Evidence for 3XMM J185246.6003317 as a massive magnetar with a low magnetic field

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Evidence for 3XMM J185246.6+003317 as a massive magnetar with a low magnetic ﬁeld

Rafael C. R. de Lima,a, Jonas P. Pereira,b,c, Jaziel G. Coelho,c,d, Rafael C. Nunes,d,e, Paulo E. Stecchini,d,f, Manuel Castro,g, Pierre

Gomes,a, Rodrigo R. da Silva,d, Claudia V. Rodrigues,d, Jos´

e C. N. de Araujo,d, Michał Bejger,b,h, Paweł Haensel,b, J. Leszek

Zdunikb

aUniversidade do Estado de Santa Catarina, Joinville, 89219-710, SC, Brazil

bNicolaus Copernicus Astronomical Center, Polish Academy of Sciences, Warsaw, 00-716, Poland

cN´ucleo de Astrof´ısica e Cosmologia (Cosmo-Ufes) &Departamento de F´ısica, Universidade Federal do Esp´ırito Santo, Vit´oria, 29075-910, ES, Brazil

dDivis˜ao de Astrof´ısica, Instituto Nacional de Pesquisas Espaciais, S ˜ao Jos´e dos Campos, 12227-010, SP, Brazil

eInstituto de F´ısica, Universidade Federal do Rio Grande do Sul, Porto Alegre, 91501-970, RS, Brazil

fInstituto de Astronomia, Geof´ısica e Ciˆencias Atmosf´ericas, Universidade de S˜ao Paulo, S˜ao Paulo 05508–900, SP, Brazil

gRECOD.ai, Institute of Computing, University of Campinas, Campinas, 13083-852, SP, Brazil

hINFN Sezione di Ferrara, Ferrara, 44122, Italy

Abstract

3XMM J185246.6+003317 is a transient magnetar located in the vicinity of the supernova remnant Kes 79. So far, observations

have only set upper limits to its surface magnetic ﬁeld and spindown, and there is no estimate for its mass and radius. Using

ray-tracing modelling and Bayesian inference for the analysis of several light curves spanning a period of around three weeks, we

have found that it may be one of the most massive neutron stars to date. In addition, our analysis suggests a multipolar magnetic

ﬁeld structure with a subcritical ﬁeld strength and a carbon atmosphere composition. Due to the time-resolution limitation of the

available light curves, we estimate the surface magnetic ﬁeld and the mass to be log10(B/G) =11.89+0.19

−0.93 and M=2.09+0.16

−0.09 M⊙

at 1σconﬁdence level, while the radius is estimated to be R=12.02+1.44

−1.42 km at 2σconﬁdence level. They were veriﬁed by

simulations, i.e., data injections with known model parameters, and their subsequent recovery. The best-ﬁtting model has three

small hot spots, two of them in the southern hemisphere. These are, however, just ﬁrst estimates and conclusions, based on a

simple ray-tracing model with anisotropic emission; we also estimate the impact of modelling on the parameter uncertainties and

the relevant phenomena on which to focus in more precise analyses. We interpret the above best-ﬁtting results as due to accretion

of supernova layers/interstellar medium onto 3XMM J185246.6+003317 leading to burying and a subsequent re-emergence of the

magnetic ﬁeld, and a carbon atmosphere being formed possibly due to hydrogen/helium diﬀusive nuclear burning. Finally, we

brieﬂy discuss some consequences of our ﬁndings for superdense matter constraints.

1. Introduction

The X-ray pulsar 3XMM J185246.6+003317 (hereafter

3XMM J1852+0033) was discovered in the ﬁeld-of-view of

an XMM-Newton observation of the supernova remnant Kes 79,

which hosts a central compact object (CCO) (Seward et al.,

2003). These observations were independently analysed by

Zhou et al. (2014) and Rea et al. (2014), who reported a bright

point-like source, located 7.4′away from the CCO just outside

the southern boundary of Kes 79, having a very prominent pe-

riodic modulation of P≈11.6 s. The source is increasing its

period at a rate ˙

P<1.4×10−13 s/s, and its X-ray luminosity

is higher than its spin-down luminosity, ruling out a rotation-

powered nature (see, e.g., Coelho et al., 2017). This implies

a surface dipolar magnetic ﬁeld strength B<4.1×1013 G,

and a characteristic age τage >1.3 Myr. The foreground ab-

sorption (NH) toward 3XMM J1852+0033 is similar to that of

Kes 79, suggesting a similar distance of ∼7.1 kpc (see Sun et al.,

2004; Zhou et al., 2014, 2016, for details). 3XMM J1852+0033

has been classiﬁed within the Soft Gamma Repeaters (SGRs)

and the Anomalous X-ray Pulsars (AXPs) class, usually called

magnetars, which are neutron stars (NSs) characterized by a

quiescent soft X-ray (2 −10 keV) luminosity of the order of

1030 −1035 erg/s, spin period in the range 2 −12 s, and a spin-

down rate from 10−15 to 10−10 s/s (see, e.g., Olausen and Kaspi,

2014; Turolla et al., 2015; Kaspi and Beloborodov, 2017). In

particular, the low dipolar magnetic ﬁeld inferred from the spin-

down suggests that this source is a transient magnetar with low-

B (Rea et al., 2014).

Since magnetars are usually isolated NSs, inferring their

macroscopic properties is a complicated task; it is usually as-

sumed that they have a canonical mass of 1.4M⊙. However,

the existence of high-mass NSs is also well-known (in bina-

ries): PSR J1614–2230 has a mass M=1.97 ±0.04 M⊙(De-

morest et al., 2010); the mass of PSR J0348+0432 is 2.01 ±

0.04 M⊙(Antoniadis et al., 2013), and PSR J0740+6620 has an

estimated mass of 2.08 ±0.07 M⊙(Fonseca et al., 2021). Ob-

servationally, the probability distribution for known NS masses

presents a two component Gaussian mixture model, with mean

values around 1.34 M⊙and 1.8M⊙, and standard deviations of

∼0.1M⊙(see Alsing et al., 2018, for details).

This paper reports on our analysis of the XMM-Newton X-ray

data of 3XMM J1852+0033 using ray-tracing modelling. We

assume that its X-ray pulse proﬁle is due to the emission of hot

Preprint submitted to High Energy Astrophysics April 3, 2024

arXiv:2210.06648v3 [astro-ph.HE] 2 Apr 2024

spots on its surface. Our main motivations are: (i) magnetars

are usually slowly rotating NSs in which ray-tracing models

are simple and relativistic phenomena are important; (ii) as far

as we are aware of, there are no inferences of masses and radii

of magnetars by means of ray-tracing techniques.

Ray-tracing modeling, as explored in recent studies, is piv-

otal for simulating X-ray light curves and understanding NS

physics. This technique accounts for general relativistic eﬀects,

crucial for depicting the propagation of light near these com-

pact objects. By incorporating detailed models of hot spots on

the NS surface, ray-tracing allows for the accurate reproduction

of observed pulse proﬁles. These simulations are instrumen-

tal in constraining NS physical parameters, such as mass and

radius, by matching theoretical predictions with observational

data. Studies like those of (Beloborodov, 2002), (Turolla and

Nobili, 2013), and (de Lima et al., 2020), (Riley et al., 2019),

highlight the method’s utility in revealing the complex interplay

between NS magnetic ﬁelds, surface temperature distributions,

and geometric factors. Therefore, ray-tracing allows us to learn

more about the physics taking place around magnetars (and any

other class of NSs) and independently complement what other

phenomena/models already tell us about them.

In Sect. 2 we describe aspects of the data selection and its re-

duction. Section 3 is devoted to the description of the model and

the parameter estimation. The best-ﬁtting results for the pulse

proﬁle of 3XMM J1852+0033 are presented and discussed in

Sect. 4. Finally, Sec. 5 summarizes our main ﬁndings. Ap-

pendix A contains details about the pulse proﬁle model. Fur-

ther details about the atmosphere models for NSs are given in

Appendix B.

2. Data selection, reduction, and preparation

2.1. The Observations

The ﬁeld around 3XMM J1852+0033 was monitored by

XMM-Newton on several occasions from 2004 to 2009. The

source entered a bright state at some time before 2009; it is

unclear whether it went into a quiescent stage in 2009 (see

Zhou et al., 2014, and references therein). We chose to re-

trieve ﬁve observations during the bright state, namely ObsIDs

0550670201 (2008 Sep. 19), 0550670301 (2008 Sep. 21),

0550670401 (2008 Sep. 23), 0550670501 (2008 Sep. 29) and

0550670601 (2008 Oct. 10), which we refer to as epochs A,

B, C, D and E, respectively. The above choice is mainly due

to data quality and due to reported characteristic timescales for

signiﬁcant hot spot motions. With relation to data quality, we

have that for epochs away from the outburst the net source count

rate is approximately one order of magnitude lower (than dur-

ing it). Also, no glitches/anti-glitches have been reported in

3XMM J1852+0033. Regarding hot spot motions, we made

use of knowledge stemming from observations of other mag-

netars. Careful monitoring of SGR 1830-0645 by NICER, for

instance, has shown that characteristic timescales are on the or-

der of a month (Younes et al., 2022), suggesting that ﬁxed hot

spots for smaller timescales would be a reasonable approxima-

tion. 1Hence, observations spanning no more than a couple of

weeks may be combined, which increases the quantity of data

to be ﬁt, and improves the quality of the statistics.

2.2. Science products extraction

During the observations, the instrument EPIC-pn (Str¨

uder

et al., 2001) was operating in small window mode and did

not have 3XMM J1852+0033 within its ﬁeld-of-view. EPIC-

MOS (Turner et al., 2001) cameras were operating in full win-

dow mode and did contain 3XMM J1852+0033; however, for

MOS 1, the source fell into a CCD that was switched oﬀin

two of the observations. Thus, we only make use of data

from MOS 2. Standard data reduction and ﬁltering procedures

were conducted with the XMM-Newton Science Analysis Sys-

tem (SAS, v.19.1.0).

Source photons were extracted, for all observations, from cir-

cular regions of 40′′ centred around the object’s position. The

background regions were chosen with the aid of the SAS task

ebkgreg. Because this task indicates the optimal background

region based solely on the detector geometry, the regions sug-

gested were slightly shrunk to avoid the inclusion of source

photons (see Figure 1).

The barycen and epiclccorr tasks were applied to ex-

tract the light curves. The former converts the photon arrival

registered time into the solar system barycenter time reference

and the latter performs a series of corrections to minimize ef-

fects that may impact the detection eﬃciency (e.g. dead time,

chip gaps, point-spread-function variation2) before producing a

background-subtracted light curve. The timing resolution was

limited by the camera’s operation mode, that is 2.6 seconds.

Light curves were extracted in two energy bands: 0.3–10 and

3–8 keV. More details are given in the next sections.

Although spectral analysis is not in the scope of this study, in

order to obtain information on the source’s ﬂux during each ob-

servation, we also extracted source and background spectra for

the same aforementioned energy-band regions. Standard tasks

rmfgen and arfgen were used to create the redistribution ma-

trix ﬁle (RMF) and the ancillary response ﬁle (ARF).

2.3. Folded light curves production

We folded the light curves (pulse proﬁles) at the periods pro-

vided by Lomb-Scargle periodograms computed for each obser-

vations’ light curves. The period values (P ∼11.56 s) found for

each set diﬀer only beyond the fourth decimal place, as already

shown by Zhou et al. (2014) and Rea et al. (2014). They also

pointed out that there is no signiﬁcant time derivative amongst

observations. This is true for either energy bands (0.3–10 and

3–8 keV). The folded light curves were binned to have 50 bins

per cycle, which will be the main input to our model. For com-

parative testing, we also produced folded light curves with 16

bins per cycle.

1The analysis of (Younes et al., 2022) suggests that the timescales for hot

spot motion could be related to properties of the solid crust, which would be

present in all NSs. Thus, analyses assuming ﬁxed hot spots should not ignore

that timescale.

2https://heasarc.gsfc.nasa.gov/docs/xmm/sas/help/epiclccorr/

118

238

474

945

Background

Source

30.0 18:53:00.0 30.0 52:00.0

50:00.0

45:00.0

0:40:00.0

35:00.0

30:00.0

Figure 1: MOS 2 raw image for observation 0550670201. The image LUT is in

log-scale; units are counts per pixel. Source and background extraction regions

for 3XMM J1852+0033 are indicated.

To derive the ﬂux emitted by 3XMM J1852+0033 during

each observation, we ﬁtted the 0.3–10 keV spectra with a sim-

ple absorbed blackbody model (phabs*bbody). We used the

X-ray spectral ﬁtting package XSPEC (Arnaud, 1996), ver-

sion 12.11.1. The overall values of the equivalent hydro-

gen column (NH∼1.2–1.5 ×1022 cm−2) and blackbody temper-

ature (kT ∼700–800 eV) provided by the best ﬁts are in agree-

ment with those reported by Zhou et al. (2014). The unab-

sorbed ﬂuxes (0.3–10 keV) for each observation were com-

puted by the flux command after setting the absorption com-

ponent to zero. To explore how the choice of model may af-

fect the unabsorbed ﬂux obtained, we added a phenomeno-

logical power-law to the previous model, i.e., the combination

phabs*(bbody+powerlaw). The blackbody model parame-

ters do not change, considering the conﬁdence range. The hy-

drogen column tends to assume slightly higher values (from 5%

to 15%), but it is also less constrained, agreeing within 90% er-

ror with the blackbody model alone; the powerlaw index is not

well constrained. These variations in the absorption component

value impact the 0.3–10 keV unabsorbed ﬂux obtained accord-

ingly. For further comparative testing, we have also computed

the unabsorbed ﬂuxes in the 3–8 keV band. In this band, the

role of the hydrogen column is much smaller, and the unab-

sorbed ﬂuxes derived for the two models agree within 2%.

Our modelling of the folded light curves relies on the shape

of each curve, meaning that it is able to ﬁt the curves regard-

less of the choice of normalization. Nevertheless, as it will be

clariﬁed in the following sections, using a sort of representative

value of the source’s emission, such as the unabsorbed ﬂuxes,

may help improve the quality of the results.

3. Model description and parameter estimation

In our previous work (de Lima et al., 2020), as well as

in the original reference that introduced the method (Turolla

and Nobili, 2013), the calculations were performed using the

normalized ﬂux, deﬁned as (Fmax +Fmin)/2. However, in

the present work, we make use of a modiﬁed normalization,

(Fmax +Fmin)/2¯

F, where ¯

Fdenotes the mean value of the ob-

served unabsorbed ﬂux in the period, derived from the spectral

ﬁtting. This modiﬁcation is of great signiﬁcance because nor-

malizing the theoretical pulse to the correct level improves the

statistical sampling and prevents the acceptance of parameters

that describe unrealistic situations, which do not correspond to

the actual ﬂux. Details are given in Appendix A.

The spacetime outside the star is well-described by the

Schwarzschild metric, i.e., we neglect rotational eﬀects, as the

source is a slow rotator. We also make use of the spectral tables

for models of magnetic NS atmospheres calculated by Ho et al.

(2007, 2008) and Mori and Ho (2007), which have been made

public and implemented in the XSPEC package (see Arnaud,

1996; Ho and Heinke, 2009; Ho, 2013). These neutron star

atmosphere models were obtained using the most up-to-date

equation of state (EOS) and opacity results for a partially ion-

ized, strongly magnetized hydrogen or mid-Z element plasma

(e.g., carbon, oxygen, and neon). The associated spectra come

from the solution to the coupled radiative transfer equations for

the two-photon polarization modes in a magnetized medium.

The atmosphere is assumed to be in radiative and hydrostatic

equilibrium. The atmosphere models depend on the NS surface

temperature, the NS surface magnetic ﬁeld strength Band its

inclination relative to the radial direction. Moreover, there is

a dependence on the NS surface gravity g=(1 +zg)GM/R2,

where the gravitational redshift is 1 +zg=1/p1−2GM/Rc2.

More precisely, the tables used for the spectra of the neutron

star atmospheres were calculated using discrete magnetic ﬁelds:

[1010,1011,1012,3.0×1013]G(nsmaxg, for an H atmosphere),

and [1012, 1013]G(nsmaxg, for a C atmosphere). For low mag-

netic ﬁelds (B≤1010 G), one can use nsx for a non-magnetic

atmosphere (H, He, and Ca). Even though we are working

with a magnetar, analysis taking into account Pand ˙

Psug-

gest that 3XMM J1852+0033 is a low-B one (Rea et al., 2014).

In addition, 3XMM J1852+0033’s proximity to SNR Kes 79

could allow magnetic-ﬁeld burying due to supernova debris;

the age of the SNR Kes 79 [estimated between 4.4 and 6.7 kyr

(see, e.g., Zhou et al., 2016; He et al., 2022)] and its proxim-

ity also suggest that 3XMM J1852+0033’s surface burial is re-

cent enough so ﬁeld re-emergence is still an ongoing process.

All the above means that NS atmosphere tables with subcriti-

cal Bs are reasonable. The tables also depend on discrete val-

ues of the surface gravity g. For a C atmosphere, we adopted

log10(g[cm/s2]) =[13.6−15.3], and for a H atmosphere,

log10(g[cm/s2]) =[13.6−15]. To be able to consider contin-

uous values of the model parameters in the Bayesian analysis,

the model emission has been interpolated using the tabulated

emission values. Further details about the atmosphere models

for NSs are given in Appendix B.

We used the Markov Chain Monte Carlo (MCMC) method

to determine the set of parameters ¯

θithat best describes the

3XMM J1852+0033 light curves. For the case of three spots,

which is the maximum number of spots we considered in the

modelling, they are

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摘要：

Evidencefor3XMMJ185246.6+003317asamassivemagnetarwithalowmagneticfieldRafaelC.R.deLima,a,JonasP.Pereira,b,c,JazielG.Coelho,c,d,RafaelC.Nunes,d,e,PauloE.Stecchini,d,f,ManuelCastro,g,PierreGomes,a,RodrigoR.daSilva,d,ClaudiaV.Rodrigues,d,Jos´eC.N.deAraujo,d,MichałBejger,b,h,PawełHaensel,b,J.LeszekZduni...

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Evidence for 3XMM J185246.6003317 as a massive magnetar with a low magnetic field

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