Upper limits on the radio pulses from magnetars and a central compact object with FAST

Magnetars and central compact objects (CCOs) are subgroups of neutron stars that show a number of properties distinguished from canonical radio pulsars. We performed radio observations of three magnetars SGR 0418+5729, 1E 2259+586, 4U 0142+61, and a CCO PSR J1852+0040 with the Fivehundred-meter Aperture Spherical radio Telescope (FAST) at 1.25 GHz, aiming to search for radio pulsations in their quiescent states. During two observation epochs, no radio pulses have been detected towards any target above a significance of signal-to-noise ratio (S/N) = 7 from either the direct folding or blind search. We provided the most stringent upper limit of radio flux (<~ 2 -- 4 $\mu$Jy) for the magnetars and the CCO. For the magnetars with long periods, the real upper limits are likely an order of magnitude larger due to the red noise. The deep radio observations suggest that these magnetars and the CCO are indeed radio-quiet sources or unfavorably beamed.


INTRODUCTION
Observations of neutron stars (NSs) in the past decades have shown a plethora of classifications, such as traditional rotation-powered pulsars, magnetars, central compact objects (CCOs), and, X-ray dim isolated neutron stars (XDINSs, Kaspi 2018).
Magnetars are a subgroup of pulsars with ultra-strong magnetic fields (typically ≳ 10 14 G) and long periods (2-12 s, Mereghetti et al. 2015).They are highly variable sources that show high energy bursts, outbursts, giant flares, quasi-periodic oscillations, and sometimes also variable radio emission (Kaspi & Beloborodov 2017).Outbursts of magnetars usually begin with the sudden brightening in the X-ray band and decay slowly in months, which can trigger a diverse emission episode, including periodic radio pulsations.
CCOs are another important subgroup of neutron stars found at the center of the supernova remnants (SNRs, De Luca 2017).In contrast to magnetars, spin measurements of three CCOs suggest this subgroup has a weak dipolar magnetic field, which could be explained as anti-magnetars (10 10 -10 11 G, Gotthelf & Halpern 2008;Halpern & Gotthelf 2010;Gotthelf et al. 2013), although there are also alternative scenarios (Viganò & Pons 2012).
So far, magnetars have been primarily discovered from the X-ray bands, while most classical rotation-powered pulsars were identified from the radio pulsations (∼ 3300 confirmed 1 Manchester et al. 2005).Radio emissions have been detected from 6 out of 30 magnetars (including 6 candidates) following outburst events (Camilo et al. 2006(Camilo et al. , 2007;;Eatough et al. 2013;Esposito et al. 2020;Bochenek et al. 2020;CHIME/FRB Collaboration et al. 2020).Only the magnetar PSR J1622−4950 has been proposed to emit highly variable radio pulsations in the X-ray quiescent phase (Levin et al. 2010).However, the follow-up X-ray study found that its X-ray flux continued to drop until 2011, suggesting that the radio activities still occurred during the decay of the X-ray outburst (Anderson et al. 2012).
CCOs are also discovered from X-ray observations and, in general, lack of emission in the other wavebands (De Luca 2017).The pulsed emission of magnetars, particularly bright at X-ray and soft γ-ray band, is in general believed to be powered by the decay of the strong magnetic fields (Duncan & Thompson 1992), while the X-rays of CCOs are blackbody emission from hot spots on the surface of neutron stars (Seward et al. 2003).
Whether magnetars and CCOs can generate persisent pulsed radio emissions or single pulses during the quiescence has been an unsolved question.In the classical paradigm, the beamed radio emission of pulsars is powered by rotational energy losses.The rotation of the magnetized neutron star induces an enormous electric field, where particles are accelerated to relativistic energies.The subsequent cascade process produces electron-positron pairs (secondary particles) that radiate curvature emission in the radio band (Ruderman & Sutherland 1975).Old pulsars with low electric potential can not support pair production and thus turn off their radio emission.As young pulsars, magnetars and CCOs should also emit radio pulsations if they share the magnetosphere geometry and radiation mechanism with normal pulsars.However, radio observations in past decades have not firmly detected any CCO or magnetar during the quiescent state (e.g., Mereghetti et al. 1996;Halpern & Gotthelf 2010;Nayana et al. 2017;Lazarus et al. 2012).With it comes whether these peculiar NSs are indeed radio-quiet or simply radio-faint.
Recently, the first Galactic Fast Radio Burst FRB 20200428 was detected from the magnetar SGR 1935+2154 (Bochenek et al. 2020;CHIME/FRB Collaboration et al. 2020), establishing that magnetars are one channel to produce FRBs.Radio pulses with 1 http://www.atnf.csiro.au/research/pulsar/psrcata large range of strengths were found from this magnetar, FRBs being just the high fluency outliers (Pleunis & CHIME/FRB Collaboration 2020; Kirsten et al. 2021;Zhu et al. 2023).It is conceivable that other magnetars may also emit FRBs.Expanding the single pulse searches in all magnetars and other peculiar pulsars will help in understanding the radio activities and FRB properties of pulsars.This motivates us to search for single pulses from magnetars and CCO.
We have performed a search of both periodic radio pulsations and single pulses in 3 magnetars, SGR 0418+5729, 1E 2259+586, 4U 0142+61 and a CCO PSR J1852+0040 in the northern sky using the Five-hundredmeter Aperture Spherical radio Telescope (FAST2 , see Nan et al. 2011;Li et al. 2018), aiming to find potential faint radio pulses or provide the most stringent constraints on the upper limit if not detected.We describe the observations of four sources in Section 2. The results of the radio pulse searches are introduced in Section 3. In Section 4, we discuss the results briefly and make a conclusion of this work in Section 5. We conducted FAST observations of 1E 2259+586, 4U 0142+61, PSR J1852+0040, and SGR 0418+5729 on April 25 and June 21, 2019 (obs.ID: 2019-059-P; PI: X.-D.Li).Integration time for each of these four FAST observations was one hour.The observation was made in the Pulsar Search Tracking Mode, using the central beam of the 19-beam receiver (Jiang et al. 2020;Li et al. 2018) with a frequency coverage of 1.05-1.45GHz and 3280 channels (122 kHz per channel).The data were 8-bit sampled every 49.152 µs, along with full Stokes polarization parameters recorded.The noise diode calibration was used at the beginning of the two observations on April 25, 2019.No outbursts or other transient signal was reported by high-energy instruments during the observation epoch, which implied that these four sources were at their quiescence.The detailed observation information of each source is listed in Table 1. 3. RESULTS

Periodicity and single pulse search
We searched for both periodic radio pulsations and single pulses using the software PRESTO (Ransom 2011), applying direct folding search, Fourier-Domain blind search with acceleration, and single pulse search (Ransom et al. 2002), respectively.Radio Frequency Interference (RFI) was removed using the command RFIFIND provided by PRESTO.
Before searching, we conducted a de-dispersion of the data by considering a broad range of Dispersion Measures (DM).The used DM range of PSR J1852+0040 is 0-3000 pc cm −3 , the upper limit of which is several times larger than the value predicted by NE2001 model (Cordes & Lazio 2002, 440 pc cm −3 ), and three times the value predicted by the Galactic electron-density model YMW16 (Yao et al. 2017, 982 pc cm −3 ) at the distance of 7.1 kpc (Case & Bhattacharya 1998;Zhou et al. 2016).The DM values of SGR 0418+5729, 1E 2259+586 and 4U 0142+61 predicted by NE2001 are 63.52, 99.71, and 103.83 pc cm −3 at distances of 2, 3.2 and 3.6 kpc, respectively (van der Horst et al. 2010;Kothes & Foster 2012;Durant & van Kerkwijk 2006).We performed the de-dispersion ranging from 0 to 535.95 pc cm −3 for the three magnetars.We used a fine DM spacing for the low DM and a slightly coarse step for the high DM (d(DM)=0.05-0.2pc cm −3 ) according to the DDplan.py(Ransom 2011), which is designed to balance the dedispersion accuracy and computing efficiency.
Since former X-ray observations had precisely measured the spin parameters of the three magnetars and the CCO (Dib & Kaspi 2014;Halpern et al. 2007;van der Horst et al. 2010;Rea et al. 2013), we extrapolated the period of each source (see Table 2) by calculating the spin period at the current epoch using the X-ray timing results.We then performed a search for periodic pulsations using a derived spin period at our observing epochs for the CCO and three magnetars in the same DM range and with the same steps as mentioned above.For this, we simply extrapolated linearly the spin period and used prepfold setting the -nosearch parameter.The extrapolated spin periods at the start of our radio observations are 0.10491264810 s, 9.0783869 s, 9.789184643 s and, 8.6885092 s for PSR J1852+0040, SGR 0418+5729, 1E 2259+586 and 4U 0142+61, respectively.No periodic radio pulsation was found at a S/N = 7 significance.
Subsequently, we performed a Fourier-Domain acceleration search (Ransom et al. 2002) for latent period sig- nals from four pulsars.We performed the acceleration search in the Fourier domain by adopting zmax = 0, 20 and the threshold of S/N = 7.Firstly, we set zmax = 0 to search for the periodic signals (including their harmonics) from these four isolated pulsars.We then chose zmax = 20 because a simple extrapolation from the old X-ray ephemeris to recent epochs could yield an imprecise spin period, especially for magnetars with large timing noise.We folded the candidates of the CCO and three magnetars by using their spin parameters, setting the same threshold S/N = 7.We did not search the derivative of spin period Ṗ , since all of the four pulsars are not found in the binary system, and their spin-down level was negligible during the observation.
Since the number of periodic candidates whose S/N > 7 is acceptable for computing resources, we folded all of them in order to search for any radio pulses that not only from these four sources but also unknown sources that emit radio periodic pulsations.The folding search was performed using the prepfold command from the software PRESTO (Ransom 2011).No significant periodic radio pulsation was found at a significance of S/N=7 during the observation campaign.
We finally searched for single pulses using the dedispersed time series (Cordes & McLaughlin 2003).We used 14 box-car width match filter grids distributed in logarithmic space from 0.1 ms to 30 ms using Note-Period P and period derivative Ṗ of all the four targets were converted to the observation date using the X-ray spin parameters (Halpern & Gotthelf 2010;Rea et al. 2013;Dib & Kaspi 2014).The DM values of these four sources were estimated using the Galactic electronic-density model NE2001 (Cordes & Lazio 2002).Smin is the upper limit of periodic pulsations at the central frequency νc =1.25 GHz.SSP is the upper limit of the single pulse, and the subscripts 30, 1, and 0.1 denote a pulse width of 30 ms, 1 ms, and 0.1 ms, respectively.The 1-σ error bars are provided for 1E 2259+586 and 4U 0142+61 based on the noise diode calibration.Smin,r is the upper limit of periodic pulses by considering the frequency-dependent noise.
single pulse search.py in the software PRESTO.For each pulsar, we grouped all the candidates obtained by the search for a time interval of 30 s and DM interval of 50 pc cm −3 to produce two-dimensional (2D) DMtime plots that we visually inspected to identify significant pulses.Significant candidates should be clustered in a high-S/N range (> 7) near a certain DM value.As shown in the 2D plot Figure 1, several significant single pulse candidates are found.We then examined the dynamic spectra of all the significant candidates with peak S/N > 7.After cross-checking the 2D plots covering the interested DMs and the dynamic spectra of significant single pulse candidates, we claim that no astrophysical single pulse was found at a threshold of S/N = 7.

Upper limit of radio periodic emission
We can constrain the upper limits of the averaged flux density of the four targets using two methods 1) theoretical estimation; and 2) noise diode-injected flux calibration.
Theoretically, the minimal detectable radio flux density S min can be estimated by applying the radiometer equation (Lorimer & Kramer 2004): where W eff = W 2 i + τ 2 scatter + ∆t 2 DM + dt 2 represents the effective width of a pulse, W i is the intrinsic pulse width, τ scatter is the scattering timescale, and t DM is the uncorrected dispersion delay within a frequency channel, introduced by the free electrons along the lineof-sight.dt is the time resolution of the FAST (see in Section 2).β is the digital correction factor, T sys is the system noise temperature, G is the gain depending on telescope performance and the zenith angle, ∆f is the observation bandwidth in MHz unit, N p is the number of polarisation channels, and t obs is the integration time.Under the assumption that the performance of FAST and the impact of the atmosphere at our observing frequency stay stable over time (Qian et al. 2020), we take the gain factor G = 16.7 K/Jy, system temperature T sys = 25.7 K (Jiang et al. 2020), β = 1.1, N p = 2, and the integration time is 1 hour.
The S/N=7 radio flux upper limits for all four sources theoretically estimated by Equation 1 are plotted in Figure 2. Neglecting the potential effects of scattering, the figures show that the radio flux sensitivity depends mainly on the DM and the intrinsic duty cycle (∼ W i /P ).The sensitivity decreases rapidly at high DM values.This is because the frequency-dependent time delay (∆t DM ) caused by large dispersion would smear the pulse width.Since this effect shares the inverse square relation with the observing frequency (∆t DM ∝ f −2 ), observations in higher frequency or with finer frequency resolution can significantly mitigate the pulse smearing and thus, the loss of sensitivity due to dispersion.
By adopting a S/N=7 significance, the radiometer equation provides the flux upper limits of 2.89 µJy for PSR J1852+0040 and 2.33 µJy for three magnetars at the intrinsic duty cycle of 10%, and assumed DMs as indicated in Table 2.These are nearly or more than one order of magnitude lower than the former results observed by GBT (Halpern et al. 2007;Rea et al. 2013;Lazarus et al. 2012).
Besides applying the radiometer equation, a switched calibration noise diode was applied in the first two minutes of observations for 1E 2259+586 and 4U 0142+61.This provides a more accurate system temperature for calculating the upper flux density limits of the observation.We extracted the calibration data and fitted the baseline and amplitude to calculate the system temper- ).The flux was cut off at DM ∼ 640 pc cm −3 because of the smearing caused by ∆tDM.We take the DM ∼ 440 pc cm −3 predicted by NE2001 model (Cordes & Lazio 2002) to estimate the theoretical upper limit.Bottom: theoretical upper limits of radio flux density for magnetars 4U 0142+61, 1E 2259+586 and, SGR 0418+5729, (assuming an intrinsic duty cycle of 10%).
ature T sys at the observation date as follows (Lorimer & Kramer 2004) where T cal is the equivalent temperature of the noise diode, OFFCAL and OFF represent the counts of system noise plus the noise diode and system noise, respectively.We considered the uncertainty of DM values predicted by NE2001 (Cordes & Lazio 2002) and the zenith-angle dependence to measure the uncertainty of sensitivity.The zenith-sensitive Gain factor with 1σ uncertainty was 12.11 +0.51  −0.51 K/Jy for 4U 0142+61 and 13.60 +0.14 −0.15 K/Jy for 1E 2259+586, respectively.We applied these calibrated Gain factors to produce the baseline calibration results for these two sources, which can be found in Table 2 and are summarized in Section 5.
Finally, we noted that the above theoretical calculation holds for ideal white noise conditions.Frequencydependent noise, such as red noise, can dominate the noise of low-frequency periodic signals (see Lazarus et al. 2015).To estimate the potential impact of red noise on our sensitivity to periodic pulses from the three magnetars, we calculated the amplitude difference of the noise in the Fourier series between the areas around the spin period of the magnetars and the CCO.We did this by using the RMS power of the neighboring bins of each spin period.

Upper limit of single pulses
The upper limit of a single pulse can be calculated by (Cordes & McLaughlin 2003) where W eff shares the same definition with Equation 1 and W i is the intrinsic pulse width.We also calculated the upper limits of single pulses for all four sources by applying Equation 3. The instrumental and calibration parameters are the same as used in Section 3.2.The results are listed in Table 2.

DISCUSSION
Our observations suggest that the CCO and three magnetars are radio-quiet during the observing epochs.We compared the upper limits of the pulsed radio luminosity (without the red noise correction for comparison purposes) from the four pulsars with those from known radio pulsars (Manchester et al. 2005), where we took the luminosity at 1.4 GHz and adopted a typical powerlaw index α = −1.6 for our sources (Lorimer et al. 1995) to extrapolate from 1.25 GHz to 1.4 GHz.As shown in Figure 3, the four pulsars in our study are over one order of magnitude dimmer than known radio pulsars with distances larger than 1 kpc.This reinforces the idea that the three magnetars and the CCO are probably radioquiet sources.The upper limits of the four pulsars are comparable or slightly lower than the theoretical estimates made by Wang et al. (2019), which calculated the coherent radiation from a twisted magnetosphere.Here we discuss a few scenarios that have been proposed to explain the non-detection of periodic radio emission in magnetars.
To explain the absence of radio emission in magnetars, Baring & Harding (1998) proposed that the ultra-strong magnetic fields can suppress electron-positron production.The quantum electrodynamic process, γ → γγ could eliminate photons from pair creation, which is thought to be the power source of radio emission in the polar cap model.Rea et al. (2012) compared the X-ray luminosity and spin-down luminosity of magnetars and high-B pulsars and proposed that the radio emission of magnetars is powered by spin-down energy (L rot ) that exceeds their quiescent X-ray luminosity L X .Swift J1834.9−0846provided a counter-example to this hypothesis, as its spin-down power is larger than its X-ray luminosity but it is not a radio-loud magnetar (Tong et al. 2013).For the radio-loud magnetars mentioned in Rea et al. (2012), the periodic radio emission was discovered during the X-ray/γ-ray outbursts (Kaspi & Beloborodov 2017) and faded in several months, which is distinctive from persistent radio pulsations.Zhou et al. (2017) considered the influence of the Equation of States (EoSs) on a pulsar's death line that distinguishes the radio-loud and radio-quiet regions.For a pulsar with a given inclination angle α between rotation and magnetic axes, the death line is determined by the maximum electric potential Φ max ≈ (Ruderman & Sutherland 1975;Shapiro & Teukolsky 1983), which depends on the moment of inertia I, and thus the equation of state.Therefore, the death line in the P -Ṗ diagram can vary with the equation of state.This might explain the non-detection of radio emission from some magnetars and CCOs, but not all of them.
Besides the aforementioned scenarios, we also considered the beaming effect as a possible reason for the nondetection of the magnetars' radio pulsations.18 of 24 confirmed magnetars were not reported to emit radio pulsations.It has been proposed that the radio beaming fraction of the pulsar f is a function of its period (Tauris & Manchester 1998): According to the relationship, we obtained a probability of 18 i=1 (1 − f i ) = 51.9% when all the 18 confirmed magnetars (Olausen & Kaspi 2014) have their radio emission beamed away from the Earth.This result implies that there is a probability that these magnetars emit radio pulses but they are unfavorably beamed.
For CCOs with low dipole magnetic fields (B ≤ 10 12 G), the lack of radio emission can not be explained with the high magnetic field scenario by Baring & Harding (1998).We estimated a non-negligible probability of 31% when the three CCOs (with spin periods measured from the X-rays) are beamed away in the radio band.Assuming that all the 10 known CCOs have a period in the range of 0.1-0.4s (De Luca 2017), the missing the emission due to the beaming effect should occur at a small probability of 0.7% ≤ p ≤ 10.0%.
The uncertainty of the beaming effect is large, since the spin periods of most CCOs are unknown and thus influence the values of the estimated beaming fraction.
Therefore, the beaming effect cannot be excluded to explain the non-detection of radio pulses in some magnetars and CCOs.It is also possible that other physical mechanisms, such as the suppression of electronpositron pair production in strong magnetic fields, the energy budget of spin-down luminosity, and the influence of the EoSs, work together with the beaming effect to prevent the detection of persistent radio pulsations from these two subgroups of pulsars.
We have not detected single pulses from the magnetars and the CCO as elaborated in Section 3.3.Since the occurrence rate of the radio pulses from these sources is unclear, missing single pulses in our observations does not mean that these sources cannot emit FRBs or other pulses beyond our observation epochs.

CONCLUSION
We have performed deep radio searches for pulsations in three magnetars and a CCO and have not found any radio periodic emission or single pulses during the observation epochs.The main results are summarized as follows: 1.The S/N = 7 upper limits of the periodic radio pulsation flux densities have been constrained to be 2.9 µJy for PSR J1852+0040, 2.3 µJy for SGR 0418+5729, 3.8 +0.8 −0.8 µJy for 1E 2259+586 and 3.5 +0.7 −0.6 µJy for 4U 0142+61, by using the radiometer sensitivity equation.These upper limits are almost or more than one order of magnitude lower than earlier results (Rea et al. 2013;Lazarus et al. 2012;Halpern & Gotthelf 2010;Gaensler et al. 2001;Burgay et al. 2006) and comparable with the faintest radio pulsars discovered in the FAST commissioning phase (Wang et al. 2021).Considering the frequency-dependent redded noise, the upper limits of the three magnetars were 32.4 µJy, 41.8 +8.8  −8.8 µJy and 38.4 +7.6 −6.6 µJy, respectively.
3. The beaming effect cannot been excluded as a potential reason for the non-detection of pulsations from these magnetars and CCOs.Extending the number of deep radio observations on magnetars and CCOs will help to improve our physical interpretation of the missing radio emission in these two subgroups of neutron stars.

Figure 1 .
Figure 1.An exemplified image of single pulse search in the DM range 50-100 pc cm −3 , 2310 -2340 s of the observation of SGR 0418+5729.The subplot on the top-right could be used to identify the single-pulse candidates.The radius of the black dots in the bottom subplot is proportional to its S/N ratio.Single pulses will be identified as bunched hollow circles.

Figure 2 .
Figure 2. Top: theoretical upper limit of the radio flux density for the CCO PSR J1852+0040 (top panel) varying with the intrinsic duty cycle (d.c.).The flux was cut off at DM ∼ 640 pc cm −3 because of the smearing caused by ∆tDM.We take the DM ∼ 440 pc cm −3 predicted by NE2001 model(Cordes & Lazio 2002)  to estimate the theoretical upper limit.Bottom: theoretical upper limits of radio flux density for magnetars 4U 0142+61, 1E 2259+586 and, SGR 0418+5729, (assuming an intrinsic duty cycle of 10%).

Figure 3 .
Figure 3.The luminosity of radio pulsars at 1.4 GHz as a function of the spin periods.Purple points represent pulsars with a distance of less than 1 kpc.Orange lower triangles denote the upper limits of periodic pulsation from four pulsars in this work.

Table 1 .
Observation information of 4 targets

Table 2 .
Spin parameters, DM, and the S/N=7 upper limits on the radio pulses of the four targets