Cyclotron Line Science with LAXPC

Dipankar Bhattacharya IUCAA, Pune

Workshop on Science with LAXPC/Astrosat, Hyderabad, 16 December 2014

Accretion powered millisecond X‐ray 

Pulsars

A High Mass X-ray Binary

Cyclotron Resonant Scattering Features

(CRSF)

arise in the accretion column of X-ray binary systems

containing high-field

Neutron Stars

Cyclotron Line in HMXB

Mound

ColumnShock

Polar accretion geometry

Romanova, Kulkarni and Lovelace 2008

Heindl 2001

B

e-

p?n

mec=p

2n(B/Bcrit)

En =q

m2ec4 + c2(p2

|| + p2?n)

; n = 0, 1, 2, ...

For

; Bcrit =m2

ec3

e~⇠ 4.4 ⇥ 1013 G

p|| = 0 and B << Bcrit~!ce ⇠ 12 B12 keV

En �mec2 = n~!ce

!ce =eB

mec⇠ (2⇡) ⇥ 3 B (G) MHz

Classical Cyclotron Frequency

!ce/�Relativistic gyration frequency:

Cyclotron resonance❖ Gyration of electrons in a

magnetic field ❖ Landau quantum levels

~!resn

mec2 =

q1 + 2n(B/Bcrit) sin2 ✓ � 1

sin2 ✓

Resonant interaction between electromagnetic wave and charged particle in a magnetic field

Absorption, Scattering, Stimulated Emission

p|| = 0for

Absorption, Emission : First order process Magneto-Compton scattering: Second order process. Involves resonant intermediate states

QED:

Cyclotron resonance

In X-ray binary systems, scattering is the most dominant process

3.4: Second order process 50

Figure 3.5: Plot for magneto-Compton scattering cross-section �sc versus!i, for twoangle of incidence of photon (✓i = 10�4,⇡/2 ). The cross-section is summed overfinal landau level, spin and polarization states (n f ,s f ,⇣p f ) and averaged over initialstates spin and polarization state (si,⇣pi). Photon incidence is perpendicular to themagnetic field ✓i = ⇡/2. The scattering cross-section is scaled with �T (Thompsonscattering cross-section). The cross-section is evalued at B/Bc = 0.03

Sandeep Kumar 2013

•Resonances are very sharply peaked, profoundly affect electron-photon interaction near them

•Cross section lower than Thompson at low energy

•Affects Eddington Luminosity

Resonant scattering cross section

Resonant cross sections1991ApJ...374..687H

Harding & Daugherty 1991

Absorption

Scattering

Cyclotron ResonanceGeneral resonance condition for a moving electron

cp0|| = cp|| + ~! cos✓

En = E0 + ~!

For arbitrary (!,✓,B,n) there could be 0, 1 or 2 solutions of p||These are the electrons the resonant scattering will occur from. Scattering probability will depend on the electron distribution at these momenta

0

0.2

0.4

0.6

0.8

1

-100 -50 0 50 100

f(p)

cp

cp║

f(p║) kTe=5 keV

5.3: Energy and angular re-distribution due to 0-0 and other scatterings 95

Figure 5.7: The distribution of the momentum pi of the electrons chosen to interactwith the photons at the first scattering after injection (blue solid line) and in allscatterings (green dashed line). The input parameters for the simulation are thesame as in Fig. 5.3.

tons are scattered heavily which have rest frame energy !0i close to the resonanceenergy !res

n . As mentioned earlier the distribution of the energy after scattering ! f

peaks at resonance energies in the lab frame. This suggest that in a large number ofscattering events the parallel momentum pi is close to zero, for which the resonaceenergies in the rest frame and the lab frame are nearly equal. This is corroborated bythe green dashed curve for all scatterings in Fig.5.7, which shows a large excess nearpi ! 0 over the blue solid curve representing only the first scattering. In conclusionit can be stated that very large number of scatterings the electrons has very smallparallel momentum pi ! 0.

Photons are re-distributed in angle after scattering. The distribution of thecosine of angleµ f after scatterings is plotted in Fig.5.6. We have injected an isotropiccontinuum which is flat in µi, but after scatterings photons are depleted in the angleµi ! 0, ✓i ! 90� and peak develop in the directions µi = ±1.

S. Kumar 2013

Scattering line profiles

Sandeep Kumar 2013

4.7: Numerical implementation 79

Figure 4.2: This figure depicts plot of the line profile Psc(B0,!i, µi) versus energy !i.

Figure is plotted for 4 di↵erent cosines of viewing angles µi = 0.1, 0.3, 0.5 0.8. andfor B0 = 0.03, Te = 5Kev. The figure in the top panel is plotted for energy range(0 � 150) Kev. The figure in bottom panel is the zoomed version of the same figurefor first 4 harmonics.

B’ = 0.03 kTe = 5 keV

Gruber et al 2001

5 10 20 50 100

Energy (keV)

Cyclotron line sources known (24)

Swift J1626.6-5156 KS 1947+300 4U 0115+63 IGR J17544-2619 4U 1907+09 IGR J18179-1621 4U 1538-522 Vela X-1 V 0332+53 Cep X-4 Cen X-3 X Per IGR J19149+1036 RX J0520.5-6932 MXB 0656-072 4U 1822-37 XTE J1946+274 4U 1626-67 GX 301-2 Her X-1 1A 0535+262 GX 304-2 1A1118-61 GRO J1008-57

Ecyc (keV)

10 12.5 14,24,36,48,62 17 18,38 20.8? 22,47 24,52 27,51,74 28 29 29 31 31 33 33 36 37 37 41 50,110 54 55 88? 79?

The Astrophysical Journal, 795:154 (8pp), 2014 November 10 Tendulkar et al.

Table 2Spectral Fits to NuSTAR Observations

Component Parameter ObservationI II

const*tbabs*cflux(powerlaw*fdcut)const CFPMB

a 1.022+0.004−0.004 1.026+0.003

−0.003

log10(Flux)b −8.917+0.002−0.002 −8.879+0.002

−0.001

powerlaw Γ 0.91+0.03−0.02 0.76+0.02

−0.02

fdcut Ecutoff (keV) 12.9+0.6−0.6 11.4+0.5

−0.5

Efold (keV) 6.2+0.1−0.1 6.24+0.07

−0.07

χ2/dof 1.499/1286 1.589/1424const*tbabs*cflux(powerlaw*fdcut*gabs+gauss)

const CFPMBa 1.022+0.004

−0.004 1.026+0.003−0.003

log10(Flux)b −8.910+0.002−0.002 −8.874+0.002

−0.002

powerlaw Γ 0.87+0.04−0.04 0.74+0.03

−0.03

fdcut Ecutoff (keV) 10+2−2 9+1

−1

Efold (keV) 7.9+0.3−0.3 7.7+0.3

−0.2

gabs ECRSF (keV) 31.3+0.8−0.7 31.5+0.7

−0.6

σCRSF (keV) 5.9+0.7−0.6 5.8+0.6

−0.5

τCRSFc 0.60+0.08

−0.07 0.57+0.07−0.07

gauss EFe (keV) 6.58+0.05−0.05 6.58+0.05

−0.05

σFe (keV) 0.38+0.02−0.02 0.46+0.07

−0.06

normd 1.1+0.2−0.2 1.5+0.2

−0.2

χ2/dof 1.045/1280 1.006/1418const*tbabs*cflux(nthcomp*gabs+gauss)

const CFPMBa 1.022+0.004

−0.004 1.026+0.004−0.004

log10(Flux)b −8.910+0.002−0.002 −8.875+0.002

−0.002

nthcomp Γ 1.46+0.01−0.01 1.47+0.01

−0.02

kTe (keV) 5.1+0.2−0.2 5.1+0.2

−0.2

kTbb (keV) 1.00+0.04−0.05 0.84+0.05

−0.05

gabs ECRSF (keV) 32+1−1 32+1

−1

σCRSF (keV) 8.6+1.0−0.9 8.2+1.2

−0.8

τCRSFc 0.8+0.2

−0.1 0.7+0.2−0.1

gauss EFe (keV) 6.5+0.1−0.1 6.62+0.05

−0.05

σFe (keV) 1.0+0.2−0.1 0.51+0.08

−0.08

normd 4.0+1.0−0.7 5.5+0.3

−0.3

χ2/dof 1.090/1280 1.062/1418const*tbabs*cflux(cutoffPL*gabs+gauss+bbody)

const CFPMBa 1.022+0.004

−0.004 1.026+0.003−0.003

log10(Flux)b −8.910+0.002−0.002 −8.874+0.002

−0.002

cutoffPL Γ 0.6+0.1−0.1 0.7+0.1

−0.1

Efold (keV) 8.4+0.8−0.6 9.2+0.7

−0.6

gabs ECRSF (keV) 31+1−1 30.8+0.6

−0.5

σCRSF (keV) 5.4+0.5−0.5 5.0+0.5

−0.5

τCRSFc 1.2+0.5

−0.3 0.9+0.1−0.1

gauss EFe (keV) 6.59+0.05−0.05 6.57+0.05

−0.05

σFe (keV) 0.35+0.09−0.08 0.49+0.08

−0.07

norm (10−2)d 1.4+0.2−0.2 2.0+0.2

−0.2

bbody kT (keV) 4.5+0.3−0.3 4.0+0.2

−0.1

norm (10−2)d 9.1+0.4−0.4 11.7+0.7

−0.8

χ2/dof 1.046/1279 1.006/1417

Notes. The photo-electric absorption NH was also frozen to theestimated Galactic value of 1.8 × 1021 cm−2.a The value of CFPMB was tied across both epochs but allowed to varyfor each fit. The value of const was frozen to unity for all FPMAdata.b 3–79 keV flux in units of erg cm−2 s−1.c Optical depth of cyclotron absorption.d Because the cflux model is used to compute the total flux, thenormalization of the gauss model is dependent on the normalizationof the power law, which is frozen to 1 photxons keV−1 cm−2 s−1 at1 keV. norm is specified in units of 10−2 photons cm−2 s−1.

Figure 2. Top: NuSTAR spectra from both observations. The colors cor-respond to the following data sets: black: Obs I FPMA, red: Obs I FPMB,green: Obs II FPMA, and blue: Obs II FPMB. Second panel: ratio of thecontinuum-only model—const*tbabs*cflux*(powerlaw*fdcut)—to thedata. The Fe emission line at 6.5 keV and the CRSF at ≈30 keV areclearly visible. Third Panel: ratio of the full model—const*tbabs*cflux*(powerlaw*fdcut*gabs+gauss)—fit to the data plotted with the absorptionand emission line strength set to zero. The continuum is accurately fit by thepower law with an exponential cutoff. Bottom panel: ratio of the full model—const*tbabs*cflux*(powerlaw*fdcut*gabs+gauss)—to the data.(A color version of this figure is available in the online journal.)

epoch. Based on the residual χ2 of all the fits from Table 2,we adopt a powerlaw*fdcut continuum (“best-fit model”)hereafter unless otherwise specified. The const*tbabs*cflux(cutoffPL*gabs+gauss+bbody)model converges to a black-body temperature T ≈ 4 keV, which is significantly larger thanusually observed for accreting neutron stars, and hence we donot consider the third model to be physically plausible. The Feemission line and CRSF parameters are relatively insensitive tothe exact continuum model used, affirming the robust detectionand measurement of these features.

The fitting of CRSF features is highly dependent on themodel of the continuum. In fact, Muller et al. (2013) showedthat the variation between ECRSF and LX in 4U 0115+634(reported by Nakajima et al. 2006, Tsygankov et al. 2007,and Muller et al. 2010) disappeared when the continuummodel was improved. To explore the correlations betweenparameters, we stepped through the parameter values forthe const*tbabs*cflux*(powerlaw*fdcut*gabs+gauss)model. Table 3 shows the typical variation of parameters as thepower-law index Γ is frozen to values between 0.5 and 1.1. Weobserve that Γ is tightly correlated with Ecutoff . We observe thatour measurement of the CRSF parameters is robust to variationsin the continuum fitting. If columns 1 and 2 are compared, one

4

RXJ0520.5-6932 NuSTAR

Tendulkar et al 2014 Ginga, BeppoSAX, CGRO, RXTE, INTEGRAL,Suzaku, NuSTAR,...

Cyclotron Lines (CRSF) in HMXB

Estimate magnetic field from: Ec ≈ 12 B12 keV (fundamental) Key unknowns:

Location of line formation, field geometry Source and nature of the continuum Distribution and dynamics of plasma Short-term and secular evolution

Important observational indicators Ec  vs LX and pulse phase, line shape, harmonic spacing Energy-resolved timing Continuum shape, phase dependence

Astrosat advantage:

More effective area in cyclotron line bands (LAXPC) than any other previous mission.

Simultaneous broad-band coverage provides characterisation of underlying continuum, which is crucial for the study of cyclotron lines

Key objective: Sensitive study of cyclotron line behaviour as a function of pulse phase and luminosity

Paul 2004

10−210

−110

1 ISGRIV 0332+53

JEM−X

Rev. 273Rev. 278

Rev. 287Rev. 284

Energy (keV)30

0332

+53/

Cra

b

V0332+53: En-ergy of fun-damental cy-clotron linechanges overoutburst

(Mowlavi et al., 2006)Mowlavi et al 2006

Time evolution of cyclotron spectrum

4U0115+63

Ferrigno et al 2009

Phase resolved spectroscopy

Cyclotron line Energy vs Lx

Tsygankov et al 2010

V0332+53 Her X-1

Vasco et al 2011

0.000.020.040.060.080.100.120.14

BA

T c

ou

nts

cm!

2 s!

1

29 1 8 15 22

2009 August

40 45 50 55 60 65 70MJD!55000

4344

45

46

47

48

4950

Ecyc [

ke

V]

RXTEINTEGRALSuzaku

0.000.020.040.060.080.100.120.14

BA

T c

ou

nts

cm!

2 s!

1

29 1 8 15 22

2009 August

40 45 50 55 60 65 70MJD!55000

4344

45

46

47

48

4950

Ecyc [

ke

V]

RXTEINTEGRALSuzaku

A0535+26

MJD - 55000

Ecy

c (ke

V)

BAT

Cou

nts

Ecy

c (ke

V)

Lbol (1037 erg/s)

Caballero et al 2011

Three types of behaviour seen: •Positive Correlation •Negative Correlation •No Correlation

Cyclotron line Energy vs Lx

GX 304!1V 0332"53A 0535"26Her X!14U 0115"63

LX#Lcrit

LX#Lcoul

RADIATION

BRAKING

COULOMB

BRAKING

GAS

SHOCK

0.1 0.5 1.0 5.0 10.0 50.0

10

50

20

30

15

70

LX !1037ergs sec!1"

Ecyc!keV"

Becker et al 2012

Ec-Lx correlation depends on continuum modelS. Müller et al.: No anticorrelation between cyclotron line energy and X-ray flux in 4U 0115+634

5

2

10

1

0.6

0.4

0.2

12

10

8

6

4

2

10

8

4

3.5

3

2.5

0.4

0.2

706050

2

1.5

1

0.552 101

L

3−50keV

XΓ

Efold

[keV

]A

Fe

EG

[keV

]σ

G[keV

]A

G

time (MJD-54500)

χ

2 red

L

3−50 keV

X

Fig. 5. Left temporal evolution and right luminosity dependence of thecontinuum parameters (see text for definitions) and 10 keV feature forthe fits with the CutoffPL continuum. The color gradient from reddishto blueish data points indicates the temporal evolution of the outburst.The data points show results from the initial fit run, where a variablenumber of cyclotron lines was used. Green data points in the left columncorrespond to the second fit run with a fixed number of three cyclotronlines (only in the left column), which was been performed as a consis-tency check (see text for details). Where no green points are visible,both fits gave the same results. LX is in units of 1037 erg s−1. AG and AFeare in units of photons s−1 cm−2, while AFe is in multiples of 10−3.

on the other hand, it is obvious that rather than describing nar-row cyclotron lines, the multiplicative broad line model stronglyinfluences the continuum. As discussed above, our spectral fitsshow that during the brightest phases of the outburst a signifi-cant hardening of the continuum emission is observed, togetherwith a change of the exponential cutoff. While this is also seenin the variation of the continuum parameters, it is very likely thatthe luminosity dependence of the CRSF in the NPEX fits is due tothe line partially modeling this behavior of the continuum, andnot a real physical effect.

706050

12

11

10

time (MJD-54500)

52 101

15

14

13

12

11

10

L

3−50 keV

X[1037 erg s−1]

E0[keV

]

Fig. 6. Luminosity and time dependence (inset) of the energy of thefundamental CRSF using the CutoffPL continuum model. The colorcoding is the same as in Fig. 5. Cyan data points (diamonds) show theresults when using the NPEX continuum.

Using the results from the CutoffPL plus 10 keV featurefits for the line energy also solves another problem found in ear-lier spectral modeling. Here, using NPEX fits, the ratios betweenthe fundamental and higher cyclotron lines were often found todeviate significantly from integers. While slightly non-integerratios are expected when taking relativistic quantum mechan-ics into account (see the discussion by Pottschmidt et al. 2005),the large deviations from integer multiples seen previously (e.g.,Tsygankov et al. 2007; Nakajima et al. 2006; Heindl et al. 1999;Santangelo et al. 1999) require rather complex model assump-tions which introduce second order effects such as strong verticalB-field gradients, crustal field structures on small scales, or ther-momagnetic effects for their explanation (see Schönherr et al.2007, and references therein for a discussion). Figure 9 showsthat we can recover these non-integer ratios in our NPEX fits, butwhen using the CutoffPL plus 10 keV feature model, these ra-tios are mostly in agreement with integer values, or at least onlyslightly higher, as expected from the most simple models for cy-clotron line formation. We conclude that also from a physicalpoint of view, the CutoffPL continuum with the 10 keV featuregives a much more satisfactory description of the data.

Finally, we check the dependence of the line position onother free fit parameters when using the CutoffPL continuummodified by the 10 keV feature. Since the origin of the 10 keVfeature remains still an open questtion, possible relations be-tween the CRSF centroid energy and the parameters of the10 keV feature have to be investigated, and other continuum pa-rameters such as Efold or Γ could influence the results for the cy-lotron line parameters. Figure 10 shows the behavior of ∆χ2 inthe vicinity of the best fit values for three epochs representativefor the early phase, peak, and late phase of the 2008 outburst forselected combinations of important fit parameters. These contourplots show that the line energy is not affected by cross correla-tions with other parameters, i.e., possible variations in the lineenergy of the fundamental cyclotron line are not due to variations

A6, page 7 of 10

NPEX

CutoffPL

Müller et al 2013

4U0115+63

Mass : 5.1 × 10-13 M⊙ Mass : 9 × 10-13 M⊙

Mass : 1.6 × 10-12 M⊙ Mass : 2.1 × 10-12 M⊙Mukherjee & DB 2012

Field distortion caused by mound of

accreted matter

110 Chapter 6. E�ects on observables

0.0 0.2 0.4 0.6 0.8 1.0Radius in km

0.0

0.5

1.0

1.5H

eig

ht

in k

mFilled parabolic mound, Zc=50 m

0.2 0.4 0.6 0.8Radius in km

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Hei

gh

t in

km

BGS/Bdip for filled parabolic mound, Zc=50m

0.42

0.74

1.05

1.36

1.68

1.99

2.30

0.8

0.80.9

0.9

0.95

0.95

1.0

1.0

1.0

1.02 1.05

1.1

1.2

0.80.90.951.01.021.051.11.2

0.0 0.2 0.4 0.6 0.8 1.0Radius in km

0.0

0.2

0.4

0.6

0.8

1.0

Hei

gh

t in

km

Hollow mound, Zc=38 m

0.2 0.4 0.6 0.8Radius in km

0.2

0.4

0.6

0.8

Hei

gh

t in

km

BGS/Bdip for hollow mound, hc=38m

0.46

0.69

0.93

1.16

1.40

1.64

1.87

0.80.9

0.951.0

1.01.

01.0

1.02

1.02

1.02

1.05

1.05

1.051.1

1.1

0.80.90.951.01.021.051.1

Figure 6.8: Left: GS solutions with full vertical domain shown. In black are the fieldlines derived from the solution while the dash-dotted red lines represent undistorted dipolefields. Right: Ratio of field strength derived from GS solution to the dipole value withcontours showing the level of departure from dipole value. The top panels are for moundswith parabolic profile with Zc = 50 m (eq. 3.24, Chapter 3). The bottom panels are for ahollow mound with Zc = 38 m. The Paczynski EOS (eq.3.17) has been used for both thesolutions. For the parabolic mound the deviation is & 20% for z . 200m. Beyond z ƒ 1km, the field lines become dipolar. For the hollow mound, distortions can be noticed up toa height of ≥ 500 m.

Magnetic field distortion in accretion column due to the presence of a filled / hollow mound

Mukherjee, DB, Mignone 2014

Mukherjee & DB 2012, 2013

Hotspot emission viewing geometry

Light  bending:  cos  α  ≃  u  +  (1  -­‐  u)  cos  ψ  ;    u  =  2GM/c2r  dF  ∝  cos  α  (d  cos  α/d  cos  ψ)  dS  (Beloborodov  2002)

Gravita?onal  redshi@:  E∞  =  (1-­‐u)1/2  E0

C.2: Shielding of radiation from inner walls of hollow mounds 137

Figure C.3: Top: A 3-D schematic representation of the hollow mound. The vectors nÂ

and rc ≠ r denote the plane where the path of the emitted ray to the observer lie. Bottom:a cross section of the mound along the plane of the emitted ray to the observer, and thelocation where the plane cuts the mound on the opposite side.

and nl as :cos ◊–l = n– · nl = C1 cos ◊rl + C2 cos ◊Âl (C.11)

where again C1 and C2 are the coe�cients of r and n respectively from eq. (C.5),eq. (C.6) and eq. (C.7) whichever is applicable. The angles ◊rl and ◊Âl are obtainedfrom:

cos ◊rl = r · nl = (› + Rs ≠ msfl)/(rÒ

1 + m2s)

cos ◊Âl = n · nl = ms1 + m2

s

[(cos i sin ÷p ≠ sin i cos Ê cos ÷p) sin „

≠ sin i sin Ê cos „] + 1

1 + m2s

[sin i cos Ê sin ÷p + cos i cos ÷p]

(C.12)

C.2 Shielding of radiation from inner walls of hollowmounds

For the CRSF simulations of hollow mounds presented in Sec. 6.3.2 (Chapter 6),special attention has been paid to properly evaluate the e�ect of shielding of emissionfrom inner walls. Some of the photons emitted by the inner wall will not reach the

Shadow effect in a Hollow mound

CRSF profile

l Multi-peaked structure due to large variation of surface field strength.

l Broader and more complex profiles for hollow mounds.

l High resolution and sensitivity required to probe line shapes

Filled mound

Hollow mound

10% energy resol

Profiles of fundamental features only; computed using basic CRSF shapes from Schonherr et al (2007)

Mukherjee, DB, Mignone 2012, 2013

Degeneracy pressure dominated structures

CRSF profiles from accretion mounds

Priymak et al 2014

Cyclotron lines from accreting neutron stars 2721

Figure 10. Instantaneous (ω = 3π/2, left-hand panel) and phase-averaged (right-hand panel) cyclotron spectrum for scenario (a) (thermal mountain withoutmagnetic burial) with (ι,α) = (π/4, π/4) and u = 0.4. The results for strong and weak magnetic fields, and ‘hotspot’ and quadrupole surface temperaturedistributions, are colour-coded as follows: ψ∗ = 1.6 × 1024 G cm2 (blue curves), ψ∗ = 1.6 × 1020 G cm2 (red curves), (δT10, δT20) = (0.1, 0) (dotted curves),and (δT10, δT20) = (0, 0.1) (solid curves).

Figure 11. Left-hand panel: instantaneous (ω = 3π/2, purple curves) and phase-averaged (black curves) spectra for scenario (b) (thermal mountain withmagnetic burial) with ψ∗ = 1.6 × 1024 G cm2, (δT10, δT20) = (0.1, 0) (dotted curves), and (δT10, δT20) = (0, 0.1) (solid curves). Other parameters as for Fig. 10.Right-hand panel: same as left-hand panel, but for scenarios (c) (solid curves) and (d) (dotted curves) (magnetic mountain with uniform and magneticallymodified surface temperature profile, respectively).

two troughs at Ecyc, 1 ≈ 15 keV and Ecyc, 2 ≈ 23 keV. The formeris marginally deeper than the latter for δT10 = 0 and vice versafor δT20 = 0, while the line widths are the same. The right-handpanel exhibits a single absorption feature at ≈18 keV for δT10 =0 and ≈23 keV for δT20 = 0. The pole dominates in the lattercase. In comparison, for δT10 = 0, the flux-dominating region shiftsequatorwards, where |B| is weaker. The instantaneous spectrumexhibits two troughs in the narrow window 1.3 ! ω/π ! 1.7 andone trough elsewhere, so the single trough dominates the phaseaverage.

At low magnetization, e.g. ψ∗ = 1.6 × 1020 G cm2 (red curvesin Fig. 10), a single CRSF appears at ! 5 keV in both the instanta-neous and phase-averaged spectra, with D ≈ 0.99 and F ≈ 4 keV.This feature is likely to be interpreted as the non-CRSF contin-uum in observational data. Note that at low ψ∗ (B/Bcrit ≪ 10−2),our calculations lie outside the regime of validity of the scatter-ing cross-section formulas in Schonherr et al. (2007). A correcttreatment falls outside the scope of this paper.

How does magnetic burial of the sort described in Section 2 affectthe CRSF from a predominantly thermal mountain? The left-handpanel of Fig. 11 displays instantaneous (ω = 3π/2, purple curves)and phase-averaged (black curves) spectra for scenario (b) withψ∗ = 1.6 × 1024 G cm2, (δT10, δT20) = (0.1, 0) (dotted curves), and(δT10, δT20) = (0, 0.1) (solid curves). Compared to the right-handpanel of Fig. 10, the single CRSF in the phase-averaged spectrumis wider (F ≈ 23 keV) and shallower (D ≈ 0.996), especially forδT10 = 0, to the point where the feature at Ecyc ≈ 22 keV is ill-defined. In the instantaneous spectrum, magnetic burial increasesthe energy splitting (Ecyc, 1 ≈ 8 keV, Ecyc, 2 ≈ 23 keV). The δT10

perturbation deepens and suppresses the feature at Ecyc, 1 more thanEcyc, 2, because burial compresses the magnetic field (compare Ecyc, 1

and Ecyc, 2 in the left-hand panels of Figs 10 and 11).In scenarios (c) and (d), magnetic burial dominates ϵ and also

modifies the cyclotron spectrum. The surface temperature is uniformor magnetic-pressure-corrected, respectively. The right-hand panelof Fig. 11 displays the instantaneous (ω = 3π/2, purple curves)

MNRAS 445, 2710–2724 (2014)

at Inter-University C

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y and Astrophysics on D

ecember 10, 2014

http://mnras.oxfordjournals.org/

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Thermal Magnetic

Distinction between thermal and magnetic pressure dominated structures

Cyclotron line: Spin Phase Dependence

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6.4: Accretion column 133

Figure 6.24: The figure shows the redshifted spectra with light bending for PLCUTcontinuum for the same parameters as in Fig.6.21. The angle between spin axes andmagnetic axes is taken to be 10�.

4.2: Photon Injection 62

rb

rt

θhz

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zt

zc

rc

rtt

rbb

Figure 4.1: This figure depicts the geometry of the column for the Case-III inTable.4.1. The structure in the blue colour is a cone cut at the top. The surface ofthe cone is defined such that it lies at a fixed optical depth below the surface of thecylindrical column.

Accretion Column

Sandeep Kumar & DB 2013

Monte Carlo Spectra i=10o

Interchange mode instability observed in 3D MHD simulation of mounds with PLUTO code

The more massive the mound, the quicker is the growth of the instability

Mukherjee, DB & Mignone 2013

Density fluctuation spectrum in

MHD instabilities

82 Chapter 5. 3D simulations

1D toroidal PSD of density for r ~ 700 m, z ~ 25 m

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Figure 5.2: Left: 1D power spectral density at r ≥ 700m and z ≥ 25m at times t ≥ 0.2tA

and ≥ 0.6tA respectively (corresponding to the first two panels in Fig. 5.1). The x axisgives the mode number (see text). A line is drawn parallel to the PSD in the second plot toshow the powerlaw nature of the Fourier spectra. Right: Stacked 1D power spectral densityof perturbed density at di�erent radii and times (corresponding to the panels in Fig. 5.1).In the beginning (t ≥ 0.25tA), power is concentrated over certain modes and instability islocalized to small radial extent near the outer edge. With time, the power spreads over allscales, and more of the mound is disrupted from equilibrium.

where Q is any physical parameter (e.g. density) and Q is its Fourier transform,„l = lfi/(2N◊) is the azimuthal coordinate and N◊ is the total number of cells inthe azimuthal direction. The corresponding frequencies in the Fourier domain areun = n/(fi/2). The power spectral density (PSD) of the evaluated Fourier transformis defined as

P (un) =

------1

N◊

N◊≠1ÿ

l=0Q(„l)e≠i4n„l

------

2

(5.3)

where m = 4n is the mode number for Fourier modes defined over the whole domainof [0, 2fi]. We present in the left panel of Fig. 5.2 the 1D PSD of perturbed densityalong the toroidal direction at two di�erent times (t = 0.25 tA and 0.6 tA), evaluatedat radius r ≥ 700 m and height z ≥ 25 m. On the right panel of Fig. 5.2 we presentcolour contour plots of toroidal 1D PSDs evaluated at di�erent radii stacked together.These plots correspond to the same height and time slices as of the density plots inFig. 5.1 (top right and bottom panels).

Mukherjee, DB & Mignone 2013

Timing signature of MHD instabilities112 Chapter 6. E�ects on observables

Intensity vs time

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Figure 6.10: Left: Light curve from the top of a mound with developed MHD instabilitiesassuming I Ã fl2. Right: Power spectral density of the light curve. The simulation wascarried out for a total time of 10tA = 3.5 ◊ 10≠3 s.

towards any line of sight. To illustrate this, we have evaluated the CRSF arisingfrom the field distribution at the top of the PLUTO domain at the end of thesimulation run (≥ 3.6tA) of a Zc = 50m mound. This exercise does not representa realistic line profile, as the PLUTO box lies well inside the mound where opticaldepth is high, while line formation takes place in low density regions higher up.Comparing the CRSF profile before and after the onset of instabilities, we clearlysee (Fig. 6.9) the enhanced broadening of the total feature.

Dynamic structures contributed by the instabilities may also produce observabletiming signatures from accreting neutron stars. With the previous caveat that oursimulations do not access the primary radiation zone, we can still expect the observedintensity to be modulated by the oscillations set up in the mound. The MHDinstabilities result in rapid formation of density streams within a few Alfven timesand subsequent oscillations in similar time scales. This will inject power in thefluctuation spectrum at frequencies corresponding to local instability growth rates.We present in Fig. 6.10 the power spectral density (PDS) of the Fourier transform ofa simulated light curve from a hollow mound of Zc = 45m. We assume the intensityof the emission to depend on the local density as I Ã fl2. We integrate this intensityover the top surface of the PLUTO domain to get the net light curve. The PDSshows a broad excess at ≥ 800 Hz (Fig. 6.10) resulting from the repetitive patternsin the light curve. Some features occurring at kilohertz frequencies correspondingto local Alfven time scales are also seen. Thus the onset of instabilities will result inexcess noise in the high frequency regime of the PDS. The result shown here is fora highly unstable mound near the GS threshold. In smaller mounds the instability

Mukherjee, DB & Mignone 2013

Proton Cyclotron Feature in Magnetars?

The Astrophysical Journal, 790:60 (9pp), 2014 July 20 An et al.

Table 3Best-fit Spectral Parameters for the Spectrum of the First 150 s after T0 for Burst 5

Modela NHb kT /Γ LBB/FPL

c EGd σG NG χ2/dof

(1022 cm−2) (keV) (keV) (keV) (photon cm−2 s−1)

BB 0.97 4.1(2) 30(2) · · · · · · · · · 70/42BB + Gauss 0.97 3.8(2) 25(2) 13.2(3) 1.3(3) 2.1(5) × 10−3 39/39PL 0.97 0.83(7) 12(1) · · · · · · · · · 108/42PL + Gauss 0.97 1.0(1) 0.8(1) 12.7(2) 1.7(3) 3.4(6) × 10−3 44/39

Notes. Uncertainties are at the 1σ confidence level.a BB: blackbody, PL: power law, Gauss: Gaussian line profile.b Frozen.c Bolometric luminosity in units of 1035 erg s−1 for the blackbody model, and the absorption corrected 3–79 keVflux in units of 10−9 erg s−1cm−2 for the power-law model.d Subscript G is used for the Gaussian parameters: line energy (EG), line width (σG), and normalization (NG).

Figure 6. Blackbody plus Gaussian line fit for the 150 s NuSTAR spectrum ofburst 5.(A color version of this figure is available in the online journal.)

not. However, as we increased the integration time, we startedseeing an enhancement in counts at ∼13 keV for burst 5.

In order to see if a line feature is statistically requiredfor the bursts and their tail emission, we first extracted aspectrum from the first 150 s of the brightest burst (burst 5).The background was extracted from the pre-burst interval inthe source region. We then fit the spectrum in the 3–30 keVband with continuum models (blackbody, power law, andbremsstrahlung), and found that none could describe the datawell with χ2/dof of 70/42 (blackbody), 108/42 (power law),and 147/42 (bremsstrahlung). We also tried combinations ofthe continuum models, but none improve the fit significantlywith χ2/dof being 67/40, 108/40, 67/40, 67/40 for a doubleblackbody, a double power-law, a blackbody plus power-law,and a blackbody plus bremsstrahlung models, respectively.In particular, in all these two-component trials, the best-fitparameters of the second component are trivial; the amplitudeis not constrained at all, and kT or Γ become ridiculously smallor large. However, adding a Gaussian line to a blackbody modelprovided an acceptable fit (χ2/dof = 38/40). We show thespectrum and the blackbody plus Gaussian fit in Figure 6, and theresults are presented in Table 3. We repeated the same procedurefor spectra in different time intervals (e.g., 100 s, 200 s, and300 s), and found that the fit improves significantly (∆χ2 ! 20)by adding a Gaussian line to the blackbody model, from which

we draw the same conclusion as we did with the 150 s spectrum.We conducted the same analysis with the other bursts and foundthat a blackbody model alone was able to describe their spectrawell (for example, χ2/dof = 39/35, p ∼ 0.1 for burst 6).

We used simulations in order to calculate the true significanceof the feature in burst 5 and its tail. The spectrum of the sourcefollowing a burst evolved on a timescale of 150 s. Therefore,we conducted simulations with temporally evolving blackbodyspectra. We first divided the 150 s spectrum of burst 5 intofive time intervals as shown in Figure 5 and the T90 interval,and fit the six spectra to blackbody models after removing theenergy range of the feature (11.5–14 keV). We then simulatedthe six spectra using fakeit in XSPEC with the response andbackground for the actual data, and merged them into onespectrum that represents a 150 s spectrum. For each simulation,we first fit the spectrum to a blackbody, and then calculatedthe improvement of the fit (∆χ2) by adding a Gaussian line.For the latter fit, we scanned the energy range of the spectrum(4–22 keV) with a step of 1 keV for the initial value of the lineenergy because the narrow feature can make the fit fall in a localminimum around the initial value. We counted the number ofoccurrences in which the improvement of the fit in a simulationwas larger than that seen in the actual data fit (∆χ2 = 31),and found that this did not occur in 10,000 simulations. Thesignificance of the feature would be even higher if we scan onlya smaller energy range (e.g., 11–15 keV) for the Gaussian lineenergy guided by the previous RXTE measurements.

We found that a blackbody model fits the spectra of thefeature-removed 150 s data as well as the above simulations.Therefore, we also conducted simulations with a single black-body continuum model, and found that improvement of fit mea-sured by ∆χ2 by adding a Gaussian line model was alwayssmaller than 31 in 10,000 simulations.

We investigated if the feature exists in the spectra without theburst. We removed the T90 interval from burst 5 and extractedtail spectra for 100 s, 150 s, 200 s, and 300 s exposures. Wethen applied the same fitting procedure and found that thesame conclusion is valid; for example, single or combinationsof continuum models do not fit the 150 s spectrum wellwith χ2/dof of 75/39 (blackbody), and 164/39 (power law)while adding a Gaussian line to a blackbody improves thefit significantly, making it acceptable (χ2/dof = 42/36). Thebest-fit Gaussian line parameters are statistically consistent withthose we obtained above.

We checked if the spectral feature shifts in energy with phaseas seen in the magnetar SGR 0418+5729 (Tiengo et al. 2013).We produced a two-dimensional energy versus phase image asshown in Tiengo et al. (2013), and found no evidence of a shift.

7

SGR 1806-20 1E 1048.1-5937

Ibrahim et al 2002 An et al 2014

If proton cyclotron resonance, then the features imply B ~ 1015 G

LAXPC cyclotron line targets•Persistent HMXB pulsars ‣spin-phase resolved spectroscopy ‣ luminosity dependent variation ‣fast timing in resonance band

•Transient HMXB pulsars ‣time resolved spectroscopy near outbursts

•Magnetar outbursts ‣hunt for proton cyclotron signature

Simultaneous fitting of pulse profile and cyclotron spectra using radiative transfer models, to probe the emission region

Average Fluxes of persistent cyclotron line sources

0

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Vela  X-­‐1 GX301-­‐2 Cen  X-­‐3 4U1626 Her  X-­‐1 4U1538 4U1907 IGR16493

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x  (m

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Determining the continuum

CompTT  vs  HighEcut  Vela  X-­‐1  15  ks

50  ks  

SXT  39  c/s  CZTI  98  c/s  LAXPC  3000  c/s

SummaryLAXPC, along with CZTI, has the capability to seriously push to the envelope of cyclotron line science. Should be a key science programme

Better estimate of continuum to better define the line

Systematic study of dependence of line on pulse phase, luminosity changes, orbital phase and time in accreting NS systems of ∼ a dozen sources.

Campaign for discovery of new cyclotron line sources - Be transients at outbursts, magnetar bursts

Devoting a couple of megaseconds on this study over the mission lifetime would be well worth the effort