Relativistic Iron Line Emission from the Neutron Star Low-mass X-ray Binary 4U 1636-536
aa r X i v : . [ a s t r o - ph ] M a y Published in the Astrophysical Journal
Preprint typeset using L A TEX style emulateapj v. 03/07/07
RELATIVISTIC IRON LINE EMISSION FROM THE NEUTRON STAR LOW-MASS X-RAY BINARY4U 1636-536
Dirk Pandel and Philip Kaaret
Department of Physics and Astronomy, University of Iowa, Iowa City, IA 52242
Stephane Corbel
Universit´e Paris 7 Denis Diderot and Service d’Astrophysique, UMR AIM, CEA Saclay, F-91191 Gif sur Yvette, France
ABSTRACTWe present an analysis of
XMM-Newton and
RXTE data from three observations of the neutron starLMXB 4U 1636-536. The X-ray spectra show clear evidence of a broad, asymmetric iron emission lineextending over the energy range 4–9 keV. The line profile is consistent with relativistically broadenedFe K α emission from the inner accretion disk. The Fe K α line in 4U 1636-536 is considerably broaderthan the asymmetric iron lines recently found in other neutron star LMXBs, which indicates a highdisk inclination. We find evidence that the broad iron line feature is a combination of several K α linesfrom iron in different ionization states. Subject headings: accretion, accretion disks — binaries: close — stars: individual (4U 1636-536) —stars: neutron — X-rays: binaries — X-rays: stars INTRODUCTION
Relativistically broadened, asymmetric Fe K α linesfrom the inner accretion disk have been observed inmany supermassive and stellar-mass black holes (e.g.Fabian 2006). In neutron star binaries, however,the iron lines are weaker, and until recently observa-tions did not clearly reveal a relativistic line profile.Bhattacharyya & Strohmayer (2007) found an asymmet-ric Fe K α line in XMM-Newton spectra of the low-massX-ray binary (LMXB) Serpens X-1 and showed that theline profile is consistent with fluorescent iron line emis-sion from the inner accretion disk. Similar asymmet-ric Fe K α lines were found by Cackett et al. (2008) in Suzaku spectra of the neutron star LMXBs Serpens X-1,4U 1820-30, and GX 349+2. In this paper we present
XMM-Newton and
RXTE observations of the neutronstar LMXB 4U 1636-536. We analyze the X-ray spectrato determine the profile of the relativistic Fe K α line andconstrain the properties of the inner accretion disk.4U 1636-536 (V801 Ara) is a well-studied, burst-ing LMXB consisting of a neutron star in a 3.8 hrorbit with a 0.4 solar mass, 18th magnitude star(van Paradijs et al. 1990) and is located at a distanceof ∼ XMM-Newton and
RXTE . We present an analysis of theX-ray spectrum over the 0.5–100 keV energy range andour results from modeling the continuum and relativis-tic Fe K α line emission. We use the Fe K α line profileto derive constraints on the disk inclination and innerdisk radius. We show that the line profile is not consis-tent with a single relativistic Fe K α line from a neutronstar accretion disk and that at least two lines from dif-ferent ionization states of iron are needed to adequatelydescribe the line profile. Finally, we discuss the impli-cations of our findings for measurements of neutron starradii based on Fe K α line profiles. OBSERVATIONS
4U 1636-536 was observed with
XMM-Newton (Jansen et al. 2001) on 2005 August 29 (observation ID0303250201), on 2007 September 28 (observation ID0500350301), and on 2008 February 27 (observation ID0500350401). The EPIC PN camera (Str¨uder et al. 2001)collected 30.0 ks of data starting at 18:24 UT duringthe 2005 observation (hereafter observation 1), 30.6 ks ofdata starting at 15:45 UT during the 2007 observation(observation 2), and 38.6 ks of data starting at 04:16 UTduring the 2008 observation (observation 3). The EPICPN was operated in timing mode and with the mediumblocking filter. We processed the PN data from ob-servations 1 and 2 with the
XMM-Newton
SAS version7.1.0 using the latest calibration files. The data fromobservation 3 required special processing by the
XMM-Newton
Science Operations Center because of the verylarge number of events. We extracted source photonsfrom the timing mode data using CCD rows RAWX =30–46 (29–45 for observation 3) and background photonsusing RAWX = 2–18. The full range of CCD columns Pandel, Kaaret, and CorbelRAWY was used. We selected only events with PAT-TERN ≤ − for observation 1,470 s − for observation 2, and 620 s − for observation 3.These rates are below the 800 s − timing mode pile-uplimit above which the spectral response would be dete-riorated by photon pile-up ( XMM-Newton
User’s Hand-book). The background count rate was less than 2% ofthe source count rate and did not exhibit significant flar-ing. We find a strong line-like feature in the backgroundspectrum near 0.45 keV. We interpret this feature as theelectronic noise peak for double events that is also presentfor PN imaging modes but is shifted to higher energiesin timing mode.4U 1636-536 was observed with
RXTE (Bradt et al.1993) simultaneously with each
XMM-Newton observa-tion. The
RXTE observations were somewhat longerthan the
XMM-Newton observations and completelyoverlapped with the EPIC PN exposures. No Earth oc-cultation occurred during these observations and the tar-get was observed continuously with
RXTE . In this paperwe consider only the data obtained with the HEXTEdetector (Rothschild et al. 1998). We did not use thePCA data because of their lower energy resolution com-pared to the EPIC PN data and because the PCA spec-trum in the 3–12 keV energy range showed an up to 30%higher flux than the EPIC PN spectrum. Similar ex-cesses of the PCA flux compared to other instrumentshave previously been reported (e.g. Tomsick et al. 1999;Courvoisier et al. 2003). It was not possible to correctfor the higher PCA flux by including a multiplicativecross-calibration factor because the flux excess is stronglyenergy dependent ( ∼
30% at 3 keV and ∼ < SPECTRAL ANALYSIS
For the spectral analysis, we removed all X-ray burstsfrom the data (three for observation 1 and one each forobservations 2 and 3). The EPIC PN spectra were binnedat about 1/3 of the FWHM detector resolution and werefitted simultaneously with the HEXTE data. We didnot include a multiplicative cross-calibration factor be-tween the two instruments. The spectral fitting was per-formed using XSPEC version 12.4 (Arnaud 1996). Forthe EPIC PN spectrum from observation 3, we find sig-nificant residuals between data and model at ∼ α line, we simply excluded the data near the absorptionedges with the largest residuals. The following energyranges were excluded from the fits: < α line which, according to the diskline modelin XSPEC (Fabian et al. 1989), is limited to the 3–10 keVenergy range for accretion disks around neutron stars.The X-ray spectra of LMXBs are typically characterizedby a hard component interpreted as Comptonization ofsoft photons by a hot corona, a soft component thoughtto be blackbody radiation from the accretion disk, and abroad Fe K α line at 6.4 keV (e.g. Barret et al. 2000).To fit the X-ray spectrum of the continuum emissionwe therefore combined a compTT component (Titarchuk1994) for a Comptonizing corona or boundary layer, a diskbb disk blackbody component (e.g. Makishima et al.1986), and a vphabs component for photoelectric absorp-tion with variable abundances (model 1). In the compTT model we used the approximation for a disk geometryand fixed the redshift at 0. In the vphabs model we onlyvaried the elemental abundances for O, Ne, Si, and Fe.Abundances for the other elements were not well con-strained by the fit and were fixed at their solar valuesaccording to Wilms et al. (2000). The spectra from thethree observations are reasonably well fitted by model 1with χ ν values of 1.44, 1.80, and 1.28 (Table 1).We find that the fit can be significantly improvedby adding a second blackbody component ( bbodyrad )elativistic Iron Line Emission from 4U 1636-536 3 TABLE 1Fits of Various XSPEC Models to the X-Ray Spectra of 4U 1636-536
Observation 1 Observation 2 Observation 3Spectral Model χ ν ( χ /dof) χ ν ( χ /dof) χ ν ( χ /dof)1. vphabs*(compTT+diskbb) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.44 (172.5/120) 1.80 (178.2/99) 1.28 (122.8/96)2. vphabs*(compTT+diskbb+bbodyrad) . . . . . . . . . . . . . . . . . . . . 1.36 (161.0/118) 1.43 (139.0/97) 0.97 (91.4/94)3. vphabs*(compTT+diskbb+bbodyrad+diskline) . . . . . . . . . . 1.23 (314.2/255) 1.22 (285.3/234) 1.18 (272.4/231)4. vphabs*(compTT+diskbb+bbodyrad+diskline+diskline) Note . — The χ values for fits of various XSPEC models to the EPIC PN and HEXTE spectra of 4U 1636-536. Shown arethe reduced χ ( χ ν = χ /dof), the χ , and the number of degrees of freedom (dof). For models 1 and 2 the energy range 3–10keV was excluded from the fit. with a temperature of ∼
200 eV (model 2). The ad-ditional component improves the χ ν for the three ob-servations to 1.36, 1.43, and 0.97, respectively. A sec-ond blackbody component with a similar temperaturewas also introduced by Fiocchi et al. (2006) in their fit-ting of BeppoSAX spectra of 4U 1636-536 obtained dur-ing the high/soft state. The region associated withthe blackbody component has an apparent radius of ∼
100 km, which suggests that this emission originatesfrom the accretion disk. We note that the diskbb model(Makishima et al. 1986) was constructed for accretiondisks around black holes and may not correctly describethe temperature profile in accretion disks around neu-tron stars which are subjected to significant central illu-mination from the stellar surface. The second blackbodycomponent may represent deviations of the temperatureprofile in the neutron star accretion disk from the diskbb model. No further improvement in the fit was achievedby adding a third blackbody component or other com-mon spectral components. The remaining discrepancybetween data and model is probably caused by small cal-ibration uncertainties that are noticeable because of thevery high signal-to-noise ratio of the data and, as men-tioned above, by the overly simplified modeling of someabsorption edges.For our further analysis we included the data in the3–10 keV energy range which were previously excludedwhen fitting models 1 and 2. The data in this energyrange show a clear excess over the continuum flux pre-dicted by model 2 which is likely caused by relativisticallybroadened Fe K α line emission. In order to fit the pro-file of this Fe K α line, we added to model 2 a diskline component (Fabian et al. 1989) which describes relativis-tically broadened line emission from a neutron star ac-cretion disk (model 3). All parameters of the diskline model were allowed to vary during the fit. We initiallyattempted to vary only the diskline parameters and fixall other parameters at their values from model 2, but wefound that a better fit can be achieved by allowing thecontinuum model parameters to vary as well. This is anindication that the spectrum outside the 3–10 keV energyrange is insufficient to correctly determine all continuummodel parameters. Model 3 provides a good fit to thedata with χ ν values of 1.23, 1.22, and 1.18, respectively.Figure 1 shows the observed spectra for the three obser-vations, the best fit with model 3, the individual modelcomponents, and the residuals between data and model.The excess of the line emission over the continuum modelis shown in Figure 2. The figure clearly shows a broadand asymmetric Fe K α line with a peak flux of 5%–8%over the continuum. The line profile is well described by the diskline model. The best-fit parameters of thecontinuum and line components for model 3 are shownin Tables 2 and 3. Also shown are the uncertainties ofthe parameters at a 90% confidence level (95% for up-per and lower limits). When calculating the confidenceregions, all continuum and line parameters were allowedto vary. We found that the commonly used error and steppar commands in XSPEC frequently failed to con-verge or underestimated the uncertainties. We thereforecalculated the confidence regions for many of the param-eters by manually searching for the parameter value thatproduced the appropriate change in χ .The continuum parameters for model 3 are gener-ally consistent between the three observations, althoughthe fit indicates a higher disk temperature and strongerComptonization component for the later observations.We find a significant difference in the rest-frame energy E of the Fe K α line. For observations 1 and 3, E isconsistent with 6.4 keV for weakly ionized iron, whereas,for observation 2, E is close to 7.0 keV for highly ion-ized Fe xxvi . The power-law index β of the emissivityprofile is in the typical range found for iron lines fromblack hole accretion disks. The diskline model provideslower limits on the disk inclination of 81 ◦ for observa-tions 1 and 3 and 64 ◦ for observation 2. A lower limitof 81 ◦ is clearly inconsistent with the fact that 4U 1636-536 is not an eclipsing system as well as with the resultsby Casares et al. (2006), who constrained the orbital in-clination to 36 ◦ –74 ◦ using phase-resolved spectroscopy.The high limit on the disk inclination for observations 1and 3 is likely the result of a slightly broader line profilecompared to observation 2. Our fit with the diskline model suggests that the line profile is broader than phys-ically possible for a single Fe K α emission line. One pos-sible explanation for a broader line profile is a smallerradius of the inner disk edge R in . However, the best-fit value of R in for observations 1 and 3 is already at6 R g ( R g = GM/c ), the lower limit of the diskline model and the radius of the innermost stable circular or-bit (ISCO) for a nonrotating neutron star. An inner diskradius much smaller than 6 R g , while possible for rotat-ing black holes, is unlikely for the accretion disk aroundthe neutron star in 4U 1636-536, which is rotating at arate of 581 Hz. The most likely explanation for a broaderline profile is the presence of several blended Fe K α lineswith different rest-frame energies. The presence of ironin more than one ionization state is already indicated bythe difference in E between the three observations (6.30and 6.43 keV vs. 7.06 keV).To test whether blended Fe K α lines are a viable ex-planation, we added a second diskline component to Pandel, Kaaret, and Corbel − − − . . P ho t on s c m − s − k e V − − R e s i dua l / E rr o r Energy (keV) Obs. 1 (2005) − − − . . P ho t on s c m − s − k e V − − R e s i dua l / E rr o r Energy (keV) Obs. 2 (2007) − − − . . P ho t on s c m − s − k e V − − R e s i dua l / E rr o r Energy (keV) Obs. 3 (2008)
Fig. 1.—
EPIC PN and HEXTE spectra of 4U 1636-536 for thethree observations. The top panels show the observed flux ( errorbars ), the best fit with model 3 ( solid line ), and the individualadditive model components ( dotted lines ). The individual modelcomponents are, from left to right, bbodyrad , diskbb , compTT , and diskline . The bottom panels show the residuals between the ob-served flux and the model divided by the 1 σ error of each datapoint. . . D a t a / C on t i nuu m m ode l . . . D a t a / C on t i nuu m m ode l . D a t a / C on t i nuu m m ode l Obs. 1 (2005)Obs. 2 (2007)Obs. 3 (2008) Energy (keV)
Fig. 2.—
Relativistic iron line profiles in 4U 1636-536. Shownare the observed flux ( error bars ) and the model flux ( solid line ),normalized to the continuum flux from model 3 (i.e. the model fluxwithout the diskline component). the model (model 4). Because the iron lines are broadand significantly blended, the parameters of the two diskline components are strongly correlated, and it isnot possible to fit all line parameters independently. Wetherefore fixed the line energy of the diskline compo-nents at 6.4 and 7.0 keV, respectively, and linked the diskinclination parameters. We also found that the outer diskradius R out is poorly constrained by the fit, so we keptit fixed at 1000 R g . The continuum parameters, whichwere allowed to vary simultaneously with the line param-eters, did not change significantly compared to model 3.Adding the second line component does not significantlyimprove the fit (Table 1), but it does result in more rea-sonable line parameters (Table 3). The lower limits onthe disk inclination change to 64 ◦ and 65 ◦ , respectively,which, unlike for model 3, are now consistent with the36 ◦ –74 ◦ constraint by Casares et al. (2006). The innerradius R in for the 7.0 keV component appears to be gen-erally smaller than for the 6.4 keV component as is ex-pected for an accretion disk in which the temperature in-creases towards the center. The flux ratio of the 7.0 keVand the 6.4 keV component increases from 0.9 to 1.6 to4.9 between the three observations, indicating that ironis generally in a higher ionization state for the later ob-servations. This is consistent with the increase in X-rayflux between observations. We conclude that the pres-ence of iron at different ionization states is a viable ex-elativistic Iron Line Emission from 4U 1636-536 5planation for the unusually broad line profiles and thatat least two blended Fe K α lines are necessary to obtainconsistent line parameters. DISCUSSION
We have analyzed X-ray spectra of the neutron starLMXB 4U 1636-536 obtained with
XMM-Newton and
RXTE in 2005, 2007, and 2008. The very high signal-to-noise ratio of the spectra allowed us to clearly de-tect a broad, relativistic Fe K α line from the inner ac-cretion disk. The line is significantly broader than theasymmetric Fe K α lines recently found in other neu-tron star LMXBs (Bhattacharyya & Strohmayer 2007;Cackett et al. 2008). The broader line profile is likely theresult of a high disk inclination in 4U 1636-536. The incli-nation angles derived from iron line profiles in other neu-tron star LMXBs have so far been comparatively low. Aspointed out by Cackett et al. (2008), this is likely a selec-tion effect because the narrower lines in low-inclinationsystems are more easily detectable. With the high signal-to-noise ratio of the 4U 1636-536 spectra, we have nowbeen able to measure the broader line profile in a highinclination LMXB. Our analysis of the Fe K α line pro-file places a lower limit of 64 ◦ on the disk inclinationin 4U 1636-536. This limit is consistent with the 36 ◦ –74 ◦ constraint on the orbital inclination by Casares et al.(2006) and with the nondetection of eclipses.When fitting the iron line profile with a single rela-tivistic line component, we find a significant differencein the rest-frame line energy between the three obser-vations. This difference is likely caused by a change inthe ionization profile of the disk related to the changein X-ray luminosity between the three observations. Theline energy derived for the second observation is close to6.97 keV, the K α line energy of Fe xxvi , which suggeststhat Fe xxvi contributes significantly to the observedline profile. According to our fit with a disk-blackbodymodel, the highest temperature in the disk is ∼ xxvi , itis evident that the ionization profile in the disk is stronglyaffected by photoionization.We find that the Fe K α line profile for two of the ob-servations is too broad to be adequately described bya single relativistic emission line with physically reason-able values of disk inclination and inner disk radius. Thebroader than expected line profile can be explained byoverlapping K α lines from iron in different ionizationstates. The presence of multiple ionization states is alsoindicated by the difference in the fitted line energy be-tween the three observations. It is evident that multi-ple line components need to be considered to adequatelymodel the relativistic iron line profiles in neutron starLMXBs. We obtained reasonable line parameters whenfitting two iron lines with different rest-frame energies.This is obviously an oversimplification, since many ion-ization states are probably contributing to the iron lineprofile. However, because the lines are broad and overlapconsiderably, it is not possible to constrain the param-eters of all line components independently. Even withonly two line components, the fit parameters are alreadystrongly correlated, leading to larger parameter uncer-tainties than a fit with a single line component. In order to adequately model the contribution from multiple ion-ization states when fitting relativistic Fe K α line profiles,improved models are needed that can predict the ioniza-tion profile in the accretion disk.The Fe K α line profiles in neutron star LMXBs canin principle be used to place upper limits on the neu-tron star radius by constraining the inner disk radius(Cackett et al. 2008). Previously, these line profiles havebeen fitted with only a single line component. However, ifmore than one ionization state contributes significantlyto the Fe K α emission, the line profile will be broaderthan for a single relativistic line, and a fit with a sin-gle line model may underestimate the inner disk radiusand thus the limit on the neutron star radius. This canbe clearly seen for two of our observations for which theupper limit on R in increases from 6 . R g to 11 . R g and10 . R g , respectively, when the iron line profile is fittedwith two line components instead of a single line compo-nent. In contrast, the upper limit on R in for the secondobservation decreases from 13 . R g to 9 . R g . It is evidentthat the constraints on the inner disk radius strongly de-pend on the assumptions made about the contributingionization states of iron and that a better understandingof the ionization profile in the disk is needed to obtain re-liable limits on the neutron star radius. The contributionof multiple ionization states may also be important forthe interpretation of some iron line profiles in accretingblack holes. We note that the disk inclination and in-ner disk radius are strongly anti-correlated when fittingbroad iron line profiles, which can lead to large uncer-tainties of the two parameters. Prior knowledge of thedisk inclination can significantly reduce the uncertaintyof the inner disk radius.It was shown by Laurent & Titarchuk (2007) thatbroad iron line features can also be produced by Comp-ton scattering of line photons in a strong outflow. Theexpected line profiles for this process are generally char-acterized by a narrow line at ∼ ∼
5% of the Eddington luminosity, which suggests thatthe rate of any outflow in 4U 1636-536 was significantlybelow the Eddington mass accretion rate. It thereforeseems unlikely that a large fraction of the observed ironline emission was produced in an outflow.The authors thank Sudip Bhattacharyya for helpfuldiscussions. D. P. and P. K. acknowledge partial supportfrom NASA grants NNG05GQ18G and NNX07AV06G.This work is based on observations obtained with
XMM-Newton , an ESA science mission with instruments andcontributions directly funded by ESA member states andthe USA (NASA).
Facilities:
XMM, RXTE Pandel, Kaaret, and Corbel
TABLE 2Fit Parameters of the Continuum Components of Model 3
Parameter Observation 1 Observation 2 Observation 3 vphabs a N H (10 cm − ) . . . . . . . . . . 3 . ± .
12 3 . ± .
10 3 . ± .
08O abundance . . . . . . . . . . . . . . 1 . ± .
04 1 . ± .
03 1 . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± .
10 1 . ± .
11 1 . ± . compTT b T (keV) . . . . . . . . . . . . . . . . . . 0 . ± .
02 1 . ± .
02 1 . ± . T C (keV) . . . . . . . . . . . . . . . . . . 14 . ± . > > τ C . . . . . . . . . . . . . . . . . . . . . . . . 2 . ± . < < − ) . . . . . 9 . ± . ± ± − erg cm − s − ) 6.1 8.2 10.0 diskbb c T disk (eV) . . . . . . . . . . . . . . . . . 640 ±
30 780 ±
20 900 ± ±
30 200 ±
13 152 ± R disk √ cos i (km) . . . . . . . . . . 7 . ± . . ± . . ± . − erg cm − s − ) 4.5 13.5 18.3 bbodyrad d T bb (eV) . . . . . . . . . . . . . . . . . . 174 ± ± ± ) . . . . . . . 29 ± ± ± R bb (km) . . . . . . . . . . . . . . . . . 102 ±
11 102 ±
14 91 ± − erg cm − s − ) 1.9 2.0 2.3 Note . — Uncertainties are given at a 90% confidence level and limits at a 95% confidence level. Fluxes for individual modelcomponents are unabsorbed and for the energy range 0.5–10 keV. R disk √ cos i and R bb were calculated from the model normalizationsassuming a distance of 6 kpc (Galloway et al. 2006). a Photoelectric absorption model with variable abundances. N H is the neutral hydrogen column density. Elemental abundances aregiven relative to their solar values according to Wilms et al. (2000). Abundances for elements not shown were fixed at their solar values. b Comptonization model according to Titarchuk (1994). T is the temperature of the soft seed photons, T C the temperature of theComptonizing plasma, and τ C the optical depth. A disk geometry was assumed for the model, and the redshift was fixed at 0. c Disk-blackbody model (e.g. Makishima et al. 1986). T disk is the temperature at the inner disk edge, R disk the apparent inner diskradius (see Kubota et al. 1998), and i the disk inclination. d Blackbody model. T bb is the blackbody temperature and R bb the apparent radius of the emitting region. TABLE 3Fit Parameters of the Iron Line Components of Models 3 and 4
Model 3Parameter Observation 1 Observation 2 Observation 3 E (keV) . . . . . . . . . . . . . . . . . . 6 . ± .
09 7 . ± .
10 6 . ± . β . . . . . . . . . . . . . . . . . . . . . . . . . . − . ± . − . ± . − . ± . R in ( GM/c ) . . . . . . . . . . . . . . < < < R out ( GM/c ) . . . . . . . . . . . . 820 +2900 − +630 − +180 − i (deg) . . . . . . . . . . . . . . . . . . . . > > > − ) . . . . . 1 . ± .
13 0 . ± .
20 2 . ± . − erg cm − s − ) 15.7 10.2 21.5Model 4Parameter Observation 1 Observation 2 Observation 3Line 1 Line 2 Line 1 Line 2 Line 1 Line 2 E (keV) . . . . . . . . . . . . . . . . . . (6.4) (7.0) (6.4) (7.0) (6.4) (7.0) β . . . . . . . . . . . . . . . . . . . . . . . . . . − . ± . < –2.7 < –2.6 − . +0 . − . < –2.7 − . ± . R in ( GM/c ) . . . . . . . . . . . . . . < < . +5 . − . < < < R out ( GM/c ) . . . . . . . . . . . . (1000) (1000) (1000) (1000) (1000) (1000) i (deg) . . . . . . . . . . . . . . . . . . . . > > > > > > − ) . . . . . 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . ± . . ± . − erg cm − s − ) 7.7 7.0 5.7 8.9 3.0 14.6 Note . — E is the rest-frame energy of the iron emission line, β the power-law index of the emissivity dependence on radius, R in and R out the inner and outer disk radius (in units of GM/c with M being the neutron star mass), and i the disk inclination. Also shownis the equivalent line width and the integrated flux for each diskline component. Uncertainties are given at a 90% confidence level andlimits at a 95% confidence level. Values in parenthesis indicate that the parameter was fixed during the fit. elativistic Iron Line Emission from 4U 1636-536 7elativistic Iron Line Emission from 4U 1636-536 7