A STRONGLY MAGNETIZED PULSAR WITHIN THE GRASP OF THE MILKY WAY'S SUPERMASSIVE BLACK HOLE

In the ACIS-S observations, a number of sources were detected besides SGR J1745–2900. In particular, four known sources present in an X-ray catalog (Muno et al. 2009) were located within ∼30'' from the SGR and could be employed to refine the absolute astrometry. We used the four source positions, calculated with wavdetect, to register the ACIS-S images on the catalog by optimizing a roto-translation (using the CIAO script reproject_aspect). The fit yielded an average rms of ∼80 mas. The estimated coordinates (also taking into account the accuracy of the reference positions) of SGR J1745–2900 are R.A. = 17^h45^m40169, decl. = −29°00'2984 (J2000.0) with a 95% confidence level uncertainty radius of 03 (see Figure 1).

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Because of the complex shape and variability of the three peaked pulse profile (Figure 2), we decided not to use a pulse template for the timing analysis (which might artificially affect the phase shift), instead using two parallel methods: fitting a sinusoid to the profile at the fundamental period and fitting the highest peak in all the observations with a Gaussian. We used 12 phase bins to produce a folded pulse profile. We built up our timing solution from the phases of the second Chandra pointing which has the highest number of counts. The resulting best-fit period for this Chandra observation was P = 3.763554(2) s (at TJD 16424.5509871; TJD = JD − 2440000.5 days). The accuracy on this measure of the period, 2 μs, is enough to coherently phase-connect adjacent observations. At each step, we checked that the timing solution was accurate enough to univocally determine the phase of the following observation. To this end, we propagated the error affecting the best-fitting parameters of the solution obtained at any step to the epoch of the newly added observation. We never obtained a phase uncertainty larger than 0.4, which allowed us to tentatively maintain the phase connection. The phase-coherent solution obtained considering the phases of the best-fit fundamental harmonic component has a period P = 3.7635537(2) s and period derivative $\dot{P} = 6.61(4)\times 10^{-12}$ s s⁻¹ (epoch TJD 16424.5509871), with a reduced chi-squared of 0.85 for 5 degrees of freedom (dof). On the other hand, when comparing this results with the timing solution derived considering the phases of the best-fit Gaussian to the main peak, we find compatible numbers for the period and the period derivative, but with marginal evidence for a cubic component (resulting in a possible $|\ddot{P}|=4(3)\times 10^{-19}$ s s⁻²).

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In the Chandra observations, the pileup in the ACIS-S3 detector was ∼5%–15%, therefore an annular region with 075 inner radius (1.5 pixels) and 2'' outer radius was selected to extract the source spectrum. For the background we used an annular region of maximum radius 8'' around the source. The point source spectrum was rebinned to have at least 50 counts per energy bin.

We modeled the spectra using the XSPEC v.12.8.0j analysis package. An absorbed single blackbody component (BB) provides a good fit to the data of the three ACIS-S observations ($\chi _r^2\sim 1.13$ with 313 dof); the best-fit parameters are N_H = 1.03(4) × 10²³ cm⁻² (abundances and cross-section from Anders & Grevesse 1989 and Balucinska-Church & McCammon 1998), with a temperature cooling from kT = 0.95(2) keV to kT = 0.90(2) keV, and then kT = 0.88(2) keV for the three observations, respectively. The BB radius remains constant within errors at R_BB ≃ 1.4 km (assuming a 8.3 kpc distance). The 1–10 keV source flux (see Table 1) corresponds to a luminosity of 2.1, 1.8, and 1.6 × 10³⁵ erg s⁻¹ (assuming a 8.3 kpc distance).

However, we note that the fit residuals are not optimal at higher energies, possibly due to the presence of a non-thermal component. By fitting with a power-law function, we also obtain a good modeling ($\chi _r^2\sim 1.04$ with 313 dof), with N_H = 1.73(4) × 10²³ cm⁻², with photon index of Γ = 3.9(1), 4.1(1), and 4.2(1) for the three observations. The residuals are slightly better shaped at higher energy. A composition of a BB plus power-law model is not statistically required by the data, and does not improve the fit.

The X-ray flux decay can be modeled with an exponential function of the form $F(t)=F_\circ \,e^{(-(t-t_\circ)/\tau)}$ ($\chi ^2_\nu =1.44$ for 80 dof). We fixed t_○ at the time of the first burst detected; the resulting best-fit parameters are F_○ = 1.72(3) × 10⁻¹¹ erg cm⁻² s⁻¹ and e-folding time τ = 144(8) days. This is a rather slow flux decay when compared with other outbursts (Figure 1).

The difference between the column densities of SGR J1745–2900  (see Section 2.3) and Sgr A* (Baganoff et al. 2003) translates into $|N_{\mathrm{H,\,J1745}} - N_{\mathrm{H,\,SgrA^*}}| \lesssim 0.6\times 10^{23}$ cm⁻² (at 90% confidence level). Given that the Central Molecular Zone (CMZ) has a particle density N_CMZ > 10⁴ cm³ (Morris & Serabyn 1996), this yields an upper limit on the distance between the two sources $d_\mathrm{max}=|N_{\mathrm{H,\,J1745}} - N_{\mathrm{H,\,SgrA^*}}|/N_{\mathrm{CMZ}} \sim$ 2 pc.

SGR J1745–2900 and Sgr A* relative distance ranges between that implied by their angular separation on the sky, d_min = 0.09 ± 0.02 pc, and d_max ∼ 2 pc. With an estimated neutron star density in the Galactic disk ≈3 × 10⁻⁴ pc⁻³ (Faucher-Giguère & Kaspi 2006), we expect ∼0.2 neutron stars in a cone of aperture 24 that encompasses the Galactic Center and reaches out to the rim of the Galaxy (the assumed distance from the Sun is 20 kpc). This estimate comprises all neutron stars born during the Galaxy lifetime in about 1 Gyr. The probability of SGR J1745–2900 being a neutron star wandering across the line of sight, with an age ≲9 kyr, and lying at such a small angular distance from Sgr A* is then ∼1.8 × 10⁻⁶. This makes the possibility that SGR J1745–2900  is a foreground or background object quite unlikely.

On the other hand, estimates of the neutron star population in the Galaxy (Freitag et al. 2006) suggest that there are about 2 × 10⁴ neutron stars within 1 pc from the Galactic center. Since this is the total population born during the entire lifetime of the Galaxy (about a Gyr), a new neutron star is born in the same region every ∼10⁵ yr. Even on an observational ground alone, about 80 ordinary radio pulsars (Wharton et al. 2012) are expected to be visible with 1 pc from Sgr A*, compatible with us seeing only one young radio pulsar with a characteristic age <10 kyr. The magnetar nature of this young radio pulsar so close to Sgr A* suggests that there might possibly be as many magnetars as ordinary pulsars in the Galaxy (Rea et al. 2010), and/or the Galactic center region is a favorable place for magnetar formation, possibly because of its high density of very massive stars.

The projected position of SGR J1745–2900 places it within the disk of young and massive stars observed within 0.5 pc of Sgr A* (Paumard et al. 2006; Lu et al. 2009), which is most likely its birthplace (see Figure 4). SGR J1745–2900  is probably the end product of one of the young massive stars born during a recent star formation activity within the dense gaseous disk around Sgr A*, now accreted into the black hole (Levin & Beloborodov 2003).

The probability of SGR J1745–2900 being in a bound orbit around Sgr A* depends on the distance and the kick velocity of the neutron star at birth. In order to estimate the probability that SGR J1745–2900 is in a bound orbit around Sgr A*, we performed numerical simulations by integrating the equations of motion in the gravitational potential of the central black hole for a large number (∼10⁶) of stars; Newtonian gravity was assumed throughout. For each orbit, the initial radial distance d (0.05 pc ⩽ d ⩽ 5 pc) was fixed and the star position on the sphere was selected by generating two uniform deviates. The modulus of the initial velocity was drawn from a Gaussian distribution with specified standard deviation σ (200 km s⁻¹ ⩽ σ ⩽ 600 km s⁻¹); the velocity direction was determined by generating two further uniform deviates. Orbits were calculated in the time interval 0 ⩽ t ⩽ T, where T = 9 kyr is the estimated age of SGR J1745–2900. Stars which at t = T are at a projected radial distance of 0.07–0.11 pc are sorted according to the value of their total energy, E. Finally, the fraction of bound orbits is computed as N(E < 0)/N_tot. Since a large number of runs are required to explore with sufficiently small uncertainties the d and σ ranges, we resorted to a two-dimensional (2D) model in which orbits are in the plane of the sky only. We checked that results from the 2D calculations are in good agreement with those of the complete three-dimensional (3D) case for the present purposes. The Monte Carlo simulations are summarized in Figure 3, which shows the fraction of bound orbits as a function of d and σ; if the magnetar was born within 1 pc of Sgr A* (where most of the massive stars are located), then the probability of being in a bound orbit around the black hole is ∼90%. For a circular orbit of radius 0.1 pc, the orbital period would be 1430 yr, while the minimum orbital period would be 500 yr with the pulsar being now at the apastron of a strongly eccentric orbit (Liu et al. 2012). Orbital periods for different eccentricities and semi-major axes can reach periods of several kyrs.

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Studies of the Galactic center environment led to the discovery of Fe Kα emission (Koyama et al. 1997) from molecular clouds within ∼300 pc from Sgr A* (Figure 4). The fast variability of these Fe emission features (Ponti et al. 2010; Clavel et al. 2013) supports an interpretation in terms of irradiation from one or more radiation fronts passing through the different molecular clouds in the Galactic Center emitted ∼100 yr ago. The luminosity needed to explain the Fe fluorescence can be calculated as L_8 keV ∼ 6 × 10³⁸ × f erg s⁻¹ (Sunyaev & Churazov 1998), where f is a parameter taking into account flares with duration Δt shorter than the cloud light-crossing time: f ≃ (R_cloud/c)/Δt. The total required fluence is then ≈L_8 keV × T_echo ∼ 10⁴⁶–10⁴⁷ erg, where T_echo ≈1–10 yr is the light crossing time of the fastest echoing clouds (Clavel et al. 2013). This energy could have been emitted by a powerful giant flare (similar to the one observed from SGR 1806–20; Hurley et al. 2005) from SGR J1745–2900  about a century ago. Unfortunately, a reliable measure of the soft X-ray flux of the peak of SGR 1806–20's giant flare is not available (Hurley et al. 2005; Inan et al. 2007); however, for the SGR 1900+14's giant flare the study of the ionosphere disturbance could give an estimate of its 3–10 keV flux as a factor of ∼9 times the hard X-ray emission level (Inan et al. 1999). This is also in line with the idea of the softer component being due to the thermal emission from an expanding fireball, which in smaller scale bursts are observed to have a spectrum consistent with a BB with kT ∼ 7–10 keV. The non-thermal hard X-ray emission during the flare peak is instead due to non-thermal processes deriving from the particle acceleration caused by the fireball. The >50 keV peak flux of SGR 1806–20's giant flare was estimated to be ∼20 erg s⁻¹ cm⁻² by GEOTAIL measurements (the only instrument providing a good estimate of the first <1 s flare flux; Terasawa et al. 2005). Assuming a distance of 15 kpc (McClure-Griffiths & Gaensler 2005), this translates into a luminosity (>50 keV) of ∼5 × 10⁴⁶ erg s⁻¹. A good guess of the 3–10 keV emission during the SGR 1806–20's giant flare would then be about an order of magnitude higher luminosity, large enough to be the cause (or a substantial part) of the photon flux responsible for the observed Fe emission. Furthermore, the requirement that a very energetic event from SGR J1745–2900 occurred ∼100  yr ago is compatible with the estimated outburst rate of a magnetar with such properties, which is approximately one every 50–100 yr (Viganò et al. 2013; Perna & Pons 2011).

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