Spectral-Timing Analysis of the Lower kHz QPO in the Low-Mass X-ray Binary Aquila X-1
DD RAFT VERSION O CTOBER
17, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
SPECTRAL–TIMING ANALYSIS OF THE LOWER KHZ QPO IN THE LOW-MASS X-RAY BINARY AQUILA X-1 J ON S. T
ROYER , E DWARD
M. C
ACKETT Department of Physics & Astronomy, Wayne State University, 666 W. Hancock St, Detroit, MI 48201, USA
Draft version October 17, 2018
ABSTRACTSpectral–timing products of kilohertz quasi-periodic oscillations (kHz QPOs) in low–mass X-ray binary(LMXB) systems, including energy- and frequency-dependent lags, have been analyzed previously in 4U 1608-52, 4U 1636-53, and 4U 1728-34. Here, we study the spectral–timing properties of the lower kHz QPO of theneutron star LMXB Aquila X-1 for the first time. We compute broadband energy lags, as well as energy-dependent lags and the covariance spectrum using data from the
Rossi X-ray Timing Explorer (RXTE). We findvery similar characteristics to other previously studied systems, including soft lags of ∼ µ s between the 3.0– 8.0 keV and 8.0 – 20.0 keV energy bands at the average QPO frequency. We also find lags that show a nearlymonotonic trend with energy, with the highest energy photons arriving first. The covariance spectrum of thelower kHz QPO is well fit by a thermal Comptonization model, though we find a higher seed photon tempera-ture compared to the mean spectrum, which was also seen in Peille et al. (2015), and indicates the possibilityof a composite boundary layer emitting region. Lastly, we see in one set of observations, an Fe K componentin the covariance spectrum at 2.4- σ confidence which may raise questions about the role of reverberation in theproduction of lags. Subject headings: accretion, accretion disks — stars: neutron — X-rays: binaries — X-rays: individual (AqlX-1) INTRODUCTIONAccretion of matter onto compact objects (black holes andneutron stars) offers an avenue to study the effects of stronggravity as well as potentially constrain the mass and size-scaleof these ultra-dense objects. Accreting neutron stars and blackholes occur in binary systems in which the companion acts asa matter donor. In low-mass X-ray binary systems (LMXB) –systems where the companion star has a mass ≤ M (cid:12) – thecompanion star overflows its Roche lobe and matter is trans-ferred from the companion to the compact object via accre-tion. See van der Klis (2000) for a more detailed overviewof accretion and oscillations in LMXB systems. The distancescale of the inner accretion flow is expected to be on the orderof the neutron star radius. This implies dynamical velocitiesand timescales of the order of (cid:39) .
5c and (cid:39) µ s respec-tively (van der Klis 2000; Wagoner 2003). We therefore ex-pect signals that carry the causal signatures of this region tohave the same timescale. The shortest timescale (highest fre-quency) oscillations observed are the kilohetrz quasi-periodicoscillations (kHz QPOs).kHz QPOs were discovered shortly after the launch ofNASA’s Rossi X-ray Timing Explorer (RXTE) (Bradt et al.1993) in December 1995. See van der Klis (1998) for a his-tory of the early days of RXTE’s discoveries of kHz QPOs.The discovery of two distinct kHz QPOs in nearly every neu-tron star LMXB system containing QPOs led to twin kHzQPO becoming a signature of neutron star systems (van derKlis 2006). The QPOs occur in the 300 - 1200 Hz range andwere quickly thought to be associated with orbital frequen-cies of the inner accretion flow - a characteristic shared by amajority of the models that attempt to explain the origin ofkHz QPOs (Miller et al. 1998; Stella & Vietri 1999; Lamb &Miller 2001). However, there are models that do not associatethe kHz QPOs with the orbital frequencies of the inner ac- [email protected] cretion flow (see e.g., Lee et al. 2001; Kumar & Misra 2014,2016). See van der Klis (2000, 2006) for a review of variouskHz QPO models.Since kHz QPOs occur on timescales of the inner accre-tion flow of neutron star LMXB systems, we wish to applyspectral-timing techniques in order to probe the geometry ofthese systems. See Nowak et al. (1999) and Uttley et al.(2014) for detailed reviews of spectral-timing analysis tech-niques. The first energy-dependent soft lags of a neutron starLMXB (4U 1608-52) were found in Vaughan et al. (1998).Soft lags occur when the higher energy photons associatedwith a correlated variation in flux arrive before the lower en-ergy photons. Additionally, soft lags were also found in otherneutron star LMXB systems (Kaaret et al. 1999; Barret 2013;de Avellar et al. 2013; Peille et al. 2015), black hole binariesand AGN (see Uttley et al. 2014, for a review of reverberationin black hole systems).While Vaughan et al. (1998) and Kaaret et al. (1999) werethe first works to study soft time lags in kHz QPOs in 4U1608-52 and 4U 1636-53 respectively, more recent analyseshave been done for a total of three neutron star LMXBs. Softlags of kHz QPOs have been studied in 4U 1608-52 in deAvellar et al. (2013) and Barret (2013), in 4U 1636-53 in deAvellar et al. (2013, 2016), and 4U 1728-34 in Peille et al.(2015). These studies have all shown for the lower kHz QPO:soft broadband lags and a near monotonic trend of lag with en-ergy, with the higher energy photons arriving first. The mag-nitudes of the soft broadband lags have all been on the order ofthe size scale of the neutron star inner accretion disk/boundarylayer.The additional spectral analysis done in Peille et al. (2015)for 4U 1608-52 and 4U 1728-34 shows: a harder covarianceComptonization component compared with the time-averagedComptonization component, as well as a better spectral fitwhen the seed photon temperature of these two componentsare decoupled. For that analysis, the covariance seed photon a r X i v : . [ a s t r o - ph . H E ] N ov Troyer & Cacketttemperature was found to be systematically higher than themean spectrum Comptonization component.In this paper we apply spectral-timing analysis techniquesto Aql X-1 with data from
RXTE/PCA . We discuss our anal-ysis approach, data reduction, and the various data productsis Section 2. In Section 3 we note similarities between ourresults and results of previous studies of other neutron starLMXB systems and review some of their implications. Fi-nally, in Section 4, we summarize the most important results. DATA ANALYSIS2.1.
Overview
We searched the entire
RXTE/PCA archive for observationsof Aql X-1 in modes compatible with spectral-timing analy-sis. In all cases, we required better than 128 µ s timing resolu-tion and 64 energy channels. Once such observations wereidentified, we required significantly detected kHz QPOs inorder to obtain sufficient statistics for meaningful analysis.Using Barret et al. (2008), we were able to select observa-tions with significantly detected QPOs up to July 2007. Itshould be noted that in the case of Aql X-1, only a singlekHz QPO - likely the lower kHz QPO (Méndez et al. 2001)- is detected well enough to perform spectral-timing analysis(Barret et al. 2008). Following Barret (2013), we evaluatedkHz QPOs by computing the power spectral density (PSD)for each time bin of the lightcurve. We used a binning time of256 s, ensuring the bins did not cross individual observations.We computed the discrete Fourier transform, calculated theperiodogram (Uttley et al. 2014), and left it in counts units.We then searched the PSD for power excess and used the χ method to fit a constant plus a Lorentzian with three param-eters: centroid frequency ( ν ), full-width half maximum fre-quency ( ∆ ν ), and normalization ( I lor ). Thus, we obtained asingle QPO frequency for each 256 s bin. A QPO is consid-ered significant if the ratio I lor / ∆ I lor ≥ RXTE , an OB-SID is a grouping of observations within a single, contiguouspointing. In this case there are no issues of changing sourcestate or instrument response since the time intervals betweenexposures are much shorter than the observation times. Prob-lems arise however in obtaining sufficient S/N to obtain mean-ingful results. In order to expand our analysis, the approachwe take is to combine observations in which the instrumentresponse does not vary significantly. Since the spectral prop-erties of the source itself can change between observations,what we present is an average over the times selected. Thecriteria we used to choose how to combine observations wasto first verify that the energy channels of interest were thesame. We considered energies from 3.0 keV to 20.0 keV,above which the background begins to dominate. Even withthe same energy channels, between observations the energyranges in each bin fluctuate by small amounts. It is thereforenecessary to rebin in energy so that the energy range fluctu-ation per bin is much smaller than the energy bin width (seee.g., Peille et al. 2015). Within all observation groups, themaximum fractional fluctuation of the centroid energy of a We searched all mode compatible observations after July 2007. Therewas a single OBSID (94076-01-05-00) with a single observation where thelower kHz QPO was significantly detected. However, due to the short dura-tion (2.3 ks) of this observation, we could not produce any spectral-timingproducts because of the limited statistics.
Table 1
Aql X-1 Observation Group 1: Observation PropertiesObsID Date Event Mode Exposure Significantmm/dd/yyyy Counts Time (s) QPOs20092-01-01-02 08/13/1997 1434551 911 320092-01-02-01 08/15/1997 2378037 1391 120092-01-02-03 08/17/1997 1470468 833 320092-01-05-01 09/06/1997 22695778 14263 320098-03-07-00 02/27/1997 5888675 4538 1420098-03-08-00 03/01/1997 5793703 5776 1330072-01-01-01 03/03/1998 2498232 1393 530072-01-01-02 03/04/1998 3310253 1510 430072-01-01-03 03/05/1998 3168559 1314 6
Table 2
Aql X-1 Observation Group 2: Observation PropertiesObsID Date Event Mode Exposure Significantmm/dd/yyyy Counts Time (s) QPOs40047-02-05-00 05/31/1999 13061454 9456 240047-03-02-00 06/03/1999 13043680 10777 440047-03-03-00 06/04/1999 12172425 9831 16
Table 3
Aql X-1 Observation Group 3: Observation PropertiesObsID Date Event Mode Exposure Significantmm/dd/yyyy Counts Time (s) QPOs50049-02-13-00 11/07/2000 5828947 3011 250049-02-15-03 11/13/2000 7268319 5456 1450049-02-15-04 11/14/2000 4918301 5034 950049-02-15-05 11/15/2000 9864954 9747 150049-02-15-06 11/16/2000 1807040 1949 570069-03-01-01 03/07/2002 2727478 2429 670069-03-01-02 03/07/2002 1836713 1647 370069-03-02-01 03/10/2002 1460966 813 470069-03-03-06 03/18/2002 918008 918 270069-03-03-07 03/18/2002 3268159 3264 470069-03-03-09 03/19/2002 1388293 1288 370069-03-03-14 03/21/2002 2092049 2690 2 bin is 0.17% and the maximum fluctuation of an energy binwidth is 0.18%. Overall we present three contiguous observa-tional groupings shown in Tables 1, 2, and 3. All uncertaintiesthroughout the paper are quoted at the 1 σ level.2.2. Data Reduction
To produce the spectral-timing products, we use the
RXTE/PCA event mode data listed in Tables 1, 2, and 3.First, in order to determine the conversion from channel toenergy, we extract spectra and create associated response ma-trices using seextrct and pcarsp . We applied good timeintervals (GTI) to account for PCUs turning on and off, Earthlimb avoidance, and avoidance of the South Atlantic Anomaly(SAA). From the response matrices we get the energy rangeassociated with each binned channel, and determine the abso-lute channel values using chantrans .For each observation group, we analyzed all event modefiles and computed the fast Fourier transform (FFT) at 4.0seconds (s) intervals which are then averaged over 256 s bins.Data gaps in the GTIs are windowed and the averaged FFTsare not permitted to cross observations. Each 256 s bin wasthen searched for excess power and fit with a 3-parameterpectral–timing analysis of Aql X-1 3
Table 4
Aql X-1 lag-energy linear fitObservation A BGroup ( µ s ) ( µ s keV − )1 49 ± − ±
12 70 ± − ±
23 53 ± − ± Note . — Parameters are from the best fit relation y = A + Bx Lorentzian as described above. We discarded any QPOs withsignificance < 3.0. Any bursts were not included in our anal-ysis. 2.3.
Lags vs. Frequency
To establish the presence of any lags, and if there is any fre-quency dependence, we computed lags between two broad en-ergy bins: 3.0 keV – 8.0 keV and 8.0 keV – 20.0 keV. We com-puted the cross spectrum for each 256 s data segment betweenthe two energy bins and averaged across the QPO FWHM. Inorder to correct for dead time induced cross-talk (van der Kliset al. 1987; Peille et al. 2015), we subtracted Fourier ampli-tudes between 1350 Hz - 1700 Hz from the cross-spectrum.We then compute the time lag from the phase of the crossspectrum. To further characterize the results and highlightany possible trends, we fit a straight line to the data and foundfits consistent with no significant dependance of the lag onQPO frequency. The mean lags for observation group 1, 2,and 3 are 28 ± µ s, 38 ± µ s and 29 ± µ s, respectively,and the mean lag when considering all observations togetheris 30 ± µ s. Additionally, we rebinned the lag-frequencydata using 10 equally-spaced frequency bins to further illus-trate the consistency of lag with frequency. The lag frequencydata for each observation group are shown in Figure 1 and thelag frequency data combining observations are show in Figure2. The average lags are all soft lags and positive by conven-tion, indicating that the higher energy band variations lead thelower energy band variations.2.4. Lag Energy Spectrum
In order to compute the full lag-energy spectrum, we com-puted the cross-spectrum within the FWHM of the mean QPOfrequency, for each 256 s segment of data, between each en-ergy band — channel of interest (CI) — and the remainingenergy channels (3.0 keV - 20.0 keV) — reference band. Werebinned in energy, decreasing the number of bins by a factorof 2 in order to increase the signal to noise ratio per bin andto reduce the effect of small energy fluctuations that occur atthe channel boundaries between observations mentioned pre-viously. We then averaged the centroid QPO frequencies andshifted and added (Méndez et al. 1998) each cross spectrum tothe mean QPO frequency. We eliminate correlated errors (Ut-tley et al. 2011, 2014) by not including the CI in the referenceband. We then computed the time lag from the phase of meancross spectrum. The lag-energy spectra, shown in Figure 3, allshow nearly monotonic trends with energy, where the highestenergy photons arrive before the lower energy photons. We fiteach lag-energy spectrum with a straight line to characterizeany trend(s). The data were fit to the function y = A + Bx andare shown in Figure 3. The fit parameters are shown in Table4. The best-fitting linear relations are consistent between all3 observation groups. QPO Frequency (Hz)
Lag ( µ s )
700 750 800 850 900 − − Observation Group 1
840 850 860 870 − − Observation Group 2
650 700 750 800 850 − − Observation Group 3
Figure 1.
Frequency-dependent lags for each observation group. Each datapoint (small black dot) is the lag from a 256 s bin with a significantly detectedkHz QPO. The mean lag between the 3.0 - 8.0 keV and 8.0 - 20.0 keV bandsare shown in red. Additionally, the lags are binned into 10 equally-spacedfrequency bins (blue triangles) between the minimum and maximum QPOfrequency.
Troyer & Cackett
650 700 750 800 850 − − − − Lag ( µ s ) All Observation Groups
Figure 2.
Lag as a function of frequency for all observation groups com-bined. The mean lag is shown in red. The rebinned data are shown in bluetriangles.
Covariance Spectrum
The covariance spectrum (Wilkinson & Uttley 2009; Uttleyet al. 2011) is yet another analysis tool useful in understandingthe nature of kHz QPOs and is computed quite easily along-side the lag-energy spectrum. The equations and methodol-ogy for calculating a covariance spectrum are given in detailin Uttley et al. (2014). The covariance spectrum describesthe spectral shape of the portion of the CI which is correlatedwith the reference band. Put another way, it is equivalent tothe rms spectrum when both are correlated. The first covari-ance spectrum of a kHz QPO was computed for 4U 1608-52and 4U 1728-34 in Peille et al. (2015). We computed the rawcovariance spectrum over the same energy range, and with thesame binning and frequencies as the lag-energy spectrum.In order to compare the covariance spectrum with the time-averaged spectrum, we need to fold the covariance spectrumthrough the instrument response for the same observation in-terval. In this way, we can investigate the amount of correlatedvariability present in each segment of the spectrum. To get anaverage instrument response for the covariance spectrum overthe observation interval, we expanded the individual responsematrices and averaged each entry across observations withina group by weighting it with the fraction of significant QPOtime.We extracted the Standard 2 spectra for all observations,adding 0.6 % systematic errors and creating background andresponse files for each. We used the most recent bright back-ground model and SAA history. We verified that the shape ofthe responses within each observation group were the same(ignoring normalization), with the exception of ObservationGroup 3, and added the spectra, background and responses.To calculate the fractional rms (covariance) we calculatethe ratio of the covariance spectrum to the mean spectrumby first rebinning the mean spectrum to match the covariancespectrum binning. The fractional rms for Aql X-1 is shownin Figure 4. This shows an increase in the fraction of thespectra that is variable with increasing energy, fractional rms(covariance), which becomes nearly constant above approx-imately 12 keV. This compares well to previous analyzes ofthe energy-dependence of the rms in kHz QPOs (e.g., Mén-dez et al. 2001).Observation Group 3 showed (3) distinct instrument re-sponse profiles in their Standard 2 spectra, which made com-bining these spectra impossible. We attempted to break thisobservation group into (3) corresponding groups, but lack ofstatistics prevented meaningful calculation of the lag/energyand covariance spectra. We could therefore not perform anyfurther comparative spectral analysis of Observation Group 3.
Energy (keV)
Lag ( µ s ) − − − − − − Figure 3.
Lag-energy spectrum for each observation group. The lags arecomputed with respect to a 3.0 keV – 20.0 keV reference band. By con-vention, positive lags indicate photons from that energy bin arrive after thereference band. Hence the highest energy photons arrive first. Note that thehighest energy bin for observation group 2 could not be calculated due topoor S/N. The best fit linear relations are also shown. The best fit parametersare listed in Table 4. pectral–timing analysis of Aql X-1 5 C o v a r i an c e (r e l a t i v e R M S ) Observation Group 1Observation Group 2
Figure 4.
Covariance in relative RMS units, which can be thought of thefraction of the spectrum that is variable on the kHz QPO timescale. Themean spectrum rebinned to match the covariance spectrum binning. We notean increase in fractional RMS (covariance) with energy up to approximately12 keV where it levels off.
Spectral Analysis
We simultaneously fit the mean spectra with the covari-ance spectra over the 3.0 keV – 20.0 keV (above 20.0keV the background dominates) energy range using
XSPEC12.8.2 (Arnaud 1996). We use the model combina-tion phabs*(diskbb+nthcomp+gaussian) for the fits (seeZdziarski et al. 1996; ˙Zycki et al. 1999, for a description of nthcomp ), though we note that the X-ray spectra of LMXBsare degenerate and can be fit equally well by other modelchoices (e.g., Lin et al. 2007). We fix the photoelectric ab-sorption column density at 0.3 × cm − (Kalberla et al.2005). For the Fe-line component we use a simple Gaussianmodel, with centroid constrained between 6.4 keV and 6.97keV. Following Gilfanov et al. (2003); Peille et al. (2015)for the covariance spectrum, we use the model combination phabs*nthcomp initially with the idea that the covariancespectra might represent the boundary layer emission.We find as in Gilfanov et al. (2003); Peille et al. (2015)for 4U 1608-52 and 4U 1728-34, good fits with the chosenmodel configuration. We attempted fitting schemes by sys-tematically untying one parameter at a time. These were: theelectron temperature (kT e ), photon index ( Γ ) and seed photontemperature (kT seed ). In order to obtain a good fit, only theseed photon temperature can be untied between the spectra.All other configurations resulted in poor fits. We find as inPeille et al. (2015) the seed photon temperature to be system-atically higher for the covariance spectrum. Additionally, inthe case of observation group 1, the spectra are fit better whenan Fe K Gaussian is included in the covariance spectrum. Inthis case, we tied the Gaussian centroid and width of bothspectra allowing only the normalizations to vary. With the ad-ditional Gaussian in the covariance spectrum, we get a changeof ∆ χ = 10 . σ confidence level using anF-test. In order to further test the presence of the covariancegaussian, we compared fits with no parameters tied betweenthe mean spectrum and covariance spectrum with and with-out covariance Gaussian. In this case we also obtain betterfits including the covariance Gaussian with a ∆ χ = 6 .
21 for1 additional degree of freedom. This corresponds to a betterfit at the 2.0- σ confidence level using an F-test. The spec-tral decompositions are shown in Figure 5 and the best-fittingparameters are listed in Table 5. The model begins to over es-timate the covariance spectrum at higher energies. This is anartifact produced by allowing only a single model parameter to be free for the fits. This artifact vanishes when both Γ andkT seed are freed, with a negligible ∆ χ .Finally, It should be noted that modeling a covariance spec-trum with an XSPEC model implicitly assumes that only thenormalization is oscillating, but the covariance spectra couldalso be produced by the average spectrum changing shape,e.g. the seed photon temperature or the optical depth. DISCUSSIONWe have analyzed all
RXTE data of Aql-X1 that show sig-nificant kHz QPOs and that were in modes with adequate res-olution in time (< 128 µ s ) and energy (64 channels). Thiswork was motivated by the desire to expand the scope ofspectral–timing analysis of kHz QPOs to a wider array of neu-tron star LMXB systems. We only analyzed the lower kHzQPO of Aql-X1 due to the poor S/N of the upper kHz – whichwas only discovered in Barret et al. (2008). All analyses areassociated with the lower kHz QPO. As in Barret (2013); deAvellar et al. (2013); Peille et al. (2015), for objects 4U 1608-52, 4U 1636-53, and 4U 1728-34 respectively, we found softlags between the high energy X-ray photons and low energyX-ray photons. The magnitude of lags in Aql X-1 were on theorder of 30 µ s and comparable to all the previous studies ofneutron star LMXB systems. Additionally, over the QPO fre-quencies, we find large dependencies of lag on frequency areexcluded, consistent with de Avellar et al. (2013); Peille et al.(2015). We note that Barret (2013) does find some variationof lag with QPO frequency, since that work used a larger dataset for 4U 1608-52 than de Avellar et al. (2013). See Barret(2013) for a discussion of the magnitude of the average lagand its implication on the geometry of neutron star systems.The shape and magnitude of the lag-energy spectra for Aql-X1 is also consistent with the other objects previously men-tioned. This includes a smooth decrease in the lags towardhigher energies. The exact mechanism and source of lagsis poorly understood. One possibility is that thermal Comp-tonization in the boundary layer causes the lags. See Lee et al.(2001); Kumar & Misra (2014, 2016) for a discussion of dif-ferent models of Comptonization and how they produce lags.Another possible explanation of the production of lags is X-ray reflection. In the reflection scenario, soft lags are thoughtto be associated with reverberation. Here, a hard source ofphotons – possibly the neutron star boundary layer formed atthe point where the faster Keplerian motion of the accretionflow encounters the slower rotating neutron star surface – im-pinges on and is reprocessed by the accretion disk. Whereashard lags are thought to arise due inward propagating accre-tion rate variations which modulate the hard Comptonizedflux via seed photon fluctuations. Additionally, lags can alsobe due to intrinstic, coherent spectral softening (Kaaret et al.1999) or due to temperature oscillations between two differentnon-isothermal Comptonizing sources (e.g., de Avellar et al.2013; Peille et al. 2015) which might indicate a compositeComptonizing source.Peille et al. (2015) point out that because the lag-energyspectrum drops at energies where the accretion disk does notcontribute a significant amount of flux, there must be someproperty associated with Comptonization alone that must con-tribute to the lags. Also, relative rms (covariance) increasesabove energies where the accretion disk should contribute tothe flux and therefore the variations there are likely modulatedby a harder source of photons, possibly the boundary layer(see e.g., de Avellar et al. 2013). Recently, Cackett (2016)modeled the lag-energy spectrum of 4U 1608-52 in order to Troyer & Cackett − k e V ( P ho t on s c m − s − k e V − ) r a t i o Energy (keV) − k e V ( P ho t on s c m − s − k e V − ) r a t i o Energy (keV)
Figure 5.
Top:
Time-averaged spectrum (black triangles) and covariance spectrum (red squares) for observation group 1 ( left ) and observation group 2 ( right ).Solid lines indicate the best-fitting overall model. The nthcomp (black dashed), disk blackbody (blue dotted) and Gaussian (green dashed dotted) componentsfor the time-averaged component are shown, while the nthcomp (red dashed) and Gaussian (magenta dashed dotted) components are shown for the covariancespectrum. There is no Gaussian for the covariance spectrum for observation group 2.
Bottom:
Ratio of the data to the best-fitting model.
Table 5
Spectral Fit ParametersObs. group 1* 1 2N H (10 cm − ) 0.3 (fixed) 0.3 (fixed) 0.3 (fixed)kT disk (mean) 0 . ± .
04 0 . + . − . . ± . disk + − + − + − kT seed (mean) 1 . ± .
06 1 . + . − . . + . − . kT seed (cov) 1 . ± .
05 1 . ± .
04 1 . ± . e (tied) 3 . ± + .
13 3 . + . − . . + . − . Norm nthcomp (mean) (6 . + . − . ) × − (6 . + . − . ) × − (7 . ± . × − Norm nthcomp (cov) (2 . ± . × − (2 . ± . × − (1 . ± . × − Γ (tied) 2 . ± . . ± .
02 3 . + . − . E line (tied) 6 . + . − . . + . − . . ± . σ line (tied) 0 . + . − . . + . − . . + . − . Norm E line (mean) (2 . + . − . ) × − (2 . ± . × − (1 . + . − . ) × − Norm E line (cov) (4 . ± × − χ ν Note . — Obs. group 1* includes a Gaussian in modeling the covariance spectrum. All other fits have no Gaussian in the covariance spectrum model. Allenergies are given in keV. test whether reverberation could produce the observed lags.While finding that reverberation could account for the lags be-low 8 keV, the behavior of the lags above 8 keV was markedlydifferent than predicted.Our spectral fits of the mean and covariance spectra in AqlX-1 yield similar results as Peille et al. (2015). We find sys-tematically higher seed photon temperatures for the covari-ance spectra over the mean spectra. Additionally, the covari-ance spectra are harder than the mean spectra, a result seenin all neutron star LMXBs to date and is well fit by a thermalComptonized component (Gilfanov et al. 2003; Peille et al.2015). The implications of these findings are discussed in de-tail in Peille et al. (2015).Finally, we have discovered that in one set of observa-tions, the covariance spectrum is better fit with a combina-tion of a thermal Comptonized component and a Fe K lineGaussian profile. This hints at the possibility of a reflec-tion/reverberation signature that contributes to the lags, atleast in part, or that some other mechanism can modulate the Fe K line at the frequency of the lower kHz QPO. Interest-ingly, by taking the ratio or the iron line normalization in thetime averaged and covariance spectra, the fractional RMS is (cid:39)
24% which is much higher than the observed fractionalRMS which never exceeds (cid:39)
10% in this component of thespectrum; see Figure 4. This implies that Fe K line is morevariable at the QPO frequency than the overall hard emission.We do not have a physical explanation of this.Currently, there are no models that explain all the spectral-timing properties of neutron star LMXBs. CONCLUSIONWe have studied the spectral-timing properties of the neu-tron star LMXB Aql X-1. We found similar behavior in thelag-frequency and lag-energy relationships as well as covari-ance spectral decompositions as seen previously in other neu-tron star LMXBs that have been studied. This adds an addi-tional source to those where detailed spectral-timing analysisof kHz QPOs has been done, and provides further support forthe conclusions reached in all cases. Specifically, the covari-pectral–timing analysis of Aql X-1 7ance spectra is well fit by a thermal Comptonized componentand spectral fits indicate a higher seed photon temperature forthe covariance spectrum. This implies a possible compositeboundary layer emitting region.We also find for one set of observations, the covariancespectrum is fit better with a thermal Comptonized componentand Fe K line with 2.4- σ confidence. The implications of thisare less clear. While tempting to attribute this to reverberation,more information is needed. Moreover, neither 4U 1608-52,nor 4U 1728-34 show this feature in their respective covari-ance spectra. Spectral-timing analysis of additional sources isneeded to determine if this result is more common in neutronstar LMXBs. Also, future missions with better spectral reso-lution – while maintaining the high timing capability of RXTE – might unlock this feature and help answer questions aboutthe fundamental nature of accretion and emission of these ob-jects.JST and EMC gratefully acknowledge support from the Na-tional Science Foundation through CAREER award numberAST-1351222. The authors would like to thank Didier Bar-ret, Philippe Peille and the participants of the Lorentz Centerworkshop ‘The X-ray Spectral-Timing Revolution’ (February2016), for useful discussions. The authors also thank the ref-eree for his careful review and comments which contributedsignificantly to the quality of this work.– might unlock this feature and help answer questions aboutthe fundamental nature of accretion and emission of these ob-jects.JST and EMC gratefully acknowledge support from the Na-tional Science Foundation through CAREER award numberAST-1351222. The authors would like to thank Didier Bar-ret, Philippe Peille and the participants of the Lorentz Centerworkshop ‘The X-ray Spectral-Timing Revolution’ (February2016), for useful discussions. The authors also thank the ref-eree for his careful review and comments which contributedsignificantly to the quality of this work.