Simultaneous 2.25/8.60 GHz observations of the newly discovered magnetar -- Swift J1818.0-1607

Swift J1818.0-1607 discovered in early 2020 is not only the fifth magnetar known with periodic radio pulsations but also the fastest rotating one. Simultaneous 2.25 and 8.60 GHz observations of Swift J1818.0-1607 were carried out with Shanghai Tian Ma Radio Telescope (TMRT) from MJD 58936 to 59092. The spin-frequency $\nu$ and first-order derivative $\dot\nu$ of this magnetar were obtained with piecewise fitting method because of its instable timing properties. We found that the amplitude of short-term $\dot\nu$ fluctuations decreased with time, and the long-term declining trend of $\nu$ discovered previously continued in our observations. The best fitted long-term $\dot\nu$ were about $-2.25 \times 10^{-11}~s^{-2}$ using our observation data spanning 156 days. The derived characteristic age was about 522 yr, supporting the recent viewpoint that this magnetar may be older than initially thought shortly after its discovery. The flux density of this magnetar was increased at both 2.25 and 8.60 GHz during our observations, and its radio spectrum became flatter at the same time. We also detected bright-quiet type emission mode switching in Swift J1818.0-1607.


INTRODUCTION
Magnetars are a special class of young neutron stars with extremely strong magnetic fields (10 13 − 10 15 G). They sometimes show dramatic variabilities across the electromagnetic spectrum, especially at high energy band, such as giant flares (Mereghetti 2008). The decay of enormous internal magnetic fields of magnetars is thought to power these emissions, as they are too bright to be powered by the loss of rotational energy or the accretion power (Duncan & Thompson 1992). By the end of 2020, there were 31 magnetars and candidates discovered (Olausen & Kaspi 2014;Coti Zelati et al. 2021) 1 . Compared with other neutron stars, magnetars generally rotate slower and spin down faster because of their stronger magnetic braking effects Gao et al. 2019). Though magnetars show dramatic outbursts at high energy, only 6 magnetars had been detected with radio pulse radiation until the end of 2020 (Olausen & Kaspi 2014) 1 . ⋆ E-mail: yanzhen@shao.ac.cn 1 http://www.physics.mcgill.ca/~pulsar/magnetar/main.html Typically, magnetar shows variable integrated profiles on timescales from hours to days and relatively flat spectra with typical spectral indices (α) greater than −0.8 at radio band (Camilo et al. 2007b;Torne et al. 2015Torne et al. , 2017, which is different from normal pulsars that usually show stable integrated profiles and steeper radio spectra with typical α around −1.6 (Jankowski et al. 2018).
Swift J1818.0−1607 was firstly captured as an X-ray burst by the Swift Burst Alert Telescope on March 12th 2020. It was confirmed to be a magnetar with a spin period (P ) of 1.36 s by the follow-up observations of Neutron star Interior Composition Explorer (Enoto et al. 2020), making it the magnetar with the shortest P known so far. Furthermore, it was shown to be the 5th radio magnetar known, as its radio pulsations were detected by Effelsberg telescope (Karuppusamy et al. 2020). Shortly after the X-ray burst, its integrated profile could only be detected below 8.0 GHz, though high frequency observations were arranged (Rajwade et al. 2020;Lower et al. 2020b,c;Ridolfi et al. 2020;Majid et al. 2020b;Champion et al. 2020a). About 27 days later, it was detected in several high frequencies ob-servations, such as 8.4 GHz (Majid et al. 2020a), 22 GHz (Liu et al. 2020), 31.9 GHz (Pearlman et al. 2020, 86 and 154 GHz (Torne et al. 2020). Its spectrum got flatter with α > −0.97. In most cases, Swift J1818.0−1607 showed integrated profile with single peak. Secondary peak component on the right of main peak was sometimes detected at 3.8 GHz (Lower et al. 2020b), 1.37 and 2.55 GHz (Champion et al. 2020a). Furthermore, Lower et al. (2020a) detected integrated profile with triple peaks at 2.368 GHz using Parkes Ultra-Wideband receiver.
As more timing observation data obtained, it was discovered that its rotation frequency derivativeν showed drastic fluctuations, though there was a long-term declining trend of ν. Besides the glitch detected in Swift J1818.0−1607 (Champion et al. 2020a;Hu et al. 2020a), it also possibly showed an anti-glitch (Hu et al. 2020a).
Long-term simultaneous multi-frequency observations are vital for studying changes in radio emission of magnetars in both frequency and time. Simultaneous 2.25/8.60 GHz observations of Swift J1818.0−1607 were arranged at Shanghai Tian Ma Radio Telescope (TMRT) to do further studies on its radiation and rotational properties. Information about observations is provided in Section 2. The data reduction methods and results are given in Section 3. Finally, further discussions are presented in Section 4.

OBSERVATIONS
Simultaneous 2.25/8.60 GHz observations were carried out ranging from MJD 58936 (Mar 28th 2020) to MJD 59092 (Aug 31st 2020) with the TMRT by taking advantage of the parallel working capabilities of the 2.25/8.60 GHz dualfrequency receiver and the digital backend system (DIBAS) which consisted of 3 pairs of analog-to-digital converters and Roach-2 boards (Yan et al. 2018). The dual-frequency receiver is a cryogenically cooled, dual-polarization receiver with the frequency coverage of 2.20-2.30 GHz and 8.20-9.00 GHz, respectively. The total bandwidth was divided into channels with a width of 1 MHz (at 2.25 GHz) and 2 MHz (at 8.60 GHz) with the DIBAS to remove the dispersion effects and radio-frequency interferences (RFIs) (Yan et al. 2015). The incoherent de-dispersion and online-folding observation mode were used in our observations. Each rotation period was divided into 1024 pulse phase bins and folded with 30 s subintegration length. The observation data were written out as the 8-bit PSRFITS format (Hotan et al. 2004).
After removing RFIs with the pazi command of the Pulsar Archive analysis software (PSRCHIVE) (Hotan et al. 2004), the data was compressed by scrunching all frequency channels and polarizations together with the pam command.
There was no flux calibrator observations arranged before MJD 59039. By assuming the off-pulse root-mean-square (RMS) noise following radiometer equation, we estimated the peak flux density of Swift J1818.0−1607 based on typical system equivalent flux density (SEFD), and the SEFD of the TMRT is about 46 Jy and 48 Jy at the corresponding frequencies (Yan et al. 2018). Then, the mean flux density was obtained by dividing the integrated flux density from the on-pulse bins by the total number of phase bins. The uncertainty in mean flux density was obtained from offpulse RMS noise divided by square root of the number of phase bins. (Zhao et al. 2017). For the observations later than MJD 59039, we estimated its flux density with both SEFD method and calibrator 3C 295. According to our calculations, these two methods are in agreement with each other within the error bar.

Evolution of spin frequency and DM
Both the integrated profile and rotational properties of Swift J1818.0−1607 were found to change irregularly during our observations, which makes constructing a phase−coherent timing solution very difficult. Thus, we divided our observations into segments and carried out timing analysis to each of them separately, similar to the strategy presented in previous work such as Levin et al. (2012). The template profiles of 2.25/8.60 GHz were respectively obtained based on the integrated profile of 2.25/8.60 GHz with typical SNRs >10.28 in the middle of each segment. Then, the time-of-arrivals (ToAs) of pulses was obtained by crosscorrelating integrated profiles with the standard template of corresponding frequencies with pat command. Next, we combined the ToA sets from 2.25/8.60 GHz after removing the delay of the receiver system, and carried out timing analysis with TEMPO2 software package (Hobbs et al. 2006) to measure the spin properties of the magnetar. The length of each segment lasted until there were obvious changes in the integrated profiles or the error of fittedν exceeded 2.70 × 10 −12 s −2 which was about 10% of meanν (Champion et al. 2020a). In Table 1, two adjacent segments are distinguished with differ- It's clear that the long-term decline trend of ν previously reported by Champion et al. (2020a) and Hu et al. (2020a) went on in our observations, thoughν still changes erratically on short time-scale. We did a linear fit to the ν measurements with the least square method base on only ours and all observation results shown in the top panel of Fig.1. The best-fitteḋ ν was about −2.25(1) × 10 −11 s −2 and −2.41(2) × 10 −11 s −2 , respectively. Champion et al. (2020a) also reported a similar fittedν of −2.37 × 10 −11 s −2 using the data spanning nearly 100 days. Combined with all observations, theν showed continuous oscillations instead of random variations after the discovery burst. It also was noticed that the amplitude of

Integrated profiles
Integrated profiles of pulsars provide important information of the structure of the radiation beam. With updated ephemeris, the integrated profiles for each epoch of 2.25/8.60 GHz observations were obtained and showed chronologically in Fig. 2. For easier comparison, they are normalized, aligned with respect to the peak of the profile and centered at the zero rotation phase. Three phase areas which are usually giving out radiation are labeled with P 1, P 2 and P 3 from left to right. From the plots in Fig. 2, we can see that the integrated profiles of Swift J1818.0−1607 can keep stable in several days at both 2.25 and 8.60 GHz. The integrated profile morphology in each epoch of our observations is also listed in the last column of Table 1. In most cases, its integrated profile showed single peak-structure at 8.60 GHz, whereas it usually showed dual-peak structure at 2.25 GHz. It is noticed that the integrated profile shapes at 2.25/8.60 GHz only showed synchronized changes during MJD 59086-59092 on the P 3 component. We fitted three Gaussian components to each profile to obtain the width at 50% of peak (W50) of each component. The curves showing how W50 of each component changed with the time are shown in the fourth panel of Fig. 1. The W50 of P 2 at 8.60 GHz is generally narrower than that at 2.25 GHz except on MJDs from 59030 to 59051. Normally, the W50 of two other components is wider than the W50 of P 2 both at 2.25 and 8.60 GHz.

Flux densities and spectral index
The estimated flux density at 2.25/8.60 GHz (S2.25 and S8.60) are appended in the 3rd column of Table 1 and also shown in 5th panel of Fig. 1. Though S2.25 decreased before MJD 58944 shortly after discovery X-ray burst, there was a steady rising trend in both S2.25 and S8.60 after MJD 59036. For each epoch, we fitted a power-low model (Sν ∝ ν α ) to the measured flux densities, and showed the spectral index α in the 4th column of Table 1 and also gave related plots in the bottom panel of Fig. 1. It can be seen that magnetar changed from steep spectrum with α < −1.48 (MJD 58936-58944) to flat spectrum with α > −0.63 (MJD 59015-59092).
Our α results are consistent with previous values obtained below 32 GHz (Majid et al. 2020a,b;Pearlman et al. 2020;Liu et al. 2020). Compared the α = +0.5 obtained by us on MJD 59076, Torne et al. (2020) reported α = −1.4 with observations from 86 to 154 GHz on same day. So, we guess there should be at least a spectra turnover at high frequency.

Mode switching
Besides mild changes, Swift J1818.0−1607 showed obvious short time-scale flux density variations on MJDs 59039, 59050 and 59051. It seems to switch between quasi-stable bright (B) and quiet (Q) radiation state. Diagnostic plots for its B-Q radiation state are shown in Fig. 3 along with relating plots for its normal radiation state. By comparison, it is a little easier to judge whether it is a mode switching or not using data from MJD 59051 than the other two data because of its relatively higher average flux density. Subfigure (a) of Fig. 3 shows the flux density changes at 2.25 and 8.60 GHz on MJD 59051 with the 'hot' and 'jet' style phase-time plots, respectively. Its mean flux density changes with the time are shown in the subpanel above each waterfall plot with the black solid curve. To avoid being contaminated by adjacent data of different states, a typically B and Q state that lasted relatively longer were selected and labeled with red dash and green solid square, respectively. The black dash line in the same panel stands for 10% of the average flux of B state labeled with the red dash square. It can be seen that this magnetar switched between B and Q state synchronously at 2.25/8.60 GHz. The integrated profiles obtained the Q state data in green solid squares with same color are shown in right subpanels. Meanwhile, the integrated profiles of its B state obtained same style curve data in the red dash squares are shown with the red line in the right subpanel of Fig.3. We can see the difference in shapes of red and green integrated profiles, especially for 8.60 GHz observation. In Q state, its  integrated profile manifested as an additional bump trailing the main peak at 8.60 GHz, but the bump vanished in B state. Furthermore, it can be clearly seen in subfigure (c) of Fig.3 flux density distribution for 8.60 GHz observation on MJD 59051 shows a double-peak structure. Therefore, we think the magnetar exhibited mode switching on MJD 59051 (plots for the B-Q mode switching on MJD 59039 and 59050 will be given in supporting materials).

DISCUSSIONS
Swift J1818.0−1607 showed irregular timing properties. As shown in the 2nd panel of Fig. 1, it seems that theν of Swift J1818.0−1607 oscillated but not a stochastic process. The amplitude ofν oscillations seemed to get smaller as time went. Similar timing phenomena were observed in the magnetar 1E 1048.1−5937 and 17 ordinary pulsars but with timescales of years (Lyne et al. 2010;Archibald et al. 2020). Theseν fluctuations may be caused by certain types of unstable torque that may be affected by stronger magnetic braking (Camilo et al. 2007a;Levin et al. 2012;. Assuming an idealized magnetic dipole model in a vacuum (braking index n = 3) and much faster spin at birth, its characteristic age τc was initially reported as 265, 310 and 240 yr (Champion et al. 2020b;Hu et al. 2020b;Esposito et al. 2020), making it be the youngest magnetar known. Theν of Swift J1818.0−1607 fluctuated more than 12 times from MJD 58930 to 58940 (Champion et al. 2020a). Though theν showed obvious fluctuations in short time-scale, there was obvious linear decrease trend of ν in long timescale. Using much longer observation data spanning about 100 days, Hu et al. (2020a) and Champion et al. (2020a) fitted the averageν then got relatively older τc age of 470 and 500 yr, respectively. We found the long-term linear decrease of ν went on in our observations. Base on the best fittedν obtained with only ours and all the data in Fig. 1, the τc inferred with the above assumptions should be 522 and 489 yr, respectively. So, the τc of Swift J1818.0−1607 is not as young as 300 yr.
Normally, radio-loud magnetars show a flat spectrum typically with α > −0.8 (Eatough et al. 2013;Torne et al. 2017). In our observations of Swift J1818.0−1607, there was a long-term flux density increase trend at both 2.25 and 8.60 GHz. The α changed from less than −1.48 to greater than −0.63 as time went on. Judging from plots in Fig. 1, we think its steep spectrum that lasted tens of days was the main reason for no successful detection of integrated profile above 8.0 GHz (Gajjar et al. 2020;Lower & Shannon 2020;Majid et al. 2020a). The steep radio spectrum was temporarily detected on some magnetars in time-scale of several hours (Lazaridis et al. 2008;Pearlman et al. 2019). A steep magnetar radio spectrum that lasted for tens of days has so far only been observed in J1745−2900, soon after its early outburst (Pennucci et al. 2015).
Magnetars usually change their integrated profile shapes dramatically on timescales from hours to days (Pennucci et al. 2015). Besides integrated profile with singlepeak and dual-peak structure usually detected at frequencies from 0.8 to 154 GHz, we also detected triple-peaked structure at 2.25 GHz near MJD 59087 as Parkes (Lower et al. 2020a). Though two new components showed at 8.60 GHz, they were not seen at 2.25 GHz from MJD 58936 to 58944 in our observations. Hankins et al. (2015) also detected phenomena in which new component dominated profile at high frequency in the Crab Pulsar. Lower et al. (2020a) reported two types of mode switching of Swift J1818.0−1607 at 0.7-4.0 GHz. Swift J1818.0−1607 was quasi-periodically switching between B-mode and Qmode on MJD 59009, and varying between two longitudinally distinct modes (P-and M-mode) on MJD 59047. Swift J1818.0−1607 switched between B-mode and Q-mode synchronously at 2.25/8.60 GHz in 3 days of our observation. Though the mode switching detected by us took place only 3 days later than 'P-M' mode switching on MJD 59047, its flux density fluctuation was more similar to 'B-Q' mode switching on MJD 59009. But, the right bump of integrated profile appeared in the Q-mode of our observation at 8.60 GHz was not so strong as Lower et al. (2020a)'s result in which it was brighter than the left peak component.