Phase lags of quasi-periodic oscillations across source states in - - PowerPoint PPT Presentation

Phase lags of quasi-periodic oscillations across source states in the low-mass X-ray binary 4U 1636–53

de Avellar, M., M´ endez, M., Altamirano, D., Sanna, A., Zhang, G. (2016) Marcio G B de Avellar April 28, 2016

J W Goethe Universit¨ at / Universidade de S˜ ao Paulo NewCompStar Meeting 2016, Istanbul

Table of contents

• 1. Quasi-periodic Oscillations (QPOs) and source states
• 2. Frequency correlations: benchmarks
• 3. Time/phase lags
• 4. Marcio @ ITP

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Quasi-periodic Oscillations (QPOs) and source states

QPOs

0.0001 0.001 0.01 0.1 Power Box 20 Lb2 Lb LhHz Ll Lu Summed

• 2

2 1 10 100 1000 Residual ν [Hz]

Figure 1: We fit the components with Lorentzians. The appearance of the components depend of the source position in the CCD.

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Source states

0.6 0.7 0.8 0.9 1 1.1 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 HC SC 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Sa = 2 Sa = 1

Figure 2: We divided the CCD in 37 regions. The line parametrises the position via the parameter Sa. We averaged the observations within each box.

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Where do we find QPOs?

We see QPOs in very different systems:

• AGNs,
• ULXs,
• CVs recall the talk by Solen

Balman,

• LMXBs ...

The “common structure” is some kind of the accretion flow.

Figure 3: LMXBs scheme; we focus

• n the inner edge of the disc where

the dominant emission is in X-rays.

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Frequency correlations: benchmarks

Frequency correlations

0.1 1 10 100 1000 100 1000 νmax (Hz) νu (Hz) Lb2 Lb LhHz Lh Llow Ll 4U 1636-53

Figure 4: Altamirano (2008) plus Marcio’s data. Pay attention to the νl-νu relation in the upper right corner.

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Time/phase lags

Concepts

Time/phase lags are Fourier-frequency-dependent measurements of the time (phase) delays between two concurrent and correlated signals, i.e. two light curves of the same source, in two different energy bands, s(t) and h(t). If Sxx = S(ν)∗S(ν) = |S(ν)|2 is PDS of s(t) and Hyy = H(ν)∗H(ν) = |H(ν)|2 is PDS of h(t), ∆φ(ν) = arctan Im(S(ν)∗H(ν)) Re(S(ν)∗H(ν))

• and the corresponding time lags

∆t = ∆φ ν . Differences in photon arrival times give information about the source size and propagation speeds.

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Concepts

We then studied the frequency dependence, the position dependence and the energy dependence of the phase lags of each QPO, since:

• Dependence on frequency/Sa ⇒ geometry of the medium.
• Dependence on energy ⇒ physical conditions of the medium (T, ρ,

radiative processes). We look for trends of the phase lags with the quantities.

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Frequency dependence

• 0.2
• 0.1

0.1 0.2 0.3 0.4 2 4 6 8 10 ∆φ/2π ν [Hz]

Lb2

• 0.1
• 0.05

0.05 0.1 10 20 30 40 50 ∆φ/2π ν [Hz]

Lb

• 0.04
• 0.02

0.02 0.04 10 20 30 40 50 ∆φ/2π ν [Hz]

Lh

• 0.1
• 0.05

0.05 0.1 80 100 120 140 160 180 200 ∆φ/2π ν [Hz]

LhHz

• 0.06
• 0.04
• 0.02

0.02 0.04 500 550 600 650 700 750 800 850 900 950 ∆φ/2π ν [Hz]

Ll

• 0.04
• 0.02

0.02 0.04 0.06 500 600 700 800 900 1000 1100 1200 ∆φ/2π ν [Hz]

Lu

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Position dependence

• 0.2
• 0.1

0.1 0.2 0.3 0.4 1.8 1.85 1.9 1.95 2 2.05 2.1 2.15 ∆φ/2π Sa

Lb2

• 0.1
• 0.05

0.05 0.1 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 ∆φ/2π Sa

Lb

• 0.04
• 0.02

0.02 0.04 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 ∆φ/2π Sa

Lh

• 0.1
• 0.05

0.05 0.1 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 ∆φ/2π Sa

LhHz

• 0.04
• 0.02

0.02 0.04 1.9 1.95 2 2.05 2.1 2.15 2.2 2.25 2.3 ∆φ/2π Sa

Ll

• 0.04
• 0.02

0.02 0.04 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 ∆φ/2π Sa

Lu

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Energy dependence

• 0.04
• 0.03
• 0.02
• 0.01

0.01 0.02 0.03 0.04 2 4 6 8 10 12 14 16 18 20 ∆φ/2π E [keV]

Lb2

• 0.04
• 0.03
• 0.02
• 0.01

0.01 0.02 0.03 0.04 2 4 6 8 10 12 14 16 18 20 ∆φ/2π E [keV]

Lb

• 0.03
• 0.02
• 0.01

0.01 0.02 0.03 0.04 0.05 0.06 2 4 6 8 10 12 14 16 18 20 ∆φ/2π E [keV]

Lh

• 0.03
• 0.02
• 0.01

0.01 0.02 0.03 0.04 0.05 0.06 2 4 6 8 10 12 14 16 18 20 ∆φ/2π E [keV]

LhHz

• 0.03
• 0.02
• 0.01

0.01 0.02 2 4 6 8 10 12 14 16 18 20 ∆φ/2π E [keV]

Ll

• 0.04
• 0.02

0.02 0.04 0.06 0.08 2 4 6 8 10 12 14 16 18 20 ∆φ/2π E [keV]

Lu

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Summary and implications

Recalling, we looked for trends in the phase lags with ν, Sa and E.

• Dependence on frequency/Sa ⇒ geometry of the medium.
• Dependence on energy ⇒ physical conditions of the medium.

Except for the lower kHz QPO, the phase lags of all the other QPOs are independent of the frequency or Sa. Except for the lower kHz QPO and the hump QPO, the phase lags of all the other QPOs are independent of the energy. ps: when we say “there is no trend” we actually mean that we cannot discern with these data a constant from a linear increase/decrease.

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Models that involve reflection off the disc or Comptonization

c∆t ⇒ upper limit to the size of the medium in which the time lags are produced. a ∼ c∆t kbTe mec2 4τ ln(E2/E1).

Table 1: a is the size scale and ne is the electronic density of the medium. Here, E2 = 16.0 keV, E1 = 7.1 keV, kbTe = 5 keV, τ = 5, ne = τ/(aσT). QPO c∆t [km] a [km] ne [1020 cm−3] Lb2 2610 ± 630 628.6 ± 151.7 0.0012 ± 0.0003 Lb 15 ± 27 3.6 ± 6.5 0.21 ± 0.37 Lh 240 ± 30 57.8 ± 7.2 0.013 ± 0.002 LhHz 2.4 ± 10.5 0.58 ± 2.53 1.3 ± 5.7 Ll 6.3 ± 0.6 1.52 ± 0.14 0.50 ± 0.05 Lu 3.0 ± 0.6 0.72 ± 0.14 1.04 ± 0.21

Notice the very low densities.

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BHC systems

• M´

endez et al (2015): for GRS 1915+105: the (soft) lags of ν1 = 35 Hz are inconsistent with the (hard) lags of ν2 = 67 Hz. Similarly to the kHz QPOs of 4U 1636–53.

• LhHz in NS-LMXBs could be related to the QPOs of BHC in the

180-450 Hz range.

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Placing the upper kHz QPO

• Bult and van der Klis (2015): SAX J1808.4-3658 ⇒ νu results from

azimuthal motion at the inner edge of the disc.

• Bachetti (2010) and Romanova and Kulkarni (2009): can produce

high frequency QPOs with 3D simulations of the accretion flow onto a magnetized neutron star. SAX J1808.4-3658 is a accreting ms X-ray pulsar classified as an atoll source (like 4U 1636–53). We suggest that:

• The phase lags of the upper kHz QPO encode the properties of

the medium at the magnetospheric radius (where the upper kHz QPO would be produced, 6 to 11 km from the surface in our estimations).

• The phase lags of the lower kHz QPO encode the properties of

the medium at the boundary layer and nearby (where the lower kHz QPO would be produced).

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What about the energy dependence of the lags?

• Lee, Misra, Taam (2001): up-scattering Comptonization Model for

the soft lags of Ll where the corona and disc temperatures

• scillates coherently at the QPO frequency ⇒ a ∼ 5 km; explain

also the rms% vs E. Cannot explain the other lags.

• Kumar and Misra (2014): a thermal Comptonizing plasma that
• scillates at QPO frequency. The soft lags of Ll are seen only when

the heating rate of the corona varies and a significant fraction

• f the photons impinge back onto the source of soft photons

⇒ a ∼ 1 km; explain also the rms% vs E. Cannot explain the other lags.

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Picture to have in mind

Figure 5: From Falanga and Titarchuk (2007).

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Conclusion

• Peille et al (2015): QPO spectrum is compatible with a black body

spectrum with Tbb > Tcontinuum; lags of Ll are systematically different from the lags of Lu. Their scenario: if lags of Lu are reverberation-dominated, then Lu comes simply from variation in luminosity at the inner edge of the disc, a response to variations in ˙ M onto the boundary layer. ⇒ The similarity between the lag-energy spectrum of Lu and of the Lb, Lh, LhHz found here would imply similar origins.

If extended to include all the other QPOs, these models provide an opportunity to study the dynamic and physical conditions of the Comptonising corona in neutron-star low-mass X-ray binaries.

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Marcio @ ITP

Using observational data we want

Identify frequencies, not only νl and νu, but also other frequencies that could be linked to other QPOs and infer the neutron star parameters.

lo=3.806213523 rcusp=4.55 rmax=8.43 rext=16.56 Rns=4.55 Mns=1.7 Msun Rns=11.42 km Torus Size = 12.01 = 30.15 km

Figure 6: The biggest torus around this star. Constant angular momentum distribution.

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Questions? Thanks.

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