Comprehensive Timing and X-ray Spectral Analysis of GX 1+4
M.M. Serim, S. Sahiner, D. Cerri-Serim, S.C. Inam, A. Baykal
aa r X i v : . [ a s t r o - ph . H E ] A p r MNRAS , 1–20 (2017) Preprint 15 September 2018 Compiled using MNRAS L A TEX style file v3.0
Comprehensive Timing and X-ray Spectral Analysis ofGX 1+4
M. M. Serim ⋆ , ¸S. ¸Sahiner ⋆ , D. ¸Cerri–Serim ⋆ , S. ¸C. ˙Inam ⋆ and A. Baykal ⋆ Physics Department, Middle East Technical University, 06531 Ankara, Turkey Department of Electrical and Electronics Engineering, Ba¸skent University, 06790 Ankara, Turkey
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
We present analysis of RXTE–PCA observations of GX 1+4 betweenMarch 3, 2001 and January 31, 2003 together with the CGRO–BATSE X-ray flux and frequency derivative time series between 1991 and 1999. Fromthe timing analysis of RXTE-PCA observations, we are able to phase con-nect pulse arrival times of the source within two different time intervals andobtain corresponding timing solutions. Using these pulse arrival times, wecontribute to long term pulse frequency history of the source. We look forepisodic correlations and anti-correlations between torque and X-ray luminos-ity using CGRO–BATSE X-ray flux and frequency derivative time series andfind that correlation state of GX 1+4 seems to change on ∼ f − ). We achieve to measure the longest observed timescale for a noise processamong accretion powered X-ray pulsars by extending the noise estimate fora time scale ranging from 31 days to 44 years. Spectral analysis of individualRXTE-PCA observations indicates a significant correlation between iron lineflux and unabsorbed X-ray flux. Pulse phase resolved spectra of the sourceindicate a broadening of iron line complex at the bin corresponding to thepulse minimum. Key words:
X-rays: binaries – pulsars: individual: GX 1+4 – stars: neutron– accretion, accretion discs ⋆ E-mail: [email protected] (MMS); [email protected] (¸S¸S); [email protected] (D ¸CS); [email protected] (S ¸C˙I); [email protected] (AB)c (cid:13)
M. M. Serim, ¸S. ¸Sahiner, D. ¸Cerri–Serim, S. ¸C. ˙Inam, and A. Baykal
Accretion powered pulsar GX 1+4 was discovered in 1970 with the pulsations of abouttwo minutes period (Lewin et al. 1971). It showed strong spin-up during 1970s (White etal. 1983). Subsequent to an undetectable low luminosity state era during early 1980s, thesource was redetected after it had undergone a torque reversal (Makishima et al. 1988).After this torque reversal event, GX 1+4 has been usually observed to be spinning down(Gonzales-Galan et al. 2012).GX 1+4 is in a low mass X-ray binary (LMXB) system and its optical counterpart is anM6III type red giant star V2116 Oph which underfills its Roche Lobe (Glass & Feast 1973;Chakrabarty & Roche 1997a; Hinkle et al. 2006). Distance to this system was estimated tobe about 4.3 kpc (Hinkle et al. 2006).GX 1+4 is the first example of an accretion powered pulsar residing in a symbiotic X-raybinary system in which the compact object accretes mass via the dense wind of the M-typegiant companion (Corbet et al. 2008). Presence of a long-term accretion disc around thepulsar was suggested and standard accretion disc theory (Ghosh & Lamb 1979; Wang 1987)was used to explain the pulse period evolution, torque reversal and transition to faint state(Dotani et al. 1989; Cui & Smith 2004).Magnetic field strength of GX 1+4 was inferred from two methods: Implementing stan-dard accretion disc theory and using marginal evidence of cyclotron resonance scatteringfeature (CRSF). With the standard accretion disc theory, the surface magnetic field strengthof the pulsar was estimated to be quite high, ∼ − Gauss (Dotani et al. 1989; Cui& Smith 2004). On the other hand using the relation between magnetic field and cyclotronline energy, magnetic field strength was calculated to be rather ordinary among accretionpowered pulsars, ∼ Gauss (Rea et al. 2005; Ferrigno et al. 2007).Although the optical companion of GX 1+4 is known, orbital parameters of the systemhave not been conclusively determined yet. From X-ray measurements of the spin periodvariations during both spin up and down era (between 1991 and 1998), an orbital periodof 304 days has been suggested (Cutler et al. 1986, Pereira et al. 1999, Braga et al. 2000).On the other hand, infrared observations of the source have indicated a 1161-day periodwithout any sign of 304-day periodicity (Hinkle et al. 2006). Recently, 1161-day period hasbeen supported by suggesting a potential neutron star eclipse from the variability of hard( >
17 keV) X-ray emission (Ilkiewicz et al. 2017).
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X 1+4 β emission along with iron K α (Reaet al. 2005) and a narrower iron K β line is found to be present for moderate luminosities aswell (Naik et al. 2005).In this paper, we present timing and spectral analysis of 90 pointing RXTE–PCA ob-servations of GX 1+4 between March 3, 2001 and January 31, 2003 with a total exposureof 276 ks. We also look for episodic correlations and anti-correlations between torque andX-ray luminosity using CGRO–BATSE X-ray flux and frequency derivative time series be-tween 1991 and 1999. In Section 2, we briefly introduce the observations. In Section 3.1, wepresent pulse timing analysis of RXTE–PCA observations and resulting measurements ofpulse frequencies. In Section 3.2, we present power spectrum of the pulse frequency deriva-tive fluctuations. In Section 3.3, we present analysis of CGRO–BATSE data for episodictorque luminosity correlations and anti-correlations. In Sections 4.1 and 4.2, we presentanalysis of time resolved and pulse phase resolved spectra of RXTE–PCA data. In Section5, we summarize and discuss our results. The
Rossi X-ray Timing Explorer (RXTE) was an X-ray satellite which had been launchedinto low-Earth orbit on December 30, 1995 and operated until January 5, 2012. It hadProportional Counter Array (PCA) composed of proportional counter units (PCUs), eachof which had an effective area of 1300 cm . The PCA was sensitive to the photons within2–60 keV energy range. GX 1+4 was monitored with RXTE–PCA between March 3, 2001and January 31, 2003. During this time interval, 90 pointing observations were carried out. MNRAS , 1–20 (2017)
M. M. Serim, ¸S. ¸Sahiner, D. ¸Cerri–Serim, S. ¸C. ˙Inam, and A. Baykal
Table 1.
Observation log of GX 1+4Proposal Number of Total Time RangeID observations exposure (ks) (MJD)60060 40 120.9 51974-5232070064 40 124.6 52338-5259370065 8 28.9 52390-5258570425 2 1.5 52662-52670total 90 276.0 51974-52670 P C A C oun t R a t e ( c t s / s ) Time (Days Since MJD 51974.7) " "(a) (b)
Figure 1.
Total exposure of these observations is around 276 ks while the exposure for each observationvaries between 0.5 and 18 ks (see Table 1 for details).The data reduction is carried out with the
HEASOFT v6.19 software. We select the dataconsidering the electron contamination to be less than 0.1, offset angle to be less than 0.02 ◦ and elevation angle to be greater than 10 ◦ . We extract lightcurves from GoodXenon modeevents with 1s bin time. Then, barrycentric correction is applied to the photon arrival timesin the lightcurve. As the active number of PCUs in each observation varies, we correct thecount rates with
CORRECTLC command as if all five PCUs were operating at the same time.For the spectral analysis we use
Standard2f mode data which have 128 energy channels.Spectra are extracted only from PCU2 data. Furthermore, we construct pulse phase resolvedspectra with the tool
FASEBIN . The PCA background estimator models (Epoch 5a and 5b)supplied by the RXTE Guest Observer Facility (GOF) are used for background subtraction.Spectral analysis is performed with
XSPEC V.12.9.0 . A systematic error of 0.5% is appliedas it is recommended by the PCA team.
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X 1+4 BATSE (Burst and Transient Source Experiment) onboard CGRO (Compton Gamma RayObservatory) consisted of eight detector modules located at the corners of CGRO. Thesedetectors enabled continuous all sky monitoring of both pulsed and unpulsed sources above 20keV between 1991 and 2000. BATSE not only continously monitored daily pulse frequencyand X-ray flux changes of persistent and previously known transient accretion poweredpulsars, but also discovered and monitored new transients (Bildsten et al. 1997).This paper makes use of BATSE 20-60 keV band X-ray flux and pulse frequency derivativetime series of GX 1+4 obtained from the ftp site ”gammaray.nsstc.nasa.gov/batse/pulsar/”.These time series cover time span between 1991 and 1999.
For the timing analysis, we follow phase coherent timing approach and use barycentricRXTE–PCA lightvurve between MJD 51974–52593. In order to search for periodicity in thedata, we fold the lightcurve over trial periods (Leahy et al 1983). Using χ test, we obtainthe template pulse profile that gives the maximum χ . We create the pulse profiles with 20phase bins for each observation and represent them in terms of Fourier harmonics (Deeter& Boynton 1985).Then, by cross correlating each pulse with the template pulse profile, we calculate thearrival times of pulses (TOAs). In order to avoid cycle count ambiguity, we construct TOAswithin each 50 days and measure the best period of that time span. Then, using the over-lapping time intervals, we align the slopes of TOAs in consecutive time spans. And phaseconnected pulse arrival times are fitted by; φ ( t ) = φ + ν ( t − t ) +
12 ˙ ν ( t − t ) +
16 ¨ ν ( t − t ) + ... (1)where t is the start time of epoch folding, ν , ˙ ν and ¨ ν are the spin frequency, its first derivativeand second derivative, respectively. Since there is a gap of 60 days within the data betweenMJD 52228–52288, we phase connected the pulse arrival times of the source in two differenttime intervals ”a” ( ≃
250 days) and ”b” ( ≃
300 days) (illustrated in Figure 1). We are able toobtain a timing solution for each interval (parameters are listed in Table 2). We find thatthe source is spinning down with a rate of ˙ ν ≈ − × − Hz/s. We present the pulse arrival
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M. M. Serim, ¸S. ¸Sahiner, D. ¸Cerri–Serim, S. ¸C. ˙Inam, and A. Baykal −200−150−100−500 C yc l e C oun t s (b) −100 0 100 200−505 R e s i dua l s Time (Days Since MJD 52390.0) " Figure 2.
Pulse arrival times of GX 1+4. (a) Pulse arrival times of interval ”a” and its residuals after the removal of thirdorder polynomial. (b) Pulse arrival times of interval ”b” and its residuals after the removal of third order polynomial. times and their residuals after the removal of cubic trend for the intervals ”a” and ”b” inFigure 2.We construct the pulse frequency history (see Figure 3) of the source by using the slopesof linear fits to each 3 consecutive TOAs (approximately 20-30 days). We calculate the errorbars of frequency measurements from the uncertainties of the slopes. The pulse frequencymeasurements of GX 1+4 were previously conducted by Cui & Smith (2004) for the time
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X 1+4 Table 2.
Timing parameters of GX 1+4 for interval ”a” and ”b”.Parameter Interval a Interval bMJD Range 51974.7–52227.9 52288.2–52593.7Time Span (Days) 253.2 305.5Epoch (MJD) 51974.0 52390.0Frequency (mHz) 7.225369(8) 7.2571253(8)Period (s) 136.3257(2) 137.795(6) ˙ ν (10 − Hz/s) -2.022(2) -1.9892(2) ¨ ν (10 − Hz/s ) 0.033(2) 1.240(4) span corresponding to interval ”b”. Our measurements are presented together with the mea-surements by Cui & Smith (2004) in the lower panel of Figure 3. In order to investigate torque noise characteristics of GX 1+4, we construct power spectrumof the pulse frequency derivative fluctuations by employing root mean square (rms) residualstechnique developed by Cordes (1980) and Deeter (1984). In this technique, mean squareresidual for the data spanning an interval of length T can be expressed as S r T r − , whereS r corresponds to r th -order red noise strength. The mean square residuals, after removing apolynomial of degree m over a time span T can be given as, < σ R ( m , T ) > = S r T r − < σ R ( m , > u , (2)where < σ R ( m , > u is the normalization (proportionality factor) which can be estimated bymeasuring the variance of residuals by removing the degree of polynomial m for unit noisestrength S( r = ).The power spectrum of pulse frequencies was constructed before from BATSE data byBildsten et al. (1997). It was shown that noise strengths corresponding to pulse frequencyderivatives obey f − law. Therefore, we simulate time series of GX 1+4 for f − noise (see Scottet al. 2003). We estimate the normalization of the simulated series by removing quadraticpolynomial of degree m = . After determining the normalization, we estimate noise strengthsfor different time spans (T, T/2, T/4,...). Then, we construct power spectrum of the pulsefrequency derivatives by taking the logarithmic average of the noise estimates for each timespan and we present inverse of time spans as frequency in Figure 4.Our power spectrum of the pulse frequency derivatives is constructed by using all pulsefrequency measurements since 1972, whereas Bildsten et al. (1997) used only the measure-ments between 1991 and 1999. It is evident that the power law index and noise strengths MNRAS , 1–20 (2017)
M. M. Serim, ¸S. ¸Sahiner, D. ¸Cerri–Serim, S. ¸C. ˙Inam, and A. Baykal −3 −3 −3 −3 −3 F r equen cy ( H z ) Days (MJD) F r equen cy ( m H z ) Time (Days Since MJD 51974.0)
Figure 3.
Upper panel shows the complete frequency history of GX 1+4 (see Gonzales-Galan et. al. (2012) and referencestherein). The frequencies measured in this work are located between the dashed lines. A closer view of this time range is givenin the lower panel. Our measurements and the measurements of Cui & Smith (2004) are represented by empty circles and filledsquares respectively. still agree with the power spectrum estimate presented by Bildsten et al. (1997). As seen inFigure 4, power spectrum estimate obeys f − (or flicker noise) for the frequency interval from1/44 yr − to 1/31 d − . The time scale of this power spectrum is the longest ever measured foraccretion powered X-ray pulsars. The noise strength level changes between S = . × − Hzs − and S = . × − Hz s − . MNRAS000
Upper panel shows the complete frequency history of GX 1+4 (see Gonzales-Galan et. al. (2012) and referencestherein). The frequencies measured in this work are located between the dashed lines. A closer view of this time range is givenin the lower panel. Our measurements and the measurements of Cui & Smith (2004) are represented by empty circles and filledsquares respectively. still agree with the power spectrum estimate presented by Bildsten et al. (1997). As seen inFigure 4, power spectrum estimate obeys f − (or flicker noise) for the frequency interval from1/44 yr − to 1/31 d − . The time scale of this power spectrum is the longest ever measured foraccretion powered X-ray pulsars. The noise strength level changes between S = . × − Hzs − and S = . × − Hz s − . MNRAS000 , 1–20 (2017)
X 1+4 −9.5 −9 −8.5 −8 −7.5 −7 −6.5 −6 − − − − − − ( S ( s − )) Log (Freq.(1/s))
Figure 4.
Power Spectrum of the pulse frequency derivatives of GX 1+4. Crosses indicate measuremental noise level.
Torque-luminosity correlations of GX 1+4 are examined by using CGRO-BATSE 20 – 60keV band X-ray flux and pulse frequency derivative time series. These time series cover atime span of ∼ days lying within the era of long term spin-down trend of the source.We systematically search for X-ray flux and pulse frequency derivative correlations andanti-correlations in ∼ − day long intervals. Assuming that the bolometric luminosityis correlated with the pulsed X-ray flux, finding such correlations or anti-correlations will bea direct indication of episodic torque luminosity correlations and anti-correlations.We find that the source occasionally enters ∼ − days long intervals that showeither correlation (Pearson correlation coefficient (PCC) > < -0.6) between X-ray flux and pulse frequency derivative. Outside these episodes, there is nosignificant correlation or anti-correlation between X-ray flux and pulse frequency derivative(-0.6 < PCC < ∼ day long) intervals with mid MJD’s of 49700 and51250. These samples are the ones that show the strongest correlation and anti-correlationbetween frequency derivative and X-ray flux respectively. PCC for the plots on the left MNRAS , 1–20 (2017) M. M. Serim, ¸S. ¸Sahiner, D. ¸Cerri–Serim, S. ¸C. ˙Inam, and A. Baykal
Figure 5.
Time variation of Pearson correlation coefficient (PCC) between frequency derivative and pulsed flux. Correlationanalysis is performed for ∼ − day long intervals of CGRO-BATSE observations of GX 1+4. −10 −10 −10 −10 −10 − . × − − . × − . × − F r equen cy D e r i v a t i v e ( H z / s ) −10 −10 −10 −10 −10 − . × − − . × − − . × − − . × − F r equen cy D e r i v a t i v e ( H z / s ) Figure 6.
Frequency derivative as a function of 20 – 60 keV BATSE pulsed flux for two data sets of ∼ days long episodesthat show correlation (PCC=0.89, left panel) and anti-correlation (PCC=-0.75, right panel) respectively. and right panels of Figure 6 are 0.89 and -0.75 with the corresponding null hypothesisprobabilities calculated from the Student’s t-distribution (two tailed) of . × − and . × − respectively. MNRAS000
Frequency derivative as a function of 20 – 60 keV BATSE pulsed flux for two data sets of ∼ days long episodesthat show correlation (PCC=0.89, left panel) and anti-correlation (PCC=-0.75, right panel) respectively. and right panels of Figure 6 are 0.89 and -0.75 with the corresponding null hypothesisprobabilities calculated from the Student’s t-distribution (two tailed) of . × − and . × − respectively. MNRAS000 , 1–20 (2017)
X 1+4 Spectral fitting of individual
RXTE –PCA observations are performed in 3 – 25 keV energyrange. We basically model the spectra with an absorbed power law and a high energy cutoff.We also add a simple Gaussian line profile around 6.4 keV. Generally, this model successfullydefines the spectra of observations with higher flux ( > × − erg cm − s − in 3 – 20 keV). Inmost of the cases, the circumstance of short ( ∼ . × − erg cm − s − to . × − erg cm − s − , hence aflux variation of two orders of magnitude is observed within ∼
700 days. Equivalent hydrogencolumn density ( n H ) measurements given in the second panel are in the range . × cm − – . × cm − . The n H results are demonstrated logarithmically for a better visualizationof the variability. We commonly observe higher n H values for the spectra in which we couldnot resolve the cutoff. The third panel shows the variation of the photon index ( Γ ), whichis varying from 0.4 to 2.4. Steeper power law is more common for the spectra in which wecould not resolve the cutoff (28 of 40 no-cutoff spectra have larger indices than the average).Cutoff energy ( E cut ) and e-folding energy ( E fold ) variations are given in fourth and fifth panels,respectively. E cut values are consistent with a constant value of 7.8 keV. The variation of E fold is stochastic; when cutoff is resolved in a low flux spectrum, E fold is generally below 25 keVwhile it is usually above 30 keV for the high flux spectra.A set of low flux observations are sorted through the observations that we could notresolve the cutoff individually, with the purpose of increasing the SNR of low flux spectrum.Seven observations between MJD 52498.9 – 62642.1 (Obs.IDs: 70064-01-19-00, 70064-01- MNRAS , 1–20 (2017) M. M. Serim, ¸S. ¸Sahiner, D. ¸Cerri–Serim, S. ¸C. ˙Inam, and A. Baykal F − k e V n H Γ E c u t E f o l d R ed . χ Days (since MJD 51974.7)
Figure 7.
Best fit spectral parameters for individual
RXTE − PCA observations. Error bars indicate uncertainties at 90per cent confidence level. Empty circles or triangles represent parameters measured by fitting cutoff power law model[ wabs*(pow*high+gau) ] or a simple power law model [ wabs*(pow+gau) ], respectively. From top to bottom; variations in 3–20 keV unabsorbed flux in units of − erg cm − s − , equivalent hydrogen column density in units of cm − , photon index,cutoff energy [keV], e-folding energy [keV] and reduced χ are plotted, respectively. n H and photon index values are measured to be similar. For the constructedspectrum, a simple power law fit without cutoff gives a reduced χ value of 2.5 which is sta-tistically unacceptable. The fit is improved by adding the cutoff model component, resultingin a reduced χ value of 0.7.We also check whether the time variability of spectral parameters is related to X-ray fluxor not. We only find a significant correlation for Fe line flux. For individual RXTE –PCAspectra, the flux contributions of the Fe line are measured using the CFLUX model in
XSPEC and they are plotted against 7 – 20 keV flux measurements in Figure 8. In order to test thesignificance of the correlation, we calculate the Pearson correlation coefficient between thetwo parameters and it is found as 0.82. The null-hypothesis probability calculated from theStudent’s t-distribution (two-tailed) is . × − . MNRAS000
XSPEC and they are plotted against 7 – 20 keV flux measurements in Figure 8. In order to test thesignificance of the correlation, we calculate the Pearson correlation coefficient between thetwo parameters and it is found as 0.82. The null-hypothesis probability calculated from theStudent’s t-distribution (two-tailed) is . × − . MNRAS000 , 1–20 (2017)
X 1+4 −10.5 −10 −9.5 −9−12−11.5−11−10.5−10 Log ( F F e ) , [ e r g s c m − s − ] Log (F ) , [ergs cm −2 s −1 ] Figure 8.
Flux variation of the Fe emission line with respect to 7 – 20 keV unabsorbed flux from RXTE − PCA observations.Single parameter errors are calculated at 90 per cent confidence level.
We construct pulse phase resolved spectra of GX 1+4 from the observation sequence on MJD52390.9, which is one of the brightest observations with a long exposure time. The timingsolution for the corresponding time is appended to the timing file of the
FASEBIN tool andthe pulse period is divided into ten equal segments each of which having an exposure of ∼ . × cm − .For the Gaussian emission representing the iron K α line around 6.4 keV, the equivalentwidth is the only parameter of the line that varies with pulse phase. The spectrum of thephase that coincides with the pulse minimum shows an increase in the EW of Fe line, withoutany significant change in line flux. MNRAS , 1–20 (2017) M. M. Serim, ¸S. ¸Sahiner, D. ¸Cerri–Serim, S. ¸C. ˙Inam, and A. Baykal N o r m a li z ed C oun t R a t e Γ E c u t E f o l d −10.5−10.4−10.3 Log ( F F e ) E W F e Pulse Phase
Figure 9.
Best fit spectral parameters of the 10 phase-binned spectra from the
RXTE − PCA observation sequence on MJD52390.9. The pulse profile is given at the uppermost panel for comparison. All uncertainties are calculated at the 90 per centconfidence level. For clarity, the data points are repeated for a cycle.
GX 1+4 is a persistent accretion powered X-ray pulsar and a peculiar source residing ina symbiotic X-ray binary. Long term spin rate evolution of the source has been monitoredcontinuously since it was discovered in 1970s (see Gonzales-Galan et al. (2012) and referencestherein). From the pulse timing analysis of RXTE-PCA observations, we are able to phaseconnect the pulse arrival times of the source within two different time intervals of ∼ and ∼ days long as shown in Figure 2. Therefore, we obtain timing solutions corresponding tothese two intervals (see Table 2 including interval-wise measurements of the first and secondderivatives of pulse frequency. Morever, using these pulse arrival times, we contributed to MNRAS000
GX 1+4 is a persistent accretion powered X-ray pulsar and a peculiar source residing ina symbiotic X-ray binary. Long term spin rate evolution of the source has been monitoredcontinuously since it was discovered in 1970s (see Gonzales-Galan et al. (2012) and referencestherein). From the pulse timing analysis of RXTE-PCA observations, we are able to phaseconnect the pulse arrival times of the source within two different time intervals of ∼ and ∼ days long as shown in Figure 2. Therefore, we obtain timing solutions corresponding tothese two intervals (see Table 2 including interval-wise measurements of the first and secondderivatives of pulse frequency. Morever, using these pulse arrival times, we contributed to MNRAS000 , 1–20 (2017)
X 1+4 Table 3.
RXTE–PCA spin rate measurements for the intervals with different flux levelsInterval 1 Interval 2 Interval 3MJD Range 51974.7-52227.9 52288.2-52343.6 52450.6-52593.7Time span (days) 253.2 146.4 143.1 ˙ ν ( − Hz/s) -2.0585(3) -2.3860(7) -0.8334(8)3–20 keV Unabsorbed Flux ( − erg cm − s − ) 6.22(2) 9.90(3) 2.21(1) long term pulse frequency history of the source with our new pulse frequency measurements(see Figure 3).GX 1+4 was a spinning-up source in 1970s before it underwent a torque reversal in 1980s.The source was found to show correlation between spin-up rate and X-ray flux before thetorque reversal, which was interpreted as an indication of a persistent prograde accretiondisc (see Ghosh& Lamb 1979, Wang 1987).After the source underwent torque reversal, the prograde accretion disc scenario wasfound to be inconsistent with the spin rate and X-ray flux behaviour of the source. By usingCGRO-BATSE data, Chakrabarty et al. (1997b) found that there is a general anti-correlationtrend between spin rate and pulsed flux (or in other words correlation between negative ofspin rate and pulsed flux) during the continuous spin-down interval between 1991 and 1995,which is the opposite of expected in the presence a prograde accretion disc. However, theyalso reported that anti-correlation state of GX 1+4 is not perpetual and there is a marginalevidence of a positive correlation between X-ray flux and spin rate for a prolonged spin-up( ∼
200 days long) interval. Similar spin rate and X-ray flux anti-correlation was also foundfrom the analysis of ∼
600 day long Fermi/GBM and Swift/BAT data (Gonzales-Golan etal. 2012). In order to investigate the correlation state from RXTE-PCA observations, wemeasure spin down rates for 3 different time intervals with different flux levels (see Table 3).The measurements indicate that spin down rate is scaling up with the flux level, therefore ageneral anti-correlation state can be inferred during RXTE observations.
Torque noise fluctuations and noise strengths of pulse frequency fluctuations have beenstudied for several accretion powered X-ray pulsars (Bildsten et al. 1997; Baykal & ¨Ogelman1993). Red noise (random walk) in pulse frequency fluctuations or white noise in the pulsefrequency derivatives are resonable models for wind accreting X-ray binaries like Vela X-1,4U 1538-52 and GX 301-2 (Bildsten et al., 1997). These sources have power spectra withwhite noise strengths in the range − − − Hz s − . The persistent long-term spinning- MNRAS , 1–20 (2017) M. M. Serim, ¸S. ¸Sahiner, D. ¸Cerri–Serim, S. ¸C. ˙Inam, and A. Baykal down source 4U 1907+09 (Baykal et al. 2001, Baykal 2006) also shows random walk in thepulse frequency history (¸Sahiner et al. 2012) with noise strength . × − Hz s − for afrequency interval between 1/1300 d − and 1/75 d − . For this source, formation of an episodictransient accretion disc around the neutron star was suggested to explain the random walkmodel in pulse frequency (¸Sahiner et al. 2012).Accretion powered pulsars in low mass X-ray binaries like Her X-1 and 4U 1626-67 accretevia persistent accretion discs and their pulse frequency time series are also consistent withthe random walk model. Their pulse frequency derivatives have white noise strengths in therange − to − Hz s − . Since the power spectra of these sources lie in a narrow range,possibility of red noise in the pulse frequency derivative can not be excluded (Bildsten et al.1997).Cen X-3 accretes via disc and and the noise strength varies from low to high frequenciesas − , − Hz s − (Bildsten et al. 1997).The power law index of the power spectrum inthis system is ∼ − which implies that disc accretion dominates at short time scales.OAO 1657-415 has a power law index of . with noise strength − Hz s − (Baykal1997). This source also shows marginal correlation with spin-down rate and X-ray luminosity(Baykal 2000).X Per has the lowest noise strength among accretion powered pulsars in high mass X-raybinaries with − − − Hz s − for frequencies between 1yr − and 1/35 yr − (Acuner et al.2014). The steep power law index in pulse frequency derivative indicates that it could havea transient accretion disc.SAX J2103.5+4545 has the steepest power law index with 2.13 among high mass X-ray binaries (Baykal et al. 2007). The steep power law index suggests that accretion viaaccretion disc at shorter time scales possesses low timing noise therefore power densityspectrum becomes more steeper compared to the other persistent high mass X-ray binaries.In GX 1+4, we observe flickering noise ( f − ) which agrees with the power spectrumestimate of Bildsten et al. (1997). It is important to note that we extend the estimate fora time scale ranging from 31 days to 44 years. Thus, we achieve to describe a noise processfor the longest timescale among accretion powered X-ray pulsars. We find that the noisestrength level of the source changes between S = . × − Hz s − and S = . × − Hz s − .The torque noise power spectrum of GX 1+4 has a unique trend among accretion poweredpulsars, showing f − power law trend in the longest timespan. In other words, timing noiseincreases with time. Recently Ilkiewicz et al. (2017) supported the orbital period of 1162 MNRAS , 1–20 (2017)
X 1+4 >
17 keV) X-ray observations. This orbital period was originally suggestedby Hinkle et al. (2006) using radial velocity measurements from infrared observations. Hinkleet al. (2006) found the projected semi-major axis of the orbit as a / c sin i ∼ lt s. Theeffect of Doopler shifts due to the orbital modulation on pulse frequency time series is thus δν ∼ π P orbit P spin ac sin i ∼ . × − Hz. Using the torque noise spectrum (see Figure 4), the noisestrength at the frequency corresponding to orbital period ( / (1162 ∗ = . × − Hz)is S ∼ × − Hzs − , we estimate the deviation on frequencies due to the noise processas √ ∆ ν = √ S T = . × − which is two orders of magnitude greater then Doppler shiftsexpected due to orbital modulation. Therefore it is not possible the resolve Doppler shiftmodulations in pulse frequency time series, since the noise process dominated. Moreover, ∼ days observation time of RXTE is short compared to the suggested orbital period.Continuous monitoring of the source using future observatories such as LOFT (Ferroci etal . 2012) might be useful to resolve Doppler shift modulations from pulse arrival data andobtain orbital parameters of the system from X-ray observations. In contrast to previous studies that concentrates on searching for ”general” correlation oranti-correlation states between X-ray flux and spin rate (Chakrabarty et al. 1997b; Paul et al.1997; Gonzales-Golan et al. 2012), we search for episodic correlations and anti-correlationson shorter time scales ( ∼ ∼ MNRAS , 1–20 (2017) M. M. Serim, ¸S. ¸Sahiner, D. ¸Cerri–Serim, S. ¸C. ˙Inam, and A. Baykal states continues for several decades of orbital cycles. The accretion process in GX 1+4 isunique as it is qualitatively seen from correlation – anti-correlation episodes and torque noisepower law trend.Future monitoring observations of GX 1+4 will be useful to further understand the torque − X-ray luminosity relation.
We investigate X-ray energy spectrum of the source using absorbed power law model withor without cut-off, including a Gaussian line for Iron line complex. Analysis of the timeresolved spectra by using individual RXTE-PCA observations indicate a significant correla-tion between iron line flux and unabsorbed X-ray flux for the first time for GX 1+4. Similarcorrelation was found before for the accretion powered X-ray pulsars OAO 1657-415 (Jai-sawal & Naik 2014), SWIFT J1729.9–3437 (¸Sahiner et al. 2013), Her X-1 (Naik & Paul2003; ˙Inam & Baykal 2005) and LMC X-4 (Naik & Paul 2003). This correlation might bean indication of the fact that the iron lines originates from the cool matter near the neutronstar (Makishima 1986).Pulse phase resolved spectra of the source are also studied. Using the same spectral modelused for the analysis of time resolved spectra, it is found that the spectral bin correspondingto the pulse minimum has significantly higher cutoff energy, lower photon index and lowere-folding energy indicating a harder spectrum for pulse minimum. Moreover, the same pulsephase shows an increase in equivalent width of Fe line whithout any significant change inline flux. A constant line flux over all the pulse phases might be an indication of the fact thatthe line emitting region surrounds the pulsar, whereas broadening of Fe line on continuumof minimum phase might be a consequence of the blending of K α and K β lines at 6.4 and7.05 keV, while K β at 7.05 keV is smothered due to enhanced emission on the continuum ofother phases. ACKNOWLEDGMENT
We acknowledge support from T ¨UB˙ITAK, the Scientific and Technological Research Coun-cil of Turkey through the research project MFAG 114F345. We would like to thank theanonymous referee for valuable comments which helped to improve the manuscript.
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