---
abstract: 'The *Neutron Star Interior Composition Explorer* ([*NICER*]{}) has extensively monitored the August 2019 outburst of the 401 Hz millisecond X-ray pulsar SAX J1808.4–3658. In this Letter, we report on the detection of a bright helium-fueled Type I X-ray burst. With a bolometric peak flux of $(2.3\pm0.1){\ensuremath{\times 10^{-7}} }$[[erg[s$^{-1}$]{}[cm$^{-2}$]{}]{}]{}, this was the brightest X-ray burst among all bursting sources observed with [*NICER*]{}to date. The burst shows a remarkable two-stage evolution in flux, emission lines at $1.0$ keV and $6.7$ keV, and burst oscillations at the known pulsar spin frequency, with $\approx4$% fractional sinusoidal amplitude. We interpret the burst flux evolution as the detection of the local Eddington limits associated with the hydrogen and helium layers of the neutron star envelope. The emission lines are likely associated with Fe, due to reprocessing of the burst emission in the accretion disk.'
author:
- Peter Bult
- 'Gaurava K. Jaisawal'
- 'Tolga G[ü]{}ver'
- 'Tod E. Strohmayer'
- Diego Altamirano
- Zaven Arzoumanian
- 'David R. Ballantyne'
- Deepto Chakrabarty
- Jérôme Chenevez
- 'Keith C. Gendreau'
- Sebastien Guillot
- 'Renee M. Ludlam'
title: 'A NICER thermonuclear burst from the millisecond X-ray pulsar SAX J1808.4–3658'
---

Introduction {#sec:intro}
============

The proto-typical accreting millisecond X-ray pulsar (AMXP) SAX J1808.4–3658 (hereafter [SAX J1808]{}), was first discovered through the detection of a thermonuclear (Type I) X-ray burst with the *BeppoSAX* satellite in September 1996 [@Zand1998]. With X-ray outbursts recurring every $2-4$ years, this source has been extensively monitored ever since, leading to the first detection of accretion-powered millisecond pulsations [@Wijnands1998a], and the confirmation that X-ray burst oscillations correspond with the stellar spin frequency [@Chakrabarty2003].

In each of the eight outbursts from [SAX J1808]{}that occurred between 1996 and 2015, at least one X-ray burst has been detected [@Zand2001a; @Bult2015b; @Patruno2017b; @Sanna2017c]. The majority of these bursts showed burst oscillations [@Bilous2019] and were observed near peak luminosity of their respective outbursts, when the accretion rate was $\approx(3-5){\ensuremath{\times 10^{-10}} }$[$M_{\odot}$]{}[yr$^{-1}$]{} [@Bult2015b]. Detailed modelling of a well sampled burst train observed with the *Rossi X-ray Timing Explorer* ([*RXTE*]{}) in October 2002 [@Galloway2006] demonstrated that these events are examples of X-ray bursts in the “delayed helium" regime [@Narayan2003; @Galloway2017]. In brief, these bursts are due to a thermonuclear flash in a nearly pure helium layer of the neutron star envelope. This layer of helium builds up on a timescale of one to a few days, through a stable $\beta$-limited CNO cycle at the base of a hydrogen layer. The hydrogen layer, in turn, is replenished by the continuous accretion of gas supplied by a hydrogen-rich brown dwarf companion star, which resides in a 2.01 hour orbit around the pulsar [@Chakrabarty1998; @Bildsten2001].

The X-ray bursts of [SAX J1808]{}have also reliably shown photospheric radius expansion (PRE; see, e.g., @Galloway2008, for a review). Such PRE may drive the ejection of burning ashes, whose presence could cause discrete spectral features in the burst emission [@Weinberg2006; @Yu2018]. Measuring such spectral lines gives a window into the thermonuclear burning reactions, and can potentially be used to constrain the neutron star compactness. Additionally, a large fraction of the burst emission is expected to be intercepted and reprocessed by the accretion disk [@Ballantyne2005; @Degenaar2018; @Fragile2018], providing an opportunity to characterize the state of the accretion disk through the spectrum of the reflected burst emission.

Launched in June 2017, the *Neutron Star Interior Composition Explorer* ([*NICER*]{}; @Gendreau2017) combines good spectral resolution with superb time-resolution and high throughput in the ${0.2-12}$[[keV]{}]{}energy band. These properties make [*NICER*]{}an ideal instrument to study the evolution of PRE in Type I X-ray bursts [see, e.g., @Keek2018b; @Keek2018a; @Jaisawal2019], and search for discrete spectral features [@Strohmayer2019]. Hence, when [SAX J1808]{}began a new outburst in August 2019 [@ATelRussell19; @ATelGoodwin19; @ATelParikh19c; @ATelBult19c], we triggered an extensive [*NICER*]{}monitoring campaign. During this campaign we detected two X-ray bursts; the first occurred on August 9 and was relatively faint, the second was seen on August 21 and was much brighter. In this Letter we report on the unusual properties of the August 21 X-ray burst. The detailed analysis of the earlier burst and the full [*NICER*]{}campaign will be presented elsewhere.

Observations {#sec:observations}
============

On 2019 August 21 at 02:04 UTC, [*NICER*]{}observed a bright X-ray burst from [SAX J1808]{}. These data are available under the [*NICER*]{}ObsID 2584010501. We processed the data using <span style="font-variant:small-caps;">nicerdas</span> v6a, which is packaged with <span style="font-variant:small-caps;">heasoft</span> v6.26. We applied standard screening criteria, keeping only those time intervals when the pointing offset was $<54\arcsec$, the Earth limb elevation angle was $>15\arcdeg$, the elevation angle with respect to the bright Earth limb was $>30\arcdeg$, and the instrument was outside of the geographic region of the South Atlantic Anomaly. Additionally, standard background screening criteria were applied, which reject all epochs where the rate of saturating particle events (overshoots) is greater than $1$[ct[s$^{-1}$]{}]{}[detector$^{-1}$]{}, or greater than 1.52 \* <span style="font-variant:small-caps;">cor\_sax</span>$^{-0.633}$, where <span style="font-variant:small-caps;">cor\_sax</span>[^1] gives the cut-off rigidity of the Earth’s magnetic field, in units of GeV[c$^{-1}$]{}. We then applied the <span style="font-variant:small-caps;">barycorr</span> tool to correct the observed event times to the Solar System barycenter, where we used the JPL DE405 planetary ephemeris [@Standish1998] and the optical coordinates of @Hartman2008. Finally, we estimated the background contributions to our data from [*NICER*]{}observations of the [*RXTE*]{}blank-field regions [@Jahoda2006].

Analysis and Results {#sec:results}
====================

The X-ray burst onset, $t_0$, occurred on MJD 58716.089362 TDB, which was $442{{\rm\,s}\xspace}$ into a $1063{{\rm\,s}\xspace}$ continuous exposure. In the following we focus our analysis on this exposure and express all times with respect to the noted onset time.

Light curve and phenomenology
-----------------------------

At $t_0$ the $0.3-10$ keV count-rate increased rapidly from an averaged $125$ [ct[s$^{-1}$]{}]{}to $\approx34,000$[ct[s$^{-1}$]{}]{}over a timespan of $\approx4.3{{\rm\,s}\xspace}$. The peak rate was maintained for $\approx3.6{{\rm\,s}\xspace}$, before the burst began to decay. The subsequent decay progressed on a minute-long time scale: at $t\simeq64{{\rm\,s}\xspace}$ the burst rate had dropped to below 5% of the peak rate, and by the end of the available exposure, at $t=621{{\rm\,s}\xspace}$, the source flux had fallen to $172$ [ct[s$^{-1}$]{}]{}. [ While this rate was slightly higher than the averaged preburst rate, the preburst light curve showed a modest upward trend. If we fit this trend with a linear function, then we find that the burst rate decayed to the extrapolated intensity at $t\simeq580{{\rm\,s}\xspace}$. ]{}

Two unusual features stand out in the burst light curve (Figure \[fig:lc\]). First, it shows a pronounced double peaked structure, with a local minimum of $\approx15,000$[ct[s$^{-1}$]{}]{}at $t\simeq13.1{{\rm\,s}\xspace}$ and a secondary peak of $\approx16,500$[ct[s$^{-1}$]{}]{}at $t\simeq15.5{{\rm\,s}\xspace}$. While double-peaked X-ray bursts have commonly been observed, these structures are usually caused by PRE: the temperature of the photosphere temporarily shifts out of the instrument passband, causing an apparent dip in the observed X-ray rate [@Grindlay1980]. Given its low-energy coverage, [*NICER*]{}is able to follow the temperature of the photosphere throughout the PRE phase, so any observed dip in the light curve is likely due to a dip in bolometric flux [@Keek2018b; @Jaisawal2019]. We investigate this in Section \[sec:time resolved\].

Second, there is a noticeable pause during the rise to the first peak. Initially the flux increases rapidly; however, between $t\simeq0.6{{\rm\,s}\xspace}$ and $t\simeq1.3{{\rm\,s}\xspace}$, this rise briefly stalls, with the count-rate remaining constant at $\approx13,600$[ct[s$^{-1}$]{}]{}. After this pause, the rate continues to increase toward the maximum, albeit at a slightly slower pace (Figure \[fig:lc\], inset of top panel). Simultaneously, the hardness ratio (the $3-10$[[keV]{}]{}rate over the $0.3-1$[[keV]{}]{}rate) evolves dramatically. As the count-rate begins to rise, the hardness ratio spikes. Subsequently, the hardness briefly dips, and then stabilizes. It is during the dip that the pause in count-rate is observed. Additionally, the previously mentioned dip in count-rate (at $t\simeq13{{\rm\,s}\xspace}$), coincides with a similar dip in the hardness ratio, suggesting these two features are related.

![ Top: light curve of the X-ray burst from [SAX J1808]{} at $0.1{{\rm\,s}\xspace}$ time-resolution in the $0.3-10$ keV energy band. Bottom: hardness ratio, defined as the $3-10$ keV rate divided by the $0.3-1$ keV rate. Inset: first four seconds of the same data, with the light curve in black (connected line, units of $\times10^{4}$[ct[s$^{-1}$]{}]{}) and the hardness ratio in red (vertical dashes). All panels are relative to $t_0=58716.089362$TDB. Vertical gray lines were added to guide the eye. []{data-label="fig:lc"}](burst-light-curve.pdf){width="\linewidth"}

Pre-burst emission {#sec:preburst}
------------------

We extracted a spectrum from $400{{\rm\,s}\xspace}$ prior to the burst and modelled it in <span style="font-variant:small-caps;">xspec</span> v12.10 [@Arnaud1996]. Following @DiSalvo2019, we find that the spectrum could be well described with the model

> `tbabs( diskbb + nthcomp )`,

where the `tbabs` interstellar absorption model [@Wilms2000] was used with the photoelectric cross-sections of @Verner1996, `diskbb` [@Makishima1986] is a multi-color disk blackbody component, and `nthcomp` [@Zdziarski1996; @Zycki1999] is a thermal Comptonization component. We used an absorption column density of $N_H =
  2.1{\ensuremath{\times 10^{21}} }$[cm$^{-2}$]{} [@Papitto2009; @DiSalvo2019], and electron temperature of [30]{}keV [@DiSalvo2019]. We further tied the `nthcomp` photon seed temperature to the disk temperature. Our best-fit had a reduced $\chi^2$ ([$\chi^2_r$]{}) of 1.04 for 375 degrees of freedom (dof), yielding an inner disk temperature of $kT=0.70\pm0.07$ keV and a power-law photon index of $\Gamma=2.0\pm0.4$. Using the `cflux` model we further measured the unabsorbed $1-10$ keV flux to be $(2.85 \pm
  0.05){\ensuremath{\times 10^{-10}} }\,{{\rm erg{\,s\ensuremath{^{-1}}\xspace}{\,cm\ensuremath{^{-2}}\xspace}}\xspace}$, from which we extrapolate a bolometric flux ($0.01-100$keV) of [$(4.7 \pm 0.5){\ensuremath{\times 10^{-10}} }\,{{\rm erg{\,s\ensuremath{^{-1}}\xspace}{\,cm\ensuremath{^{-2}}\xspace}}\xspace}$]{}. Assuming a distance of $3.5$kpc [@Galloway2006], a 1.4[$M_{\odot}$]{}neutron star mass, and a 10km radius, this corresponds to a mass accretion rate of $\dot M =
  2.9{\ensuremath{\times 10^{-11}} }\,{\ensuremath{M_{\odot}}\xspace}$[yr$^{-1}$]{}, which is $\approx0.3\%$ of the Eddington rate.

Burst spectroscopy {#sec:spectra}
------------------

![ Top: burst spectra at four epochs during the X-ray burst. Bottom: the residuals of the best fit models, showing the ratio of the data over the model prediction. In each case we have set the normalization of the emission line components to zero, which highlights these lines in the residuals. []{data-label="fig:spectra"}](burst-spectral-comparison.pdf){width="\linewidth"}

We investigated the spectral shape of the burst emission by extracting a spectrum from a $4{{\rm\,s}\xspace}$ interval at the peak of the burst (Figure \[fig:spectra\]). We first attempted to model this spectrum by adding a blackbody component to the preburst spectrum model, holding all parameters except for those of the blackbody constant. At a ${\ensuremath{\chi^2_r}\xspace}$ of $28$ for 631 dof, this model failed to account for a large excess below 1.5 keV and above 5 keV.

In an attempt to account for the residuals we applied a free scaling factor to the components describing the preburst spectrum [@Worpel2013], so that our model was

> `tbabs(bbodyrad + f(diskbb + nthcomp))`,

where `bbodyrad` is a blackbody component with its normalization proportional to surface area. At a [$\chi^2_r$]{}of 5.4 for 630 dof, this model failed to remove the large residuals. Additionally, at $f=159$, the magnitude of the obtained scaling factor is not realistic, as it is much larger than the ${f\sim2-10}$ that is typically observed [@Worpel2013].

In an alternative approach to account for the large soft excess, we adopted a model consisting of the fixed preburst model plus two blackbody components. This model provided a much better description of the data ([$\chi^2_r$]{}of 1.11 for 628), yielding a blackbody with $0.233\pm0.003$keV and $318\pm5$km for the soft excess, and $1.83\pm0.03$keV and $14.7\pm0.3$km for the higher energy emission (presumably the photosphere). Some structure still remained in the residuals, most prominently at 1.0keV and 6.5keV. The fit was significantly improved ([$\chi^2_r$]{}of 1.07 for 624 dof) by adding a `diskline` component [@Fabian1989] at $6.7_{-0.3}^{+0.1}$keV, along with a Gaussian line at $1.05\pm0.02$keV. The signal strength of the `diskline` was insufficient to reliably constrain the disk radius and inclination, giving respective limits of $<13\,r_g$ and $>65\arcdeg$. Instead, we fixed the inner radius to $11\,r_g$, which is the approximate magnetospheric radius [@Bult2015b], and the inclination to $65\arcdeg$, which is within the range allowed by modelling of the FeK line in the persistent emission of [SAX J1808]{}. We further note that while this inclination is inconsistent with the $\leq30\arcdeg$ limit derived by @Galloway2006, a more sophisticated analysis of the same burst data yield $69_{-2}^{+4}\arcdeg$ [@Goodwin2019]. With these parameters held constant, we obtained a line normalization of $0.62\pm0.16$[[ph[cm$^{-2}$]{}[s$^{-1}$]{}]{}]{}. Meanwhile, the 1[[keV]{}]{}Gaussian line had a normalization of $0.27\pm0.07$[[ph[cm$^{-2}$]{}[s$^{-1}$]{}]{}]{}and standard deviation of $0.05_{-0.02}^{+0.07}$keV.

In an attempt to apply a physical foundation to our modelling of these data, we also fit the spectrum using the reflection models of @Ballantyne2004b. This overall model is summarized as

> `tbabs( bbodyrad + diskbb + nthcomp + rdblur*atable{reflection} )`

where `rdblur` is a convolution component that applies the relativistic effects associated with an accretion disk around a compact object, and the `reflection` component tabulates reflection spectra calculated for a hydrogen density of $n_H=10^{18}\,{\rm cm}^{-3}$, using a grid in temperature ($kT$), ionization ($\log \xi$), and Fe abundance ($\log
  {\rm Fe}$). As before, we kept the parameters for the absorption column and preburst components fixed. The temperature parameter of the reflection table was linked to the blackbody temperature, and the `rdblur` parameters were identical to those of the `diskline` component discussed above. This model yielded a reasonable description of the continuum ([$\chi^2_r$]{}of 1.2 for 628 dof), but left a large residual at 1 keV. Adding in a Gaussian component gave a good fit to the data at a [$\chi^2_r$]{}of 0.95 for 633 dof, with a normalization of $0.86\pm0.15$[[ph[cm$^{-2}$]{}[s$^{-1}$]{}]{}]{}and standard deviation $0.09\pm0.02$[[keV]{}]{}. The best-fit parameters for the reflection component were $\log \xi=3.79_{-0.08}^{+0.11}$, $\log {\rm Fe}=0.51_{-0.24}^{+0.10}$, and an unabsorbed bolometric reflection flux of $(1.87\pm0.13){\ensuremath{\times 10^{-7}} }$[[erg[s$^{-1}$]{}[cm$^{-2}$]{}]{}]{}, indicating the reflection fraction is $F_{\rm refl} / F_{\rm bb} \approx2.3$. Finally, we note that in this model, the photosphere blackbody had a temperature of $2.05\pm0.06$keV and a radius of $6.6\pm0.7$km. While the temperature is consistent with the double blackbody model, the radius is significantly smaller.

The double blackbody and reflection models both provide a statistically acceptable description of the spectrum, and give a roughly equivalent interpretation. Since the double blackbody model is phenomenologically simpler, it can be fit robustly to much shorter integration times, yielding a higher time resolution view of the spectral evolution in the burst. In the following we will therefore focus our analysis on this model.

We extracted spectra from three other distinct time intervals during the burst: the pause (0.6[[s]{}]{}), the dip (0.7[[s]{}]{}), and the second peak (2[[s]{}]{}). Each spectrum could be described with the double blackbody spectrum plus $6.7$[[keV]{}]{}`diskline` component. The second peak additionally required an emission line at 1 keV. These spectra are shown in Figure \[fig:spectra\] and their best-fit parameters are listed in Table \[tab:spectra\].

[ l l l C C C C ]{} & & & & & &\
Soft blackbody & temperature & keV & 0.2330.003 & 0.2280.007 & 0.2100.005 & 0.220.01\
Soft blackbody & normalization & km & 318 5 & 24017 & 29718 & 23631\
Hard blackbody & temperature & keV & 1.830.03 & 2.50.2 & 2.520.14 & 1.990.11\
Hard blackbody & normalization & km & 14.70.3 & 6.20.5 & 6.80.4 & 10.50.7\
Gaussian line & line energy & keV & 1.050.02 & & & 1.050.02\
Gaussian line & standard deviation& keV & 0.05\_[-0.02]{}\^[+0.07]{}& & & 0.070.02\
Gaussian line & normalization & [[ph[cm$^{-2}$]{}[s$^{-1}$]{}]{}]{}& 0.270.07 & & & 0.260.07\
diskline & line energy & keV & 6.7\_[-0.3]{}\^[+0.1]{} & 6.70.1 & 6.70.1 & 6.80.1\
diskline & inclination & degrees & 65 & 65 & 65 & 65\
diskline & inner radius & GM/c$^2$& 11 & 11 & 11 & 11\
diskline & normalization & [[ph[cm$^{-2}$]{}[s$^{-1}$]{}]{}]{}& 0.620.16 & 0.470.14 & 0.50.2 & 0.450.16\
[$\chi^2_r$]{}/ dof & & & 1.07/624 & 1.13/182 & 1.05/264 & 1.17/487\

Time-resolved spectroscopy {#sec:time resolved}
--------------------------

To investigate the full spectral evolution of the X-ray burst, we applied high-resolution time-resolved spectroscopy. We extracted [133]{} spectra from dynamically allocated intervals. Each interval was constructed to have at least [0.125[[s]{}]{}]{} of exposure, and was increased as needed to include a minimum of [2000]{} counts. Each spectrum was then fit using the double blackbody model. For simplicity we did not include emission line components, giving in slightly poorer fit statistics. The resulting evolution in spectral parameters is shown in Figure \[fig:time resolved\].

The time resolved spectroscopy demonstrates that the hot ($\approx2$keV) blackbody in our model can be understood as the emission from a neutron star photosphere that undergoes PRE between $t\simeq1{{\rm\,s}\xspace}$ and $t\simeq13{{\rm\,s}\xspace}$. The radius expansion is moderate, reaching a maximum radius of $\approx15$km. The cool ($\approx0.2$keV) blackbody, on the other hand, maintains a stable temperature through the burst, with its emitting area closely tracking the evolution of the overall flux. This trend further supports the idea that the soft excess tracks an interaction between the burst emission and the neutron star environment, such as the disk reflection model discussed in Section \[sec:spectra\].

Considering the bolometric flux, we see that the burst emission reaches a stable peak of $(2.40\pm0.12){\ensuremath{\times 10^{-7}} }$[[erg[s$^{-1}$]{}[cm$^{-2}$]{}]{}]{}when the photosphere is at its largest extent. As the photosphere begins to contract, the flux begins to decrease. This cooling trend, however, is interrupted at $t\simeq15.5$. In the following $\approx3{{\rm\,s}\xspace}$, we see the bolometric flux holding constant, causing an excess over the cooling trend that coincides exactly with the second peak observed in the light curve. Hence, the spectroscopy confirms that the dip and second peak seen in the light curve are indeed astrophysical in origin rather than a passband effect.

Finally, we note a peculiar feature in the spectroscopic results: the temperature evolution of the photosphere shows two peaks, marking the start and end of the PRE phase. These start and end times coincide with the pause and the dip, respectively. Furthermore, both the pause and the dip have the same bolometric flux level of $(1.43\pm0.09){\ensuremath{\times 10^{-7}} }$[[erg[s$^{-1}$]{}[cm$^{-2}$]{}]{}]{}.

![ Time-resolved spectroscopy of the X-ray burst using a double blackbody model. The top panel shows the estimated bolometric flux, the middle four panels show the time evolution of the spectral parameters describing the burst emission (radii were calculated using a distance of 3.5kpc), and the bottom panel gives the reduced $\chi^2$ fit statistic. The grey band indicates the time interval where burst oscillations were detected. See text for further details. []{data-label="fig:time resolved"}](time-resolved-spectroscopy.pdf){width="\linewidth"}

Burst oscillations {#sec:oscillations}
------------------

To search for burst oscillations, we constructed a $1/8192{{\rm\,s}\xspace}$ time-resolution light curve in the $0.3-10$ keV energy band. We then searched for coherent oscillations in a [10]{}Hz region centered on the known 401Hz pulsar spin frequency by applying a sliding window search method [see, e.g., @Bilous2019 and references therein]. Specifically, we used window sizes of $T=1,2,{\rm~and~} 4{{\rm\,s}\xspace}$, with strides of $T/10{{\rm\,s}\xspace}$. For each window position, we computed a power spectrum and searched for a signal power in excess of the expected noise distribution [@Klis1989]. We detected a significant oscillation ($>3\sigma$) in all windows between $t=17.7{{\rm\,s}\xspace}$ and $t=24.6{{\rm\,s}\xspace}$. The fractional sinusoidal amplitude[^2] of the burst oscillation was $(4.0\pm0.6)\%$, while the oscillation frequency was $401$Hz and did not show any significant drift.

Given the stability of the burst oscillation frequency, we folded the event times within the noted epoch on the pulsar spin period to obtain a waveform for the burst oscillation. For comparison, we also extracted the waveform of the persistent pulsations from the full ObsID, excluding the burst emission (see @ATelBult19c for a preliminary ephemeris). Both waveforms are shown in Figure \[fig:bo\]. The burst oscillation has a similar profile and amplitude as the persistent pulsation, but appears to lead the pulse by $34\arcdeg\pm7\arcdeg$.

[ To resolve the burst oscillation with respect to photon energy, we applied a sliding window to the instrument energy channel space, using a window size of 100 channels and strides of 10 channels. At each window position, we folded the selected data and measured the burst oscillation amplitude and phase. We then repeated this method for the non-burst data. The resulting amplitude spectra are shown in Figure \[fig:bo-spectrum\]. Although the averaged profiles are similar, the energy dependence of the burst oscillation is very different from that of the pulsar. Particularly notable is that the burst oscillation amplitude is mostly constant below $\approx5$keV, but rises sharply at $6-7$keV. ]{}

![ Waveform of the burst oscillation observed in [SAX J1808]{}, compared to the waveform of the accretion-powered pulsation as seen outside the X-ray burst interval. []{data-label="fig:bo"}](bo-waveform.pdf){width="\linewidth"}

![ Top: energy dependence of the burst oscillation waveform. Bottom: same for the persistent pulsation observed outside the X-ray burst interval. Note that these data were computed using a sliding window, so adjacent points are correlated. Additionally, in order to look for decohering noise, we plot the waveform phase even if the amplitude is not formally significant. See text for further details. []{data-label="fig:bo-spectrum"}](dynamic-energy-spectra.pdf){width="\linewidth"}

Discussion {#sec:discussion}
==========

We detected a bright X-ray burst from [SAX J1808]{}with [*NICER*]{}. The burst showed a peculiar light curve, with a notable pause during the rise and a double-peaked structure. Additionally, we detected significant burst oscillations in the cooling tail of the burst and emission features in the burst spectrum. We now discuss each of these findings.

Reflection
----------

We find that the burst spectrum shows a strong excess at the lowest energies that requires the inclusion of a second blackbody in the spectral model. A similar strong soft excess was previously observed in [SAX J1808]{}by @Zand2013. In contrast to that work, however, we also observe emission features at 1 keV and 6.7keV. A similar complex of emission features has been seen in the intermediate-duration X-ray bursts from IGR J17062–6143 [@Degenaar2013; @Keek2017], which were associated with ionized FeL and FeK emission lines. Thus, the detection of these lines provides strong evidence that we are seeing the burst emission reflected from the accretion disk. Applying a physically motivated disk reflection model to our data (Section \[sec:spectra\]) indicates that such a reflection component provides a satisfactory description of the soft excess, but cannot fully account for the emission feature observed at 1keV. We suggest that this may be due to the presence of additional elements not currently incorporated in these models (e.g. Ne). Additionally, this model fit indicated a strong reflection signal, which may indicate that the accretion disk structure is significantly impacted by the burst [@He2016; @Fragile2018].

Spectral evolution
------------------

The X-ray burst light curve shows a double-peaked structure. Given that the second peak in count-rate occurs after the PRE phase, and that this peak is reproduced (albeit less prominently) in the bolometric flux, we conclude that this feature is astrophysical in origin. A very similar double-peaked structure in an X-ray burst from 4U 1608–52 was recently observed with [*NICER*]{}[@Jaisawal2019]. Although that burst showed a hotter photosphere and lacked the strong soft excess that we detect in [SAX J1808]{}, the rebrightening phase is nearly identical in both bursts. In each case, the end of the PRE phase coincides with a pronounced dip in count-rate, and is followed by a secondary peak.

@Jaisawal2019 considered a number of plausible origins for the rebrightening of the burst flux, including the ignition of fresh material [@Keek2017b], stalled thermonuclear flame spreading [@Bhattacharyya2006], and waiting points in the rp-process [@Fisker2004]. Our observation of rebrightening in the X-ray burst from [SAX J1808]{}does not rule out any of these proposed explanations. It does, however, add two new perspectives: first, in [SAX J1808]{}the rebrightening coincides with the onset of burst oscillations, which may be difficult to reconcile a flame spreading model. Second, in [SAX J1808]{}the dip appears related to the pause during the rise. If this relation is real, then whatever physical mechanism underpins these features may also be related to the rebrightening.

Burst Oscillations {#burst-oscillations}
------------------

We found that the X-ray burst shows burst oscillations at the expected 401 Hz spin frequency. Comparing these oscillations with the accretion-powered pulsations, we find that the two waveforms are remarkably similar, but the burst oscillations lead the pulsations by [$34\arcdeg\pm7\arcdeg$]{}. Similar results were reported from [*RXTE*]{}observations of burst oscillations in [SAX J1808]{}observed during the cooling phase of an X-ray burst [@Chakrabarty2003]. The fact that the burst oscillations are so closely matched to the persistent pulsations in terms of their waveform, suggests that both must arise from geometrically similar, if not the same, confined emitting region (hot-spot) on the stellar surface. With this in mind, it is interesting to note that the [*NICER*]{}data indicate the waveform energy dependence of the burst oscillations is quite different from that of the persistent pulsations. Some of the difference may simply arise from the strong reflection component, which is likely not pulsed, and thus is expected to dilute the measured burst oscillation amplitude at low energies. A detailed spectral-timing analysis may be able to determine how much each of the spectral components is oscillating. Such an analysis, however, is beyond the scope of this initial work.

Eddington limits
----------------

Finally, we note that our analysis of the light curve, the spectral evolution, and the timing behavior all indicate that each time interval where the [*NICER*]{}count-rate of [SAX J1808]{}is between 13,000 [ct[s$^{-1}$]{}]{}and 14,000 [ct[s$^{-1}$]{}]{}is somehow special. At these count rates, the burst rise pauses, the dip reaches its minimum, and burst oscillations appear. The bolometric flux measured at these times was $(1.43\pm0.09){\ensuremath{\times 10^{-7}} }$[[erg[s$^{-1}$]{}[cm$^{-2}$]{}]{}]{}, which corresponds to a luminosity of $(2.08\pm0.13){\ensuremath{\times 10^{38}} }$[[erg[s$^{-1}$]{}]{}]{}. We note that this luminosity is consistent with the expected local Eddington limit of a hydrogen envelope of a neutron star [@Lewin1993].

For spherically symmetric emission, the Eddington luminosity as measured by the observer is predicted as [@Lewin1993; @Suleimanov2017] $$L_{\rm edd} = \frac{4\pi GMc}{\kappa_{\rm T}}\frac{1}{(1+z)},$$ where $M$ is the neutron star mass, $G$ the gravitational constant, $c$ the speed of light, and $z$ the gravitational redshift. Finally, $\kappa_{\rm T}=0.2(1+X)\,{\rm cm}^2$[g$^{-1}$]{} is the Thomson electron scattering opacity, with $X$ the hydrogen abundance in the atmospheric layer. Hence, we expect that the flux level at which PRE occurs differs depending on the material composition of the neutron star envelope. For a hydrogen layer with cosmic abundances ($X=0.73$), the predicted luminosity is $\approx2.0{\ensuremath{\times 10^{38}} }$[[erg[s$^{-1}$]{}]{}]{}, whereas the luminosity of a pure helium layer ($X=0$) is larger by a factor of 1.73. In [SAX J1808]{}, the ratio in bolometric flux between the peak and pause/dip is $1.68\pm0.13$.

The following scenario now emerges for the X-ray burst evolution. As the critical ignition point is reached in the helium layer, the flame front quickly spreads across the stellar surface and an intense radiation field starts to diffuse outward. After about 0.5[[s]{}]{}, the radiation pressure reaches the local Eddington limit of the hydrogen layer, causing that layer to expand. Meanwhile, the intensity of the radiation field continues to increase, either expelling or diluting the hydrogen layer, so that the observed spectrum becomes dominated the PRE of the helium layer. Over the following 10[[s]{}]{}, we observe the full helium PRE cycle, causing the photosphere to cool and then heat, as the envelope expands and then contracts. Once the envelope touches back down on the stellar surface, the burst flux is still comparable to hydrogen Eddington limit, although at the time this touchdown occurs, there will likely have been some mixing of the atmospheric layers. Subsequently, the photosphere cools, while the radius grows, and then, after about $4-5{{\rm\,s}\xspace}$, the rebrightening mechanism activates and quickly thereafter the burst oscillations appear. The photosphere continues to cool, and after about 10[[s]{}]{}both the rebrightening and oscillations switch off.

The flux levels of the pause and peak are highly suggestive that we are seeing both the hydrogen and helium Eddington limits in a single X-ray burst. The evolution of the hardness ratio around the pause further supports the interpretation that this stall in the rise is related to the expanding hydrogen layer. The link between the pause and the dip is weaker, but highly suggestive, and may yet provide the insight required to uncover the physics behind intrinsic rebrightening during the tail of an X-ray burst.

This work was supported by NASA through the [*NICER*]{}mission and the Astrophysics Explorers Program, and made use of data and software provided by the High Energy Astrophysics Science Archive Research Center (HEASARC). P.B. was supported by an NPP fellowship at NASA Goddard Space Flight Center. D.A. acknowledges support from the Royal Society.

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[^1]: The <span style="font-variant:small-caps;">cor\_sax</span> parameter is based on a model for the cut-off rigidity that was originally developed for the *BeppoSAX* satellite, and has no specific relation to [SAX J1808]{}.

[^2]: Sinusoidal amplitudes are a factor of $\sqrt{2}$ larger than fractional rms amplitudes.
