On the Curious Pulsation Properties of the Accreting Millisecond Pulsar IGR J17379–3747

To investigate the pulse and its evolution, we performed a coherent timing analysis of the pulsations. For any of the data selections considered, we first assumed a binary ephemeris and adjusted the photon arrival times to the binary barycenter. Then, we folded the data on the pulse period to construct a pulse profile. This profile was modeled with a constant for the nonpulsed contribution, and k sinusoids, each with fixed frequency kν_p. Hence, k = 1 described the fundamental pulsation, k = 2 the second harmonic, and so forth. A harmonic was considered to be significantly detected if its measured amplitude exceeded the 99% confidence amplitude threshold of the noise distribution. If so, the pulse amplitude is expressed in terms of its sinusoidal fractional amplitude. That is,

$$\begin{eqnarray}&&r=\displaystyle \frac{{A}_{k}}{{N}_{\gamma }-B},\end{eqnarray} \tag{ 1 }$$

where A_k is the measured amplitude of the kth harmonic, N_γ the number of photons in the data set, and B the number of photons contributed by the background emission. If a harmonic amplitude was not significantly detected, we calculated an upper limit as the minimum signal amplitude that would have produced a measurement in excess of the noise threshold 95% of the time.

Next, we further refined our model parameters by applying a phase-coherent analysis to the binary period. For each segment we optimized the time of ascending node through a grid search method: we constructed a grid with varying T_asc around its preliminary value, propagated to be near the observational time window. This grid spanned one orbital period using 1000 steps. For each trial on the grid, we then measured the pulse amplitude and picked the trial with the largest amplitude as the best timing solution. This method gave us 16 measurements of successive ascending node passages, which we modeled as

$$\begin{eqnarray}&&{T}_{\mathrm{asc},k}={T}_{\mathrm{asc},\mathrm{ref}}+{P}_{b}{N}_{k},\end{eqnarray} \tag{ 2 }$$

where N_k gives the number of orbital cycles between the reference epoch and the kth measurement. The resulting best-fit parameters were⁹ T_asc = 58209.200270, P_b = 6772.2681 s, and a_x = 0.0729 lt-s. This solution proved to be sufficiently accurate to allow for a coherent analysis of the pulsations.

Finally, we considered all ObsIDs. For each segment of continuous exposure we constructed a pulse profile and measured the pulse time of arrival. We fit these arrival times with a constant frequency and a circular orbital model using tempo2 (Hobbs et al. 2006) and refolded the data using the improved ephemerides. We iterated through this procedure until the timing solution had converged. The best-fit parameters are listed in Table 2, and the resulting pulse amplitudes and phase residuals are shown in Figure 1. We note that our timing solution is statistically consistent with the long-term timing solution reported by Sanna et al. (2018).

Table 2.  Timing Solution for the 2018 Outburst of IGR J17379

Parameter	Value	Uncertainty
ν (Hz)	468.083266605	7 $\times {10}^{-9}$
$\dot{\nu }$ (Hz ${{\rm{s}}}^{-1}$)	$\lt (-1.2\pm 1.7)\times {10}^{-14}$
${a}_{x}\sin i$ (lt-ms)	76.979	1.4 $\times {10}^{-2}$
Pb (s)	6765.8388	1.7 $\times {10}^{-3}$
Tasc (MJD)	58,208.966409	4 $\times {10}^{-6}$
	$\lt 5\times {10}^{-4}$
χ2/dof	192/119

Note. Uncertainties give the 1σ statistical errors, and the upper limit is quoted at the 95% c.l. The parameter gives the orbital eccentricity.

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A robust analysis of the accretion geometry implied by the observed pulse shapes requires a numerical treatment of beaming, light bending, and other relativistic effects (see, e.g., Salmi et al. 2018, and references therein), which is well beyond the scope of this work. Nonetheless, we may still obtain some first-order constraints on the viewing geometry from the results of our pulse-phase-resolved spectral analysis.

All three of our spectral groups indicate a thermal component that oscillates in normalization. While the fractional amplitude of the oscillation varies wildly between the groups, the absolute amplitudes of modulation imply that the emission area shows a gradual evolution. From the first to third group, we find that the apparent area of modulation seen at infinity is ${R}_{\infty }=\left\{3.8,2.9,1.8\right\}$ km. Following Poutanen & Gierliński (2003), we can then estimate the angular size of the hot spot as

$$\begin{eqnarray}&&\rho =\displaystyle \frac{{R}_{\infty }}{R}{Q}^{-1/2},\end{eqnarray} \tag{ 3 }$$

where

$$\begin{eqnarray}&&Q=\displaystyle \frac{{R}_{g}}{R}+\left(1-\displaystyle \frac{{R}_{g}}{R}\right)\cos i\cos \theta \end{eqnarray} \tag{ 4 }$$

and R_g = 2GM/c² is the gravitational Schwarzschild radius, with G the gravitational constant, M the neutron star mass, and R its radius. In Figure 6 we show the regions of allowed spot sizes as a function of θ for a choice of inclinations and radii and a canonical neutron star of $1.4\,{M}_{\odot }$. The inclination of IGR J17379 is only weakly constrained. All we know is that the source does not exhibit eclipses, and hence the system is not viewed edge-on (Sanna et al. 2018). Presuming that the neutron star rotation is aligned with the orbital plane, this implies i ≲ 75°. Due to the large pulse fraction, we suggest that the inclination is unlikely to be small, so we choose a lower bound of 30°. Based on these weak limits, we find that the spot size is likely constrained to 8°–18°, independent of the alignment angle, but we note that larger inclinations favor larger spot sizes.

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Two of three spectral groups also show an oscillation in blackbody temperature. In both cases, the oscillation fractional amplitude is on the order of 10%, which we note is consistent with the upper limit derived for the other spectral group. We further found that in both our measurements the temperature oscillation leads the maximum in blackbody area by about 150°. This implies that the apparent temperature is largest as the hot spot starts to rotate toward the observer, which immediately suggests an origin in a rotational Doppler boost. We note that the largest Doppler boost achievable is observed when the system is viewed edge-on and the spot is located at the equator, with the boosting factor given by

$$\begin{eqnarray}&&\beta (R)=\displaystyle \frac{2\pi R\nu }{c}.\end{eqnarray} \tag{ 5 }$$

Accounting for the alignment angle and system inclination, we can relate this boosting factor to the observed change in blackbody temperature as (Gierliński et al. 2002)

$$\begin{eqnarray}&&\displaystyle \frac{{{kT}}_{\max }}{{{kT}}_{\min }}\sim \displaystyle \frac{1+\beta (R)\sin (i)\sin (\theta )}{1-\beta (R)\sin (i)\sin (\theta )},\end{eqnarray} \tag{ 6 }$$

so that we obtain an approximate relation between the viewing angles (i and θ) and the neutron star radius. In Figure 7 we plot this relation for two assumed inclinations and a temperature variation of 10%. While these trends are approximate and have substantial uncertainty regions, they still demonstrate that for realistic radii (8–15 km) IGR J17379 strongly favors large inclination (i ≳ 45°) and alignment angles (θ ≳ 25°).

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In addition to a modulation of the blackbody emission parameters, we find that the Comptonized emission independently oscillates at the pulse period. Comparing the two spectral groups where this power-law emission is present, we see that both fractional amplitude and hard emission phase remain practically unchanged. The main differences are that the mean intensity goes down and that the second harmonic shows a phase shift, thus increasing the asymmetry of the hard pulse profile. Both the stability of the hard emission and the presence of a second harmonic support our interpretation that this emission originates in a radially extended region, as such a region would be far less sensitive to small changes in the hot spot location or shape. Also, different heights above the surface would experience slightly different Doppler boosts, which would naturally produce an asymmetric pulse profile (Gierliński & Poutanen 2005). A rather interesting property of our measurements is the apparent oscillation in photon index, which is nearly out of phase with the power-law flux. Qualitatively, this relation might also be explained by the viewing geometry: the effective area of the accretion column is smallest when the hot spot points toward the observer, yet that is the phase at which the optical depth is maximized; thus, the photon index should be out of phase.

Perhaps the most striking result of our pulse-phase-resolved analysis comes from the second spectral group, where we find a >62% fractional amplitude for the blackbody normalization and an apparently asymmetric profile (from the evidence for a second harmonic). While we caution that this measurement has substantial statistical and modeling uncertainty (see Table 3 and Section 3.6), this apparent deviation of the pulse profile could indicate that the hot spot is being partially obscured by the neutron star. According to Beloborodov (2002), such partial obscuration occurs when

$$\begin{eqnarray}&&\cos \left(i+\theta \right)\lt \displaystyle \frac{{R}_{g}}{{R}_{g}-R},\end{eqnarray} \tag{ 7 }$$

which we have drawn as dot-dashed lines in Figure 7. We find that the conditions to partial obscuration of the hot spot are indeed broadly consistent with the geometry requirements obtained from the blackbody temperature variation, and again we prefer a system with a large magnetic misalignment angle.

The halting outburst progression we observed in IGR J17379 is not unique to this source. Similar reflares have been reported in other sources under various names, including "rebrightenings," "echo-outbursts," "mini-outbursts," and "flaring-tails." This behavior has been reported for dwarf novae (e.g., Robertson et al. 1995; Kuulkers et al. 1996; Patterson et al. 2002), Galactic black hole binary systems (e.g., Bailyn & Orosz 1995; Kuulkers et al. 1996; Tomsick et al. 2004), and nonpulsating accreting neutron stars (e.g., Šimon 2010; Allen et al. 2015). Perhaps the most pertinent example of such reflaring behavior, however, may be found in the canonical AMXP SAX J1808.4–3658 (Wijnands et al. 2001; Patruno et al. 2009a).

As in SAX J1808.4–3658, the reflares observed in IGR J17379 have a roughly weeklong duration and peak at luminosities of ∼10³⁵ erg ${{\rm{s}}}^{-1}$. This similarity may reflect the fact that these two AMXPs are also very similar in terms of their orbital parameters and their respective stellar companions (Chakrabarty et al. 2003; Sanna et al. 2018). Important differences, however, exist also: the main outbursts of SAX J1808.4–3658 are longer than those of IGR J17379 (Bult & van der Klis 2015). Additionally, SAX J1808.4–3658 is known to show a prominent aperiodic 1 Hz modulation (van der Klis et al. 2000; Patruno et al. 2009b), which is absent in IGR J17379. A very similar aperiodic 1 Hz modulation has been reported in the outburst of NGC 6440 X-2 (Patruno & D'Angelo 2013), a different AMXP whose outbursts are reminiscent of reflares in terms of duration and peak luminosity (Altamirano et al. 2010; Heinke et al. 2010). This 1 Hz modulation has been attributed to episodic accretion onto the neutron star (D'Angelo & Spruit 2010, 2012) and hence is likely a signature of the magnetosphere/disk interaction, rather than being a signature of the reflare itself. Furthermore, the 1 Hz modulation has also been reported to occur in the main outburst (Bult & van der Klis 2014), suggesting that the underlying instability has two mutually exclusive branches: it occurs either around 10³⁵ erg ${{\rm{s}}}^{-1}$ during the reflares or around 10³⁶ erg ${{\rm{s}}}^{-1}$ during the main outburst. Hence, the absence of such a 1 Hz modulation in IGR J17379 may not be meaningful.

It is not clear what causes some X-ray transients to show reflares toward the end of their outbursts. Nonetheless, as this phenomenon has been observed across source types, it is likely caused by the same ionization instability (Osaki 1974; Lasota 2001) that is generally assumed to cause the X-ray outbursts themselves. This common interpretation essentially views each reflare as a separate mini-outburst: a small change in the disk temperature causes hydrogen to partially ionize. This, in turn, increases the disk opacity, which further increases its temperature. As this instability grows, the mass accretion rate through the disk increases rapidly, and hence the source is observed to brighten in X-rays. The reason why this instability can be triggered several times in a row is unclear, both from an observational and a theoretical perspective (Dubus et al. 2001; Lasota 2001; Kotko et al. 2012). The NICER X-ray data alone are not especially informative on the matter. Constraints on the origin of these reflares should come from either a population study or a multiwavelength observing effort (see, e.g., Patruno et al. 2016). In this light, however, we point out that IGR J17379 appears to have a comparatively short and stable recurrence time and has reported counterparts in both radio (van den Eijnden et al. 2018a) and the optical/near-infrared (Curran et al. 2011). Hence, we suggest that this source might make a compelling target for future multiwavelength investigations.

Following the reflares, we observed IGR J17379 to transition into a prolonged low-activity state. In this state the source X-ray luminosity was about $5\times {10}^{33}$ erg ${{\rm{s}}}^{-1}$, placing it in the ≲10³⁴ erg ${{\rm{s}}}^{-1}$ luminosity regime in which accreting neutron stars are usually considered to be in quiescence (Verbunt et al. 1984). In tandem with the decrease in luminosity, the source spectrum was observed to soften. Such late-outburst spectral softening is commonly observed in both black hole (Wu & Gu 2008; Plotkin et al. 2013) and neutron star binaries (Wijnands et al. 2015, and references therein). The soft spectrum of a quiescent neutron star can be attributed either to residual low-level accretion or to the gradual cooling of the stellar surface. It is often difficult to disentangle which of these two mechanisms applies, or, at least, which one dominates the observed emission (see, e.g., Fridriksson et al. 2011). In IGR J17379, however, we continue to detect coherent pulsations, which is a clear indication that at least some channeled accretion continues even at the lowest luminosities.

Interestingly, very similar behavior has been reported for two of the three confirmed transitional millisecond pulsars (tMSPs; Archibald et al. 2015; Papitto et al. 2015), the class of millisecond pulsars that bridge the gap between traditional AMXPs and rotationally powered millisecond pulsars observed in the radio (Papitto et al. 2013). Both PSR J1023+0038 and XSS J12270–4859 have shown coherent X-ray pulsations at luminosities of order 10³³ erg ${{\rm{s}}}^{-1}$. In both cases, the X-ray pulsations were highly sinusoidal and had pulse fractions of 5%–15%, similar to the X-ray pulsations seen in AMXPs. Neither of these two tMSPs, however, has shown the 10³⁶ erg ${{\rm{s}}}^{-1}$ X-ray outburst cycle of an AMXP, so the link between these two populations of pulsars has always been based on the similarity of their pulse profiles. The third confirmed transitional millisecond pulsar, IGR J18245–2452, did show a high-luminosity outburst (Papitto et al. 2013), but that outburst was highly atypical for an LMXB, and no X-ray pulsations have been detected at quiescent luminosities (Linares et al. 2014). In IGR J17379, however, we observed both the outburst cycle and the low-activity state, and our pulse-phase-resolved spectroscopy demonstrates that the character of the pulsations does not change substantially with luminosity. Hence, IGR J17379 gives us strong evidence that the X-ray pulsations in the low-activity state are indeed accretion powered.

A second characteristic property that transitional pulsars show in their low-activity regime is a stepwise mode switching between a "low" and "high" luminosity state that differs in observed flux by a factor of 10 (Archibald et al. 2015; Bogdanov et al. 2015; Papitto et al. 2015). Unlike the transitional pulsars, IGR J17379 does not appear to be showing this characteristic mode switching. Indeed, if we construct a histogram of count rates measured in 10 s bins (Figure 8), then we see no evidence of a bimodal population.

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A caveat to this discussion is that the distance to IGR J17379 is not well constrained. If the source were substantially farther away than the presumed 8.5 kpc, then we may be underestimating the luminosity by up to a factor of a few. We note, however, that the one X-ray burst observed from IGR J17379 had a double-peaked profile and an estimated maximum luminosity near the Eddington limit (Chelovekov & Grebenev 2010). If one assumes that this burst was Eddington limited (Kuulkers et al. 2003), then the inferred distance would place IGR J17379 at ≈8 kpc (van den Eijnden et al. 2018a). Hence, while the source distance used in this work is uncertain, it is probably not too far off.

While the detection of X-ray pulsations at low luminosity in IGR J17379 (and likewise in the transitional pulsars) indicates that magnetically channeled accretion is taking place, it is not at all clear how to reconcile these observations with accretion theory. In the standard view of disk accretion the rotating magnetosphere of the neutron star imposes a centrifugal barrier (Illarionov & Sunyaev 1975), such that accretion onto the star can proceed only while the disk is truncated inside the corotation radius

$$\begin{eqnarray}&&{r}_{c}\simeq 28\,{\rm{km}}{\left(\displaystyle \frac{\nu }{468\mathrm{Hz}}\right)}^{-2/3}{\left(\displaystyle \frac{M}{1.4{M}_{\odot }}\right)}^{1/3}.\end{eqnarray} \tag{ 8 }$$

If the disk is truncated outside this corotation radius, then the propeller effect should inhibit accretion and instead drive a mass outflow. We can consider the radius of the magnetosphere as the distance at which the magnetic field is strong enough to force the orbiting material of a Keplerian disk into corotation (Spruit & Taam 1993; D'Angelo & Spruit 2010),

$$\begin{eqnarray}\begin{array}{rcl}{r}_{m} & \simeq & 100\,{\rm{km}}{\left(\displaystyle \frac{M}{1.4{M}_{\odot }}\right)}^{-1/10}{\left(\displaystyle \frac{B}{{10}^{8}{\rm{Gauss}}}\right)}^{2/5}\\ & & \,\times {\left(\displaystyle \frac{R}{10{\rm{km}}}\right)}^{6/5}{\left(\displaystyle \frac{\dot{M}}{{10}^{-13}{M}_{\odot }{{\rm{yr}}}^{-1}}\right)}^{-1/5}\\ & & \,\times {\left(\displaystyle \frac{\nu }{468\mathrm{Hz}}\right)}^{-3/10},\end{array}\end{eqnarray} \tag{ 9 }$$

where B gives the stellar magnetic field strength and $\dot{M}$ the mass accretion rate onto the neutron star. If the observed $5\times {10}^{33}$ erg ${{\rm{s}}}^{-1}$ luminosity is entirely due to accretion, we can estimate the mass accretion rate at $\dot{M}=3\times {10}^{-13}\,{M}_{\odot }\,\,{{\rm{yr}}}^{-1}$, which places the disk truncation outside the light-cylinder radius r_lc = 100 km. Hence, one would expect this system to be well inside the propeller regime, such that channeled accretion is not expected. There are three scenarios proposed in the literature that could resolve this issue (see, e.g., Archibald et al. 2015; Papitto et al. 2015; Patruno et al. 2016):

• 1.  
  As the accretion rate drops, the innermost region of the disk may transition into a radiatively inefficient accretion flow, allowing the formation of an optically thin, geometrically thick disk (Rees et al. 1982). Such a disk would convert less energy into radiation, so that the accretion rate may be much higher than inferred from the X-ray flux. A similar transition has been proposed to explain the late-outburst spectral softening in black hole binaries (Plotkin et al. 2013). However, it is not clear that this interpretation extends to neutron stars as well (Wijnands et al. 2015). Additionally, there is considerable theoretical uncertainty surrounding the properties of such a flow and how it might interact with the stellar magnetic field (Menou & McClintock 2001; Dall'Osso et al. 2015), which makes it difficult to explore this scenario in depth.
• 2.  
  If the propeller ejects a very large fraction of the inflowing disk material, then it is possible that the neutron star magnetosphere is experiencing a much greater inward pressure from the disk than what is inferred from the X-ray flux (Lasota et al. 1999). Plausibly, this disparity may be large enough to place the inner edge of the disk near corotation, thus allowing channeled accretion to proceed. In practice, the outflow rate would have to be roughly two orders of magnitude larger than the rate obtained from the X-ray flux, which again implies that the accretion flow must be radiatively inefficient, since otherwise direct emission from the disk would have dominated our spectrum.
• 3.  
  Depending on the detailed microphysics governing the magnetosphere/disk interaction, the magnetosphere may not be able to drive an outflow (Spruit & Taam 1993). Instead, the disk truncation radius could be "trapped" near corotation (Sunyaev & Shakura 1977; D'Angelo & Spruit 2010). Indeed, this is the scenario invoked to explain the 1 Hz modulation in SAX J1808.4–3658 and NGC 6440 X-2 (Patruno et al. 2009a; Patruno & D'Angelo 2013).

All three scenarios imply in one way or another that the X-ray flux is a poor estimate of the accretion rate onto the neutron star. Some independent evidence for this argument can be found in the parallel track phenomenon of LMXBs (van der Klis 2001), and in the structured relation between the kHz QPOs and pulse amplitude of SAX J1808.4–3658 (Bult & van der Klis 2015). However, there are also secondary consequences to this argument.

First, if there is a large mass outflow, one might expect an observational signature of that outflow in the radio data. The detection of a flat-spectrum radio counterpart (van den Eijnden et al. 2018a) supports this scenario, although we note that the radio data were not contemporaneous with the low-activity state, and detailed modeling would be required to determine whether the observed radio flux is consistent with the mass ejection rate required by our X-ray data.

Second, for the magnetosphere to drive an outflow, a significant spin-down torque would have to be applied to the neutron star. The magnitude of this torque would have to be consistent with the long-term spin evolution of the pulsar. The rate at which the neutron star spin changes owing to an outflow can be estimated as (Hartman et al. 2008)

$$\begin{eqnarray}\begin{array}{rcl}\dot{\nu } & \gtrsim & -2.4\times {10}^{-13}\,{\rm{Hz}}\,{s}^{-1}\,n{\left(\displaystyle \frac{{r}_{m}}{{r}_{c}}\right)}^{1/2}{\left(\displaystyle \frac{I}{{10}^{45}{g\mathrm{cm}}^{2}}\right)}^{-1}\\ & & \times \,\left(\displaystyle \frac{-\dot{M}}{{10}^{-11}\,{M}_{\odot }\,{{\rm{yr}}}^{-1}}\right){\left(\displaystyle \frac{M}{1.4{M}_{\odot }}\right)}^{2/3}{\left(\displaystyle \frac{{\nu }_{s}}{468{\rm{Hz}}}\right)}^{-1/3},\end{array}\end{eqnarray} \tag{ 10 }$$

where n gives a scaling parameter capturing the detailed physics and I is the neutron star moment of inertia. Roughly, we can assume n = 0 when the disk edge is inside r_c and n ≃ 1 when the disk edge is in the propeller regime (Ekşi et al. 2005). Since Sanna et al. (2018) report a lower limit on the long-term spin frequency derivative of $\dot{\nu }\gtrsim -{10}^{-12}$ Hz ${{\rm{s}}}^{-1}$, it follows that even if only 1% of the accretion flow passes through the barrier imposed by the propeller effect, the resulting spin-down torque is still sufficiently small to be consistent with the observed long-term spin evolution limits. We note, however, that the spin frequency derivative measurement for IGR J17379 is currently limited by the relatively poor spin frequency measurement during the 2004 outburst (see Sanna et al. 2018). If a future outburst were well sampled with NICER or a similarly capable timing instrument, the sensitivity to the spin frequency change would improve by 3 orders of magnitude. This, in turn, would allow for a physically interesting constraint on the ratio of accreted to ejected material.

Finally, we note that Archibald et al. (2015) hypothesize that the mode switching seen in tMSPs may be a result of the disk transitioning between a propeller and trapped disk state. If so, then the absence of mode switching in IGR J17379 may simply mean that this source is in a more stable trapped disk state during our observations. Similar to a propeller, a trapped disk must also apply a spin-down torque on the neutron star in order to remain stable (D'Angelo & Spruit 2010). However, the loss in angular momentum for this mechanism is smaller compared to that predicted by mass ejection (D'Angelo & Spruit 2012).

The X-ray spectrum of IGR J17379 during the low-activity state is softer than the spectra observed in the tMSPs at similar luminosities (Coti Zelati et al. 2014; Bogdanov et al. 2015; Papitto et al. 2015) and shows an additional blackbody component at the lowest energies. The origin of this blackbody is not immediately clear, although any thermal emission can generally be attributed to either the stellar surface or the accretion disk. If we interpret this low-temperature component as coming from the disk, then the normalization gives us an implied inner disk radius of 34 (82) km at 75° (30°) inclination. Alternatively, if the emission is originating from the neutron star, its nonpulsed nature suggests that it has an isotropic temperature profile. It could possibly be generated from radiative cooling of the neutron star crust if the crust was heated out of equilibrium during the outburst (Brown et al. 1998). While the expected crust temperature depends on the outburst light curve, the temperature and luminosity of this blackbody component match the emission one might expect from a cooling neutron star crust (Ootes et al. 2016). Some of this uncertainty might be resolved if future outbursts could be followed further into quiescence to see whether the source luminosity decreases over time. In order to determine the neutron star luminosity after cooling down from an accretion episode, we must first estimate the long-term averaged mass accretion rate for this system.

Integrating the 2018 outburst count rate observed with Swift/BAT, we find that NICER observed roughly 10% of the total outburst fluence. The NICER data, in turn, can be approximated as a linear decay, allowing us to measure the observed fluence as $8.4\times {10}^{-6}$ erg cm⁻². Hence, we can roughly estimate the total fluence for this outburst at 10⁻⁴ erg cm⁻². If we assume this fluence to be typical for all outbursts of IGR J17379 and we consider a recurrence time of 4 yr, we can then estimate the long-term averaged mass accretion rate onto the neutron star to be

$$\begin{eqnarray}&&\langle \dot{M}\rangle \simeq 6\times {10}^{-13}\,{M}_{\odot }\,\,{{\rm{yr}}}^{-1}.\end{eqnarray} \tag{ 11 }$$

This long-term averaged accretion rate is substantially lower than those estimated for other neutron star binaries (Heinke et al. 2010). If this estimate reflects the real accretion rate onto the neutron star, then we may expect the source to show a quiescent luminosity of $5\times {10}^{31}$ erg ${{\rm{s}}}^{-1}$ through deep crustal heating (Brown et al. 1998).

Our estimate of the long-term mass accretion rate is subject to a number of systematic uncertainties. For one, the distance to the source may be larger than assumed, which would cause us to underestimate $\langle \dot{M}\rangle$. Additionally, IGR J17379 is a faint source, so it is conceivable that a number of its outbursts have not been recorded (as evidenced by our Swift/BAT analysis; see Section 3.2). Since $\langle \dot{M}\rangle$ scales linearly with the recurrence time, a shorter-than-assumed recurrence would again imply that we are underestimating the mean accretion rate.

Finally, if the neutron star is less compact than assumed, e.g., if its radius is 15 km rather than the canonical 10 km used in our calculations, then again the mass accretion rate is underestimated.

However, even if we take all these uncertainties in aggregate, we can increase $\langle \dot{M}\rangle$ by no more than one order of magnitude. Under such fine-tuning IGR J17379 would still be on par with the low end of the population and have an implied quiescent luminosity of ≲10³² erg ${{\rm{s}}}^{-1}$.