Broad-band X-ray spectra and timing of the accretion-powered millisecond pulsar Swift J1756.9-2508 during its 2018 and 2019 outbursts
Z. S. Li, L. Kuiper, M. Falanga, J. Poutanen, S. S. Tsygankov, D. K. Galloway, E. Bozzo, Y. Y. Pan, Y. Huang, S. N. Zhang, S. Zhang
AAstronomy & Astrophysics manuscript no. ms_SwiftJ1756 © ESO 2021February 24, 2021
Broad-band X-ray spectra and timing of the accretion-poweredmillisecond pulsar Swift J1756.9 − Z. S. Li , L. Kuiper , M. Falanga , J. Poutanen , , , S. S. Tsygankov , , D. K. Galloway , , E. Bozzo , Y. Y. Pan , Y.Huang , S. N. Zhang , and S. Zhang Key Laboratory of Stars and Interstellar Medium, Xiangtan University, Xiangtan 411105, Hunan, P.R. Chinae-mail: [email protected] SRON-Netherlands Institute for Space Research, Sorbonnelaan 2, 3584 CA, Utrecht, The Netherlands International Space Science Institute (ISSI), Hallerstrasse 6, 3012 Bern, Switzerland Department of Physics and Astronomy, University of Turku, FI-20014, Finland Space Research Institute of the Russian Academy of Sciences, Profsoyuznaya str. 84 /
32, 117997 Moscow, Russia Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden School of Physics and Astronomy, Monash University, Australia, VIC 3800, Australia OzGRav-Monash, School of Physics and Astronomy, Monash University, Victoria 3800, Australia University of Geneva, Department of Astronomy, Chemin d’Ecogia 16, 1290, Versoix, Switzerland Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, 19B Yuquan Road,Beijing 100049, ChinaReceived xx / Accepted xx
ABSTRACT
The accreting millisecond X-ray pulsar Swift J1756.9 − XMM-Newton , NuSTAR , INTEGRAL,
Swift and
Insight -HXMT. The two outbursts exhibited similar broad-band spectra and X-ray pulseprofiles. For the first time, we report the detection of the pulsed emission up to ∼
100 keV observed by
Insight -HXMT during the2018 outburst. We also found the pulsation up to ∼
60 keV observed by NICER and
NuSTAR during the 2019 outburst. We performeda coherent timing analysis combining the data from two outbursts. The binary system is well described by a constant orbital periodover a time span of ∼
12 years. The time-averaged broad-band spectra are well fitted by an absorbed thermal Comptonization model compps in a slab geometry with the electron temperature kT e = τ ∼ .
3, blackbody seed photontemperature kT bb , seed ∼ N H ∼ . × cm − . We searched the available data for type-I (thermonuclear) X-ray bursts, but found none, which is unsurprising given the estimated low peak accretion rate ( ≈ .
05 of theEddington rate) and generally low expected burst rates for hydrogen-poor fuel. Based on the history of four outbursts to date, weestimate the long-term average accretion rate at roughly 5 × − M (cid:12) yr − for an assumed distance of 8 kpc. The expected masstransfer rate driven by gravitational radiation in the binary implies the source can be no closer than 4 kpc. Swift J1756.9 − Key words. pulsars: individual: Swift J1756.9 −
1. Introduction
Swift J1756.9 − Swift -BAT during its2007 outburst (Krimm et al. 2007a; Linares et al. 2008). Co-herent X-ray pulsations at a frequency of ∼
182 Hz confirmedthe compact object to be an accreting millisecond X-ray pulsar(AMXP) (Markwardt et al. 2007). In the following observations,carried out by
Swift and
RXTE , the orbital period of 54.7 minhas been measured and from its mass function the mass of thecompanion star – a highly evolved white dwarf – has been deter-mined in the range 0 . − . M (cid:12) (Krimm et al. 2007b). TheAMXPs are rapidly spinning, old, recycled neutron stars (NSs)hosted in low-mass X-ray binaries (LMXB). As a binary system Send o ff print requests to : Z. Li evolves through phases of accretion onto the NS, it gains angu-lar momentum from the accreted material, which is su ffi cient tospin-up the NS to a rotation period equilibrium in the millisec-ond range, i.e., recycling of old radio-pulsars to millisecond pe-riods (Alpar et al. 1982; Wijnands & van der Klis 1998; Falangaet al. 2005b; Papitto et al. 2013). On the other hand, between theoutbursts, long-term monitoring shows some AMXPs to exhibitspin-down in quiescence (see, e.g., Hartman et al. 2009; Patrunoet al. 2010; Papitto et al. 2010). For reviews of the propertiesof these objects, we refer to Wijnands (2006), Poutanen (2006),Patruno & Watts (2021), Campana & Di Salvo (2018), Papittoet al. (2020), and Di Salvo & Sanna (2020).The source, Swift J1756.9 − Article number, page 1 of 12 a r X i v : . [ a s t r o - ph . H E ] F e b & A proofs: manuscript no. ms_SwiftJ1756 | ˙ P orb | < . × − s s − from the total 11 years spanof the observations, consistent with the prediction of a conser-vative mass transfer in the binary system (Bult et al. 2018a).Swift J1756.9 − | ˙ ν | (cid:46) × − Hz s − measuredby Patruno et al. (2010), | ˙ ν | ∼ . × − Hz s − by Bult et al.(2018a) and a smaller value | ˙ ν | ∼ . × − Hz s − by Sannaet al. (2018c). Assuming that the rotational energy loss due tothe magnetic dipole emission dominated the spin evolution ofSwift J1756.9 − − × G (see,e.g., Patruno et al. 2010; Bult et al. 2018a; Sanna et al. 2018c,and references therein).Most NSs hosted in LMXB systems exhibit type I X-raybursts (Galloway et al. 2020). Type I bursts are thermonuclearexplosions on the surface of accreting NS triggered by unstablehydrogen or helium burning. They are typically characterizedby a fast rise time of ∼ − kT bb ≈ L Edd ≈ × erg s − , and the to-tal burst energy release is of the order ∼ erg (see Lewin et al.1993; Strohmayer & Bildsten 2006; Galloway et al. 2008, for areview). Several thousand bursts have been observed to date (see,e.g., Galloway et al. 2008, 2020). However, seven sources (in-cluding Swift J1756.9 − − − −
300 keV), two
NuSTAR (3 −
79 keV), one
XMM-Newton (1 −
10 keV), eight NICER (0 . −
12 keV), nine
Swift andfive
Insight -HXMT (5 −
250 keV) observations during the 2018outburst from Swift J1756.9 − NuSTAR , one
Swift and seven NICER observations during its 2019 outburst.All monitoring observations will shed light on the physical pro-cesses acting in Swift J1756.9 −
2. Observations and data reduction
We reduce the data from Swift J1756.9 − − NuSTAR , and
Swift observedSwift J1756.9 − Table 1.
The observations of Swift J1756.9 − a Exposure(d) (ks)2018 outburst
NuSTAR / FPMB 8.36 39.590402313004 FPMA / FPMB 14.13 61.0NICER 1050230101 XTI 3.64 7.51050230102 XTI 4.61 7.11050230103 XTI 7.89 2.41050230104 XTI 8.02 10.71050230105 XTI 9.33 4.11050230106 XTI 10.02 6.21050230107 XTI 11.06 5.01050230108 XTI 25.85 1.5
XMM-Newton / MOS / PN 8.09 66INTEGRAL 1936, 1937 ISGRI -1.23, 1.42 1291939 (ToO) ISGRI 7.68 851940 ISGRI 10.011942 ISGRI 14.91 190 b Insight -HXMT P011469200101 ME & HE 5.13 4.3P011469200102 ME & HE 5.33 1.1P011469200103 ME & HE 5.47 0.3P011469200104 ME & HE 5.60 1.2P011469200105 ME & HE 5.71 5.9
Swift
NuSTAR / FPMB 11.85 37.7NICER 2050230101 XTI 9.10 1.52050230102 XTI 9.56 3.62050230103 XTI 11.10 5.42050230104 XTI 11.50 11.72050230105 XTI 16.51 1.12050230106 XTI 19.02 1.72050230107 XTI 21.16 1.1
Swift
Notes. ( a ) The start time of the observations since MJD 58208 and58644.5 for the 2018 and 2019 outbursts, respectively. ( b ) The total ex-posure time of Rev. 1940, 1942 and 1944. the data reduction part for all instruments and provide in Ta-ble 1 a log of all observations during the 2018 and 2019 out-bursts. We adopted Solar System ephemeris DE405 and the X-ray position of Swift J1756.9 − NuSTAR (Sect. 2.3),
XMM-Newton (Sect. 2.4) and
Insight -HXMT (Sect. 2.5) obser-vations.
Our INTEGRAL (Winkler et al. 2003) data-set comprises all theobservations covering the 2018 outburst. It consists of 160 stablepointings (science windows, ScWs) with a source position o ff setfrom the center of the field of view (cid:46) ◦ .
0. The di ff erent satellite Article number, page 2 of 12. Li et al.: High-energy characteristics of Swift J1756.9 − Fig. 1.
INTEGRAL-ISGRI sky image in the 20–50 keV band (signifi-cance map, in Galactic coordinates ( l , b )), of the field of view around theAMXP Swift J1756.9 − ff ective exposure time of 248 ks (rev. 1937, 1939,and 1940 combined). The source was detected at a significance of ∼ σ . pointings in the direction of Swift J1756.9 − ∼ − ffl ine ScienceAnalysis (OSA ) version 10.2 distributed by the Integral ScienceData Center (Courvoisier et al. 2003). The algorithms used forthe spatial and spectral analysis are described in Goldwurm et al.(2003). We analyzed data from the IBIS-ISGRI coded mask tele-scope (Ubertini et al. 2003; Lebrun et al. 2003) at energies be-tween 22 and 300 keV and from the JEM-X monitor, module 1and 2 (Lund et al. 2003) between 5 and 20 keV. Because mostof the pointings were not aimed at Swift J1756.9 − < ◦ .
5. Therefore, we did not use the JEM-X data for thespectral analysis.We show in Fig. 1 part of the ISGRI field of view for 20–50 keV energy range (significance map) centered on the po-sition of Swift J1756.9 − ∼ σ in the 20–50 keVenergy range and still significant with ∼ . σ in the higher100–150 keV energy range. The best determined position is at α J2000 = h m s .
35 and δ J2000 = − ◦ (cid:48) (cid:48)(cid:48) .
8, with an asso-ciated uncertainty of 0 (cid:48) . − NuSTAR and
XMM-Newton observations (see Sect. 2.2, 2.3,2.4) and permitted the most accurate description of the source http: // / integral / analysis Time since 58206 (days) . . . . . . F l u x ( − e r g c m − s − ) NICERNuSTARSwift/XRTINTEGRALXMM-Newton/MOS20 5 10 15 20
Time since MJD 58644.5 (days) . . . . . . . . . F l u x ( − e r g c m − s − ) NICERNuSTARSwift/XRTSwift/BAT
Fig. 2.
The evolution of the bolometric fluxes (0.1–300 keV) ofSwift J1756.9 − F ∝ e − t / . and F ∝ e − t / , followed bya linear decay, respectively. averaged broad-band high-energy emission. The outburst profileis described in Sect. 3, and the averaged broad-band spectrumof the source, as measured almost simultaneously by all theseinstruments, is described in Sect. 4. We note, INTEGRAL didnot observe Swift J1756.9 − The Neutron star Interior Composition ExploreR (NICER),launched on June 3, 2017, is an International Space Station pay-load dedicated to (spectral) timing studies in the 0.2–12 keVband at an unprecedented time resolution of ∼
100 ns (Arzou-manian et al. 2014). During the 2018 outburst, NICER startedregular observations of Swift J1756.9 − − xselect . The spec- Article number, page 3 of 12 & A proofs: manuscript no. ms_SwiftJ1756 trum from Obs. ID 1050230104 was used together with thosefrom the other instruments in the 2018 outburst. The back-ground spectrum is adopted from the Obs. ID 1050230107, whenSwift J1756.9 − NuSTAR obser-vation. In order to obtain a simultaneous broad-band spectrumthe data between MJD 58656.3485 and 58656.9060 were ana-lyzed; in this case, the background spectrum is from the Obs.ID 2050230107. The redistribution matrix file and ancillary re-sponse file were taken from the o ffi cial webpage. For details on the timing analysis of NICER data we refer toSect. 5.
NuSTAR observed Swift J1756.9 − ∼ . ∼ . ∼ . − NuSTAR pipeline tool nupipeline for both FPMAand FPMB. The light curves and spectra were extracted from acircular region with a radius of 60 (cid:48)(cid:48) centered on the location ofSwift J1756.9 − nuproducts , andthe response files were produced simultaneously. To extract thebackground spectra, we chose a source-free circular backgroundregion located on the same chip with a radial aperture of 60 (cid:48)(cid:48) .In the timing analysis, we barycentered event data fromthe source region using HEASOFT multi-mission tool barycorrv2.1 with
NuSTAR fine clock-correction file µ s level (Bachetti et al. 2020). To obtainbackground corrected timing characteristics like fractional am-plitudes we used the above mentioned background region.For the observation during the 2019 outburst, similar pro-cedures were carried out as for the 2018 outburst, except thatthe spectra were cut in the same interval as the NICER Obs. ID2050230104, see also Sect. 2.2. On April 8, 2018
XMM-Newton started an observation ofSwift J1756.9 − XMM-Newton was operated in Timing Mode (TM) allowing timingstudies at ∼ µ s time resolution. The other (imaging) EPICinstrument equipped with two cameras, MOS-1 and MOS-2(Turner et al. 2001), were set in Full window and TM, respec-tively.We run the XMM-SAS pipeline analysis scripts (SAS-version18.0) for all EPIC and RGS instruments on board
XMM-Newton .We verified that the background flares were not detected, there-fore further cleaning was not performed. We extracted the sourcespectrum from MOS-2 in TM from the
RAWX interval [285, 325],while the background spectrum was extracted from MOS-2 inthe image mode from a circle region with a radius of 150 (cid:48)(cid:48) . The https: // heasarc.gsfc.nasa.gov / docs / nicer / proposals / nicer_tools.html response matrix file and ancillary response file were generatedusing rmfgen and arfgen , respectively.For the timing analysis we used data from the XMM-Newton
EPIC pn. These were subsequently barycentered us-ing the
SAS barycen 1.21 script. We further selected on theone-dimensional spatial parameter
RAWX by defining the source-region as
RAWX interval [31,44] and the background region asthe combination of
RAWX [11,19] and [55,63], chosen far fromthe source region. The latter has been used in the estimation ofbackground corrected fractional amplitudes in the pulse profileanalysis.The (non-imaging) Reflection Grating Spectrometers (RGS)(den Herder et al. 2001) on board
XMM-Newton operated in de-fault mode (HighEventRate with Single Event Selection; HER + SES), collecting spectral information in the 0.35–2.5 keV band.Two RGS spectra were extracted using rgsproc and the corre-sponding response files were created using rgsrmfgen . In orderto increase the signal-to-noise ratio, we combined the spectraof two RGS data in first order.
XMM-Newton did not observeSwift J1756.9 − Insight -HXMT
The first Chinese X-ray telescope, Hard X-ray Modulation Tele-scope (HXMT), was launched on June 15, 2017 and later dubbed
Insight -HXMT (Zhang et al. 2020). Three slat-collimated instru-ments, the Low Energy X-ray telescope (LE, 1–15 keV, 384 cm ;Chen et al. 2020), the Medium Energy X-ray telescope (ME,5–30 keV, 952 cm ; Cao et al. 2020) and the High Energy X-ray telescope (HE, 20–250 keV, 5100 cm ; Liu et al. 2020)on board Insight -HXMT provide the capability for the broad-band X-ray timing and spectroscopy.
Insight -HXMT observedSwift J1756.9 − ∼ µ s for HE, ∼ µ s for ME). We analysed thedata using the Insight -HXMT Data Analysis Software package(HXMTDAS) version 2.01. The ME and HE data were calibratedby using the scripts mepical and hepical , respectively. Thegood time intervals were individually selected from the scripts megtigen and hegtigen with the loose criteria, i.e., ELV > mescreen and hescreen , and werebarycentered by the tool hxbary . Insight -HXMT did not observeSwift J1756.9 − Swift
Totally, nine and one observations are available in the 2018and 2019 outbursts from
Swift / XRT, respectively. The
Swift / XRTlight curves were only reduced to construct the outburst profilesduring the 2018 and 2019 outbursts. We reduced the
Swift / XRTdata in the photon counting mode. The pipeline xrtpipeline was operated for each observation and the light curve was ex-tracted from a circle region centered on the source position witha radius of 25 (cid:48)(cid:48) , and corrected by the
Swift tool xrtlccorr .
3. The outburst profiles
The light curves of Swift J1756.9 − Article number, page 4 of 12. Li et al.: High-energy characteristics of Swift J1756.9 − − Time (days) − . . . . . C o un t s / s / c m ( - k e V ) − Time (days) − . . . . . . . C o un t s / s / c m ( - k e V ) Fig. 3.
Swift -BAT daily averaged (15–50 keV) profiles of the 2007(blue dots) and 2018 (magenta squares) outbursts (top panel), the 2009(red dots) and 2019 (greed squares) outbursts (bottom panel) fromSwift J1756.9 − burst was observed at the last stage during its decay phase, theflux in one day bins was estimated using the Swift -BAT data.The count-rates measured from all instruments were convertedto bolometric flux (0.1–300 keV) using the spectral analysis re-sults obtained in Sect. 4 for the respective outbursts.The profile of the outburst observed fromSwift J1756.9 − ∼ ∼ ∼ ∼ . × − erg cm − s − in the 0.1–300 keV energy range(see Fig. 2), this value is similar to all other observed outbursts,considering the same energy band (Krimm et al. 2007a; Linareset al. 2008; Patruno et al. 2009a; Sanna et al. 2018c).Such outbursts are typically described by the disk instabilitymodel (see King & Ritter 1998, for more details), which pre-dicts that both linear and exponentially decaying outbursts canbe produced. Typically for such outbursts the flux decays fromthe maximum exponentially until it reaches a break (“knee"),in our case around MJD 58217 (2018 outburst) or MJD 58656(2019 outburst), and then linearly drops to the quiescent level. Table 2.
Best parameters determined from the fits to the broad-bandemission spectra of Swift J1756.9 − phabs absorbedcomptonization model compps . In the 2018 outburst, the spectra wereobtained from the XMM-Newton , NICER,
NuSTAR and INTEGRAL.The NICER and
NuSTAR spectra were utilized for the 2019 outburst.Parameter Unit 2018 outburst 2019 outburst N H (10 cm − ) 4 . ± .
05 4 . ± . kT bb , seed (keV) 0 . ± .
01 0 . ± . kT e (keV) 41 . ± . . ± . τ T . ± .
02 1 . ± . K bb (km ) 150 ± ± χ / d . o . f . / / F bol a (10 − erg cm − s − ) 8 . ± .
06 4 . ± . Notes.
Uncertainties are given at 1 σ confidence level. ( a ) Unabsorbedflux in the 0.1–300 keV energy range.
Following Powell et al. (2007), the outer disk radius can be esti-mated by fitting the decay profile (see Fig. 2) with the expression L X = ( L t − L e ) exp[ − ( t − t t ) /τ e ] + L e , (1)where L e (the limit luminosity of the exponential decay), t t (thebreak time), L t (the luminosity at the break time t t ), and τ e (expo-nential decay time) are all free parameters. The outer disk radiusis R disk ( τ e ) = ( τ e ν KR ) / ∼ . × cm, where the value ofthe viscosity near the outer disk edge ν KR = cm s − isadopted (see King & Ritter 1998; Powell et al. 2007, for moredetails). In the 2019 outburst, we obtain the outer disk radius of R disk ∼ . × cm. For the binary inclination of 60 ◦ and theNS mass of 1 . M (cid:12) , the companion mass M c is 0 . M (cid:12) . Weadopted the relation b a = . − . q + . q − . q − . q , (2)where b is the distance between the NS and the Lagrange point L of the binary system and a is the binary separation, which hasthe accuracy of 0.5% for q between 0.0025 and 0.11 (Iaria et al.2021). The circularization radius R circ can be estimated from (seee.g., Frank et al. 2002) R circ a = (1 + q )( b / a ) . (3)We found that the outer disk radii in the 2018 and 2019 outburstssatisfy the condition R circ < R disk < b , where R circ ≈ . × cm and b ≈ . × cm.In Fig. 3, an inspection of all the Swift -BAT outburst datashows that the period of activity in 2018–19 broadly follows thepattern of the previous outbursts, with two more closely-spacedoutbursts separated by a longer interval. The 2009 outburst fol-lowed the discovery outburst in 2007 by 2.1 yr; the 2019 outburstcame 1.2 yr after 2018. However, the 2018 outburst came after amuch longer quiescent interval, of 8.7 yr.Such pairs of outbursts have only previously been observedfrom the low-mass X-ray binaries IGR J00291 + +
480 (Hartman et al. 2011), although in those systems theinter-outburst separation was 30 d. Those authors attributed thesecondary outburst to leftover material in the accretion disk thatwas not deposited on the NS during the first outburst. The atyp-ical mass distribution left in the disk when the accretion stallsduring the first outburst, leads to the unusual slow-rise shape of
Article number, page 5 of 12 & A proofs: manuscript no. ms_SwiftJ1756 − × − × − E F ( E ) e r g c m − s − − − χ Energy (keV) − × − × − E F ( E ) e r g c m − s − − − χ Energy (keV)
Fig. 4.
Unfolded and unabsorbed broad-band spectra of Swift J1756.9 − Left panel:
Spectrum for the 2018 outburst in the 1–250 keVenergy range. The data points are obtained from the combined of two
XMM-Newton
RGS instruments (magenta datapoints, ∼ XMM-Newton
EPIC-MOS2 (blue points, 2–10 keV), NICER (black points, 1.5–10 keV)
NuSTAR
FPMA / FPMB (red and green points, 3.5–80 keV),and INTEGRAL-ISGRI (cyan points, 30–250 keV).
Right panel:
Spectrum of the 2019 outburst in the 1.5–80 keV energy range. The data pointsare obtained from the NICER (black points, ∼ NuSTAR
FPMA / FPMB (red and green points, 3–80 keV). In both cases the fits areobtained with the compps model, represented with a solid line. The residuals from the best fit are shown at the bottom. the second outburst; this pattern is very similar to what is ob-served in Swift J1756.9 − − . × − erg cm − and 1 . × − erg cm − , respectively. Thefluence of each outburst arises from an accreted mass of ∆ M = π d (cid:82) F X dtQ grav ≈ π d R NS (cid:82) F X dtGM NS (4)where Q grav ≈ GM NS / R NS is the gravitational potential energyliberated during accretion. For each of the 2018 and 2019 out-bursts, the accreted mass is ∆ M ≈ × − M (cid:12) d r m − . , where d is the distance in units of 8 kpc, r the NS radius in unitsof 10 km, and m . the NS mass in units of 1 . M (cid:12) . Assuminga constant accretion rate ˙ M over the interval between the 2009and 2019 outbursts, we can solve for this quantity as well as theamount of fuel leftover following the 2018 outburst. We find asteady accretion rate of 5 × − M (cid:12) yr − d r m − . , implyingabout 45% of the material in the disk remaining after the end ofthe 2018 outburst.We can estimate a lower limit for the distance to the sourceby equating the implied long-term accretion rate above, withthe expected accretion rate driven by gravitational-wave radia-tion from the binary orbit (e.g. Bildsten & Chakrabarty 2001).Adopting the minimum companion mass M c = . × − M (cid:12) for a 1 . M (cid:12) NS (Krimm et al. 2007b), we find that d (cid:38) . m / . r − , so that d (cid:38)
4. Broad-band spectral analysis of the 2018 and2019 outbursts
We studied separately the broad-band X-ray spectra of the 2018and 2019 outbursts. For the 2018 outburst, we fit the quasi- simultaneous spectra, including the INTEGRAL-ISGRI (20-250 keV) ToO data between MJD 58215.8–58216.8, the
NuS-TAR
FPMA / FPMB (3.5–79 keV) data starting on MJD 58216.4(Obs. ID 90402313002), NICER (1.5–10 keV) data starting onMJD 58216.0 (Obs. ID 1050230104),
XMM-Newton
MOS (2–10 keV), and RGS (1–2.4 keV) data starting on MJD 58216.1.We note that the MOS spectrum showed a strong excess below 2keV, which may be a ff ected by the straylight. For the 2019 out-burst, we consider the simultaneous observations from NICER(1.5–10 keV, Obs. ID 2050230104) and NuSTAR
FPMA / FPMB(3–79 keV, Obs. ID 00033646004), respectively. All spectra aregrouped to make sure that each channel has more than 25 pho-tons. For each instrument, a multiplication factor is included inthe fit to account for the uncertainty in the cross-calibration ofthe instruments. For all fits, the factor is fixed at 1 for the
NuS-TAR
FPMA instrument. All uncertainties in the spectral param-eters are given at a 1 σ confidence level for a single parameter.The spectral analysis were carried out using Xspec version 12.10(Arnaud 1996).We fit all spectra by using the thermal Comptonizationmodel, compps , in the slab geometry (Poutanen & Svensson1996), with the interstellar absorption described by model phabs . This model has been used previously to fit the broad-band spectra of AMXPs (see e.g., De Falco et al. 2017b,a; Liet al. 2018; Kuiper et al. 2020, and references therein). Themain parameters are the Thomson optical depth across the slab, τ T , the electron temperature, kT e , the temperature of the softseed photons (assumed to be injected from the bottom of theslab), kT bb , seed , the normalization factor for the seed blackbodyphotons K bb = ( R km / d ) (with d being distance in unitsof 10 kpc), and the inclination angle θ (fixed at 60 ◦ ) betweenthe slab normal and the line of sight to the observer. The in-terstellar absorption is described by the hydrogen column den-sity, N H . The best-fit parameters for all models are reported inTable 2. For the distance of 8 kpc, the size of the blackbodyemitting region R bb = . √ K bb ≈
10 km. This is very similarto IGR J17498 − −
305 (Gierli´nski & Poutanen 2005). Such alarge size is hardly consistent with the hotspot at the NS surfaceand might indicate that the distance to the source is smaller. The
Article number, page 6 of 12. Li et al.: High-energy characteristics of Swift J1756.9 − Table 3.
Positional, rotational and orbital parameters used from otherworks and derived in this work for Swift J1756.9 − α h m s . δ − ◦ (cid:48) (cid:48)(cid:48) . P orb s 3282 . a x sin i lt-s 0 . e . ν Hz 182 .
065 803 84(3)Epoch, t MJD; TDB 58216 . − T asc , MJD; TDB 58211 .
017 52(6)Outburst - 2019 ν Hz 182 .
065 803 4(2)Epoch, t MJD; TDB 58654 . − T asc , MJD; TDB 58655 .
996 57(12) bolometric fluxes are calculated by the convolution model cflux in the 0.1–300 keV energy range. In Fig. 4 we show the best-fitspectra.We find that all multiplication cross-calibration factors arearound unity, which means the flux calibration of these instru-ments is well established and the source did not vary much be-tween the quasi-simultaneous observations. The 2018 and 2019outbursts can be characterized by similar hard spectra, see Ta-ble 2. This is indicating, that even thought the 2019 outburst wasobserved at a later outburst stage, i.e. at a flux level lower by afactor 1.9 , the decay of the outburst is characterized by a nearlyconstant spectral shape described by similar electron tempera-ture kT e , soft seed photons temperature kT bb , seed , and the op-tical depth, τ T . The spectral parameters are similar to those ofmany other AMXPs (see e.g., Falanga et al. 2011, and refer-ences therein). The spectra for the 2018 and 2019 outbursts innarrower energy ranges are well described by a power-law with aphoton index in the range ∼ N H ∼ (4 . − . × cm − .This also confirms, that all four observed outbursts are very sim-ilar (see also Sect. 3). We note that our estimate of the blackbodynormalization is at least factor of 30 larger than the normaliza-tion quoted by Sanna et al. (2018c), who used a phenomeno-logical blackbody plus cuto ff power-law model. The di ff erencecomes from the facts that in the compps model, only a smallfraction, exp( − τ T / cos θ ) ∼ .
06, of the seed blackbody photonspass through the Comptonizing slab una ff ected, the rest is scat-tered and produce the hard tail extending to 100 keV. Also in ourmodel a large fraction of the flux below 3 keV comes from theblackbody, while in a model by Sanna et al. (2018c), the powerlaw contributes most of the flux.
5. Timing analysis
Irrespective of the instrument, in timing analyses we have toconvert the Terrestial Time (TT) arrival times of the (selected)events to arrival times at the solar system barycenter (in TDBtime scale). We used in this process through-out in this work:1) the JPL DE405 solar system ephemeris, 2) the instantaneousspacecraft position with respect to Earth center, and 3) the X-ray celestial position of Swift J1756.9 − α J2000 = h m s . δ J2000 = − ◦ (cid:48) (cid:48)(cid:48) . Swift -XRT telescope(Krimm et al. 2007b).
For our timing analysis, we selected ‘cleaned’ barycenteredNICER XTI events, collected during the 2018 and 2019 out-bursts, from the standard pipeline analysis with measured en-ergies between 0.5 and 10 keV. Events with energies between12–15 keV, however, were used to flag periods with high-background levels (e.g. South Atlantic Anomaly ingress oregress, etc.) as bad, and these intervals have been ignored in fur-ther analyses. Moreover, events from noisy or malfunctioningdetectors were ignored. The screened events were subsequentlybarycentered using a (multi-instrument serving) idl procedure.For each outburst separately we determined the pulse fre-quency ν and time of ascending node T asc in a 2d-optimizationscheme based on a SIMPLEX algorithm (see, e.g., De Falco et al.2017b; Kuiper et al. 2020, for more details) finding the globalmaximum of the Z ( φ )-test statistics (Buccheri et al. 1983). Inthis approach we kept the orbital period, P orb , projected semimajor axis, a x sin i , fixed at the optimum values given by Patrunoet al. (2010) (see their Table 4). We verified that using updatedorbital ephemeris information (Bult et al. 2018a) had no impacton the T asc values derived here. The best fit values for ν and T asc along with the validity interval and epoch t for both outburstsseparately are listed in Table 3, and are used later in this work inestimating the orbital period derivative combining informationfrom all registered outbursts (see Sect. 6).Equipped with accurate timing models for both outbursts(see Table 3) we phase folded the barycentered event times fromdi ff erent instruments for di ff erent energy bands both for the 2018and 2019 outbursts. The results are shown in Figs. 5 and 6 for the2018 and 2019 outbursts, respectively.During the 2018 (also for the 2019) outburst no pulsed emis-sion has been detected below 1 keV using NICER and XMM-Newton data.
NuSTAR has detected pulsed emission up to ∼
60 keV during the 2018 outburst. Folding INTEGRAL-ISGRIbarycentered data of the 2018 outburst for the 20-60 keV bandhas not resulted in a detection of the pulsed emission in line withthe expectations given the moderate total outburst flux, low ex-posure and low pulsed fraction of < ∼
8% (see Sect. 5.2). However,with the
Insight -HXMT HE instrument, significant pulsed emis-sion has been detected up to ∼
100 keV (see lower right panelof Fig. 5) in spite of a relatively low exposure, providing a greatperspective for future observations with
Insight -HXMT of theAMXP outbursts.
We produced pulse-phase distributions in narrow energy bandsfor NICER,
XMM-Newton and
NuSTAR , covering the ∼ N ( φ ) with a trun-cated Fourier series given by F ( φ ) = A + n (cid:88) k = A k cos[ k ( φ − φ k )] . (5)For each harmonic, the maxima occur at φ max = φ k mod (2 π/ k )(in radians). Article number, page 7 of 12 & A proofs: manuscript no. ms_SwiftJ1756 . . . NICER . . . . . . XMM-Newton
NuSTAR . . . . . HXMT . . . . Pulse Phase R e l a t i v e I n t e n s i t y Fig. 5.
Pulse profiles of Swift J1756.9 − XMM-Newton , NuSTAR , and
Insight -HXMT during the 2018 outburst. . . . NICER . . . . . . NuSTAR
Pulse Phase R e l a ti v e I n t e n s it y Fig. 6.
Pulse profiles of Swift J1756.9 − NuSTAR during the 2019 outburst.
The results of these fits are shown in Fig. 7. The left panelshows the fractional amplitude, A k / A , and the right panel thephase angle, φ k , converted from radians to pulse phase, for boththe fundamental ( k =
1, in black) and the first overtone ( k =
2, in red). The di ff erent symbols indicated di ff erent instruments(NICER, 1–10 keV, squares; XMM-Newton
EPIC-pn 1–12 keV,circles, and
NuSTAR , 3–60 keV, triangles). The pulsed fractionof the fundamental component increases from ∼
4% till ∼ . ∼ . ∼
1% around 12 keV. Theseresults are consistent with those reported by Sanna et al. (2018c)(e.g. their Fig. 5). Such a behavior was also observed in othersources (see, e.g., Patruno et al. 2009b) and is likely related toan increasing contribution of an unpulsed emission from the ac-cretion disk.The phase angle plot (Fig. 7 right panel) shows that the lo-cation of both harmonics is stable up to at least 10 keV (seealso bottom panel of Fig. 2 of Bult et al. 2018a, for equivalentresults), beyond a possible small drift to smaller values occurs:from 0.7 to 0.65 for the fundamental and from 0.12 to 0.07 forthe first overtone.
6. Orbital period
From the outburst in 2019, we have an additional well deter-mined T asc value. It allows us to perform a coherent analysis ofthe orbital period evolution across a longer baseline comparedwith Bult et al. (2018a) and Sanna et al. (2018c). Following theprocedure introduced in Hartman et al. (2008), we calculate the Article number, page 8 of 12. Li et al.: High-energy characteristics of Swift J1756.9 − A k / A E [keV]
E [keV] P h a s e A n g l e Fig. 7.
Left panel:
Fractional amplitude of two harmonics (1 – fundamental, 2 – first overtone) as a function of energy using background correcteddata from NICER (squares),
XMM-Newton
EPIC-pn (circles) and
NuSTAR (triangles). The pulsed fraction of the fundamental component increasesfrom ∼
4% till ∼ .
5% from 1 to 5 keV, from where it more or less saturates at a level of ∼ . Right panel:
Phase angles φ k (divided by 2 π ) forthe two Fourier components as function of energy. They remain remarkably stable across the 1–60 keV band, with possibly a small drift for φ toslightly lower values at energies above ∼
10 keV. residual time of passage through the ascending node, ∆ T asc = T asc , i − ( T ref + NP orb ) , (6)where T asc , i is the time of ascending node determined from the i -th outburst, T ref is the reference time, N is the integer number oforbital cycles between the i -th outburst and T ref , and P orb is theorbital period. We use the orbital period reported in Table 3 andthe reference time T ref as the time of ascending node in the 2007outburst (Krimm et al. 2007b), to obtain the values of ∆ T asc forfour outbursts. The errors of ∆ T asc are from the uncertainties of T asc . In Fig. 8, we fit the ∆ T asc evolution with a parabolic func-tion, and obtain a best fit value of the orbital period derivative ˙ P of (7 . ± . × − s s − , which is consistent with the results re-ported in Sanna et al. (2018c) and Bult et al. (2018a). Hence, weconclude that the binary is well described by a constant periodover a time span of nearly twelve years.
7. The non-detection of type-I X-ray bursts
We searched for type-I X-ray bursts in all availableSwift J1756.9 − − m , which in turn determinehow much fuel must be accreted prior to ignition, and the igni-tion depth. The known AMXPs can be divided into two distinctgroups based on their orbital periods; either around 40 min, orin the range 2–11 h (see e.g., Campana & Di Salvo 2018). Stel-lar evolution models predict that AMXPs with an orbital period Δ T a s c ( s ) Fig. 8.
Orbital period evolution of Swift J1756.9 − longer than one hour should host a highly evolved, hydrogen-rich brown dwarf companion star, and the heating from steadyburning of the accreted H fuel prior to ignition will lead to burstrecurrence times of hours to days (see e.g., Galloway & Cum-ming 2006; Heger et al. 2007; Falanga et al. 2011; Ferrignoet al. 2011; De Falco et al. 2017b,a; Li et al. 2018; Kuiper et al.2020). However, “ultracompact” X-ray binaries (UCXBs) withorbital periods <
80 min are expected to have low-temperatureC, O or He white dwarf companions, i.e., hydrogen-poor, highlyevolved dwarfs (Deloye & Bildsten 2003). The mass-radius re-lation of AMXPs are shown in Fig. 9, by the assumption ofa Roche lobe-filling companion (Paczy´nski 1971). The corre-sponding M c versus R c relations for di ff erent stellar evolution Article number, page 9 of 12 & A proofs: manuscript no. ms_SwiftJ1756 − − M c /M ⊙ R c / R ⊙ Fig. 9.
The assumption of a Roche lobe-filling companion implies a mass-radius relation R c = .
082 ( M c / . M (cid:12) ) / ( P orb /
40 min) / R (cid:12) , shown inlogarithmic scale for di ff erent AMXPs with orbital periods around 40 min. From bottom up, the sources are IGR J17062 − −
294 (Campana et al. 2003), XTE J1751 −
305 (Papitto et al. 2010), XTE J0929 −
314 (Galloway et al. 2002), MAXI J0911 − − − − − − − + ◦ . We notethat from all AMXPs with the orbital period shorter than 1 hr, except MAXI J0911 −
655 and IGR J17494 − K, lower lines) or high (3 × K, upper lines) central temperatures. models are also provided in Fig. 9. The expected burst recur-rence time for such systems, even if reaching the same accretionrates during outbursts as the H-rich systems, are substantiallylower, significantly reducing the chance of detecting bursts (e.g.Cumming 2003).We can roughly estimate the likely burst recurrence timebased on the persistent flux of the source during the outburstThe local mass accretion rate per unit area onto the NS is˙ m = π d F bol (1 + z )(4 π R ( GM NS / R NS )) − , i.e., ˙ m ≈ . × d g cm − s − and ˙ m ≈ . × d g cm − s − for the 2018and 2019 outbursts, respectively. If the accreted matter is purehelium, the expected recurrence time for type-I X-ray bursts is t rec ≈ y / ˙ m ≈
116 d ( y / g cm − )( ˙ m / g cm − s − ) − , where y is the ignition depth of a helium burst (see e.g., in’t Zand et al.2007). For Swift J1756.9 − ffi cient material would accrete to produce even asingle burst.While no type-I burst events have been detected dur-ing outbursts of transient ultracompact AMXPs, includingSwift J1756.9 − −
655 (Nakajima et al. 2020; Bultet al. 2020), and two intermediate duration X-ray bursts in IGRJ17062 − − erg s − corresponding to ac-cretion rates that are likely far too low to produce thermonuclearbursts.
8. Summary
We have analyzed all public high-energy data and re-ported the outburst profiles, spectral and timing properties ofSwift J1756.9 − XMM-Newton , Article number, page 10 of 12. Li et al.: High-energy characteristics of Swift J1756.9 − NuSTAR , NICER, and
Insight -HXMT, during its 2018 and 2019outbursts. We found these two outbursts showed quite similarbehavior in several aspects. The outburst profiles showed a sim-ilar shape that can be explained by the disk instability models.The broad-band spectra in the energy range 1–250 keV for thebrighter 2018 outburst and in the range 1.5–80 keV for the fainter2019 outbursts, were well fitted by a thermal Comptonizationmodel compps with a similar set of parameters: the electron tem-perature kT e = τ ∼ . kT bb , seed ∼ − XMM-Newton data, in 3–60 keV using
NuSTAR during bothoutbursts, and in the 5–100 keV range using
Insight -HXMT dur-ing the 2018 outburst. We detected an increase of the pulse frac-tion from 4% to 7.5% from 1 to 5 keV saturating at higher en-ergies. We found no evidence for a change in the spin frequencyfrom our data set. Comparing the observed times of ascendingnode passage with the predicted values, we concluded that thebinary system had a constant orbital period since the first out-burst in 2007.Swift J1756.9 − + ff the accretion before the diskwas exhausted. There are a number of di ff erences between theoutburst pairs in the two systems; in Swift J1756.9 − + − ff erentin these two systems. Furthermore, IGR J00291 + − + − Acknowledgements.
We thank the anonymous referee for valuable comments.ZL thanks the International Space Science Institute in Bern for the hospi-tality. This work is supported by the National Key R&D Program of China(2016YFA0400800). ZL was supported by National Natural Science Founda-tion of China (U1938107, 11703021, U1838111, 11873041), and Scientific Re-search Fund of Hunan Provincial Education Department (18B059). JP and SSTwere supported by the grant 14.W03.31.0021 of the Ministry of Science andHigher Education of the Russian Federation and the Academy of Finland grants317552, 322779, 324550, 331951, and 333112. SZ and SNZ were supported byNational Natural Science Foundation of China (Nos. U1838201 and U1838202).This research has made use of data obtained from the High Energy AstrophysicsScience Archive Research Center (HEASARC), provided by NASA’s GoddardSpace Flight Center, and also from the HXMT mission, a project funded by theChina National Space Administration (CNSA) and the Chinese Academy of Sci-ences (CAS).
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Article number, page 11 of 12 & A proofs: manuscript no. ms_SwiftJ1756