MILLIHERTZ QUASI-PERIODIC OSCILLATIONS AND THERMONUCLEAR BURSTS FROM TERZAN 5: A SHOWCASE OF BURNING REGIMES

We report the discovery of several instances of mHz QPOs during the peak of the T5X2 outburst, on 2010 October 16, 18, 19, 20, and 21 (MJDs 55485–55490; Linares et al. 2010a for the initial report of mHz QPOs on 2010 October 18 and 19). Two examples of mHz QPO light curves are shown in Figure 3, each spanning one RXTE orbit. Table 2 shows the main QPO properties: fractional rms amplitudes between 1.3% and 2.2% (in the 2–60 keV band) and ν_QPO in the range 2.8–4.2 mHz (note that the lower end of this frequency range corresponds to our mHz QPO definition; Sections 2 and 3). Figure 4 presents LSPs of two cases, on October 16 and 18, clearly showing the change in ν_QPO as well as the harmonic structure (up to four overtones are visible in the LSPs). By inspecting the power spectra obtained from 2048 s long FFTs, we find that the mHz QPO power is in all cases spread over one or two frequency bins, from which we derive a limit on the FWHM ≲ 1 mHz. For the 2.8–4.2 mHz QPO frequencies this corresponds to a lower limit on the quality factor (Q ≡ ν_QPO/FWHM) of Q ≳ 3, which reveals a fairly coherent QPO (a fairly constant t_wait).

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Table 2. Properties of the mHz QPOs from T5X2

Date	ObsIDa	νQPOb	rmsQPO	Lpers/1037	$\dot{m}$/104
(MJD)		(mHz)	(%)	(erg s−1)	(g cm−2 s−1)
55485.46	04–00 [1]	2.75 ± 0.2	1.9 ± 0.1	9.1 ± 0.4	4.5 ± 0.2
55485.63	04–01 [1,2,3]	3 ± 0.5	2.2 ± 0.1	9.9 ± 0.4	4.9 ± 0.2
55487.43	06–000 [1,4]	4.2 ± 0.2	1.3 ± 0.1	11.4 ± 0.4	5.6 ± 0.2
55487.62	06–00 [1,2]	4.2 ± 0.2	1.7 ± 0.2	12.1 ± 0.5	6.0 ± 0.2
55488.26	07–00 [1]	4.0 ± 0.5	1.4 ± 0.1	12.0 ± 0.5	5.9 ± 0.2
55489.59	08–00 [1]	3.75 ± 0.2	2.1 ± 0.1	9.6 ± 0.5	4.8 ± 0.2
55490.63	09–00 [1,2]	2.9 ± 0.2	2.2 ± 0.1	9.1 ± 0.4	4.5 ± 0.2

Notes. ^aObservation (from proposal-target 95437-01) where the mHz QPOs are detected, orbit numbers used indicated between square brackets. ^bFor comparison, the reported values for the "low-L_pers mHz QPOs" are in the following ranges: ν_QPO = [7–14.3] mHz; rms_QPO = [0.7–1.9]% (2–5 keV); L_pers = [0.6–3.5] × 10³⁷ erg s⁻¹ (Section 4.2; Revnivtsev et al. 2001; Altamirano et al. 2008).

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We present in Figure 5 light curves folded at the mHz QPO period, showing folded burst/QPO profiles for the same two dates, October 16 and 18. In both cases the burst/QPO profile is peaked and highly non-sinusoidal (as seen also in the raw, unfolded light curves; Figure 3), which explains the harmonic content. On October 18, when ν_QPO was highest (Table 2), we find a nearly symmetric burst/QPO profile. On October 16 the burst/QPO profile is slightly asymmetric, with the rise faster than the decay. We measure a mHz QPO fractional rms amplitude in the range 1.3%–2.2%, in the total (∼2–60 keV) PCA band. Furthermore, from our measurements of the mHz QPO amplitude at different energies (Section 2 and Figure 6) we find that its fractional rms amplitude increases between ∼2 and ∼20 keV, from ∼1.4% to ∼2.8% in the two cases presented in Figure 6. At energies higher than 20 keV the mHz QPO is not visible by the naked eye in the light curves, nor is it conclusively detected using LSPs, FFTs, or folded light curves. The presence of red noise with variable strength gives rise to different upper limits on the fractional rms amplitude of the mHz QPO above 20 keV (between 1.4% and 3%; Figure 6). As discussed in Section 4.2, such an increase in QPO amplitude up to 20 keV is in contrast with mHz QPOs from other bursting NSs, which showed a fractional amplitude decreasing with increasing energy between 2 and 5 keV (Revnivtsev et al. 2001).

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We present in this section the relation between burst properties and $\dot{m}$, as inferred from L_pers, including the faintest and most frequent bursts which form the mHz QPOs (see above). Figure 2 shows L_peak, E_b, and t_rec as a function of the Eddington-normalized L_pers and $\dot{m}$ (Section 2). The overall trend is that of an anticorrelation between L_peak, E_b, and t_rec on the one hand and L_pers on the other (see also Figure 1 in Linares et al. 2011; Motta et al. 2011). Closer inspection of the burst properties over the full L_pers range (0.1–0.5 L_Edd; see Figure 7) reveals a more complex and interesting behavior, namely, four different bursting regimes.

• 1.  
  At the lowest persistent luminosities, 0.1 < L_pers/L_Edd < 0.2, when L_pers increases both L_peak and E_b (and possibly t_rec) decrease moderately, from L_peak ≃ 4.6 × 10³⁷ erg s⁻¹, E_b ≃ 1.6 × 10³⁹ erg to L_peak ≃ 3.7 × 10³⁷ erg s⁻¹, E_b ≃ 1.3 × 10³⁹ erg. We refer to this 0.1–0.2 L_Edd regime as slow decrease, or regime A (see Figure 7).
• 2.  
  At higher persistent luminosities, 0.2 < L_pers/L_Edd < 0.3, we find L_peak and E_b to be steeply anticorrelated with L_pers, while t_rec also decreases from 200 s to 400 s with increasing L_pers. We refer to this 0.2–0.3 L_Edd regime as fast drop, or regime B (see Figure 7).
• 3.  
  At the highest persistent luminosities (L_pers > 0.3 L_Edd), when mHz QPOs are detected, burst peak luminosity and energy reach approximately constant values (saturation, or regime C): L_peak  ≃  1.2 × 10³⁷ erg s⁻¹ and E_b  ≃  0.3 × 10³⁹ erg. The burst recurrence time, however, keeps decreasing with increasing L_pers from t_rec  ≃  400 s down to ∼240 s on 2010 October 18 (Figure 7 and Table 2).
• 4.  
  Finally, during incursions into the flaring/normal branches near the outburst peak, when T5X2 showed Z source behavior (Altamirano et al. 2010a), neither bursts nor mHz QPOs were detected. These few episodes without bursting activity, which we refer to as regime D, were associated with moderate (∼30%) short (hour-long) drops in L_pers and occurred between MJDs 55486 and 55496 (while L_pers ≳ 0.3 L_Edd). They are noted with square brackets in Table 1.

Interestingly, regimes C and D show similar L_pers (0.3–0.5 L_Edd), but their variability and spectral properties differ (i.e., they constitute different "accretion states"; see D. Altamirano et al. 2012, in preparation). We summarize the main bursting properties of all four regimes in Table 4.

In order to quantify the anticorrelations explained above and to characterize the bursting regimes present in T5X2, we fit the L_peak, E_b, t_rec versus L_pers relations with broken power-law functions. The results are shown in Figure 8 and Table 3, and confirm that the two "breaks" or transitions occur at L_pers  ≃  0.2 L_Edd and L_pers  ≃  0.3 L_Edd. Due to the large scatter some of the fits are statistically poor, yet they allow us to constrain the slope and transition luminosity of the three bursting regimes (Figure 8). Remarkably, the t_rec–L_pers relation that we find in regime B (L_pers ∼ 0.2–0.3 L_Edd) is far from linear, as would be expected from a t_rec ∝ $\dot{m}^{-1}$ relation if $\dot{m}$ ∝ L_pers (see Section 4.1 for further discussion). Instead, it is close to t_rec ∝ L⁻³_pers: we measure a t_rec–L_pers power-law index in regime B of −3.2 ± 0.5 (see further discussion in Section 4). We also calculate the mean alpha parameter (α ≡ L_pers × t_rec/E_b) from the daily-averaged values reported by Linares et al. (2011) and, after applying the bolometric correction we obtained from broadband X-ray spectral fits (Section 2), we find a mean α of 102, with a standard deviation of 27. Figure 9 shows that α increases from ∼60 to ∼120 with increasing L_pers until L_pers  ≃  0.3 L_Edd (regimes A and B), and decreases at higher luminosities (regime C) to again reach values close to 60. Figure 9 also shows the burst duration and rise time as a function of L_pers: the general trend is for bursts to become shorter and have slower rise when L_pers increases.

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In this section we compare in detail the T5X2 burst properties with theoretical predictions. Models of nuclear burning in the envelope of (non-magnetic, non-rotating) accreting NSs predict four different burning regimes on an NS accreting a mixture of hydrogen (H; mass fraction X₀), helium (He; mass fraction Y₀), and heavy elements (mainly CNO, mass fraction Z; see Woosley & Taam 1976; Fujimoto et al. 1981; Taam 1981; Bildsten 1998; Cumming & Bildsten 2000, and references therein). At the highest accretion rates, close to or higher than $\dot{m}_\mathrm{Edd}$, both H and He burn stably and no bursts are expected (Section 4.2). For accretion rates

$$\begin{equation} \dot{m} > \dot{m}_\mathrm{sHb} \simeq 0.008 \dot{m}_\mathrm{Edd}\left(\frac{0.7}{X_0}\right)\left(\frac{Z}{0.01}\right)^{1/2}, \end{equation} \tag{ 1 }$$

(Bildsten 1998; where we assumed an opacity of 0.04 cm² g⁻¹ and the value of $\dot{m}_\mathrm{Edd}$ given in Section 2), H burns stably between bursts at a constant rate, via the so-called (β-limited) hot-CNO cycle (Bildsten 1998; Cumming & Bildsten 2000, and references therein). In this range all bursts are triggered when He burning at the base of the accreted layer becomes thermally unstable (He ignition). The column depth (or density) at the base of the burning layer when ignition occurs is known as ignition depth, y_ign, and the time between bursts is simply $t_\mathrm{rec}=y_\mathrm{ign}/\dot{m}$.

As H burns at a constant rate (temperature and $\dot{m}$ independent, but proportional to Z), the time it takes to consume all H in a sinking fluid element depends only on X₀ and Z:

$$\begin{equation} t_\mathrm{burn}=27 \,\mathrm{hr} \left(\frac{X_0}{0.7}\right)\left(\frac{0.01}{Z}\right) (1+z)/1.31 \end{equation} \tag{ 2 }$$

(as seen by an observer; e.g., Galloway & Cumming 2006), where 1+z = (1–2GM/Rc²)^−1/2 = 1.31 is the gravitational redshift on the surface of a NS with mass M = 1.4 M_☉ and radius R = 10 km. The longest burst recurrence time that we measure in T5X2 is t_rec  ∼  1 hr. For solar abundances this implies that t_rec ≪ t_burn, i.e., there is no time to consume all H between the T5X2 bursts unless the fuel is substantially H-poor and/or metal-rich (see below). In general, for accretion rates

$$\begin{equation} \dot{m} > \dot{m}_\mathrm{dep} \simeq 0.04 \dot{m}_\mathrm{Edd}\left(\frac{0.7}{X_0}\right)\left(\frac{Z}{0.01}\right)^{13/18} \end{equation} \tag{ 3 }$$

(Bildsten 1998; for M = 1.4 M_☉ and R = 10 km), there is no time to burn the accreted H before reaching ignition conditions (i.e., t_rec < t_burn) so that He ignites in a mixture of H and He. In this regime y_ign does not depend sensitively on $\dot{m}$, and a simple $t_\mathrm{rec} \propto \dot{m}^{-1}$ relation is expected. For $\dot{m} < \dot{m}_\mathrm{dep}$ instead, there is enough time to deplete all H before the base of the accreted layer reaches ignition conditions. Bursts are then triggered in the absence of H (pure He ignition). In this regime y_ign decreases with increasing $\dot{m}$, which results in a steeper decline of the burst recurrence time as $\dot{m}$ increases, close to $t_\mathrm{rec} \propto \dot{m}^{-3}$ (Cumming & Bildsten 2000).

This transition between pure He and mixed H/He ignition regimes can be seen in the $E_\mathrm{b}\hbox{--}\dot{m}$ and $t_\mathrm{rec}\hbox{--}\dot{m}$ relations in Figure 11, where we show two semi-analytic models from Cumming & Bildsten (2000) with different compositions. Even though the transition from pure He to mixed H/He ignition is expected at $\dot{m}_\mathrm{dep}\sim 0.05\,\dot{m}_\mathrm{Edd}$ for the case of solar abundances, Figure 11 and Equation (3) clearly show that changes in the accreted composition can increase $\dot{m}_\mathrm{dep}$ by a factor of at least 10. In particular, Figure 11 shows that ignition models with low-H abundance, [X₀ = 0.1, Z = 0.02], can reproduce the change in slope of both the E_b–L_pers and t_rec–L_pers relations that we observe in T5X2 at L_pers  ≃  0.3L_Edd, i.e., at the transition between regimes B and C (Section 3.2, Tables 3 and 4). With such low X₀, H can be depleted before reaching He ignition at accretion rates much higher than in the case of solar abundances, which highlights the importance of fuel composition in the burning regimes.

The average T5X2 accretion-to-burst energy ratio (α = Q_grav(1+z)/Q_nuc), 〈α〉 = 102, corresponds to a total nuclear energy release during the bursts Q_nuc  ≃  2.8 MeV nucleon⁻¹ (see also Motta et al. 2011). Taking Q_nuc = 1.6 + 4〈X〉 MeV nucleon⁻¹ (which assumes complete burning of the accumulated fuel and ∼35% neutrino energy loss; Galloway et al. 2008 and references therein) we find an average H mass fraction over the burning layer 〈X〉  ≃  0.3. Such low inferred Q_nuc lends support to the low-H fraction fuel scenario for T5X2 proposed above. In summary, the slopes of the E_b–L_pers and t_rec–L_pers relations as well as the α values observed during the T5X2 outburst indicate a low accreted H fraction and strongly suggest a transition from the pure He ignition regime to the mixed H/He ignition regime happening during the outburst rise when $\dot{m}$ increases above ∼0.3 $\dot{m}_\mathrm{Edd}$. It is worth noting that the reverse transition is observed during the outburst decay when $\dot{m}$ drops below 0.3 $\dot{m}_\mathrm{Edd}$ (i.e., the outburst rise and decay tracks overlap and no hysteresis is seen in Figures 7 and 8).

We stress that the link between the observed T5X2 bursting regimes and the theoretical burning regimes that we put forward is based on the t_rec–L_pers and E_b–L_pers relations. Modeling and interpretation of the individual burst light curves is beyond the scope of this work, yet we note that different burst light curves and peak luminosities are predicted in the different ignition regimes (e.g., Woosley et al. 2004). Pure He bursts are expected to show faster rise times than mixed H/He bursts. This agrees qualitatively with the identification of regime B as pure He ignition: t_rise is shorter in regime B than in regime C (Figure 9). The large change in L_pers, however, could influence the observed timescales along the burst rise and decay, as these are measured after subtracting the persistent emission. It should also be noted that at low accretion rates (near $\dot{m}_\mathrm{sHb} \,{\simeq}\, 0.08 \dot{m}_\mathrm{Edd}$ for X₀ = 0.1, Z = 0.02) there should be a transition to H-ignited bursts, not included in the models discussed in this section (Cumming & Bildsten 2000).

If the link between bursting and burning regimes that we propose is correct, to our knowledge this is the first time that the transition between pure He and mixed H/He ignition is observed in a single source. There is, however, a systematic and interesting discrepancy evident in Figure 11. Even when including compressional heating or when increasing the base heat flux from the NS crust (up to 2 MeV nucleon⁻¹; fixed at 0.1 MeV nucleon⁻¹ in Figure 11; Cumming & Bildsten 2000), ignition models predict higher burst energies and longer recurrence times than those we find in T5X2, by a factor close to 10 in most cases (i.e., larger than the distance uncertainty on L_pers and E_b, Section 2). This large difference between the observed and predicted values of E_b and t_rec, together with the lack of detailed modeling of the T5X2 burst light curves, prevents a conclusive identification of the observed bursting regimes.

We propose that such discrepancy could be explained by the presence of an extra source of heat in the NS envelope not accounted for by ignition models (which typically consider only hot-CNO heating). Additional heat would act to reduce y_ign and thereby decrease E_b and t_rec, explaining the T5X2 observations presented herein. Several interesting possibilities for the nature of this extra source of heat have been partially investigated, including: (1) heating due to stable He burning (triple alpha reaction rates have been recently debated; e.g., Ogata et al. 2009; Dotter & Paxton 2009; Peng & Ott 2010); (2) heating due to deep burning of residual H (e.g., Taam et al. 1996, who already pointed out that it can lead to weaker and more frequent bursts than expected); (3) thermal inertia, "hot ashes" or heat from previous bursts, which could become important for T5X2 as it features t_rec ∼ 200 s, the shortest recurrence times between thermonuclear bursts ever observed (time-dependent simulations of a series of bursts are needed to investigate this in detail; e.g., Heger et al. 2007b); and (4) turbulent friction at the base of the spreading layer, which could release substantial amounts of heat (Inogamov & Sunyaev 2010). It is worth noting that an independent study of the same source (Degenaar et al. 2011) reached similar conclusions, suggesting the presence of a "shallow heat source" in T5X2 in order to reconcile quiescent observations and crust heating/cooling theory. Without regard to the exact nature of this heat source, we have shown in the present work that the burst properties of T5X2 place new constraints on the thermal properties of a fast-accreting and frequently bursting NS.

The mHz QPOs from T5X2 (Section 3.1; see also Linares et al. 2010a) have distinctive properties that clearly set them apart from the previously known mHz QPOs (Section 1; Revnivtsev et al. 2001; Altamirano et al. 2008). The persistent luminosity that we measure in T5X2 when mHz QPOs are present is about 10 times higher than that observed in previous mHz QPO sources (L_pers higher by a factor of 4–25 taking into account the observed ranges: 0.02–0.1 L_Edd in atoll sources as opposed to 0.4–0.5 L_Edd in T5X2; Table 2). For this reason we refer to the previously known mHz QPOs as "low-L_pers mHz QPOs."

Bright bursts and low-L_pers mHz QPOs alternate, while remaining clearly distinguishable. Instead, in T5X2 bursts smoothly evolve into mHz QPOs and vice versa (Section 3.1), a phenomenon never observed before. Strikingly, the same qualitative evolution from bright infrequent bursts to faint and frequent bursts, mHz QPOs, and ultimately stable burning is predicted to happen as $\dot{m}$ increases by both one-zone models and detailed simulations of nuclear burning on NSs accreting near the boundary between unstable and stable He burning (Heger et al. 2007b). We can therefore identify with confidence the mHz QPOs from T5X2 with marginally stable burning on the NS surface. The evidence that links low-L_pers mHz QPOs with marginally stable burning is less conclusive, but remains valid (see Revnivtsev et al. 2001; Yu & van der Klis 2002; Altamirano et al. 2008 for details).

Analytic estimates place the threshold for stable He burning at

$$\begin{equation} \dot{m}_\mathrm{sb} \simeq 1.1 \dot{m}_\mathrm{Edd}\left(\frac{1.7}{1+X_0}\right)^{3/4}\left(\frac{Y_0 \mu }{0.3\times 0.6}\right)^{1/2}, \end{equation} \tag{ 4 }$$

where μ is the mean molecular weight of the accreted fuel (Bildsten 1998; assuming again M = 1.4 M_☉ and R = 10 km). The persistent luminosity where mHz QPOs are observed in T5X2 (0.4–0.5 L_Edd) is therefore closer to the expected value of $\dot{m}_\mathrm{sb}$ than what was seen in low-L_pers mHz QPOs, yet still inconsistent with the value predicted by theory, which is higher by a factor of ∼2 (unless Terzan 5 is at ∼9 kpc instead of 6.3 kpc, Section 2). Invoking H-poor fuel makes this discrepancy even larger, as it can increase the expected $\dot{m}_\mathrm{sb}$ by a factor two (for X₀ = 0.1, Z = 0.01, Equation (4)). A more massive NS can have unstable burning at higher $\dot{m}$ than a less massive star, but given the weak (M^1/2) scaling of $\dot{m}_\mathrm{sb}$ different NS masses cannot explain the large difference (factor 4–25) in L_pers between T5X2 and the other known sources of mHz QPOs. Another remarkable difference between the mHz QPOs presented herein and the low-L_pers mHz QPOs resides in their fractional rms spectrum (Section 2): we find a fractional rms amplitude that increases with energy between 2 and 20 keV (Section 3.1), while Revnivtsev et al. (2001) reported fractional amplitudes decreasing with increasing photon energy between 2 and 5 keV. The energy-averaged fractional amplitudes are, however, similar (1.3%–2.2% in T5X2; this work; 0.7%–1.9% in low-L_pers mHz QPOs; Revnivtsev et al. 2001). The increase of fractional amplitude with energy that we find is shallower than the linear increase predicted by models of temperature oscillations at the NS surface (developed in the context of burst oscillations; Piro & Bildsten 2006).

An interesting possibility is that the low-L_pers mHz QPOs trace the boundary of stable H burning (Equation (1)), whereas the mHz QPOs that we discovered in T5X2, at a higher accretion rate, occur at the boundary of stable He burning (Equation (4)). This remains speculative at present given the lack of published theoretical work on this particular topic. A specific analysis of oscillatory burning at the thermal stability boundary of H burning is needed to address this hypothesis. The oscillatory behavior at the marginally stable point is generic (Paczynski 1983) and it could also occur when H burning stabilizes. If low-L_pers mHz QPOs do happen at the H-burning stability boundary, the need to invoke confined accretion to explain their low L_pers would vanish.

Heger et al. (2007b) found that the QPO frequency is mainly sensitive to the accreted H fraction (X₀) and the NS surface gravity: increasing the surface gravity or decreasing X₀ leads to higher mHz QPO frequencies. The highest ν_QPO values that we find in T5X2 (4.2 mHz) are about a factor of three lower than those of the low-L_pers mHz QPOs (Table 2; Revnivtsev et al. 2001; Altamirano et al. 2008). If the accreted fuel has a similar composition, and if the mHz QPOs have the same origin, this would suggest a less compact NS in T5X2 than in the low-L_pers mHz QPO sources (the "atoll" sources 4U 1636−536, 4U 1608−52, and Aql X−1). Comparing with models of marginally stable burning, we find that if X₀ < 0.7 the surface gravity of the NS in T5X2 must be g = GM/R² < 1.9 × 10¹⁴ cm s⁻² (Figure 9 in Heger et al. 2007b). Even though it is subject to theoretical (based on analytic one-zone model) and observational (a new outburst of T5X2 could show higher ν_QPO) uncertainties, this illustrates how a comparison between marginally stable burning models and mHz QPO properties can be used to constrain the NS compactness.

Despite the striking similarities between the T5X2 burst properties and the general bursting behavior predicted by models of nuclear burning near the transition from unstable to stable burning (cf. Figure 1 in this work and Figure 5 in Heger et al. 2007b), interesting differences remain. First, as explained above, the $\dot{m}$ where marginally stable burning is expected (0.925 $\dot{m}_\mathrm{Edd}$; Heger et al. 2007b) is higher than the highest inferred $\dot{m}$ where we observe mHz QPOs in T5X2 (0.5 $\dot{m}_\mathrm{Edd}$). Second, Heger et al. (2007b) find a sharp transition from bursts to mHz QPOs and finally stable burning (occurring between 0.923–0.95 $\dot{m}_\mathrm{Edd}$), while we observe in T5X2 a smooth evolution from bursts to mHz QPOs, and vice versa (between 0.1 and 0.5 $\dot{m}_\mathrm{Edd}$; Section 3). Time-dependent simulations of nuclear burning tailored to T5X2 would be of high interest, in particular exploring the H-poor fuel range. Third, we find that the disappearance of the mHz QPOs in T5X2 is not linked to an increase in $\dot{m}$ but to an actual drop of L_pers that happens when the accretion state changes (from horizontal to normal and flaring branches). This suggests that the geometry/configuration of the accretion flow plays a role in setting the nuclear burning stability boundary.

While most models of thermonuclear bursts on accreting NSs assume that the NS magnetic field is negligible (Fujimoto et al. 1981; Taam 1982; Paczynski 1983; Woosley et al. 2004), Joss & Li (1980) showed that the presence of a strong (B  ≳  10¹² G) magnetic field can affect the stability of nuclear burning in different ways. A strong magnetic field reduces the (conductive and radiative) opacities, allowing for more efficient heat transport and thereby stabilizing burning. Applying disk–magnetosphere interaction models to T5X2, Papitto et al. (2011) estimated B = 2 × 10⁸–2.4 × 10¹⁰ G from the luminosity range at which pulsations were detected, whereas Miller et al. (2011) further constrained B = (0.7–4) × 10⁹ G from the Fe line profile. The fact that T5X2 shows thermonuclear bursts suggests that the magnetic field needed to suppress the thermal instability and quench thermonuclear bursts must be greater than ∼10¹⁰ G, in accordance with theoretical expectations (Joss & Li 1980).

A strong magnetic field also affects convective heat transport and mixing (e.g., Joss & Li 1980). Bildsten (1995) proposed that even in cases where thermonuclear burning is unstable the presence of a strong magnetic field can suppress convection in the NS envelope, stalling the propagation of the burning front (diffusive heat transport being slower than convection) and preventing the fast ignition that causes type I X-ray bursts (see also Bildsten 1998). Again, the mere presence of type I X-ray bursts in T5X2 strongly suggests that the magnetic field required to suppress convective burning fronts must be higher than ∼10¹⁰ G, in agreement with analytical estimates (Joss & Li 1980; Bildsten & Brown 1997). Rise times are rather long however (Figure 9), which could perhaps indicate that B is strong enough to slow down the burning fronts (Bildsten & Brown 1997). In summary, the bursting properties of T5X2 presented herein (in particular combined with refined measurements of its magnetic field strength) can place new constraints on the physics of convection and heat transport under intermediate magnetic fields (10⁸–10¹⁰ G).

Finally, a 10⁸–10¹⁰ G magnetic field can also channel the accretion flow onto the magnetic polar caps, as suggested by theoretical models of disk–magnetosphere interaction (Lamb et al. 1973) and by the presence of X-ray pulsations in T5X2 (Strohmayer & Markwardt 2010; Papitto et al. 2011). Accretion confined to the magnetic polar caps may break the spherical symmetry assumed by most thermonuclear burst models, and increase $\dot{m}$ for a given (observed) L_pers (Section 2). The impact on the burning properties depends on the size of the polar caps and on how soon the accreted fuel spreads laterally while sinking into the NS envelope under the influence of a magnetic field. Bildsten & Brown (1997) found that for dipolar magnetic fields B < (2–4) × 10¹⁰ G, the accreted fuel spreads before igniting and the spherically symmetric case is recovered. This suggests that the T5X2 burst properties can still be compared to spherically symmetric ignition models (Section 4.1).

As the size and "depth" of the polar caps are nevertheless ill-constrained quantities, we explore a simple scenario in which the fuel in T5X2 is confined into a 10% of the NS surface down to ignition depth, y_ign. From geometrical considerations, assuming the same y_ign predicted by ignition models (Cumming & Bildsten 2000), in this confined scenario bursts would be 10 times less energetic and 10 times more frequent than in the spherically symmetric case, which would explain the mismatch between predicted and observed E_b and t_rec (Section 4.1). However, the accretion rate per unit area would also increase by a factor 10, which for the observed L_pers implies that unstable burning would operate at $\dot{m}$ as high as ∼5 times $\dot{m}_\mathrm{Edd}$. This is well above the predicted threshold for stable steady burning of H and He ($\dot{m}_\mathrm{sb}$, Equation (4); see also Bildsten 1998), and we therefore consider this scenario unlikely. If the accreted material contains no H, however, $\dot{m}_\mathrm{sb}$ can be several times larger than $\dot{m}_\mathrm{Edd}$ (Bildsten 1998).

The unique bursting behavior in T5X2 is, in essence, much closer to what theory predicts than any other burster known to date. Theoretical burning regimes were mostly based on models that assume a non-rotating NS and radial infall of the accreted mass (Fujimoto et al. 1981; Bildsten 1998). These are admittedly simplistic assumptions, as NSs in LMXBs can have spin frequencies in excess of 600 Hz and the orbital frequencies in the innermost accretion disk are well above 1000 Hz. The accretion of matter with angular momentum onto a spinning NS introduces a shear in its surface layers (Piro & Bildsten 2007; Keek et al. 2009, and references therein). The main effect of rotation which may have an impact on burning regimes is turbulent mixing. In particular, Keek et al. (2009) found that such rotationally induced turbulent mixing stabilizes He burning, decreasing the burning stability boundary ($\dot{m}_\mathrm{sb}$).

Motivated by the stronger magnetic field (factor ∼10) and slower spin (factor ≳20) of T5X2 compared to the rest of bursters, we speculate that rotationally induced turbulent mixing is what sets T5X2 apart from the rest of thermonuclear burst sources. The stronger B field could channel a large fraction of the accreted matter into the NS magnetic poles and produce a more radial inflow which would then spread over the whole surface, minimizing shear, and turbulent mixing. Therefore T5X2 seems to meet to a greater extent the assumptions of zero spin and radial infall mentioned above, which can explain the better agreement with theory. This in turn suggests that, as argued by Piro & Bildsten (2007) and Keek et al. (2009), the effects of rotation must be considered to explain the behavior of most bursters.