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 19, 2016 J W Goethe Universit¨ at / Universidade de S˜ ao Paulo

Table of contents 1. About Marcio 2. Quasi-periodic Oscillations (QPOs) and source states 3. LMXBs 4. Motivation 5. Frequency correlations: benchmarks 6. Time/phase lags 7. The paper 8. Marcio @ ITP 2

About Marcio

Professional data Post-doc at IAG-USP, S˜ ao Paulo, Brasil, under supervision of prof. Dr. Jorge Horvath. Now, visiting ITP under supervision of prof. Dr. Luciano Rezzolla. Research: • Information Theory applied to equation of state of compact objects; • Entropy along stellar evolution; • Magnetic field evolution in the context of red backs and black widows (in progress); • Hybrid neutron stars (in its beginnings); • X-ray astrophysics of low-mass X-ray binaries (QPOs and time/phase lags). 4

Quasi-periodic Oscillations (QPOs) and source states

Light curve and PDS Light curve of an observation ⇔ time series. 14 13 12 11 counts/sec 10 9 8 7 6 5 4 5.01967 5.01967 5.01967 5.01968 5.01968 5.01968 5.01968 5.01968 5.01969 5.01969 sec [10 8 ] Figure 1: X-ray light curve of one observation of 4U 1636–53. We look for periodicities and patterns ⇒ Fourier transform. 6

Components of the PDS and their appearance We find many features in the PDS: 1.1 1.0 Hard color (Crab) -1 log 10 ( L / L Edd. ) 0.9 0.8 0.7 -2 0.6 0.5 1608 Aql X-1 1705 1.1 1.0 Hard color (Crab) -1 log 10 ( L / L Edd. ) 0.9 0.8 0.7 -2 0.6 0.5 1636 0614 1728 1.1 Hard color (Crab) 1.0 -1 log 10 ( L / L Edd. ) 0.9 0.8 0.7 -2 0.6 0.5 1820 1735 GX 3+1 0.8 1 1.2 1.4 1.6 0.8 1 1.2 1.4 1.6 0.8 1 1.2 1.4 1.6 Soft color (Crab) Soft color (Crab) Soft color (Crab) Figure 2: Left: PDS of a X-ray light curve (Altamirano 2008). Right: colour-colour diagram (CCD) plus luminosity (Linares 2009, thesis). Pay attention to the kHz QPOs. 7

Fits and related quantities λ P ν = 2 ) 2 , ( ν − ν 0 ) 2 + ( λ 0.1 Box 20 Lb2 Lb LhHz where λ is the FWHM and ν 0 is the Ll 0.01 Lu Summed Power centroid frequency. 0.001 Q ≡ ν 0 λ ( quality factor ) . 0.0001 Residual 2 0 -2 Conventionally Q ≥ 2 for QPOs. 1 10 100 1000 ν [Hz] � Figure 3: We fit the components rms ∝ P 1 / 2 where P = P ν d ν. with appropriate functions, i.e., a Lorentzian. Pay attention to the kHz Positive detection if P ≥ 3 σ . QPOs. A Lorentzian is the Fourier transform of a signal of the type x ( t ) ∝ e − t /τ cos (2 πν 0 t ) where τ = 1 πλ. 8

Where do we find QPOs? We see QPOs in very different systems: • AGNs, • ULXs, • CVs, • LMXBs ... The “common structure” is some kind of the accretion flow . 9

LMXBs

System configuration LMXBs are binary systems with a neutron star or a black hole and an ordinary low-mass star ( M � 1 . 3 M ⊙ ) in the following configuration: Figure 4: LMXBs scheme; we focus on the inner edge of the disc where the dominant emission is in X-rays. 11

Motivation

RG and EoSs Possibility to study extreme physics not possible in laboratories: • v φ = ( GM / R ) 1 / 2 ∼ 0 . 5 c ⇒ τ dyn ∼ 0 . 1 − 2 ms. • Turbulence and magnetic structures ⇒ emission varies due to motion of inhomogeneities. • 90% of gravitational energy is released in the inner 100 km of the system. ( T ∼ 10 7 K ⇒ X-rays.) Extreme physics: motion of matter in strong gravitational field regime and the physics of dense matter in neutron stars. It is thought that the kHz QPOs can probe the inner regions of the disc, very near the central compact object. 13

Frequency correlations: benchmarks

Frequency correlations 1000 L b2 L b L hHz L h L low L l 4U 1636-53 100 ν max (Hz) 10 1 0.1 100 1000 ν u (Hz) Figure 5: Altamirano (2008) plus Marcio’s data. Pay attention to the ν l - ν u relation in the upper right corner. 15

Frequency correlations 125 25 Q upper kHz 5 1 0.2 125 25 Q lower kHz 5 1 0.2 125 25 Q hHz 5 1 0.2 440 660 880 1100 1320 ν u [Hz] 16

Frequency correlations 20 RMS of L b2 (%) RMS of L b (%) 15 10 5 0 20 RMS of L hHz (%) RMS of L h (%) 15 10 5 0 20 RMS of L u (%) RMS of L l (%) 15 10 5 0 220 440 660 880 1100 1320 220 440 660 880 1100 1320 ν u [Hz] ν u [Hz] 17

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). As mentioned we Fourier transform the signals: � ∞ � ∞ f ( t ) e − i (2 πν t ) dt ⇔ f ( t ) = F ( ν ) e + i (2 πν t ) d ν. F ( ν ) = −∞ −∞ Differences in photon arrival times give information about the source size and propagation speeds. 19

Concepts Thus, if S xx = S ( ν ) ∗ S ( ν ) = | S ( ν ) | 2 is PDS of s(t) and H yy = H ( ν ) ∗ H ( ν ) = | H ( ν ) | 2 is PDS of h(t), we can find the phase lags of h(t) with relation to s(t) calculating the cross-density spectrum (CDS): G xy = S ( ν ) ∗ H ( ν ) ∼ e ∆ φ ( ν ) , or � Im ( G xy ) � ∆ φ ( ν ) = arctan Re ( G xy ) and the corresponding time lags ∆ t = ∆ φ ν . ps: the * is the conjugate. 20

Beautiful and easy in theory... Alert: real signals are discrete and finite • in dealing with low frequencies, we need to clean the signal of from bursts, instrumental spikes and dropouts; • better statistics if we divide the signal and pieces, Fourier transform each piece and average the pieces; • we need to take into account the gain of the instrument and its ageing; • we need to clearly state what a positive detection is; • etc. It is a very delicate work. 21

The paper

Observations • 511 RXTE observations up to May 2010 in which Sanna et al (2012) detected kHz QPOs ⇒ make use of the correlations in frequency. • Seven narrow energy bands whose mean energies are 4.2 keV, 6.0 keV, 8.0 keV, 10.2 keV, 12.7 keV, 16.3 keV and 18.9 keV. • Two broad bands whose mean energies are 7.1 keV and 16.0 keV. • In 15 years the gain of the instrument changed significantly ⇒ adjustment of our channel selections for different groups of observations, depending upon the epoch. • We ordered the observations chronologically and cleaned the observations. • We subtracted the Poisson noise. • etc. 23

Assumption Our assumption: The variability features depend on the position of the source in the CCD. Sa = 1 1.1 1 27 0.9 26 HC 25 0.8 23 24 21 22 20 Sa = 2 0.7 18 19 6 3 9 12 15 4 7 10 13 2 1 17 5 8 11 14 16 0.6 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 SC Figure 6: We divided the CCD in 37 regions. The line parametrises the position. We statistically compared the individual PDSs in each box in order to 24 verify our assumption. We averaged the observations within each box.

What do we see? A few examples Table 1: Detected QPOs of the NS-LMXB 4U 1636–53 through the colour-colour diagram. Box Detected QPOs ... Box 3 L b L hHz L l L u Box 4-1 L b 2 L b L hHz L l L u Box 4-2 L h L l Box 5 L b 2 L b L hHz L l L u ... Box 27 L b L h L hHz L u We then studied the frequency dependence , the position dependence and the energy dependence of the phase lags of each QPO, since: • Dependence on frequency/ S a ⇒ 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. 25

Frequency dependence 0.4 0.1 L b L b2 0.3 0.05 0.2 ∆φ /2 π ∆φ /2 π 0.1 0 0 -0.05 -0.1 -0.2 -0.1 0 2 4 6 8 10 0 10 20 30 40 50 ν [Hz] ν [Hz] 0.1 L h 0.04 L hHz 0.05 0.02 ∆φ /2 π ∆φ /2 π 0 0 -0.02 -0.05 -0.04 -0.1 0 10 20 30 40 50 80 100 120 140 160 180 200 ν [Hz] ν [Hz] L l 0.04 0.06 L u 0.02 0.04 0 0.02 ∆φ /2 π ∆φ /2 π -0.02 0 -0.04 -0.02 -0.06 -0.04 500 550 600 650 700 750 800 850 900 950 500 600 700 800 900 1000 1100 1200 26 ν [Hz] ν [Hz]

Position dependence 0.4 0.1 L b L b2 0.3 0.05 0.2 ∆φ /2 π ∆φ /2 π 0.1 0 0 -0.05 -0.1 -0.2 -0.1 1.8 1.85 1.9 1.95 2 2.05 2.1 2.15 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 S a S a 0.1 L h 0.04 L hHz 0.05 0.02 ∆φ /2 π ∆φ /2 π 0 0 -0.02 -0.05 -0.04 -0.1 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 S a S a L l L u 0.04 0.04 0.02 0.02 ∆φ /2 π ∆φ /2 π 0 0 -0.02 -0.02 -0.04 -0.04 1.9 1.95 2 2.05 2.1 2.15 2.2 2.25 2.3 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 27 S a S a