Subsecond periodic radio oscillations in a microquasar

Nature | www.nature.com | 1
Article
Subsecondperiodicradiooscillationsin
amicroquasar
Pengfu Tian1,2,16
, Ping Zhang1,2,16
, Wei Wang1,2,16✉, Pei Wang3,4,16
, Xiaohui Sun5
, Jifeng Liu2,3
,
Bing Zhang6,7✉, Zigao Dai1,8
, Feng Yuan9
, Shuangnan Zhang10
, Qingzhong Liu11
, Peng Jiang3,12
,
Xuefeng Wu11
, Zheng Zheng3
, Jiashi Chen1,2
, Di Li3,13,14
, Zonghong Zhu1,15
, Zhichen Pan3,12
,
Hengqian Gan3,12
, Xiao Chen1,2
& Na Sai1,2
Powerfulrelativisticjetsareoneoftheubiquitousfeaturesofaccretingblackholesin
allscales1–3
.GRS1915 + 105isawell-knownfast-spinningblack-holeX-raybinary4
with
arelativisticjet,termeda‘microquasar’,asindicatedbyitssuperluminalmotionof
radioemission5,6
.IthasexhibitedpersistentX-rayactivityoverthelast30 years,with
quasiperiodicoscillationsofapproximately1–10 Hz(refs.7–9)and34and67 Hzinthe
X-rayband10
.Theseoscillationsprobablyoriginateintheinneraccretiondisk,but
otheroriginshavebeenconsidered11
.Radioobservationsfoundvariablelightcurves
withquasiperiodicflaresoroscillationswithperiodsofapproximately20–50 min
(refs.12–14).Herewereporttwoinstancesofapproximately5-Hztransientperiodic
oscillationfeaturesfromthesourcedetectedinthe1.05-to1.45-GHzradiobandthat
occurredinJanuary2021andJune2022.Circularpolarizationwasalsoobserved
duringtheoscillationphase.
WeusedtheFive-Hundred-MeterApertureSphericalRadioTelescope
(FAST)15
to perform a high-sensitivity, millisecond-time-resolution
study of GRS 1915 + 105, aiming to study the fine details of jet dynam-
ics. We performed tracking mode observations on the source in the
1.05- to 1.45-GHz band with the central beam of the 19-beam receiver
and a 49.152-μs sample time starting on 25 January 2021 01:35:00
(Coordinated Universal Time, UTC). The continuous observations
lasted90 min,withfullStokespolarizationparametersrecorded.After
datareductionandcalibration(detailsareinMethods),wederivedthe
variationsofthetotalintensity,degreesoflinearpolarization(LP)and
circularpolarization(CP),andLPpositionangle(PA)overtheobserv-
ing time intervals with a time resolution of approximately 0.002 s, as
presented in Fig. 1.
To study the variation properties of radio emission, the dynamical
power spectrum of the light curve of radio flux density is calculated
and displayed in the bottom panel of Fig. 1. The power spectrum over
time shows two striped structures appearing in the middle interval
of the observations, indicating transient quasiperiodic oscillations
(QPOs) at approximately 0.196 ± 0.002 s and 0.104 ± 0.003 s in the
radiolightcurve(alluncertaintiesareatthe1σlevel).Thetwovertical
dashedlinesdividetheobservingtimeintothreetimedomains.Epoch
Aiswhenthetotalintensityfluxdensitywasinarelativelystablestate
at approximately 400–420 mJy before the appearance of the QPOs.
The radio spectral index α in the 1.05- to 1.45-GHz band varies from
approximately −0.6 to −0.5. Epoch B is the period of periodic oscilla-
tions,whichlastedforabout1,260 s.Duringtheepoch,thefluxdensity
increasedfromapproximately450 mJytoapproximately660 mJy,and
αevolvedfromapproximately−0.5to−0.35.EpochCistheepochafter
theperiodicoscillationsdisappeared.Thefluxdensityreachedastable
levelofapproximately660 mJywithαofapproximately−0.3.Onecan
see that the transient subsecond periodic oscillations only occurred
duringtheperiodofarapidincreaseofradiofluxdensity.Thechange
of α suggests the occurrence of an ejection event6,16
.
Polarizationevolutionwithfluxandtimewasalsoobserved.InFig.2,
wepresentthedistributionsofLP,CPandPAinthethreeepochsdefined
above.TheLPdegreewasdistributednormallyaround26.5%inEpochA,
increasedtoapproximately28.5%inEpochBandcontinuedtoincrease
toapproximately30.5%inEpochC.TheCPevolutionshowsadifferent
evolution behaviour with time. A clear double-peak symmetrical dis-
tributionwasobservedbeforetheQPOphase(EpochA)withbothleft
andrightCPs.ThedistributionbecameasinglepeakwithpureleftCP
inEpochB,anditswitchedbacktothedouble-peakdistributionagain
inEpochCwithalittlebitmorerightCPthanleftCP.ThelinearPAhas
similar distributions for both Epochs A and C, with the peak value of
approximately 87.5°. During Epoch B, the PA became systematically
larger, with the peak distribution around PA of approximately 88.5°.
The transient subsecond QPOs have a complicated temporal varia-
tionstructure,whichcouldbeconnectedtojetdynamicsoftheblack
https://doi.org/10.1038/s41586-023-06336-6
Received: 29 August 2022
Accepted: 16 June 2023
Published online: xx xx xxxx
Check for updates
1
Department of Astronomy, School of Physics and Technology, Wuhan University, Wuhan, People’s Republic of China. 2
WHU-NAOC Joint Center for Astronomy, Wuhan University, Wuhan,
People’s Republic of China. 3
National Astronomical Observatories, Chinese Academy of Sciences, Beijing, People’s Republic of China. 4
Institute for Frontiers in Astronomy and Astrophysics,
Beijing Normal University, Beijing, People’s Republic of China. 5
School of Physics and Astronomy, Yunan University, Kunming, People’s Republic of China. 6
Nevada Center for Astrophysics,
University of Nevada, Las Vegas, NV, USA. 7
Department of Physics and Astronomy, University of Nevada, Las Vegas, NV, USA. 8
School of Astronomy and Space Science, University of Science
and Technology of China, Hefei, People’s Republic of China. 9
Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai, People’s Republic of China. 10
Key Laboratory of
Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, People’s Republic of China. 11
Purple Mountain Observatory, Chinese Academy of Sciences,
Nanjing, People’s Republic of China. 12
Guizhou Radio Astronomy Observatory, Guizhou University, Guiyang, People’s Republic of China. 13
University of Chinese Academy of Sciences, Beijing,
People’s Republic of China. 14
Zhijiang Lab, Hangzhou, Zhejiang, People’s Republic of China. 15
Henan Academy of Sciences, Zhengzhou, People’s Republic of China. 16
These authors contributed
equally: Pengfu Tian, Ping Zhang, Wei Wang, Pei Wang. ✉e-mail: wangwei2017@whu.edu.cn; bing.zhang@unlv.edu

2 | Nature | www.nature.com
Article
hole.Wethenperformawaveletanalysisofthelightcurvesduringthe
epoch of periodic oscillations (Methods). The wavelet analysis result
of the power profiles of the radio light curve with the QPO signal is
presentedinFig.3a.Thecontoursofwaveletsshowthevariationchar-
acteristics of the QPOs in both frequency and time domains with the
95%confidencelevelfortheglobalwaveletspectrum.Thelocalwavelet
power spectrum example has a duration of 20 s, which displays a sig-
nificant 5-Hz signal across essentially the entire time span. The 10-Hz
harmonicsignalisweakerandmoresparse.Inthehigh-time-resolution
wavelet power diagram, the 5-Hz signal still shows a discontinuous
400
500
600
Flux
(mJy)
25.0
27.5
30.0
32.5
LP
(%)
–4
–2
0
CP
(%)
87
88
89
PA
(º)
–0.6
–0.5
–0.4
–0.3
Index,
α
6,500 7,000 7,500 8,000 8,500 9,000 9,500 10,000 10,500
Time (s)—MJD (59,239)
5
10
Frequency
(Hz)
0
2
4
6
8
10
12
14
Power
Epoch A Epoch B Epoch C
Fig.1|LightcurvesduringtheQPOphasein2021.Evolutionoftotalintensity
fluxdensity,degreeofLP,degreeofCP,PA,spectralindexanddynamicPDS
withobservationsfrom25January202101:35:00to25January202103:04:57
(UTC).Thetwodashedlinesdividethetimedomainintothreeregimes.For
EpochA,fluxdensityisaround400–420 mJy.ForEpochB,fluxincreased
fromapproximately450to660 mJy,andthe5-and10-HzQPOsappearedwith
adurationofapproximately1,260 s.ForEpochC,fluxshowsaplateauof
approximately660 mJy,andtheQPOsdisappeared.LPhasaslowrisingfrom
25to31%asthefluxdensityrises,whileCPevolvesfromaround0inEpoch
Atoapproximately−1to−2%inEpochBandthenreturnsto0attheendof
theobservation.PAisdeterminedtobearound87.5°inEpochsAandC,andPA
isapproximately88.5°inEpochB.Theevolutionofthespectralindexfrom
approximately−0.65towards−0.3indicatesthatthesystemisevolving
fromopticallythintotheopticallythick.Inthebottompanel,wecalculated
thedynamicalpowerspectrumbycombiningthePDSforeachdatasetof4-s
duration.TheQPOsignalsatapproximately5and10 Hzareonlydetected
duringEpochB.MJDisamodificationoftheJuliandate.

behaviour,withtheQPOsignaldisappearingsometimes.Astatistical
studyofthetimescalesofthedetectedtransientQPOsignalsfindsthe
durationofthe5-HzQPOtobeabout0.4–12 s,withapeakofapproxi-
mately0.7 s.Thetypicalduration(τ)ofthe5-HzQPOsignalatτ ≈ 0.7 s
definesacharacteristicscaleofapproximatelyτc ≈ 2 × 1010
cm,where
cisthelightspeed,whichmayberelatedtothetypicalsizeoftheQPO
emission region or lower limit of the emission height.
ToprobethevariationcharacteristicsoftheQPOs,wefoldtheradio
lightcurvesattheperiodof0.196 sfortheEpochBdata.Inthebottom
panelofFig.3,theQPOpulseprofilesforthe5-Hzsignalsarepresented.
The pulse profile shows a broad single peak covering more than 70%
of the whole phase. The pulse-folding technique also constrains a dis-
persionmeasureofapproximately230–280 pc cm−3
forGRS1915 + 105
(Methods). Additionally, we also fold the light curves of three polari-
zation parameters (LP, CP and PA) at the same period during Epoch
B, showing variations of these polarization parameters over the QPO
pulseprofile.Inparticular,theCPshowsavariationpatternsimilartothe
QPOprofile.
GRS1915 + 105hasshownvariableLPandCPofradioemissionbyrela-
tivisticelectrons,whichrevealsalarge-scalemagneticfieldstructure
intheoutflow17
.CPofapproximately−1%wasdetectedduringtheQPO
epoch. In a relativistic jet, there may be two physical mechanisms for
CP:anintrinsicCPfromsynchrotronradiationandLPtoCPconversion
(repolarizationbyFaradayconversion)17,18
.Amagneticfieldconfigura-
tionperpendiculartothelineofsightwouldinduceFaradayconversion,
especially with the presence of copious low-energy electrons18
. If the
26 28 30 32
LP (%)
0
0.2
0.4
0.6
0.8
1.0
Density
a
Epoch A
Epoch B
Epoch C
–4 –3 –2 –1 0 1
CP (%)
Density
b
86.0 86.5 87.0 87.5 88.0 88.5 89.0 89.5
PA (º)
0
0.5
1.0
1.5
2.0
2.5
3.0
Density
c
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6 Epoch A
Epoch B
Epoch C
Epoch A
Epoch B
Epoch C
Fig.2|Evolutionofthepolarizationparameters. a–c,Thevaluedistributions
oftheLP(a),CP(b)andPA(c)inthreeobservationalepochs:EpochsA,BandC.
Thesolidlinesarethekerneldensityestimationsmoothingcurves.LPrises
slowlywiththetime,whileCPandPAshowdifferentbehavioursbetweenEpoch
B(theQPOregime)andEpochsAandC(thetexthasadetaileddescription).
0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0
Time (s)
64.0
16.0
4.0
Frequency
(Hz)
a
545
546
547
548
Flux
(mJy)
b 5 Hz profile
28.05
28.10
28.15
LP
(%)
–1.20
–1.18
–1.16
CP
(%)
0 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
Phase
88.24
88.26
88.28
88.30
PA
(º)
Fig.3|FastvariationsoftheQPO.a,Inthewaveletanalysisresultoftheflux
foratimeintervalof20 sasanexample,thecontourplotsshowthedetected
periodic signals and their evolution with time. The orange dashed lines
annotatethecentroidfrequenciesoftheperiodicsignals.Thediscontinuous
andscatteringfeaturesofQPOsindicatethatthesignalsarenotdetected
sometimesandmaynotappearsimultaneously.b,Fromtoptobottom,the
pulseprofilesofthe5-HzregimeoverQPOphasesfoldedat0.2-speriodforflux
(StokesI),LP,CPandPA.Thepulseprofilesofthe5-HzQPOareLorentzianlike,
showingasinglepeak.Inaddition,thepolarizationprofiles,speciallyCP,show
similarmodulationsinphasewiththefluxprofile(amplitudevariationsof
approximately2–3%).Theerrorbarsaregivenwiththerangesof1σ.

4 | Nature | www.nature.com
Article
large-scale magnetic field along the line of sight changes orientation
with time, it also induces modulation of the observed CP.
The detection of subsecond periodic oscillations in the radio band
brings direct evidence of subsecond QPOs within the jet emission
region in a stellar-mass black-hole system. To confirm the genuine
origin of the QPO, we searched for similar subsecond QPO features in
GRS 1915 + 105 in the archived data observed with FAST from 2020 to
2022.WedetectedanothertransientQPOsignatureatapproximately
0.21 ± 0.02 s, which lasted approximately 80 s, with the observations
performed on 16 June 2022 (Fig.4), with the 19-beam receiver record-
ingthedataofallbeamssimultaneously.Duringtheobservations,the
centralbeam(M01;fieldofviewof3 arcmin)wastowardsthetargetGRS
1915 + 105,whilethebeamsM02–M19weretowardsotherskyregions
for background monitoring. We applied the fast Fourier transform
analysistoalllightcurves,includingbeamM01onGRS1915 + 105and
other beams on the off-source sky regions in the same time interval
(Fig. 4). Only the M01 data showed the QPO peak feature at around
5 Hzinthepowerspectrum.Otherbeamlightcurvesonlyshowedfluc-
tuations in the power spectra with no QPO features detected. This
strongly suggested that the subsecond QPOs at approximately 5 Hz
were again from GRS 1915 + 105. This observation confirmed the QPO
signaturedetectedinJanuary2021,suggestingthattheapproximately
5-Hzfrequencyisrepresentativeforthismicroquasarsystem.During
thesecondevent,theradiofluxwasrelativelysteadyatalevelaround
350 mJy,withthemeasuredLPapproximately6.5%,CPapproximately
−1.3% and PA approximately 96°. The spectral index α evolved from
−0.08 to approximately −0.01 during the period.
Low-frequencyQPOshavebeendetectedinblack-holeX-raybinaries
in the optical, infrared, ultraviolet and X-ray bands11,19
. These QPOs
probablyoriginatefromtheinneraccretiondisk,butotheroriginsfrom
thecoronaortheoutflowarealsopossible11
.Modelsinvokingdifferent
physical mechanisms have been proposed to interpret these QPOs
(forexample,accretionejectioninstability20
,propagatingoscillatory
shocksinthedisk21
,relativisticprecessionoftheinneraccretionflow22
or jet base23
). Radio emission directly probes jet emission. Thus, the
first detection of subsecond modulations in radio emission provides
an unambiguous connection between the QPOs and the dynamics of
the jet. The new phenomenon could arise from the precession of a
magnetizedrelativisticjetwithawarpedaccretiondisk24,25
.However,
it is not clear whether this variability can survive to the optically thin
regionofthejet,anddetailedmodellingisneededtotestthisscenario.
Whileitisinterestingtospeculateonaconnectionbetweendiskoscil-
lationsandjetoscillations,atpresentthereisnoconfirmedmechanism
to propagate oscillations from the disk to the jet.
Nowadays,GRS1915 + 105appearsinadimmingX-raystate.During
our FAST observations in both 2021 and 2022, GRS 1915 + 105 did not
show any enhancement of emission in X-rays, suggesting possible
obscuration of the X-rays (the long-term X-ray light curves and a dis-
cussion on the special state are in Methods). In general, the launch
of the jet may require a special condition at the engine, and a rapidly
10–5
10–4
10–3
10–2
10–1
100
Power
Epoch A
a
Power
Epoch B
Fit
3V
100 101 102
Frequency (Hz)
Power
Epoch C
101
Power
M01
b
101
Power
M08
101
Power
M10
10–5
10–4
10–3
10–2
10–1
100
10–5
10–4
10–3
10–2
10–1
100
100 101 102
Frequency (Hz)
Fit
3V
Fig. 4 | The power spectra of radio light curves based on the FAST
observationaldata.a,ThePDSsofthreelightcurvesselectedfromthethree
epochsobservedon25January2022(A,BandCasdefinedinFig.1).ThePDS
inEpochBisfittedwithapower-lawcomponentandtwoLorentzianfunctions.
Thecoloureddashedlineinthemiddlepanelindicatestheconfidencelevelat
3σ(thedetailsoftheuncertaintycalculationaredescribedinMethods).b,The
PDSsoftheradiolightcurvesobservedon16June2022simultaneously
recordedbythecentralbeamM01towardsGRS1915 + 105andtheotherbeams
(forexample,M08andM10)towardsotherskyregions.ThesubsecondQPOs
around5 Hzwereonlyreportedfromthetargetsource.Thepowerspectrum
fromM01isfittedwithapower-lawcomponentandaLorentzianfunction.
Thecoloureddashedlineinthetoppanelindicatestheconfidencelevelat3σ.

spinningblackholewithamagnetized,varyingaccretionflowmaybe
in operation in GRS 1915 + 105 to power these relativistic jets.
Onlinecontent
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ries,sourcedata,extendeddata,supplementaryinformation,acknowl-
edgements, peer review information; details of author contributions
andcompetinginterests;andstatementsofdataandcodeavailability
are available at https://doi.org/10.1038/s41586-023-06336-6.
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Article
Methods
Observations
TheFASTisthelargestsingledishandthemostsensitiveradiotelescope
intheworldinthe0.07-to3-GHzfrequencyrange.Thefrequencycover-
ageofthe19-beamreceiveris1.05–1.45 GHz.Thesystemtemperature
is a function of zenith angle and can be fitted with a modified arctan
function validly no more than 40° from the zenith because the back-
ground noises of this observation agree with the average level of the
long-term noise monitoring (Extended Data Fig. 1). To facilitate the
calibration,referencesignalsproducedbythenoisediodeareinjected
into the receiving system. The temperature of the reference signal
is about 1.1 K for low-power mode and 12.5 K for high-power mode15
.
Themeasuredtemperatureuncertaintyofthediodeisapproximately
1%,whichwouldleadtoapproximately2%accuracyinfluxcalibration.
Here, we have carried out a FAST observation on the microquasar
GRS 1915 + 105 in tracking mode on the 1.05- to 1.45-GHz band with
thecentralbeamofthe19-beamreceiver15
startingon25January2021
01:35:00 (UTC) with a 49.152-μs sample time for a duration of 90 min.
The resolution of the central beam is approximately 2.9′. Before and
afterthetrackingmodeobservations,thepatternoftheon–offmode
in which the noise diode was continuously switched on and off was
performed for two time intervals: from 01:25:00 to 01:30:00 (UTC)
and from 03:10:00 to 03:15:00 (UTC), which are used for calibration
processes. This led to the detection of the first QPO event.
A second event was also detected by FAST during an observation
performed on 16 June 2022 from 17:42:40 (UTC) to 17:47:30 (UTC) in
thetrackingmodeonthe1.05-to1.45-GHzbandwiththecentralbeam
of the 19-beam receiver. The data from all 19 beams were recorded
for this observation. The central beam M01 was beamed towards the
source,andtheother18beams(M02–M19)werebeamedtowardsthe
off-source sky regions. Before and after the tracking mode observa-
tions, the pattern of the on–off mode in which the noise diode was
continuously switched on and off was performed.
Extractinglightcurvesofradiofluxandpolarization
Here,weshowthemethoddetailstoreducedataandcalibratethetotal
intensity and polarization. The data of FAST are recorded in PSRFITS
format26
.First,weusetheastropypackage27
todothepreprocessingfor
FITS data files. For each of the FITS files, we do the resampling for the
originaldataandextractthefrequencybandandtimefrom4,096fre-
quencychannelsand128subints,andthen,wecombinetheresampled
preprocesseddatafiles.ThePRESTO28
producesatimeseries,whichis
theuncalibratedlightcurvefromthecombinedfile.Meanwhile,PRESTO
canfindtheradiofrequencyinterferences(RFIs)andcreateamaskto
eliminate these narrow-band signal-like noises. The noisy broadband
signal in the periodogram may be caused by RFIs (for example, the
variation of the feed source forms a 0.1-Hz noise, and the frequency
of alternating current in the electronic system may also cause a noise
of50Hzandtheharmoniccomponentinthewholeobservationtime).
RFI-removing processes.Weusedthetwo-dimensionalwavelettrans-
formmethodtomasktheRFI-contaminateddataandthen,filledthese
masked data with the median values. The two-dimensional wavelet
transformcanbeusedtoextracttime–frequencystructuralfeaturesof
RFIsfromthenoisedataalongthehorizontal,verticalanddiagonallines
ofthefeaturematrices(thatis,thenarrow-bandfrequencydomainRFI
and the border-band impulsive RFI can be extracted in the horizontal
andverticaldirections,whilethediagonalfeaturesindicatetheisolate
abnormal values). We project anomalous signals into these three fea-
turedimensions,thensmooththeobviousedgesby3σthresholdfilter-
ing and reconstruct the time–frequency dynamic spectrum by using
thetwo-dimensionalwaveletalgorithm.Thisalgorithmtendstoretain
more data than the traditional frequency channel zapping methods.
InExtendedDataFig.2,wedemonstratetheeffectofRFIremovaland
the corresponding RFI mitigation data (Extended Data Fig. 2a,b). It is
obviousfromthefrequencybandpassthatnearlyallnarrow-bandRFIs
have been masked in RFI mitigation data (Extended Data Fig. 2c), and
the histogram is consistent with a Gaussian white noise distribution
(thevalueofχ2
is5%)(ExtendedDataFig.2d).
To ensure that the RFI removal algorithm does not block the detec-
tion of QPO-like signals, we designed an experiment to simulate the
injectionof5-and10-Hztemporalmodulatedbroadbandsignalsinto
therealFASTdatatoevaluatetheeffectofthetwo-dimensionalwave-
let algorithm. The combined effect of 5- and 10-Hz temporal inten-
sity injection and RFI events, particularly the satellite bands around
1.2 GHz,isshowninExtendedDataFig.3b.Asacomparison,theresult
of RFI mitigation data (Extended Data Fig. 3c) shows not only that the
two-dimensional wavelet algorithm does not block the detection of
thecorrespondingperiodicsignalbutthatitalsoincreasesthesignifi-
cance of the detected signal (for example, from 4.2σ to 12.5σ for 5 Hz;
from 1σ to 3.4σ for 10 Hz).
WealsoworkedwiththeFASTElectromagneticCompatibility(EMC)
technical team to carefully examine the noise signals covering the
whole bandpass to check for possible QPO-related effects from the
receiver or backend instrumentation. The FAST EMC technical team
regularly conducts noise tests on the L-band receiver performance15
.
Duringeachofthenoisetests,anabsorberisusedtocoverthereceiver
feed opening (Extended Data Fig. 4, left panel) (that is, the receiver
willnotreceiveanyofexternalsignalsduringthetime).Wereanalysed
theswitch-by-switchRFIexclusionexperimentaldataon26April2019
15:35–16:05(UniversalTime(UT) + 8)and10January202110:05–10:25
(UT + 8)asdemonstratedinthecorrespondingpowerspectrumforeach
ofthetwofrequency-averagedlight-curvesegmentsinExtendedData
Fig.4(rightpanel)assumingabroadbandsignal(afewhundredmega-
hertz).Nodetectionof5-or10-Hzsignalswithinthefullfrequencyrange
(1,050–1,450 MHz) was made. The horizontal and vertical axes show
theFourierfrequencyandtheintensityinarbitraryunitsofthepower
spectrum,whiletheverticalredandbluelinesarethelocationsof5and
10 Hz,respectively.Throughouttheobservations,noQPO-likedsignal
(inparticular,for5 Hz)withanapparentintensityabove3σwasdetected.
Flux calibration.Thesystemtemperatureofthetelescopeisafunction
ofthezenithangle,
( )
T P θ P P
= ⋅ arctan 1 + − + , (1)
n
sys 0 ZA 1 2
where θZA is the zenith angle; P0, P1, P2 and n are parameters; and their
values vary with different frequencies. Table 4 and figure 12 in ref. 15
show the relationships between Tsys and θZA for different beams. The
temperature of the source is
T t T T t
( ) = ⋅
ON
CALON−ON
− ( ), (2)
src cal sys
where Tcal is the temperature of the injected reference signal from the
noise diode, CALON and ON are the intensity values with the injected
signal switched on and off for the calibration scans before and after
the tracking observations and Tsys(t) is the time-dependent system
temperature. Then, the observed flux density with time is:
t
t
T t
G
Flux( ) =
Track( )
ON
⋅ ( ) ⋅
1
, (3)
src
whereTrack(t)istheintensityvaluesduringthetrackingobservations,
G = ηG0 differsfromthemeasuredgainG0 = 25.6 K Jy−1
byafactoryη,is
thefullgainofFASTintheskycoverageandηistheapertureefficiency.
Meanwhile, there are some RFI broad peaks around channels from
1,400 to 2,380 (Extended Data Fig. 2) that are conspicuous. For a test

for the very clean database, we did another calibration and dynamic
power density spectrum (PDS) calculation for the light curve with
channels from 1,400 to 2,380 removed directly, and the results are
shown in Extended Data Fig. 5. The QPO signals are still recognizable
but a little weaker, which would be due to the reduction of observed
channels leading to the lower signal–noise ratio. In addition, we also
derive the spectral index in the band 1.05–1.45 GHz defined by
α S ν
= ∆log /∆log
ν ,whereSv istheobservedfluxdensityatafrequency
v.ThespectralindexevolutionversustimeisshowninExtendedData
Fig.5,andαvariesfrom−0.6to−0.3duringtheincreasingoftheflux.
Thechangeoftheradiospectrumgenerallyoccursbeforetheejection
event14,29
.
Polarization calibration. The original PSRFITS files of FAST observa-
tion contain the polarization components that are recorded as the
AABBCRCIform,whereAAandBBarethedirectproductsoftwochan-
nelsandCRandCIaretherealandimaginarypartsofthecrossproduct
oftwochannels,respectively.WeuseDSPSR30
andPSRCHIVE26
tofold
theoriginalfileswiththeirdurationasfoldingperiodstoproducethe
fourtimeseries.Eachofthefourtimeseriesisfullof4,096frequency
channels and 128 time subints, so it is necessary to eliminate the RFIs
manuallyforeachtimeseries.
Wecalculatethestokesparametersfromthefourrecordedchannels,
named I x
2
, I y
2
,CRandCI,respectively31
,whereCRandCIaretherealand
imaginary parts of the crossproduct of two channels Ix × Iy. Generally,
for normal devices, feeds are never perfect, and there are two quanti-
ties that should be considered and calibrated (that is, relative gain of
the electronic system and phase differences between two channels).
Inthispaper,wenamedthetwoquantitiesasleakageandphaseerror.
Additionally, stokes parameters with subscripts obs and true refer to
polarization components before and after calibration, respectively,
which normally should take the Mueller matrix32,33
of the equipment
into account. Then, considering the leakage between two channels,
for the linearly polarized signal from the diode, we find
I I f Q
Q Q f I
′ = ′ + ⋅ ′
′ = ′ + ⋅ ′ ,
(4)
obs true true
obs true true
where ′ means the injected reference signal and the leakage f =
′
′
Q
I
obs
obs
.
We calibrated the phase error asδ = arctan
′
′
V
U
er
1
2
obs
obs
; then, removing the
error from orientation, we can get the true values of the four stokes
parameters:
I
I f Q
f
Q
Q f I
f
U P δ δ
P δ δ P δ δ
V P δ δ
P δ δ P δ δ
=
− ⋅
1 −
=
− ⋅
1 −
= cos(2( − ))
= cos2 cos2 + sin2 sin2
= sin(2( − ))
= sin2 cos2 + cos2 sin2 ,
(5)
true
obs obs
2
true
obs obs
2
true er
er er
true er
er er
where P U V
= +
obs
2
obs
2
.Finally,thedegreesofLPandCPandthepolar-
ization PA are calculated as
L
I
Q U
I
V
I
U
Q
LP = =
+
CP =
PA =
1
2
arctan .
(6)
true
true
2
true
2
true
true
true
true
Dispersionmeasuretest
The dispersion measure represents the integrated column density of
freeelectronsbetweenanobserverandapulsar34
,thenobservationally
leads to a broadening of a sharp pulse when a pulsar is observed over
afinitebandwidth.Unfortunately,theverybroadandsine-likeprofile
of transient 5-Hz QPO compared with the pulses in pulsars makes it
difficult to directly detect the dispersion measure of the source from
the delay of time of arrival between different frequencies of the QPO.
In this work, we used the prepfold to fold the data during Epoch B in
January2021attheperiodoftheQPO(0.196 s)atdifferentdispersion
measure values. Here, we take the dispersion measure ranges from 0
to 700 pc cm−3
and set the step of 1 pc cm−3
. Then, we fit each folded
profiles via Lorentzians. The fitting parameters (for example, ampli-
tude (A) and full-width at half-maximum (σ)) are supposed to reach
themaximumandminimum,respectively,aroundthetruedispersion
measure value. In Extended Data Fig. 6, the evolution of A, σ and A/σ
withdispersionmeasureareplotted;thepeakofA/σcentringaround
a dispersion measure of approximately 255 pc cm−3
with an s.d. of
25 pc cm−3
(68% confidence level) indicates the possible dispersion
measure of the source.
Dynamicalpowerspectrum
Themainaimofthetiminganalysishereistosearchforthesubsecond
QPOsinradiofluxlightcurves.QPOsaregenerallystudiedintheFou-
rierdomainandshowupinthePDSasnarrowpeaks.WeusedNumpy.
fft.fft and Stingray in Python packages to perform the PDS analysis,
including the production and fitting of the PDS. We calculated the
PDS for every 4-s dataset of the calibrated flux time series and then
wearrangedtheminchronologicalordertogetasetofspectrathatis
calledthedynamicalpowerspectrum(Fig.1andExtendedDataFig.5)
for the whole observational time series on 25 January 2021. Based on
theQPOsignalevolutionbehaviour,theobservationaltimeseriescan
be divided into three time regimes: the pre-QPO regime (Epoch A),
the QPO regime (Epoch B) and the post-QPO regime (Epoch C). With
thesamemethods,wealsoderivedtheevolutionoftheradiofluxand
polarization for the second QPO event on 26 June 2022 and present
the dynamical power spectrum of the flux light curves in Extended
DataFig.7.TheQPOaround5 Hzlastedforabout80 s,whichwasalso
weaker than that detected in January 2021.
InFig.4a,wedisplaythePDSsofthethreelightcurvesselectedfrom
thethreeepochs(A,BandC)on25January2021.Theplotsofthethree
PDSs show two unambiguous peaks around 5 and 10 Hz only appear-
ing during Epoch B. There are no QPO signals during Epochs A and
C. In addition, for comparison, we also showed the PDSs of the three
light curves selected from the central beam and the other two beams
with the FAST observations performed on 16 June 2022 in Fig. 4b. The
5-Hz QPO was only reported in the central beam towards the source.
Nosignalsweredetectedinotherbeamstowardsthebackgroundsky
regions.Meanwhile,inFig.4,wedenoteasignificancelevelof3σusing
alightcurvesimulationalgorithm35
torepresentthecriterionforQPO
detection.Forthesignificance-levelcomputation,wesimulated20,000
light curves with power-law distributed noises appropriate for our
data and resampled these light curves to ensure that the resolution
matched our observation data.
Waveletanalysisresults
The dynamical PDS technique has the limit of the time resolution at
thetimeintervals(severalseconds)usedforthetimedomainanalysis.
However, the wavelet analysis method can provide accurate time–
frequencyspaceinformationwithveryhightimeresolution,andthus,
it can be used to study the detailed variation characteristics of the
periodic or quasiperiodic signals over time36
, which also have been
applied to timing analysis of X-ray light curves in the X-ray binaries to
discover the transient QPOs37–39
.

Article
WealsousedthewaveletanalysismethodtotesttheQPOsignalswe
detected in dynamical PDS, which can approach the time evolution
and variation of the signal. In wavelet analysis, we have taken the red
noiseintoaccountbycalculatingthecorrelationfunctionsofthetime
series, and a simple model to compute red noise is the univariate
lag-1 autoregressive process, so that we estimate the red noise from
α α
( + )/2
1 2 wheretheα1 andα2 arethelag-1andlag-2autocorrelations
ofthetimeseries,respectively.Basedontheχ2
distribution,ifapower
inthewaveletpowerspectrumisabovethe95%confidencelevelcom-
pared with the background spectrum, then it can be considered as a
true signal.
ThewaveletpowerspectrumwiththetimeshowsthattheQPOshave
the fine structure evolution in both the time and frequency domains
(an example of the wavelet spectrum is in Fig.3). The 5-Hz QPO signal
is stronger over the time than the 10-Hz QPO; in addition, 5-Hz QPO
can be detected in most observational time intervals during the QPO
regime,whilethe10-HzQPOsignaldistributessparsely.Then,basedon
thewaveletpowerspectrum,wecanclearlyidentifythetimeregimes
whenthe5-HzQPOisonlydetectedandwhenboth5-and10-HzQPOs
appear. Thus, we fold the light curves at the 0.2-s period to create the
pulseprofilesofthefluxdensityforthe5-Hzregime,whichshowsthe
single-peakbroadpulseprofile.Inaddition,tocheckthevariationpat-
terns of the polarization with the pulse profiles of the QPOs, we also
foldthelightcurvesofdifferentpolarizationcomponents(thatis,LP,
CP and PA) at the 0.2-s period of the QPO for the 5-Hz regime (Fig. 3).
With the time–frequency space information provided by wavelet
analysis, the variance of power with time and frequency can be easily
identified so as to distinguish the time intervals with QPOs and
non-detectionofQPOs.Theradiovariationpropertiesshouldberelated
to the jet dynamics; then, the short timescale evolution of two QPO
signalsprovidestheprobeofthecharacteristictimescalesofjetproduc-
tionanddynamics.Thus,wehavestatisticsonthetimeintervalsofthe
QPOsignalsinEpochB(ExtendedDataFig.8):thedurationdistribution
ofthe5-HzQPOs,theseparateintervaldistributionfortwoneighbour
5-HzQPOsandthedurationofthe10-Hzsignal.The5-Hzsignalisstrong
andcanbedetectedinmosttime.However,the10-Hzsignalisweaker,
the QPO feature lasts for only about 1 s or subseconds, and there are
gaps lasting for several to tens of seconds without a feature.
Wealsousethelogarithmicnormalfunctiontofitthedistributions
todeterminethepeakvaluesofthreetypicaltimeintervals,whichwill
probe the characteristic dynamical timescales of jets near the black
hole.Thedurationofthe5-HzQPOdistributesinthebroadtimescales
from0.3to12 sandthepeakaround0.7 s.Thischaracteristictimescale
would be connected to the typical emission size of the QPO emission
source in the jet (approximately cτ). Although the 5-Hz QPO signal is
the dominant component in the power spectrum, the signal would
alsonotbecontinuous,andinsometimeintervalsofEpochB,noQPO
signal can be detected.
OtherradioQPOsinblack-holeaccretionsystems
Long-periodradioQPOswiththeperiodsfromabout100 daystosev-
eralyearshavebeenreportedinsomeradioloudactivegalacticnuclei
(AGNs),especiallyblazars40–43
.TheseradioQPOsgenerallylastforabout
several to 20 cycles, which probably reflects the special dynamics of
relativistic jets powered by supermassive black holes in AGNs. Radio
oscillations with a period of approximately 15 h were also found in
a gamma-ray X-ray binary LS I + 61°303 (ref. 44), which only had two
or three QPO cycles. In addition, slow radio oscillations in the period
rangefrom20to50 minweredetectedinGRS1915 + 105(refs.12–14).
Therehavebeenafewphysicalmodelssuggestedtointerpretthese
QPOs.Forstellarmassblack-holesystems(forexample,GRS1915 + 105),
thehalf-hourradioperiodicoscillationsmaybeconnectedtotheX-ray
oscillations with the similar periods, while in LS I + 61°303, it was sug-
gestedthattheradioQPOscouldresultfrommultipleshocksinajet44
.
TheinfraredQPOsaround0.1 HzreportedinamicroqusarGX339-4are
attributedtothejetprecession45
.IntheframeworkofAGNs,radioQPO
modelsarediverse.TheyearlongQPOsaregenerallyconsideredtobe
theindicatoroftheorbitalmotionofbinarysupermassiveblack-hole
systems. Helical structures in magnetic fields and plasma trajectory
are expected in magnetically dominated jets46
, so helical motion of
blobsorshocksinrelativisticjetshavebeenincorporatedtointerpret
periodsaroundhundredsofdaysinradio,opticalorgamma-raybands
in blazars47,48
. Recently, the optical and gamma-ray periods around
0.6 daysinBLLacertaeweresuggestedtooriginatefromkinkinstabil-
ity in relativistic jets49
.
X-raymonitoringofGRS1915 + 105
We have checked the X-ray light curves by monitoring the source
based on Swift and Gas Slit Camera aboard Monitor of All-sky X-ray
Image(MAXI)from2016to2021,whicharedisplayedinExtendedData
Fig. 9. The Burst Alert Telescope aboard Swift covers the energy band
of 15–50 keV, and MAXI reports the count rates of two energy bands:
2–6 keVand6–15 keV.Asexpected,GRS1915 + 105isthestronglyvari-
able X-ray source and shows flares in the historic records. Since 2018,
GRS 1915 + 105 has unexpectedly started a peculiar low-luminosity
state that is an order of magnitude dimmer than the previous states,
with greater hardness ratio in X-rays50–55
(Extended Data Fig. 9). Even
thoughintrinsicdimmingispossible,detailedX-rayspectralanalyses
suggestedthatthesourcemayhaveenteredanobscuredstatewiththe
strongabsorption(bydiskwindsortorusintheouterdiskpart)along
theobserver’ssight51–53,55,56
duetoalargeinclinationangleofapproxi-
mately60°(ref.57).Thisinterpretationwassupportedbythedetection
of X-ray flares, which are not strongly affected by obscuration. The
observationsoffrequentradioflaresduetotheepisodicjetemissions58
are also consistent with this scenario. During the FAST observations
on25January2021and16June2022,theX-rayfluxwasweakbasedon
both Swift and MAXI observations. The radio oscillations revealed
by our FAST observations suggest that presently GRS 1915 + 105 may
stillhaveahighaccretionratetopowertransientrelativisticjets.This
adds further support to the suggested strong obscuration in X-rays.
Comparisonwithotherradioobservations
The radio flux and LP values from relativistic jets are highly vari-
able and change significantly in different radio bands and different
epochs14,17,29,59,60
. Here, we briefly compare our radio results on GRS
1915 + 105 with other observations. The Very Large Array, Very Long
BaselineArray,MeerKat,Multi-ElementRadio-LinkedInterferometer
Network (MERLIN) and other radio telescopes have monitored GRS
1915 + 105 in different radio bands. MeerKat reported a radio flux of
approximately100–900 mJyduringtheradioflaresafter201858
,which
isconsistentwiththeradiofluxofthepresentobservations.Inaddition,
MERLINhasasimilarobservationalwavebandaround1.2 GHz,report-
inganLPofapproximately(1–24%)(refs.59,60).OurFASTobservation
on 25 January 2021 has an LP of approximately (25–31%), which is a
little higher than or still approaching the previously reported values.
Thisvalueisalsophysicallyreasonable.Foramagneticallydominated
jet with an ordered magnetic field configuration, in the optically thin
emission(α < 0;forexample,thecaseofradioflares)themaximumLP
can be as high as 70% (refs. 61,62). For the observations of FAST on 25
January2021,theradioflarehasanαofapproximately−0.5,andtheLP
couldbeashighasapproximately30%foralarge-scalemagneticfield
alongthejet,consistentwiththeFASTresult.ThesomewhatsmallerLP
inearlierobservationsmaybearesultofobservingdifferentepisodesof
jetinjection.Asthejetpropagates,theLPdegreemaydegradebecause
ofthedissipationoftheorderedmagneticfieldintheemissionregion.
Ourobservationmighthavecaughttheearlyphaseofafreshlyinjected
jetthathasahigherLPdegree.Ingeneral,theLPofthepresentobserva-
tions is still similar to the previous observations and other black-hole
systems59,60,62
, which increases with decreasing randomization of the
magnetic field within the jet component29
.

Dataavailability
All relevant data for the GRS 1915 + 105 observations are available
from the Five-Hundred-Meter Aperture Spherical Radio Telescope
archive(http://fast.bao.ac.cn)one yearafterdatatakingfollowingthe
Five-Hundred-MeterApertureSphericalRadioTelescopedatapolicy.
Owingtothelargedatavolumefortheseobservations,interestedusers
are encouraged to contact the corresponding author to arrange the
data transfer. The data that support the findings of this study are
openlyavailableintheScienceDataBankathttps://doi.org/10.57760/
sciencedb.08478.
Codeavailability
CodeisavailableatPSRCHIVE(http://psrchive.sourceforge.net),DSPSR
(http://dspsr.sourceforge.net)andPRESTO(https://github.com/scot-
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Acknowledgements This work is supported by the National Key Research and Development
Program of China (2021YFA0718500 and 2021YFA0718503), the NSFC (12133007, U1838103,
U2031117, 12233002 and U2031205), the Youth Innovation Promotion Association CAS
(2021055), the CAS Project for Young Scientists in Basic Research (YSBR-006) and the
Cultivation Project for FAST Scientific Payoff and Research Achievement of CAMS-CAS.
Author contributions W.W., as the principal investigator of the Five-Hundred-Meter Aperture
Spherical Radio Telescope observations, led the data analysis and wrote the paper. P.T. and P.Z.
did the data analysis. P.W., X.S., J.L. and Z. Zheng provided the help of the radio data analysis
and software. W.W., B.Z., Z.D., F.Y., S.Z., Q.L. and X.W. constructed the scientific interpretation
of the data and B.Z. contributed to the writing of the paper. P.W., P.J., D.L., Z. Zhu, Z.P. and H.G.
aided with the Five-Hundred-Meter Aperture Spherical Radio Telescope observations. J.C.,
X.C. and N.S. provided the X-ray data. All authors have reviewed the results and manuscript.
Competing interests The authors declare no competing interests.
Additional information
Supplementary information The online version contains supplementary material available at
https://doi.org/10.1038/s41586-023-06336-6.
Correspondence and requests for materials should be addressed to Wei Wang or Bing Zhang.
Peer review information Nature thanks the anonymous reviewers for their contribution to the
peer review of this work. Peer reviewer reports are available.
Reprints and permissions information is available at http://www.nature.com/reprints.

Article
ExtendedDataFig.1|StabilityofFASTperformance.ThermsofthefluxwhenthefeedsourceispointingtothebackgroundskyduringourFASTobservations.

ExtendedDataFig.2|AdemonstrationofRFI-mitigationexperimentusing
thetwo-dimensionalwaveletalgorithm.a,signalintensityasafunctionof
frequencyandtime(waterfall)plotoftherawdataofGRS1915+105between
MJD59239.09766-59239.09997(bottomsubplot)andfrequency-averaged
lightcurve(uppersubplot).b,thereddotsatthewaterfallplotrepresentthe
maskedRFIcontaminateddatabyusingthetwo-dimensionalwaveletalgorithm
and then fill these masked data by the median values. c, comparison of
frequencybandpassfortherawdataandRFIremovalresult.d,comparison of
histogramforrawdata(white)andRFIremoveddata(blue,theredlineisthe
gaussianfittingwiththevalueofChi-squareislessthan5%).

Article
ExtendedDataFig.3|ExampleofQPOsignalsandRFIremovingsimulations.
Upperpanelsshowfrequency-averagedlightcurves,subplotsa/b/caretheraw
dataofskybackgroundmonitoring,simulatedinjectionof5-Hzand10-Hz
QPOsinthebroadbands,andthelightcurveafterremovingallRFIs,respectively.
BottompanelsshowthecorrespondingFourierpowerspectrainlogarithmic
andlinearcoordinates.Subplotcdemonstratestheapparentincreaseinthe
significanceofthedetectedQPOsignals,i.e.from4.2σto12.5σfor5Hz;
from1σto3.4σfor10Hz,comparedwiththatinSubplotb.Thesimulations
demonstratethatourRFIremovingprocessescanefficientlyreducethe
narrow-bandRFIsandkeepthebroadbandastrophysicalsignals.

ExtendedDataFig.4|The19-beamreceiverperformance.Leftpanel:anabsorberisusedtocoverthereceiverfeedopeningduringnoisetests.Rightpanel:
no-detectionof5-Hzor10-HzapparentpeaksfromFASTreceiveritselfontwooffrequency-averagedlight-curvetimesegments.

Article
ExtendedDataFig.5|Lightcurveanddynamicpowerspectrumwithless
channels. Lightcurve,spectralindexevolutionanddynamicPDSoftheradio
fluxwhichiscalibratedwithdirectlyremovingRFIpeaksfromthechannels
1400to2380.Thereare2700channelsleftafterchannelcuttingandRFI
removing.QPOsignalsat ~ 5Hzarefaintercomparedtothecasewithabout
3400channels.TheEpochsA,BandChavethesamedefinitioninFig.1,with
thetimerecordstartingfromJanuary25202101:35:00(UTC).Theindexα
variesfrom − 0.6to − 0.3duringtheEpochs.

ExtendedDataFig.6|TheDMvalueofQPOsignals.Amplitude(A)andfull
widthathalfmaximum(σ)ofthefittingLorentziansforthefoldedcurvesevolve
withDM.ThepeakofA/σislocatedatDM ~ 255 ± 25pccm−3
,whichisfittedviaa
Gaussianfunction(greendashedline),wouldindicatethepossibledispersion
measureofGRS1915+105.

Article
ExtendedDataFig.7|Lightcurvesanddynamicalpowerspectrumduring
theQPOphasein2022.Thelightcurvesoftotalintensityfluxdensity,LP,CP,
PA,spectralindexαanddynamicPDSwithFASTobservationsfrom2022-06-
16:17:42:40to2021-06-16:17:47:30(UTC).ThetransientQPOat ~ 5Hzlasting
about80secondswasdetected.Duringtheevent,theradiofluxwassteadyata
levelaround350mJy;LPwasaround6.5%andincreasedslightlyduringthe
observations;CPwasmeasuredat ~ − 1.3%,andthePAwasaround96∘
.The
spectralindexαalsoevolvedfrom − 0.08to − 0.01.Allerrorbarsaregivenat
the1σlevel.

ExtendedDataFig.8|Thedistributionsforthreetimescalesobservedin
EpochB.Thedurationdistributionofthe5-HzQPOs(top),separateinterval
distributionfortwoneighbour5-HzQPOs(middle),anddurationdistribution
ofthe10-HzQPOs(bottom),andtheredlinesarethebestfittingcurveswith
thelog-normaldistribution.

Article
ExtendedDataFig.9|X-raymonitoringduringtheradioQPOs.Top:The
X-raylightcurvesofGRS1915+105from2016-2023basedontheSWIFTand
MAXIlong-term monitorobservations.Bottom: Thezoom-inversionofthe
lightcurvesaroundJanuary252021andJune162022.Theverticaldashedlines
showthetimeofourFASTobservations.

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