Reopening the window of astronomical soft X-ray polarimetry

Hua Feng 冯骅 (Tsinghua University)on behalf of the PolarLight collaboration

1

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目录CONTENTS

Science with X-ray Polarimetry

Technique for X-ray Polarimetry

PolarLight

CubeSats in Space Astronomy

01

02

03

04

2

PART ONEScience with X-ray Polarimetry

What can we learn from X-ray polarimetry?

• Information about the magnetic field– Synchrotron radiation (PWNe, Jets)– Plasma polarization (Magnetized plasma)– QED vacuum birefringence (Neutron Stars)

• Information about the scattering medium– Thomson/Compton/InverseCompton scattering – Geometric symmetry (accretion flow, BH spin, Sgr B2, etc.)

4

Science cases• Synchrotron radiation and B-fields

Blazars GRB Jetted TDEs

(Marscher et al. 2010) Pulsar wind nebulae

5

Science cases• Accreting Pulsars

(Meszaros et al. 1988)

6

Science cases• Surface thermal emission from NSs

• QED effects (vacuum birefringence) & B-field geometry• Tested in optical (RX J1856.5-3754; Mignani et al. 2017)

– SGRs & AXPs

Simulations by R. Taverna and R. Turolla

interactionwiththe

plasmaelectrons

istaken

intoaccount;

however,thisw

illbeimportantonly

atfrequenciesbelowthe

optical!15,16".

Using

theresultofK

uboand

Nagata

!17"todescribe

thepolarization

evolutioninadielectric

birefringentmedium

,Heyland

Shaviv!7"

haveshow

nthatthis

vacuumbirefrin-

gencewillcouple

theevolution

ofthephoton

polarizationto

themagnetic

fielddirection

throughthe

equation

#s#x

3 !$

"s,

%2&

where

x3isthe

distancealong

thedirection

ofpropagation,sisthe

normalized

Stokesvector,

and$isthe

birefringentvector

previouslydescribed.

Close

tothe

neutronstar,$

islarge,and

srotates

quicklyaround

$.Thus,

asthe

directionofthe

magnetic

fieldchanges,

$willrotate

andswillfollow

itadiabatically.Farenough

fromthe

NS,the

amplitude

of$willfalland

swill

notbeable

tofollow

$any

longer.Thecondition

foradia-

baticitytohold

is!7"

l% 'k& !

!$/% (

ln!$!& !#

0.5%3&

where

listhe

scalelength

ofthe

magnetic

field.Ifone

assumesthat

thefield

surroundingthe

starhas

adipolargeom

etry,thepolarization

statesevolve

adiabaticallyif

r$rpl )"

*45+c #

1/5",

BQED sin-#

2/5

.1.2"

107"

,

1030Gcm

3 #2/5"

+

1017Hz #

1/5

"% sin

-& 2/5cm

,%4&

where

risthe

distancefrom

thecenter

ofthe

star,,isthe

magnetic

dipolemoment

ofthe

neutronstar,

and-isthe

anglebetw

eenthe

dipoleaxis

andthe

lineofsight;r

pl isthe

polarization-limiting

radius,borrowing

terminology

fromthe

studyofradio

pulsars!15".

Physically,theadiabatic

regimeisappropriate

aslong

as'n•k•l#

1,where

'nisthe

differencebetw

eenthe

indicesofrefraction,k

isthe

wave

vectorand

l/risthe

distancescale

overwhich

thephysical

variableschange.

Inother

words,

adiabaticityrequires

thatover

thephysical

lengthscale

ofthe

problem,the

twomodes

developasignificant

phasedifference

between

them.The

couplingorpolarization

limiting

radiustherefore

doesnot

dependon

therate

atwhich

$changes

direction.The

direction%and

rateof

changeindirection&

of$will,how

ever,determine

thepo-

larizationleft

beyondrpl .Since

$isinthe

1-2plane

de-scribing

linearpolarizations,

thedirection

of$atrpl w

illdeterm

inethe

linearpolarization

component

ofswhile

therate

ofchange

of$willdeterm

inethe

circularcom

ponent.

Heuristically,

becauseofvacuum

birefringenceinthe

magnetosphere,

theobserved

polarizationdirection

froma

surfaceelem

entiscorrelated

withthe

directionofthe

mag-

neticfield

farfrom

thestellar

surface.Atthis

distance,thebundle

ofrays

thatwill

eventuallybe

detectedpasses

throughasmallsolid

angle.Over

thissmallsolid

angle,thedirection

ofthe

magnetic

fieldvaries

little,sothe

observedpolarization

fromdifferentparts

alsovaries

littleand

alarge

netpolarization

results.Furtherm

ore,this

heuristicpicture

predictsthatbecause

starswithsmallerradiigenerally

resultinsmallerray

bundles,smallerstars

willexhibita

largernetpolarization.This

heuristicpicture

isborne

outby

detailedcalcula-

tions.Tocalculate

theprocess

accurately,onecalculates

thephoton

trajectoryboth

inspacetim

eand

onthe

Poincaresphere

inthe

contextofgeneral

relativity%GR

&.First,

we

incorporatelightbending

%asisgiven,forexam

ple,byPage

!18"&.Second,wehave

touse

theresultofPineault!19"w

hoshow

edthat

alongthe

bentlight

rayspresent

inGR,the

polarizationdirection

rotatesinsuch

awaythatitkeepsfixed

orientationwithrespectto

thenorm

altothe

trajectoryplane,

remaining

perpendiculartothe

wave

vector.Additionally,

GRdistorts

thedipole

magnetic

field!20"

nearthe

star.

III.RESULTS

Asam

pleresult

ofthe

integrationofthe

polarizationis

giveninFig.1,w

herethe

apparentpolarizationatinfinity

isdepicted

togetherwith

thedirection

thatthe

polarization

FIG.1.The

apparentpolarized

image

ofaneutron

starover-

layedonthe

apparentimage

ofthe

NS.The

leftpaneldepictsthe

observedmapofpolarization

directionsifone

assumesthat

thesurface

emitsonly

inthe

ordinarymode

andneglects

thevacuum

birefringenceinduced

byQED.The

rightpanelshowsthe

polariza-tion

map

includingbirefringence

forafrequency

of+

!,30 %210

17Hz.The

ellipsesand

shortlinesdescribe

thepolariza-

tionofalight

rayoriginating

fromthe

surfaceelem

entbeneath

them.The

linesand

themajoraxes

oftheellipses

pointtowards

thedirection

ofthelinearcom

ponentofthepolarization

direction.Theminorto

majoraxis

ratioprovides

theamountofcircularpolariza-

tion(s3 ).In

bothmaps,the

largedashed

curvesarelinesofconstant

magnetic

latitude%separated

by15°).The

observer’sline

ofsight

makesan

angleof30°

withthe

dipoleaxis.Forcom

parison,thenet

linearpolarizationonthe

leftis13%while

itis70%onthe

right.Inamore

realisticNS,the

valuesfor

x-rayfrequencies

would

bere-

ducedto6–10

%and

35–55%,respectively

!21",sincethe

intrinsicpolarization

ofeach

elementis

not100%butsm

aller.

JEREM

YS.H

EYLANDNIRJ.SH

AVIV

PHYSIC

ALREVIEW

D66,023002

%2002&

023002-2

~10% ~70-80%

interactionwiththe

plasmaelectrons

istaken

intoaccount;

however,thisw

illbeimportantonly

atfrequenciesbelowthe

optical!15,16".

Using

theresultofK

uboand

Nagata

!17"todescribe

thepolarization

evolutioninadielectric

birefringentmedium

,Heyland

Shaviv!7"

haveshow

nthatthis

vacuumbirefrin-

gencewillcouple

theevolution

ofthephoton

polarizationto

themagnetic

fielddirection

throughthe

equation

#s#x

3 !$

"s,

%2&

where

x3isthe

distancealong

thedirection

ofpropagation,sisthe

normalized

Stokesvector,

and$isthe

birefringentvector

previouslydescribed.

Close

tothe

neutronstar,$

islarge,and

srotates

quicklyaround

$.Thus,

asthe

directionofthe

magnetic

fieldchanges,

$willrotate

andswillfollow

itadiabatically.Farenough

fromthe

NS,the

amplitude

of$willfalland

swill

notbeable

tofollow

$any

longer.Thecondition

foradia-

baticitytohold

is!7"

l% 'k& !

!$/% (

ln!$!& !#

0.5%3&

where

listhe

scalelength

ofthe

magnetic

field.Ifone

assumesthat

thefield

surroundingthe

starhas

adipolargeom

etry,thepolarization

statesevolve

adiabaticallyif

r$rpl )"

*45+c #

1/5",

BQED sin-#

2/5

.1.2"

107"

,

1030Gcm

3 #2/5"

+

1017Hz #

1/5

"% sin

-& 2/5cm

,%4&

where

risthe

distancefrom

thecenter

ofthe

star,,isthe

magnetic

dipolemoment

ofthe

neutronstar,

and-isthe

anglebetw

eenthe

dipoleaxis

andthe

lineofsight;r

pl isthe

polarization-limiting

radius,borrowing

terminology

fromthe

studyofradio

pulsars!15".

Physically,theadiabatic

regimeisappropriate

aslong

as'n•k•l#

1,where

'nisthe

differencebetw

eenthe

indicesofrefraction,k

isthe

wave

vectorand

l/risthe

distancescale

overwhich

thephysical

variableschange.

Inother

words,

adiabaticityrequires

thatover

thephysical

lengthscale

ofthe

problem,the

twomodes

developasignificant

phasedifference

between

them.The

couplingorpolarization

limiting

radiustherefore

doesnot

dependon

therate

atwhich

$changes

direction.The

direction%and

rateof

changeindirection&

of$will,how

ever,determine

thepo-

larizationleft

beyondrpl .Since

$isinthe

1-2plane

de-scribing

linearpolarizations,

thedirection

of$atrpl w

illdeterm

inethe

linearpolarization

component

ofswhile

therate

ofchange

of$willdeterm

inethe

circularcom

ponent.

Heuristically,

becauseofvacuum

birefringenceinthe

magnetosphere,

theobserved

polarizationdirection

froma

surfaceelem

entiscorrelated

withthe

directionofthe

mag-

neticfield

farfrom

thestellar

surface.Atthis

distance,thebundle

ofrays

thatwill

eventuallybe

detectedpasses

throughasmallsolid

angle.Over

thissmallsolid

angle,thedirection

ofthe

magnetic

fieldvaries

little,sothe

observedpolarization

fromdifferentparts

alsovaries

littleand

alarge

netpolarization

results.Furtherm

ore,this

heuristicpicture

predictsthatbecause

starswithsmallerradiigenerally

resultinsmallerray

bundles,smallerstars

willexhibita

largernetpolarization.This

heuristicpicture

isborne

outby

detailedcalcula-

tions.Tocalculate

theprocess

accurately,onecalculates

thephoton

trajectoryboth

inspacetim

eand

onthe

Poincaresphere

inthe

contextofgeneral

relativity%GR

&.First,

we

incorporatelightbending

%asisgiven,forexam

ple,byPage

!18"&.Second,wehave

touse

theresultofPineault!19"w

hoshow

edthat

alongthe

bentlight

rayspresent

inGR,the

polarizationdirection

rotatesinsuch

awaythatitkeepsfixed

orientationwithrespectto

thenorm

altothe

trajectoryplane,

remaining

perpendiculartothe

wave

vector.Additionally,

GRdistorts

thedipole

magnetic

field!20"

nearthe

star.

III.RESULTS

Asam

pleresult

ofthe

integrationofthe

polarizationis

giveninFig.1,w

herethe

apparentpolarizationatinfinity

isdepicted

togetherwith

thedirection

thatthe

polarization

FIG.1.The

apparentpolarized

image

ofaneutron

starover-

layedonthe

apparentimage

ofthe

NS.The

leftpaneldepictsthe

observedmapofpolarization

directionsifone

assumesthat

thesurface

emitsonly

inthe

ordinarymode

andneglects

thevacuum

birefringenceinduced

byQED.The

rightpanelshowsthe

polariza-tion

map

includingbirefringence

forafrequency

of+

!,30 %210

17Hz.The

ellipsesand

shortlinesdescribe

thepolariza-

tionofalight

rayoriginating

fromthe

surfaceelem

entbeneath

them.The

linesand

themajoraxes

oftheellipses

pointtowards

thedirection

ofthelinearcom

ponentofthepolarization

direction.Theminorto

majoraxis

ratioprovides

theamountofcircularpolariza-

tion(s3 ).In

bothmaps,the

largedashed

curvesarelinesofconstant

magnetic

latitude%separated

by15°).The

observer’sline

ofsight

makesan

angleof30°

withthe

dipoleaxis.Forcom

parison,thenet

linearpolarizationonthe

leftis13%while

itis70%onthe

right.Inamore

realisticNS,the

valuesfor

x-rayfrequencies

would

bere-

ducedto6–10

%and

35–55%,respectively

!21",sincethe

intrinsicpolarization

ofeach

elementis

not100%butsm

aller.

JEREM

YS.H

EYLANDNIRJ.SH

AVIV

PHYSIC

ALREVIEW

D66,023002

%2002&

023002-2

7

Science cases

8

PART TWOTechnique for X-ray Polarimetry

Exploration of the new window since the 1960s

First satellite: 1974Flat Bragg crystal

Ariel 5

First precise measurement: 1975Bragg polarimeter, OSO-8P = 19.2% ± 1.0% 𝜓 = 156.4°± 1.4°Weisskopf et al. 1976, 1978

First detection: 1971Bragg polarimeterAerobee 350Crab nebula P = 15.4% ± 5.2%

First attempt: 1968Scattering polarimeterAerobee 150

X-ray astronomy started in 1962

10

X-ray polarimetry based on the photoelectric effect

dσdΩ

∝cos2ϕ

Dsptt.tfdujpo!pg!qipupfmfdusjd!fggfdu

position angle

max−minmax+min

degree

11

Technical difficulties• Short range for electrons of a few keV

– in silicon: ~μm– in gas: ~mm

• Electron tracks are not straight due to scattering

• Challenge for detector– Require 2D imaging device– Resolution < 100 μm

•600

-800

IOOC-1000 -800 -800 -400 -200 0 200 400 000 800 1000x axis (micron)

Figure 9. Simulated tracks (projected onto the detector plane) produced by 5 keV electrons in pure Ne, at pressureof 1 Atm (right). Starting directions are distributed according to equation (15), simulating photoelectrons emitted inresponse to a collimated, 100 % linearly polarized 5.9 keY photons beam. By means of a progressive "zoom out" (left),it can be clearly seen that the modulation of the track directions is more and more blurred by Coulomb scattering whilegoing away from conversion point.

direction with the principal axis of the released charge distribution. At higher energy, in fact, tracks are longerand the probability for a large angle electromagnetic scattering to occur increases as well. On the other hand, amore sophisticated algorithm which isolates the initial part of the track (like the one we use) allows to efficientlyovercome this limitation, as it is clearly confirmed by experimental data.

By means of our Monte Carlo code we have investigated the performance of a polarimeter with a 100 mreadout pitch (which is feasible with currently adopted technology and will be soon available for tests) for several

70C.)

o 60

50

40

30

20

200 400 600 800 1000Distance from convertion point (micron)

Figure 10. Modulation factor, as a function of distance from absorption point, evaluated from the distribution ofprimary ionization for 5 keV photoelectrons in pure Ne, 1 Atm.

x m ron)

- 800U,

800

400

8

200

.200 -

-400 -

) ) )))) )

I ) ) ) I

Proc. of SPIE Vol. 4843 391

•600

-800

IOOC-1000 -800 -800 -400 -200 0 200 400 000 800 1000x axis (micron)

Figure 9. Simulated tracks (projected onto the detector plane) produced by 5 keV electrons in pure Ne, at pressureof 1 Atm (right). Starting directions are distributed according to equation (15), simulating photoelectrons emitted inresponse to a collimated, 100 % linearly polarized 5.9 keY photons beam. By means of a progressive "zoom out" (left),it can be clearly seen that the modulation of the track directions is more and more blurred by Coulomb scattering whilegoing away from conversion point.

direction with the principal axis of the released charge distribution. At higher energy, in fact, tracks are longerand the probability for a large angle electromagnetic scattering to occur increases as well. On the other hand, amore sophisticated algorithm which isolates the initial part of the track (like the one we use) allows to efficientlyovercome this limitation, as it is clearly confirmed by experimental data.

By means of our Monte Carlo code we have investigated the performance of a polarimeter with a 100 mreadout pitch (which is feasible with currently adopted technology and will be soon available for tests) for several

70C.)

o 60

50

40

30

20

200 400 600 800 1000Distance from convertion point (micron)

Figure 10. Modulation factor, as a function of distance from absorption point, evaluated from the distribution ofprimary ionization for 5 keV photoelectrons in pure Ne, 1 Atm.

x m ron)

- 800U,

800

400

8

200

.200 -

-400 -

) ) )))) )

I ) ) ) I

Proc. of SPIE Vol. 4843 391

12

Gas Pixel Detector (GPD)• First demonstrated by INFN-Pisa & IAPS-Rome

(Bellazzini et al.; Costa et al. 2001)

13

Gas Electron Multiplier (GEM)

Detector assembly

14

Measured electron tracks

15

Angular modulation

2.67 keV 3.74 keV 5.33 keV

6.09 keV 7.49 keV

16

PART THREE

PolarLight

Polarimeter Light (PolarLight；极光计划)

collimator

window

GEM

ASIC chip

GPD

HV

DAQ

CubeSat

x-ray

photoelectron track

measured 2D track

PolarLight

18

Shocking test

19

Vibration test

20

Thermal vacuum

21

Launched into a low Earth orbit

October 29, 2018

22

Re-detection of X-ray polarization from the Crab nebula

23

Time variation of polarization

With pulsar emission Without pulsar emission significance level: 3σ

• Bayes factor• Bayesian posterior• BootstrapMagnetosphere altered after the glitch

glitch

24

High energy emission from pulsars

25

11 Multi-Wavelength Polarimetry of Isolated Pulsars 287

Fig. 11.3 Location of radio (blue) and high-energy emission in the outer gap (yellow), two-polecaustic (red) and current sheet (green) models in the meridional plane containing the spin andmagnetic axes of a force-free magnetosphere. The dashed black lines denote the light cylinder andthe dotted red lines show projections of the null-charge surface

site of particle acceleration. The accelerated particles radiate ! -rays through cur-vature and inverse-Compton radiation, initiating electromagnetic cascades throughone-photon pair production in the strong magnetic field (Daugherty and Harding1982; Harding and Muslimov 2002). In this model, the high-energy pulses wouldappear near the phase of the radio pulses, would be very highly polarised and exhibitthe “S-shaped” PA sweep of the RVM. Phase-resolved high-energy polarisationmeasurements were not available until fairly recently, so this property of the polarcap models could not be tested. However the Fermi Gamma-Ray Space Telescope,launched in 2008, discovered many ! -ray pulsars whose pulses appeared at phasessignificantly different from those of the radio pulses (Abdo et al. 2013). In fact,the variety of light curves agree more with predictions of models where the high-energy emission comes from the outer magnetosphere near or beyond the lightcylinder,RLC = c/", where" is the pulsar rotation rate. Such outer magnetospheremodels, such as outer gap (Cheng et al. 1986; Romani 1996), slot gap and currentsheet models had been proposed earlier (see Fig. 11.3). Naturally, polarisationpredictions also changed substantially from those of polar cap models and, as will bediscussed in the following sections, can better explain the properties of the observedpolarisation.

Cheng et al. 1986Muslimov et al. 2004Kalapotharakos et al. 2012Harding et al. 2019

Reopening the window

OSO-8 (1975)

PolarLight (2018)

IXPE in 2021(Weisskopf et al. 2016)

eXTP in 2027(Zhang et al. 2019)

26

PART FOUR

CubeSats in Astronomy

CubeSat 立方星• The CubeSat standard

– proposed in 1999 by Jordi Puig-Suari of California Polytechnic State University and Bob Twiggs of Stanford University

– an educational tool for teaching students about spacecraft hardware, electronics and programming

– Low cost1U 3U 6U

28

Astronomical CubeSats funded by NASA

• ASTERIA (Arcsecond Space Telescope Enabling Research in Astrophysics)

– to measure exoplanetary transits across bright stars with <100 ppm photometry

– launched in August 2017, one of the first CubeSats enabled for astronomical measurements

• PicSat– to observe in visible light the potential transit of the directly-

imaged giant planet β Pictoris b• HaloSat

– measure the soft X-ray emission from the hot halo of the Milky Way galaxy to resolve the missing baryon problem

• CUTE (Colorado Ultraviolet Transit Experiment)– survey of exoplanet transit spectroscopy in the near-UV

• SPARCS (Star–Planet Activity Research CubeSat)– the far- and near-UV monitoring of low-mass stars (0.2–0.6

M☉)• BurstCube

– to detect and localize GRBs

29

“CubeSat” on ADSLaunches of CubeSats

A rapid growth

30

The GRID network

GRID (Gamma Ray Integrated Detectors)

l 10+ CubeSats in LEOl Scintillation detector, ~60 cm2 eachl Localization accuracy for GRBs within 200 Mpc

ü <1°(for an on-axis event, ~0.14 yr-1)ü 10°~ 15°(for a GRB 170817A like event, ~5 yr-1)

31

Flight model & satellite

32

GRID - a student project

• Started in 2016 October• More than 50 Students from 16 universities• GRID-1 in orbit• GRID-2/GRID-3 will be launched this year

The first group Testing the detector Talking at COSPAR 2018

33

CubeSats in Astronomy• To demonstrate new techniques

– Sounding rockets vs. Balloons vs. CubeSats• Highly customized science objective

– Large missions: observatories– Small missions: dedicated

• Long-term monitoring of a single or a few targets• Student training

– Project cycle: ~3 years– All-around skills: science + engineering + leadership

34

THANK YOU!