X-ray polarimetry and other thoughts Adam Ingram – Royal Society URF Soumya Shreeram, Tom Maccarone, Michiel van der Klis, Guglielmo Mastroserio & the IXPE team Ionization 2 ) − 1 Direct keV − 1 s − 2 (Photons cm
2 ionization parameter:
0.1 1 Reflected keV ξ = 4πFx / ne 10 100 Energy (keV) e.g. Ross & Fabian (2005); Garcia et al (2013) Ionization 2 ) − 1 Direct keV − 1 s − 2 (Photons cm
2 ionization parameter:
0.1 1 Reflected keV ξ = 4πFx / ne 10 100 Energy (keV) e.g. Ross & Fabian (2005); Garcia et al (2013) Ionization profile 3
• NuSTAR observation of GRS 1915+105 in plateau state • Radial ionization profile changes the best fitting disc inner radius (but not >ISCO)
Shreeram & Ingram (2020) ) − 1 keV − 1 s − 2 Ionization profile 4 3.5 4 (Photons cm 2 keV ) ) − 1 − 1 keV keV − 1 − 1 s s − 2 − 2 3.5 4 (Photons cm (Photons cm 2 2 0.1 1 keV keV )
− 1 510 20 50
keV Energy (keV) − 1 s − 2 • Difference between models is very subtle • Need high ionization parameter => low disc density (� ≲ 10 cm ) (Photons cm 2 0.1 1 Shreeram & Ingram (2020) keV 510 20 50 Energy (keV) Scaleheight & Distance 5
Disc scale height • Currently assuming h/r=0 • For h/r finite, get more reflection from larger r (Taylor & Reynolds 2018; 2019)
F ' obs $ ()*+ ! ∝ # & % , - Can now make distance D a D model parameter instead of ξ ne, ξ Ingram et al (in prep) Linear polarization 6
p0=100% p0=100% p0=0%
p0=3% p0=24% p0=54% p0=93%
ψ0 ψ0 ψ0 ψ0
Adapted from Foster et al (2017) Basic expectations 7 Synchrotron
• �� /�� ∝ � , p~2.4
• Optically thin: � + 1 � = � ~� 72% � + 7/3 where � is order of B-field � perpendicular to B-field
• Optically thick (self-absorbed): 3 � = � ~� 11% 6� + 13 � parallel to B-field e.g. Rybicki & Lightman Basic expectations 8 Compton scattering � • �� /�Ω ∝ sin �
• Sphere + symmetric seed photon dist: No polarization
• Sphere + asymmetric seed photon dist: � ~2 − 8%
• Slab: � ~2 − 15%
Higher scattering orders have higher � , emission angle dependent e.g. Sunyaev & Titarchuk (1985) Basic expectations 9 Disc • Blackbody from mid-plane unpolarized, polarization from scattering in the Chandrasekhar (1960) atmosphere: • � ~1 − 5%, angle dependent
Reflection • � (� )~0 − 100%, � (� )~0 − 180° depending on emission angle
Relativistic effects • Mixing of emission angles (like relxill) • Parallel transport (gravitational Faraday rotation), • Returning radiation Schnittman et al (2010) X-ray polarimetry 10
• Photo-electric effect: photo-electron preferentially travels parallel / anti-parallel electric field to E-field oscillations vector • Thomson scattering: photon preferentially scattered perpendicular to its E-field oscillations incoming photon
photo -electron detector X-ray polarimetry 10 North on projected sky ψ0 = polarisation angle ψ = modulation angle electric field vector ψ ψ0
incoming photon 10 1 − photo -electron −1 −0.5 0 0.5 1 detector X-ray polarimetry 11
End p0=10% � � ∝ 1 + �� cos 2 � − � point ψ � = modulation factor 0=40°
North ) 5
Initial photoelectron path
p0=0
End ψ Counts (10 p0=10% point ψ0=40° 1.95 2 2.05
North ) 5
Interaction 0 100 200 300 Initial photoelectron path point Modulation Angle ψ (degrees) p0=0
ψ Counts (10 1.95 2 2.05
Interaction 0 100 200 300 point Modulation Angle ψ (degrees) Cyg X-1 polarization 12
Russell & Shahbaz (2014) Cyg X-1 polarization 12
• Soft X-rays, OSO-8: ~5%, but less than 3σ significance • Polarization angle aligned with jet
Long, Shanan & Novik (1980) Cyg X-1 polarization 13
• γ-rays, INTEGRAL: ~70% polarization • Polarization angle totally different to jet
Laurent et al (2011); Jourdain et al (2012) Cyg X-1 polarization 14
Toy model: • Unpolarized corona • 70% polarized optically thin synchrotron jet
Russell & Shahbaz (2014) Cyg X-1 polarization 15
• Hard X-rays, POGO+ balloon flight: ~5%, but less than 1σ significance • Polarization angle aligned with jet • Fits Russell & Shabaz’s toy model remarkable well!
Chauvin et al (2018) Lamppost model 16
• Corona unpolarized, all polarization comes from reflection • Polarization angle = 0 means it aligns with disc normal
inc = 30 degrees inc = 60 degrees
Black: spin = 0 Grey: spin = 1 Solid: h = 3 Rg Dovciak et al (2011) Dashed: h = 15 Rg Sandwich model 17
Schnittman et al (2010)
Dotted: only disc Dashed: only corona Truncated disc model 18
Schnittman et al (2010)
Dotted: only disc Dashed: only corona Lamppost model ruled out? 19
• Chauvin et al (2018) argue their POGO+ result rules out parameter space of lamppost model • The Dovciak (2011) model has many simplifications though IXPE 20 The Imaging X-ray Polarimetry Explorer • NASA Small Explorer mission • Launch: May 2021 • Passed Critical Design Review • Photo-electric effect polarimeter • Energy range: 2-8 keV
Some Science • First X-ray polarization measurements of neutron stars, stellar mass black holes and AGN • Vacuum birefringence from high B-field NSs (QED) • Astro-archeology of Galaxy center IXPE 21 Y1 Observing plan
BH XRB transients: 3 ~300 ks ToOs, each one includes a hard state and soft state pointing
BH XRB persistent sources: 4 targets are GRS1915+105, Cyg X-1, 1E1740.7-2942 & GRS1758-258 (300 ks each)
AGN: Circinus galaxy ~ 800ks MCG-5-23-16 ~ 500ks IC 4329A ~ 500ks Propagating fluctuations 22
Hard X-rays lag soft X-rays IR
Jet Optical
Cyg X-1 X-rays
Nowak et al (1999)
Disk: Soft X-rays Inner flow / Corona: Hard X-rays Propagating fluctuations 22
Infrared lags X-rays IR
GX 339-4 Jet Optical
Cross correlation function X-rays
Infrared lag (s) Casella et al (2010)
Disk: Soft X-rays Inner flow / Corona: Hard X-rays Propagating fluctuations 23
~Jet
~corona
0.1 s lag Jet: ~65% polarization, ~5% of 2-8 keV flux
• 200 ks exposure • Bright source (~GRS 1915+105) Inner flow / corona: ~5 % polarization, ~95% of 2-8 keV flux Propagating fluctuations 23
IXPE
~Jet Time Lag (ms) 024 ~corona
0.51 2 5 10 0.1 s lag Frequency (Hz) Jet: ~65% polarization, ~5% (10%) of 2-8 keV flux
• 200 ks exposure • Bright source (~GRS 1915+105) Inner flow / corona: ~5 % (10%) polarization, ~95% (90%) of 2-8 keV flux Polarization modulation 24 i = 70 degrees Ro=20Rg, a=0.98 110
100 Flux 90
12 11
p (%) 10 9 Pol degree (%) log (flux) ) 10 −5 deg
(degrees) −10 0 ψ Pol angle (
0 0.5 1 QPO cycles Ingram et al (2015) www.youtube.com/watch?v=ieZYYfCapJg&feature=youtu.be Detection 25
GRS1915+105 Can we make a time series?
• IXPE count rate ~ 100 c/s
ray Brightness • p of source < ~10%
− 0
X GRS1915+105 4000 6000 • Integration time: 0 5 10 15 20 Time (s) T ~ 4 minutes! 0
ψ ? ray Brightness So can’t probe variability on − X 4000 6000 timescales of seconds L 0 5 10 15 20 Time (s) Detection 26
Model Modulation function
1.5
Flux 1
6 10 10.5 11 (%) Fractional RMS (%) 0 p 5
−5 (deg)
−0 10 ψ Phase (cycles) 0.01 0 0.01
0246 − 0 100 200 300 Time (s) Modulation Angle ψ (degrees)
Ingram & Maccarone (2017) Detection 27
Model Modulation function
1.5
Flux 1
6 10 10.5 11 (%) Fractional RMS (%) 0
p 5
−5 (deg)
−0 10 ψ Phase (cycles) 0.01 0 0.01
0246 − 0 100 200 300 Time (s) Modulation Angle ψ (degrees) • Make light curves selected on modulation angle • Calculate QPO amplitude for each light curve • Calculate phase lag between the different light curves Ingram & Maccarone (2017) Sensitivity 28
High Inclination Low Inclination
1 1 3σ 3σ 0.1 0.1 IXPE only IXPE only 0.01 0.01
10−3 IXPE 10−3 IXPE + NICER + NICER
Hypothesis Prob. (%) 10−4 5σ Hypothesis Prob. (%) 10−4 5σ − −
−5 −5 Null 10 Null 10
246 123 Mean Polarization Degree (%) Mean Polarization Degree (%) • Mean pol degree most uncertain thing in modelling (everything else just geometry + GR) • High inclination = low amplitude pol variability; Low inclination = high amplitude pol variability • But high inclination sources expected to have higher mean pol degree • Cross-correlation with a bigger detector boosts signal Ingram & Maccarone (2017) Dealing with gaps 29
• NICER light curve has gaps (Earth occultations, ISS structures etc). • IXPE light curve has gaps at different times. • Therefore not much strictly simultaneous time L Solution
• Maximum likelihood method: Miller et al (2010); Zoghbi 3 − 10 keV Count rate
et al (2013) 2000 4000 6000 • Likelihood = 20 30 40 Days since 1st Sep 2017
Parameters (power in each frequency Matrix calculated Observed light bin) from power spectral curve model • Maximize likelihood to get e.g. cross-spectrum between IXPE and NICER • Already works on e.g. NuSTAR data (Zoghbi et al 2013) Ingram et al (in prep) Reconstruction of spin axis 30 Smile/frown diagram ψ0~max ψ0~min 6.8 6.6 Iron Line Energy (keV) Iron 6.4
-4 -7 -10 Polarisation Angle (degrees) • Detect polarization QPO with method of Ingram & Maccarone (2017) • Tomography (NuSTAR, NICER): gives disk illumination pattern • Polarization: gives orientation of corona • = reconstruction of black hole spin axis + shape of corona! The End 31