Vojtech SimonVojtech Simon

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Monitoring of low-mass Monitoring of low-mass binary X-ray sourcesbinary X-ray sources

Astronomical Institute, Academy of SciencesAstronomical Institute, Academy of Sciences251 65 Ondrejov, Czech Republic251 65 Ondrejov, Czech Republic

Talk: AXRO, Dec 10–13, 2012Talk: AXRO, Dec 10–13, 2012

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Transient X-ray sources:Transient X-ray sources: wide-field monitoring of the sky is necessary (most transients are wide-field monitoring of the sky is necessary (most transients are

discovered only by the first detection of their outburst)discovered only by the first detection of their outburst)

outbursts are usually unpredictable – only their mean recurrence outbursts are usually unpredictable – only their mean recurrence time (cycle-length) can be determined from a long (years to time (cycle-length) can be determined from a long (years to decades) series of observationsdecades) series of observations

(Quasi)persistent X-ray sources:(Quasi)persistent X-ray sources: transitions between the high/low states (and fluctuations in the hightransitions between the high/low states (and fluctuations in the high

state) are usually fast (~days) and unpredictable state) are usually fast (~days) and unpredictable

Superorbital X-ray variations:Superorbital X-ray variations: timescale of weeks and months timescale of weeks and months

stability of the cycle depends on the parameters of the system stability of the cycle depends on the parameters of the system 22

The importance of the long-term coverage (I)The importance of the long-term coverage (I)

Occasional pointing in any spectral band is not enough:Occasional pointing in any spectral band is not enough:

many pieces of information on the time evolution are lost in any many pieces of information on the time evolution are lost in any spectral bandspectral band

time allocation has to be justified (search for unexpected behavior time allocation has to be justified (search for unexpected behavior of the object is usually not approved)of the object is usually not approved)

Determining a comprehensive picture about the processes operating Determining a comprehensive picture about the processes operating in a given system (or a group of systems) requires analysis of an in a given system (or a group of systems) requires analysis of an ensemble of events.ensemble of events.

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We will discuss the activity in various X-ray bands and how We will discuss the activity in various X-ray bands and how monitoring helps.monitoring helps.

The importance of the long-term coverage (II)The importance of the long-term coverage (II)

Donor, lobe-filling starDonor, lobe-filling star

Mass streamMass stream

Compact object Compact object (NS, BH)(NS, BH)

Accretion diskAccretion disk

Donor – thermal radiation Donor – thermal radiation (optical, IR)(optical, IR)

Typical structure of lTypical structure of low-mass X-ray binariesow-mass X-ray binaries (LMXBs)(LMXBs)

Outer disk region – thermal Outer disk region – thermal radiation (UV, optical, IR)radiation (UV, optical, IR)

Jets: synchrotron (radio, IR?)Jets: synchrotron (radio, IR?)

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Inner disk region – thermal Inner disk region – thermal radiation radiation (soft X-rays ((soft X-rays (EE up to several keV)) up to several keV))

Comptonizing cloud around the Comptonizing cloud around the compact object (inverse Comptoncompact object (inverse Compton scattering – hard X-rays) scattering – hard X-rays)

Types of the long-term activityTypes of the long-term activity Outbursts vs. quiescenceOutbursts vs. quiescence – mass accumulates in the outer regions – mass accumulates in the outer regions

of the accretion disk during quiescence of the accretion disk during quiescence

– – strong accretion of matter from the disk strong accretion of matter from the disk onto the central compact object during onto the central compact object during outburstoutburst

High/low state transitionsHigh/low state transitions – transient decrease of the mass transfer – transient decrease of the mass transfer rate rate

Cyclic (superorbital) changesCyclic (superorbital) changes of luminosity (variations of the disk of luminosity (variations of the disk shape and interaction of the disk with the inflowing mass stream shape and interaction of the disk with the inflowing mass stream from the donor)from the donor)

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Low-mass binary X-ray sources – excellent Low-mass binary X-ray sources – excellent targets for monitoringtargets for monitoring

What can we expect from data from X-ray monitors?What can we expect from data from X-ray monitors?

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Various physical processes produce specific large-amplitude variations of X-ray Various physical processes produce specific large-amplitude variations of X-ray luminosity on a timescale of days, weeks, to years and decades. luminosity on a timescale of days, weeks, to years and decades.

The characteristic features (e.g. outbursts, high/low state transitions) can be The characteristic features (e.g. outbursts, high/low state transitions) can be investigated even in a single-band X-ray light curve (monitors often work with a investigated even in a single-band X-ray light curve (monitors often work with a single band (typically in soft X-rays, a few keV)). single band (typically in soft X-rays, a few keV)).

Even some model predictions are already available Even some model predictions are already available

Dividing the observed spectral region into several bands (e.g. used in ASM/RXTE) Dividing the observed spectral region into several bands (e.g. used in ASM/RXTE) or simultaneous usage of various monitors (e.g. ASM/RXTE & BAT/Swift) helps to or simultaneous usage of various monitors (e.g. ASM/RXTE & BAT/Swift) helps to distinguish between various processes influencing the luminosity.distinguish between various processes influencing the luminosity.

Properties of the basic outburst light curves in soft X-raysProperties of the basic outburst light curves in soft X-rays

(model: Dubus et al. 2001)(model: Dubus et al. 2001)

Dependence of the outburst Dependence of the outburst profile on irradiation of profile on irradiation of the diskthe disk

Simulated cycle-length Simulated cycle-length of the outburstsof the outbursts

Mas

s ac

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ion

rate

(g/s

)M

ass

accr

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/s)

Mas

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(g/s

)M

ass

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/s)

Mission: RXTE (Rossi X-Ray Timing Explorer)

Three wide-angle shadow cameras equipped with proportional counters, each with 6 x 90 degrees FOV

Collecting area: 90 cm2

Detector: Xenon proportional counter, position-sensitive

Energy range: 1.5 – 12 keV in three bands: 1.5 – 3 keV 3 – 5 keV 5 – 12 keV

Time resolution: 80% of the sky every 90 min (but one-day means are usually used to increase the sensitivity)

Spatial resolution: 3 x 15 arcmin

Sensitivity: 30 mCrab (but obs. show ~13 mCrab for one-day means)

Operation: January 1996 – 2012

ASMASM

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ASM/RXTE - monitor for soft X-raysASM/RXTE - monitor for soft X-rays

SSmooth linesmooth lines:: fits by HEC13fits by HEC13

Spectral changes can be measured in the ASM/RXTE data (band A, band B, band C)Spectral changes can be measured in the ASM/RXTE data (band A, band B, band C)

Absorption of X-rays can be measured even by monitors – it is predicted to Absorption of X-rays can be measured even by monitors – it is predicted to influence mostly the softest band influence mostly the softest band

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KS 1731-260KS 1731-260

Typical X-ray spectrum of a low-mass X-ray binary in outburst (a high state)Typical X-ray spectrum of a low-mass X-ray binary in outburst (a high state)

Simon (2012)Simon (2012)

The highest intensity in The highest intensity in the soft X-ray bandthe soft X-ray band

Steep decrease of intensity Steep decrease of intensity with growing energy – it with growing energy – it is is better to construct better to construct monitors monitors observing in soft X-ray observing in soft X-ray bandband

Narita et Narita et al. (2001)al. (2001)

ASCA ASCA spectrumspectrum

V1500 Cyg – classical nova

All-Sky Monitor (ASM/RXTE)

Z Cam – dwarf nova

View toward the Galactic centerMost detected objects are binary systems with mass-accreting neutron star or black hole.

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Composed view of X-ray sky in soft X-rays (1.5–12 keV)Composed view of X-ray sky in soft X-rays (1.5–12 keV)

Mission: NASA Swift

Aperture: Coded mask

Detecting area: 5200 cm2

Field of view: 1.4 sr (partially-coded)

Detection elements: 256 modules of 128 elements

Telescope PSF: 17 arcmin

Energy range: 15 - 150 keV (15 - 50 keV is used for monitoring of X-ray sources)

Operation: since 20041010

BAT/Swift – monitor for very hard X-raysBAT/Swift – monitor for very hard X-rays

Most X-ray binary sources concentrate toward the Galactic plane.1111

BAT/Swift monitorBAT/Swift monitor

Composed view of X-ray sky in very hard X-rays (15–50 keV)Composed view of X-ray sky in very hard X-rays (15–50 keV)

Tueller et al. (2010)Tueller et al. (2010)

ASM/RXTE (one-day means) 1.5–12 keV 1996-2008ASM/RXTE (one-day means) 1.5–12 keV 1996-2008

Outbursts in Outbursts in NS soft X-ray NS soft X-ray

transient transient

Aql X-1Aql X-1

Progress with the recent Progress with the recent monitors: monitors:

Better-defined features Better-defined features of the intense events of the intense events (e.g. outbursts or high (e.g. outbursts or high states generally) states generally)

Minor outbursts can be Minor outbursts can be resolved (important for resolved (important for the assessment of the the assessment of the activity of the object)activity of the object)

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Vela 5B (10-day means) 3–12 keV 1969-1976Vela 5B (10-day means) 3–12 keV 1969-1976

Priedhorsky & Terrell (1984)Priedhorsky & Terrell (1984)

Cou

nts

/ sC

ount

s / s

X-ray light curves from monitors: the effect of improving sensitivityX-ray light curves from monitors: the effect of improving sensitivity

Decaying branchDecaying branch (measure of (measure of propagation of the so-called cooling propagation of the so-called cooling front across the disk) – the most front across the disk) – the most stable part of outburst, its slope is stable part of outburst, its slope is independent of the peak luminosity independent of the peak luminosity of outburst. of outburst.

ASM/RXTEASM/RXTE data data (1.5 – 12 keV)(1.5 – 12 keV)

Simon (2002)Simon (2002)1313

Properties of the ensemble of outbursts Properties of the ensemble of outbursts in soft X-rays (1.5–12 keV)in soft X-rays (1.5–12 keV) Aql X-1 = V1333 AqlAql X-1 = V1333 Aql

Evolution of hardness ratios with Evolution of hardness ratios with intensity during a set of outbursts. intensity during a set of outbursts.

Big circle: peak of a given outburst Big circle: peak of a given outburst

ASM/RXTEASM/RXTE hardness ratios: hardness ratios: HR1 = Flux (3-5 keV) / Flux (1.5-3 keV)HR1 = Flux (3-5 keV) / Flux (1.5-3 keV)HR2 = Flux (5-12 keV) / Flux (3-5 keV)HR2 = Flux (5-12 keV) / Flux (3-5 keV)

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Relation between Relation between the the O-C curve and O-C curve and TTCC: :

LLinear profile of inear profile of the the O-C curve O-C curve – – constant constant TTCC

Parabolic profile ofParabolic profile of O-CO-C – – linear change of linear change of TTCC

Variations of the recurrence time TC (cycle-length) of outbursts are large, but not chaotic – occasional jumps are not explicable by the evolutionary processes.

This SXT serves as a clear evidence that the variations of Imax and TC are reliable only if also the faint outbursts are detected.

Times of the peaks of the outbursts determined from the observations of different monitors are often in good mutual agreement.

Simon (2002, 2010)Simon (2002, 2010)

Aql X-1 = V1333 AqlAql X-1 = V1333 Aql

Peak intensity Peak intensity of outburstof outburst

Evolution of residuals of Evolution of residuals of the mean recurrence time the mean recurrence time TTCC of outbursts of outbursts

WWWZWZ--ttransformransform (method of Foster 1996) (method of Foster 1996)Time evolution of the recurrence time Time evolution of the recurrence time

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Peak intensity of outburstPeak intensity of outburst

Evolution of the residuals of Evolution of the residuals of the mean recurrence timethe mean recurrence time

Recurrence time Recurrence time of outburstsof outbursts

Investigation of a relation between two parameters easily measurable by the monitor – recurrence time of outbursts, and the peak soft X-ray intensity:

TC ~ 136 days, modulated by a cycle-length of about 5.4 years.

The most luminous outbursts occur after the time of the longest TC.

WWZ-transform can be used even for seach for cycles in so transient events like outbursts

Simon Simon (2008)(2008)

Soft X-ray transient GRS 1747–312Soft X-ray transient GRS 1747–312

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GX 339 – 4 GX 339 – 4 Black hole transientBlack hole transient

ASM/RXTE (1.5-12 keV)ASM/RXTE (1.5-12 keV)

BAT/Swift (15-50 keV)BAT/Swift (15-50 keV)

Star

t of o

utbu

rst

Peak

of o

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Very large differences between the profiles of the outburst in the soft and the very hard X-rays:

Start of the outburst almost simultaneous for both bands State transition close to the peak luminosity in both bands Very fast decay of the BAT luminosity The outburst lasts much longer in the BAT band

Faint very hard outburst

Tang et al. (2011)Tang et al. (2011)

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XTE J1701-462XTE J1701-462

A very long (~600 d) outburst of the neutron star SXTA very long (~600 d) outburst of the neutron star SXT

ASM/RXTE (1.5-12 keV) BAT/Swift (15-50 keV)ASM/RXTE (1.5-12 keV) BAT/Swift (15-50 keV)

Residuals of the fit smoothed by the two-sided moving averages with various filter half-widths Q

Number of data in each meanNumber of data in each mean

conj

unct

ion

Z and atoll sourceZ and atoll sourceA borderline source between transient A borderline source between transient

and persistent neutron star systemsand persistent neutron star systems

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Typical X-ray spectrum during outburstXTE J1701-462XTE J1701-462

ASM/RXTE ASM/RXTE

Ding et al. (2011)Ding et al. (2011)

PCA/RXTE PCA/RXTE spectrumspectrum

BAT/SwiftBAT/Swift

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Time evolution of the smoothed residuals of the ASM/RXTE and BAT/Swift measurements during the outburst

The largest fluctuations during the primary peak of soft X-ray luminosity

XTE J1701-462XTE J1701-462

Primary peak Primary peak of soft X-ray of soft X-ray

luminosityluminosity

Plateau of soft Plateau of soft X-ray luminosityX-ray luminosity

Final decay Final decay of luminosityof luminosity

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XTE J1701-462XTE J1701-462

Time evolution of hardness ratio Time evolution of hardness ratio HR HR = I= IASMASM / I / IBATBAT during decline of the outburst during decline of the outburstHRHR was determined for the data included in a segment of 30 days was determined for the data included in a segment of 30 days

Primary peakPrimary peakof soft X-rayof soft X-ray

luminosityluminosity

Final decay Final decay of luminosityof luminosity

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XTE J1701-462XTE J1701-462

HEC13 fit to the fluctuations in the one-day means in the ASM/RXTE light curveHEC13 fit to the fluctuations in the one-day means in the ASM/RXTE light curve

The times of maxima and minima of the cycle in segment A and segment B were The times of maxima and minima of the cycle in segment A and segment B were determined from the HEC13 fit. determined from the HEC13 fit.

The intervals of +/-25 days from the conjunction with the Sun are marked.The intervals of +/-25 days from the conjunction with the Sun are marked.

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Segment ASegment ASegment BSegment B

Time evolution of cycle Time evolution of cycle

WWWZ (method of Foster 1996)WZ (method of Foster 1996)

XTE J1701-462XTE J1701-462

WWZ-transform of the HEC13 fit to the WWZ-transform of the HEC13 fit to the modulation in the ASM data modulation in the ASM data

The best cycle-length (in days). Only the The best cycle-length (in days). Only the segments with the amplitude larger than segments with the amplitude larger than 15 percents of its peak value. 15 percents of its peak value.

Amplitude of the cycle-length in segments Amplitude of the cycle-length in segments A and B (the horizontal lines - amplitude of A and B (the horizontal lines - amplitude of 15 percents of its peak value) 15 percents of its peak value)

Weighted wavelet Z-transform of the X-ray Weighted wavelet Z-transform of the X-ray light curve during the outburst light curve during the outburst

Residuals of the HEC13 fit to the ASM data Residuals of the HEC13 fit to the ASM data averaging through the modulation. averaging through the modulation.

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Distance between dot-dashed lines: the length of the cycle used in the ephemeris (21 days).

XTE J1701-462XTE J1701-462

O-C diagram for the times of the maxima and minima of the ASM/RXTE intensity in the cycle during the outburst (segments A and B).

Maxima of intensity (closed circles) Minima of intensity (open circles)

Segment of the ASM light curve of the Segment of the ASM light curve of the outburst with the large-amplitude outburst with the large-amplitude fluctuations fluctuations

Cyclic fluctuations are prominent Cyclic fluctuations are prominent in all ASM bands (HEC13 fits with in all ASM bands (HEC13 fits with identical parameters)identical parameters)

Vertical lines: times of the minima of Vertical lines: times of the minima of IIAA in the fit. in the fit.

ASM hardness ratios determined from ASM hardness ratios determined from the fits to the fits to IIAA, , IIBB, and , and IICC – – absorption of absorption of X-rays is NOT dominantX-rays is NOT dominant

Accompanying intensity variations in Accompanying intensity variations in the BAT data – no cyclic modulation, the BAT data – no cyclic modulation, only rapid fluctuationsonly rapid fluctuations 2424

XTE J1701-462XTE J1701-462Search for the nature of Search for the nature of the modulationthe modulation

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XTE J1701-462XTE J1701-462Time evolution of cycle Time evolution of cycle

ASM/RXTE (1.5-12 keV)ASM/RXTE (1.5-12 keV)

BAT/Swift (15-50 keV)BAT/Swift (15-50 keV)

Segment ASegment A

Segment BSegment B

Striking discrepancy between the behavior in the soft and the hard X-ray bands

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Cygnus X-2Cygnus X-2

Z source: persistent Z source: persistent neutron star systemneutron star system

ASM/RXTE (1.5-12 keV)ASM/RXTE (1.5-12 keV)

BAT/Swift (15-50 keV)BAT/Swift (15-50 keV)

Striking discrepancy between the character of activity in the soft and the hard X-ray bands:

Soft band – superorbital variations

Hard band – only rapid large-amplitude fluctuations

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Cygnus X-2Cygnus X-2

WWZ-transform of the one-day means of the ASM/RXTE intensity

Amplitude of this cycle-length

The best cycle-length (in days) - only segments with amplitude larger than 20 percents of its peak value

WWZ-transform of the HEC13 fit to the ASM curve.

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Cygnus X-2Cygnus X-2

ASM/RXTE (1.5-12 keV)ASM/RXTE (1.5-12 keV)

BAT/Swift (15-50 keV)BAT/Swift (15-50 keV)

Striking discrepancy between the behavior in the soft and the hard X-ray bands

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4U 1820-304U 1820-30 Atoll source: NS persistent sourceAtoll source: NS persistent source

Superorbital modulation probably due to Mazeh & Shaham mechanism Superorbital modulation probably due to Mazeh & Shaham mechanism ((Mazeh & Shaham 1979Mazeh & Shaham 1979;; Chou & GrindlayChou & Grindlay 2001)

State transitions occur during some episodes of minimum of soft X-ray luminosityState transitions occur during some episodes of minimum of soft X-ray luminosity

ASM/RXTE (1.5-12 keV)ASM/RXTE (1.5-12 keV)

BAT/Swift (15-50 keV)BAT/Swift (15-50 keV)

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4U 1820-304U 1820-30

ASM/RXTEASM/RXTE oone-day means of ne-day means of intensity in intensity in the 1.5-12 keV the 1.5-12 keV bandband

TTriangles riangles – times – times of maxima and minimaof maxima and minima of intensity in the 172 d cycle (Mazeh & of intensity in the 172 d cycle (Mazeh & Shaham mechanism) Shaham mechanism)

Profile of the cycle is smoothed Profile of the cycle is smoothed by the by the mmoving averages for oving averages for QQ=17 days =17 days

VVertical barsertical bars: : prominent and well covered prominent and well covered episodes of brief low states episodes of brief low states

Simon (2003)Simon (2003)

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4U 1820-304U 1820-30

Simon (2003)Simon (2003)

ASM/RXTE ASM/RXTE light curve folded with light curve folded with the the 1172 day 72 day cycle of cycle of activityactivity (the (the yeyears 1996-2002ars 1996-2002) )

FFolded data olded data are are smoothed smoothed by the by the two-sided two-sided moving moving averages averages for for the filter half-widths the filter half-widths QQ=0.05, 0.06, =0.05, 0.06, 0.08, 0.10, and 0.12 phase0.08, 0.10, and 0.12 phase..

SSkewness of the residualskewness of the residuals

NNumber of umber of datadata

Smoothed residuals Smoothed residuals of the fitsof the fits

Evolution of the hardness ratios with the 172 day cycle of activity (Mazeh & Shaham mechanism)

Smoothing by the two-sided moving averages for Q=0.05 and 0.08 phase. 3232

4U 1820-304U 1820-30

Simon Simon (2003)(2003)

ASM/RXTEASM/RXTE hardness ratios: hardness ratios: HR1= Flux (3-5 keV) / Flux (1.5-3 keV)HR1= Flux (3-5 keV) / Flux (1.5-3 keV)HR2= Flux (5-12 keV) / Flux (3-5 keV)HR2= Flux (5-12 keV) / Flux (3-5 keV)

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4U 1820-304U 1820-30

Simon (2003)Simon (2003)

DDependence of ependence of HRHR1 1 and and HRHR2 on 2 on the the 1.5-12 keV intensity1.5-12 keV intensity

SSmooth linesmooth lines: HEC13 : HEC13 fits to the fits to the wholewhole data set. data set.

EEmpty circlesmpty circles: : the arithmetic means the arithmetic means for three episodes of for three episodes of deepdeep brief low brief low states (BLS) superimposed on the states (BLS) superimposed on the 172 day cycle172 day cycle

Individual Individual data of BLS data of BLS – – dark (blue) dark (blue) points. points.

Hardness ratio vs. intensityHardness ratio vs. intensity

DDense series of ense series of X-ray X-ray observations observations from monitors from monitors covering the covering the intervals of intervals of at least at least severalseveral years years are are necessary tonecessary to investigate investigate the properties of the long-term activity of binary X-ray sources: the properties of the long-term activity of binary X-ray sources:

to to resolve the resolve the outbursts and/or outbursts and/or transitionstransitions between high and between high and low stateslow states

to place these events in the context of the long-term activity to place these events in the context of the long-term activity of a given systemof a given system

to form a representative ensemble of events in to form a representative ensemble of events in (a) a given X-ray binary system, (a) a given X-ray binary system, (b) in a type of X-ray binary systems(b) in a type of X-ray binary systems

This is important for our understanding of the physical processes This is important for our understanding of the physical processes involvedinvolved in these systems in these systems. .

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General conclusions (I)General conclusions (I)

Profiles of features of the long-term Profiles of features of the long-term activity are activity are measurable by measurable by the monitors the monitors – – a very a very large large variety existsvariety exists. S. Search earch for for the the common features is needed. common features is needed.

Search for the accompanying spectral variations (changes of Search for the accompanying spectral variations (changes of hardness ratios are measurable by some monitors – e.g. hardness ratios are measurable by some monitors – e.g. ASM/ASM/RXTERXTE or a combination of simultaneous ASM/ or a combination of simultaneous ASM/RXTERXTE & & BAT/BAT/SwiftSwift observing). observing).

We emphasize theWe emphasize the very important role of very important role of the spectral region of the spectral region of the the X-ray monitorX-ray monitor – a very hard X-ray band like the one in – a very hard X-ray band like the one in BAT/BAT/SwiftSwift sometimes maps quite a different activity (probably sometimes maps quite a different activity (probably coming from a different spectral component)coming from a different spectral component)..

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General conclusions (II)General conclusions (II)

Time evolution of the recurrence time Time evolution of the recurrence time TTCC of outbursts is very little of outbursts is very little studied mainly because of the lack of data. Only very few SXTs studied mainly because of the lack of data. Only very few SXTs with quite short with quite short TTCC of less than a year could be investigated so of less than a year could be investigated so far. far. Important:Important: measuring measuring TTCC and its time evolution can often be and its time evolution can often be made even if the individual monitors work with made even if the individual monitors work with different spectral bands – the time of the outburst different spectral bands – the time of the outburst in SXT is often comparable for the soft and the in SXT is often comparable for the soft and the hard X-ray band. Very long time segments can be hard X-ray band. Very long time segments can be thus investigated. thus investigated.

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General conclusions (III)General conclusions (III)

Acknowledgements:Acknowledgements:

This research has made use of the observations provided by This research has made use of the observations provided by the ASM/RXTE team. I also acknowledge the use of public the ASM/RXTE team. I also acknowledge the use of public data from the Swift data archive. This study was supported data from the Swift data archive. This study was supported by the grant 205/08/1207 provided by the Grant Agency of by the grant 205/08/1207 provided by the Grant Agency of the Czech Republic and the project RVO:67985815. I made the Czech Republic and the project RVO:67985815. I made use of the code developed by Dr. G. Foster and available at use of the code developed by Dr. G. Foster and available at http: //www.aavso.org/data/software/wwz.shtml. http: //www.aavso.org/data/software/wwz.shtml. I thank Prof. P. Harmanec for providing me with the code I thank Prof. P. Harmanec for providing me with the code HEC13. The Fortran source version, compiled version and HEC13. The Fortran source version, compiled version and brief instructions how to use the program can be obtained brief instructions how to use the program can be obtained via http: //astro.troja.mff.cuni.cz/ftp/hec/HEC13/. via http: //astro.troja.mff.cuni.cz/ftp/hec/HEC13/. Some images come from the web pages of HEASARC.Some images come from the web pages of HEASARC.

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