,
thus the pulse profile width would increase toward lower observing frequency.
Most of the average profiles of XTE J1810-197 at 2.3 – 22 GHz during our
observing period have a single peak and we did not find a significant phase
lag between pulse peaks at different frequencies, implying that the observed
peak would be a core component when based on the RFM model. The model is,
however, based on the dipole magnetic field structure and expects S-shaped
polarization angle swings within the framework of rotating vector model (RVM).
The dramatic changes of the polarization position angles of radio magnetars
inhibit the classical RVM to be applied for magnetars (e.g. Kramer et al.,
2007). Although the RFM model might not be plausible for the cases of radio
magnetars, the profile narrowing trend of XTE J1810-197 could give a hint for
any link between magnetar radio emission and standard pulsar emission in terms
of magnetospheric structures. However, the pulse width variations of radio
magnetars during an outburst, even only for XTE J1810-197, are yet poorly
understood, hence high-sensitive long-term investigations on the variability
in radio profiles of magnetars are required for each radio outburst.

A recent study of pulse widths for ordinary pulsars, though, estimated more
than 20 % of ordinary pulsars show positive correlations between pulse width
and observing frequency, implying the diversity in the energy spectrum
distribution across the emission regions of neutron stars (Chen & Wang, 2014).
While most radio magnetars have rather stable or slight narrowing pulse width
over frequency (e.g. Wharton et al., 2019; Lower et al., 2020), PSR J1622-4950
showed not only profile narrowing from 1.4 GHz to 6.6 GHz, but slight
broadening at 17 GHz (Levin et al., 2012). When it comes to radio-loud
magnetars, only a few atypical properties are known to be commonly seen,
hindering an integrated understanding of the radio-emitting magnetars
altogether. Searching the additional common features of magnetar radio
pulsations would enable a comprehensible understanding of them. We, therefore,
stress the necessity of the investigations into the frequency dependence of
pulse widths of radio magnetars through simultaneous multi-frequency
observations, and this would enable a better understanding of the
magnetospheric geometry of magnetars. We, in addition, note that in the long-
term, radio magnetars can provide crucial samples for studying ultra wideband
frequency dependency of pulse width with the benefit of their flat spectra.

##  5 Summary and Conclusion

We conducted an analysis of the simultaneous observations of the radio-loud
magnetar XTE J1810-197 with radio telescopes in Japan at 0.3, 2.3, 6.9, 8.4,
and 22 GHz. Our observations were organized for six months during the revived
radio outburst detected in December 2018. Significant pulsed emissions were
detected at the frequency range of 2.3 – 22 GHz and the radio pulsations
generally became fainter during our observations.

By employing the timing solutions for the early phase of this outburst from
the literature, we found the change of the spin frequency derivative has
continuously weakened since the radio outburst. We also report the duty cycle
of the magnetar during this outburst is $\sim$ 5 %, which is analogous to its
previous outburst and a number of ordinary pulsars. The pulse widths tend to
become narrower as the observing frequency goes higher.

We obtained the negative spectra in 2.3 – 22 GHz with the average spectral
index of $-0.85\pm 0.14$ at 2.3 – 8.7 GHz. By combining with the flux
densities at lower and higher frequencies from the literature, we suggest that
XTE J1810-197 would have a bimodal spectrum with a GPS feature at lower 7.6
GHz and a second peak at over 22 GHz. Considering that the magnetar radio
emission is highly variable, we put special emphasis on the importance of
long-term simultaneous broad-band observations of magnetar radio outbursts to
understand the origin and emission mechanisms of magnetar radio pulsations.

## Acknowledgements

We thank all staff of Mizusawa VLBI Observatory of NAOJ. We are grateful to
Katsunori Shibata for providing information for VERA data reduction.
Observations at the Hitachi 32-m telescope are supported by the Inter-
university collaborative project “Japanese VLBI Network” of NAOJ. This work
are supported by JSPS/MEXT KAKENHI grant numbers 17H01116 (M.H.), 18H01245
(S.K.), 18H01246 (S.K., T.T.), 19K14712, and 21H01078 (S.K.).

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