Study of Periodic Polarized X-ray Emission with IXPE

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Universit`

a di Pisa

DIPARTIMENTO DI FISICA Corso di Laurea Magistrale in Fisica

Tesi di laurea magistrale

Study of Periodic Polarized X-ray Emission with IXPE

the case of transitional millisecond pulsars

Candidato:

Nunziato Sorrentino

Relatore:

Prof. Luca Baldini

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"Amor che nella mente mi ragiona cominciò egli a dir si dolcemente che la dolcezza ancor dentro mi suona." Dante Alighieri - La Divina Commedia Purgatorio Canto II

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Introduction

Astronomical polarimetry allows to investigate physical anisotropies linked to astrophysical phenomena like non-spherical distributions of matter and ordered magnetic fields, given its distinctive link to the emission processes. In radio and optical wavelengths polarimetry is a powerful tool commonly used since the pi-oneering measurements made in 1950s, but it is an almost unexplored field at higher energies.

X-ray astronomy, nevertheless, has a vast history of successful missions and observations that include almost no polarimetric data: X-ray polarimetry counts just one target, the Crab nebula, with a highly significant and unambiguous result. The reason for such a gap is mainly due to the nature of X-ray polarimetry it-self: it requires significantly more data to produce meaningful results, if compared to ones required by spectral or photometric measurements. Moreover, polarime-ters used in the 1960s and 1970s (the only period when polarimetry missions have been performed) had low efficiency, making the measures even more difficult.

The Imaging X-ray Polarimetry Explorer (IXPE) is a mission set to be launched in the middle of 2021 and will allow again, after more than 40 years gap, to per-form polarimetric measurements in the X-ray band. IXPE will be able to inves-tigate tens of astrophysical sources, giving a whole new set of data to invesinves-tigate the physical processes happening inside and around them.

Important sources that fully satisfy these characteristics are pulsars, that are very compact objects with a high magnetic field in a geometrically asymmetric environment. Both isolated and in accretion states, pulsars are being observed over the entire electromagnetic spectrum, trying to explain their peculiar periodic behavior. The possibility of investigating the phase-resolved polarized emission with IXPE represents a suitable opportunity to understand the physical processes involved in such extreme systems.

One of the most studied pulsar systems to date are the transitional millisec-ond pulsars, characterized by some millisecmillisec-ond pulsar like peculiarities, but that have been observed with such a different multi-wavelength behavior, that have been identified as the "missing link" in the evolutionary chain between rotation-powered and accretion-rotation-powered millisecond pulsars.

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3 In Chapter 1 I will summarize the fundamental quantities and properties in-volved in polarimetric studies. In Chapter 2 I will explain what is IXPE, what are the mean scientific goals and the technical overview, then in the Chapter3 I will focus on the polarized photon sensitive Gas Pixel Detector. In Chapter 4 I will talk about the simulation framework dedicated to IXPE mission (ixpeob-ssim), to which development I have actively contributed, concentrating my thesis work on programs dedicated to the study of pulsars polarized emission. In Chap-ter 5 I will treat the case of the most observed transitional millisecond pulsar PSRJ1023+0038, simulating and analyzing it with ixpeobssim and trying to out-line an observation strategy for this kind of sources. In the end, in Chapter 6, there are the conclusions of this thesis, the contribution that led to the final stage of the simulation framework, which programs are available for all the IXPE col-laborators, the input given to the study of transitional millisecond pulsars and the significant measurements that IXPE will lead to this kind of sources.

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Chapter 1 X-ray Polarimetry

A fundamental quantity in astronomy is the polarization of photons, that brings information about the internal geometry of the source and provides a great observ-able that discriminates between different types of emission.

Imaging, timing and spectroscopy are routine observational techniques across the entire electromagnetic spectrum. The direction of photons allows to deter-mine the position and the morphology of the source, while the times of arrival provide information about the dynamical properties of the source, like periodicity or emission mechanism changes. Moreover, the energy of photons provides the source spectrum, from which a huge amount of information can be deduced, such as the chemical composition of the emitting medium and its acceleration environ-ment.

Polarimetry, instead, is a common tool in the optical and radio bands but is almost unexplored in higher energy photons band. An X-ray polarimeter with imaging timing and spectroscopy capabilities can lead to a powerful observational window in high energy astrophysics.

In this chapter I will introduce the general aspect of photons polarimetry, fol-lowing the [85] review and exploring its creation and detection in X-ray energy band.

1.1 Polarimetry of Electro-Magnetic Waves

Photons can be seen as electromagnetic waves, solution of Maxwell equation, with an electric field E, from which the polarization properties are defined. For an electromagnetic monochromatic plane wave traveling in vacuum in z direction in Euclidean coordinates (x, y, z),E can be expressed as:

E = E0cos(kz − ωt + φ0)

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CHAPTER 1. X-RAY POLARIMETRY 7 where t is the time, ω is the angular frequency, k = ω/c is the wave vector module, and φ0 is an arbitrary phase. On the z = 0 plane, the x and y components for E

are:

• Ex(t) = Ex(0) cos(ωt − φ1)

• Ey(t) = Ey(0) cos(ωt − φ2)

where φ1 and φ2 are two arbitrary phases.

Polarization is a property of electromagnetic waves which refers to the orien-tation of the electric field. Therefore, polarization is given by the relative values of Ex(0), Ey(0), φ1 and φ2. Three states of polarization can be identified:

ellip-tical, linear and circular polarization. In general, the direction of the electric field vector follows an elliptical trajectory in the x-y plane, and the wave is consid-ered elliptically polarized. The orientation of the ellipse is constant in time and this polarization is said to be right-handed in the case of a clockwise motion with respect to the z direction. Otherwise (counterclockwise motion ofE) the polariza-tion is denoted as left-handed. The polarizapolariza-tion angle χ corresponds to the angle between the positive x axis and the semi-major axis of the ellipse.

If the polarization ellipse degenerates into a circle the radiation is said to be circularly polarized. This corresponds to φ2 = φ1± π₂ and Ex(0) = Ey(0).

There is linear polarization if the ellipse degenerates into a line. This happens when φ1 = φ2 and in this case the angle χ is constant.

1.2 Polarization Statistics

Astrophysical observations do not deal with individual electromagnetic waves, but with a superposition of waves, thus they are sensitive to an ensemble of polarized and unpolarized waves. So if a certain orientation of the electric field vectors is preferred for some reason, the light polarization property will becomes the prob-ability of measuring a wave as polarized, called polarization degree. Let’s define it as:

P = IP

I ∈ [0; 1]

where I denotes the total intensity of the light and IP denotes the intensity of

polarized light. Since the total polarization state of radiation can be described as a superposition of linear and circular polarization, these ones can be defined separately: PL= IL I ∈ [0, 1] PC = IC I ∈ [−1, 1]

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CHAPTER 1. X-RAY POLARIMETRY 8 The positive (negative) sign is assigned to PC by convention to light which is

mostly right-handed (left-handed).

1.2.1 Stokes Parameters

Considering the statistic treated above, the polarization state of a set of photons can be described by means of three independent parameters, called Stokes Param-eters:

• I = hE2

xi + hEy2i

• Q = hE2

xi − hEy2i

• U = 2hExEysin δi

• V = 2hExEycos δi

where Ex/yare function of time, δ = φ2− φ1and h...i represents the average over

the ensemble, that under ergodicity is also equal to the time average taken over times much larger than2π/ω.

I represents the total intensity of the radiation, Q quantifies the difference in the intensities in x and y, thus it provides information on linear polarization. U , instead, denotes the intensities at 45◦ and 135◦, likewise probing linear polariza-tion. Finally and V corresponds to the circularly polarized intensity.

For individual waves the Stokes parameters are related to each other: I2 = Q2_{+ U}2_{+ V}2

thus the number of free parameters in case of fully polarized radiation is three. In the general case of superimposed polarized and unpolarized radiation the Stokes parameters are related via:

I_P2 = Q2_{+ U}2_{+ V}2 _{≤ I}2

and the number of free parameters increases to four.

Therefore, according to the definitions of PL, χ and PC, the Stokes parameters

are related to that with:

PL= pQ2 _{+ U}2 I ∈ [0, 1] χ= 1 2arctan U Q ∈ −π 2, π 2

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CHAPTER 1. X-RAY POLARIMETRY 9

PV =

V

I ∈ [−1, 1] and the total degree of polarization is given by:

P = pQ

2_{+ U}2_{+ V}2

I ∈ [0, 1]

1.3 Polarized Photons Creation

In this section I will treat the radiation phenomena that produce X-ray polarized photons from astrophysical sources, which represent the basis of emission models proposed by astronomers.

1.3.1 Scattered Photons

The scattering of a photon with a free electron leads to a characteristic linear po-larization of the scattered light. This process is referred to as Compton scattering or, at lower energies in classical regime, as Thomson scattering.

Thomson Scattering

Following [59], this is the case of unpolarized photon radiation that scatters elas-tically with a free electrons distribution at rest with energy E mec2 ≈ 0.5

MeV. The scattered intensity can be written in terms of differential cross-section of scattering process: dσT dΩ unpol = r 2 e 2(1 + cos 2_α)

where r2_e is the electron classical radius and α is the angle between the direc-tion of the incident radiadirec-tion and the line of sight. If a polarized incident flux is considered, the formula is:

dσT dΩ pol = r2 esin2α

The total cross section is the same for polarized and unpolarized incident radiation and it is constant: σT = 8π 3 r 2 e ≈ 0.665 × 10 −24 cm2

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CHAPTER 1. X-RAY POLARIMETRY 10 The incident beam can be considered as the superposition of two linearly polarized beams with orthogonal axes. The angle dependence of differential cross-sections implies that the scattered radiation is linearly polarized with a degree of polariza-tion:

PL =

1 − cos2_α

1 + cos2_α

Thus, radiation scattered by means of Thomson scattering is polarized. An unpo-larized radiation acquires a degree of polarization and becomes completely polar-ized for α= 90◦_.

Compton Scattering

The classical description of the scattering between a photon and an electron is no longer valid when the photon energy approaches mec2. In many astrophysical

process we have relativistic electron populations that are scattered by Compton mechanism. The elementary process is:

γ+ e−−→ γ + e−

The photon transfers part of its energy to the electron, thus the scattered photon will have an energy Ef different from the incident photon energy Ei. The relation

between the energy transfer and the scattering angle θ can be obtained by means of conservation of energy and momentum and is equal to:

Ef =

Ei

1 + Ei

mec2(1 − cos θ)

The differential cross-section for Compton scattering (the Klein-Nishina cros-section) in the case of a completely polarized incident beam is [47]:

dσT dΩ pol = r 2 e 2 Ef Ei 2_E f Ei + Ei Ef − 2 sin2_θ_cos2_φ

where φ is the azimuthal angle of scattering, i.e the angle between the electric field direction and the plane of scattering. This cross-section has a maximum at φ = 90◦ _{and φ} _{= 270}◦_{, thus linearly polarized photons are preferentially}

scat-tered perpendicularly to the direction of polarization. The polarization degree of scattered photons is:

PL = 2 1 − sin2_θ_cos2_φ Ef Ei + Ei Ef − 2 sin 2_θ_cos2_φ <1

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Figure 1.1: Polarization degree due to unpolarized photons scattering with Comp-ton effect as a function of the scattering angle and the incident phoComp-ton energy. Image from [56].

have a reduced linear polarization degree with a photon energy dependence. In the non-relativistic case in which Ei = Ef (Thomson scattering) PL = 1 is recovered,

as expected. In the case of unpolarized incident radiation, the differential cross-section is: dσT dΩ _unpol = r 2 e 2 Ef Ei 2_E f Ei + Ei Ef − sin2θ

and the scattered photons are partially polarized, with a polarization degree equal to: PL= 1 − sin2_θ Ef Ei + Ei Ef − sin 2_θ <1

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Figure 1.2: Radiation emitted by an electon in a magnetic field in the non-relativistic (left) and non-relativistic (right) case. Image from [10].

which depends on the energy of the incident photons and on the scattering angle as shown in Fig.1.1.

A related process of interest in the astrophysical context is the Inverse Comp-ton scattering. In this process low-energy photons are scattered by relativistic electrons to higher energies. Electrons with γ = 1000, for example, can scatter optical photons up to γ-rays [58]. Thanks to this process, as for the Compton scattering, unpolarized radiation acquires a linear polarization degree.

1.3.2 Syncrotron Radiation

Synchrotron radiation is the electromagnetic radiation emitted by relativistic charged particles (usually electrons and positrons) gyrating around magnetic field lines, which can be static or time-varying. Assuming a magnetic field B in the z direc-tion and a particle with a non-zero velocity along z, the Lorentz force causes the electron to have an helical trajectory around z and its acceleration causes the photon emission, respecting the Larmor formula [59] (see Fig.1.2). In the non-relativistic case the radiation is emitted with a dipole pattern with a gyro-frequency of the electron:

νg =

eB 2πme

In the relativistic case, due to the effect of aberration, the radiation is emitted in the direction of the particle motion into a narrow cone with half opening angle θ '1/γ, where γ is the Lorentz factor. The orbit of the electron is a projected el-lipse, thus the radiation emitted by a single electron is elliptically polarized. In the astrophysical case, instead, there is not a single electron/positron that accelerates,

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CHAPTER 1. X-RAY POLARIMETRY 13 but an ensembles of particles, each with a right-handed or left-handed electron orbits, with equal probability. Therefore the elliptical component of the radiation averages out and, macroscopically, the synchrotron radiation results in a partially linearly polarization emission, with the direction of polarization perpendicular to the direction of the magnetic field projected onto the plane of the sky. The lin-ear polarization degree PL depends on the spectrum of the synchrotron radiation

which in turn depends on the distribution of the electron energies. In the case of a power-law distribution of electrons, the number of these particles varies with the energy E as:

N ∝ E−p

where p is the index of electron power-law distribution. The polarization degree can be found and it is:

PL=

p+ 1 p+7 3

Thus, for a typical value of p ≈ 2.6 and in the case of a uniform magnetic field, the polarization of synchrotron radiation is expected to be about 73%.

1.4 Polarized Photons Detection

The current technology available for X-ray polarimetry allows to measure only linear polarization. Different physical processes are considered in order to per-form this measurement, depending on the photon energy (see Fig.1.3). Diffraction on crystals is used below 1 keV, while the photoelectric effect is used up to some tens of keV and finally the Compton scattering is exploited in the 100 keV en-ergy range [40]. In this section the basic concepts and techniques used for X-ray polarimetry are presented [22].

Polarization Measurement

A X-ray polarimeter is ultimately an instrument composed by a detector and an analyzerthat measure a certain azimuthal modulation around the polarization an-gle φ0 of the incident radiation:

R(φ) = A + B cos2_{(φ − φ}

0) (1.1)

where the measured angle φ depends on the type of polarimeter (for example, in the case of a photoelectric effect polarimeter, it is the azimuthal component of the angle of the photoelectron track), while A and B are two generic parameters which depend on the instrument. Eq.1.1 can be also written as:

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Figure 1.3: Photon total cross section as a function of energy in Carbon. Note the "jump" at binding energy of the K-shell, that is the innermost shell and is exploited in photoelectric polarimeters. Image from[72].

where C is a normalization constant that represents the number of photons de-tected and m = B

B+2A is the modulation amplitude. The m and φ0 quantities are

the ones that must be measured for the reconstruction of the X-ray polarization. In the case of 100% polarized photons the modulation amplitude is denoted as modulation factor (µ) and it is in general 0 < µ < 1. This means that in a real polarimeter the modulation factor depends on the physics of the interaction chosen for the detection and on the properties of the polarimeter, which lead to an energy dependence of the quantity (µ ≡ µ(E)). Thus µ represents a fundamental parameter, since it quantifies the ability of the polarimeter to measure the

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polar-CHAPTER 1. X-RAY POLARIMETRY 15

Figure 1.4: Response curves (number of photons over the φ bin) of a generic polarimeter in the two cases of unpolarized radiation (left) and 100% polarized radiation (right). Image from [40].

ization degree of the event (Fig.1.4 right panel). On the other hand, in the case of an unpolarized beam the detector response should be statistically flat, since there is no preferred direction (Fig.1.4 left panel).

There are two ways for measuring linear polarization with a X-ray polarimeter. The first follows what has been said above: the distribution of the event-by-event azimuthal angles φi (the modulation curve) is accumulated and then fitted with

Eq.1.2. The polarization angle φ0 and the modulation amplitude m are the results

of the fit. Thus given µ the polarization degree is:

P = m

µ

An alternative approch is based on Stokes parameters and is presented in [55]. The steps start with the definition of event-by-event Stokes parameters:

ii = 1, qi = cos(2φi) ui = sin(2φi)

Since the Stokes parameters are additive, the ones calculated for a sample of N events are given by:

I = N X i=1 ii, Q= N X i=1 qi, U = N X i=1 ui

So the normalized Stokes parameters are:

Q = Q

I , U =

U I

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Figure 1.5: Polarization degree values obtained both with stokes parameters es-timator and fitting the modulation curve. The φ are generated randomly from m = 10% and µ = 1. It is clear that the binning affect the measurement if we apply a fit to data. Indeed, using too much bins, the number of events per bin is too small for a correct χ2 _{test statistics. Using Stokes parameters, the problem is}

avoided.

and the polarization degree and angle can be recovered: P = 2 µ p Q2_{+ U}2_, _φ 0 = 1 2arctan U Q (1.3) With respect to the method of fitting the modulation curve, the Stokes parame-ters method avoids the information loss associated with the azimuthal binning of events and lead to a better estimation of polarization degree (see Fig.1.5).

Minimum Detectable Polarization

Statistical fluctuations in the instrumental azimuthal response of a polarimeter cause there to be always a probability of measuring an amplitude of modulation,

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CHAPTER 1. X-RAY POLARIMETRY 17 even if the source is unpolarized. Assuming that the number of events in each azimuthal bin is described by a Poisson distribution and that there is no back-ground, the modulation amplitude which has a 1% probability of being exceeded by chance for an unpolarized source is [91]:

m99% =

4.29 √

N

where N is the number of counts. The corresponding polarization degree, which is a fundamental figure of merit in X-ray polarimetry, is the Minimum Detectable Polarization (MDP) at a 99% confidence level, given by

MDP99% =

4.29

µ√N (1.4)

Therefore, if the measured polarization degree is higher (less) than the MDP, this means that the probability that the detection is due to statistical fluctuations is less (more) than 1%. If the background is not negligible Eq.1.4 changes as follows:

MDP99% = 4.29 µ√t √ S+ B S

where S and B are the signal and background counting rates and t is the time of observation. Using Eq.1.4 we are able to calculate the counts NM DP required

to achieve a particular MDP. Assuming, for example, an ideal polarimeter with µ= 1, the number of counts needed to achieve a MDP= 1% is:

NM DP = 4.29 µMDP99% 2 ' 1.84 × 105

This result highlights the fact that X-ray polarimetry requires a large number of photons, with respect to spectroscopy, imaging and timing, to hold a sufficient sensitivity. It is important to point out that the MDP is not the uncertainty in the polarization measurement, but the mean quantity needed to establish the sig-nificance of a polarimetric measurement. In particular, it can be shown that the number of counts necessary to measure the modulation amplitude corresponding to a certain value of the MDP with βσ of significance is:

Nβ = NM DP

β2

4

Thus, a polarization measurement at5σ, requires an integration time at least 6.25 times longer than that required to simply establish a detection at the confidence level set by the MDP.

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Figure 1.6: Bragg reflection. The two outgoing waves are in phase if the difference in path length for scattering from two adjacent crystal planes,2d sin θ, where d is the crystal plane spacing and θ is the angle of incidence, is an integer multiple of the photon wavelength, λ. Image from [53].

1.4.1 Bragg Crystal Polarimeters

X-rays that incident on a crystal can be scattered by the atoms in the its lattice. When scattered electromagnetic waves interfere constructively they give rise to an intense reflected radiation and happens the phenomenon of the Bragg reflection (Fig.1.6). The constructiveness occurs when the difference in path length due to scattering from two adjacent crystal planes is an integer multiple of the radiation wavelength, that is when Bragg’s law is satisfied:

2d sin θ = nλ

where d is the distance between the lattice planes, θ is the scattering angle, λ is the radiation wavelength and n is a positive integer. A flat crystal oriented at45◦

to a parallel beam of X-rays acts as a perfect polarization analyzer, satisfying Bragg’s law [77]. On the other hand, when θ = 45◦_{, only photons whose electric field}

vec-tors are perpendicular to the plane of incidence are reflected, as shown in Fig.1.7. It follows that, if the incident radiation is partially polarized, the rotation of the crystal around the incident direction causes the diffracted flux to be modulated, with a µ ' 1. However, for a nearly perfect crystal, an efficient reflection can

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Figure 1.7: Schematic view of an X-ray polarimeter exploiting Bragg diffraction, one with a non-focusing flat crystal and one with a focusing curved crystal. The two configurations are shown in [77].

be obtained only for X-rays satisfying Bragg’s law within less than 1 eV and this energy bandwidth is too small for astronomical applications[77].

In order to improve the bandwidth, imperfect crystals (a mosaic of small crys-tal with random orientation) can be used. An X-ray incident on an imperfect crystal traverses many domains until it finds one oriented to satisfy the Bragg’s law. Due to the random orientation of the crystals, domains greatly the possibility of a simultaneous reflection and the range of photon energies is increased to some tens of eV (see Fig.1.8, right panel).

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Figure 1.8: In left panel there are the components to the polarization measurement of the Crab Nebula by OSO-8. In right panel there is the increased bandwidth of the mosaic crystal produced by Gaussian distribution of perfect crystals. Image from [22].

1.4.2 Scattering Polarimeters

Scattering polarimeters exploit the sensitivity of Thomson or Compton scatter-ing (discussed in Sec.1.3.1) to the linear polarization of the incident photons. As shown in Fig.1.9, a scattering polarimeter usually consists in two detector ele-ments: a scattering component, where the scattering takes place, and an absorber (or calorimeter), which detects the scattered photons and records the distribution of the azimuthal scatter angles (φ) [64]. From this distribution, the direction and degree of polarization of the incident beam can be measured. In the case of a 100% linearly polarized incident beam the resulting azimuthal distribution is modulated with a maximum in the direction perpendicular to the polarization one. The mod-ulation factor for this kind of detectors is:

µ(E) = sin 2_θ E Ef + Ef E − sin 2_θ <1

where θ is the scattering angle and E and Ef are respectively the energies of the

incident and scattered photon. The modulation factor is maximum at θ = 90◦

and decreases as E increases. The fact that µ < 1 makes a Compton polarimeter intrinsically not a perfect polarization analyzer. As showed in Sec.1.3.1, in the Thomson limit and at θ = 90◦

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Figure 1.9: A Compton/Thomsom polarimeter, composed by a scattering part that brings the photon to an absorbtion stage. Image from [53].

so a perfect polarization analyzer can be obtained. A preferred relative placement of the two detectors is typically chosen to maximize scattering at θ = 90◦_{, where}

the modulation factor is maximum.

A scattering detector is usually chosen to be composed of a low atomic number material to minimize photoelectric interactions, while the absorber is often an high atomic number material that absorbs the total energy of the scattered photon. Moreover, at low X-ray energies, in the Thomson regime, where the electron recoil is negligible, only the scattered photons are detected and the scattering detector is made of a passive light element, such as Lithium. In the Compton regime, instead, the produced electron can be detected using something like a plastic scintillator. The scattering detector can be readout in coincidence with the absorber, reducing instrumental background.

1.4.3 Photoelectric Polarimeters

The photoelectric effect is the dominant interaction process of X-rays with matter in the 1-10 keV energy band. In this process a photon of energy Eγis absorbed by

an atom, which becomes ionized and emits an electron denoted as photoelectron (see Fig.1.10). The process emits a this particular electron with a kinetic energy:

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Figure 1.10: Angular distribution of the photoelectron emitted by interaction of a linearly polarized photon with an atom. The photoelectron is emitted preferen-tially along the photon electric field, but not exactly parallel to the electric field. The direction of emission is described by two angles: φ is the azimuthal angle relative to the photon electric field vector, θ is the emission angle relative to the photon momentum vector. The Auger electron emission is the most probable sys-tematic effect of the detection. The concentrated energy loss near the end of the track is the Bragg peak. Image from [53].

where Eb is the binding energy of the electron in its original shell. In this process,

the nucleus absorbs the recoil momentum. This energy can be released emitting a fluorescence photon or a second electron, called Auger electron. The emission of an Auger electron is the most probable process (respect to fluorescence) for elements with low atomic number (close to 100% at Z <10).

The photoelectric cross section as a function of the photon energy presents characteristic discontinuities (absorption edges) in correspondence of the bind-ing energies of electrons in the different shells of the absorber atom (Fig.1.3). The last edge corresponds to the binding energy of the innermost electron shell (named K-shell). When the photon energy is above the K-shell, the photoelecton almost always is ejected. If this is assumed, and if the photon is lineary polar-ized, the differential cross-section distribution of the photoelectric effect, in the non-relativistic approximation, is [23]: dσ dΩ = r 2 0 Z5 1374 mc2 Eγ 7₂ 4√2 sin2_{(θ) cos}2_(φ) (1 − β cos(θ))4 (1.5)

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CHAPTER 1. X-RAY POLARIMETRY 23 ejected electron (from K-shell), φ is the photoelectron azimuthal angle with re-spect to the polarization vector, Z is the atomic number of the absorbing material, r0 is the classical radius of the electron and β is the photoelectron speed, in units

of the light speed. The term sin2_{θ at the numerator means that the}

photoelec-tron is emitted meanly in a plane orthogonal to the direction of propagation of the photon. The angle at which the cross section is maximum is:

θmax ≈ cos−1(2β)

Thus, at energies of few keV, photoelectrons are essentially emitted at θ = 90◦ _.

In this plane, the direction of the photoelectron is 100% modulated by the X-ray polarization, following acos2_{(φ) angular dependence. So, in the few keV energy}

range, which is interesting for X-ray astronomers, the photoelectric effect in the K-shell is a good polarization analyzer.

In order to measure polarization exploiting the photoelectric effect it is neces-sary to measure the emission direction of the photoelectron, trying to overcome the two main limitations deriving from this technique:

• electrons, once emitted, propagate in matter less then photon at the energies of interest (short tracks);

• electrons scatter on atoms, randomizing their original direction while their energy decreases and during their motion toward the collecting electrode. Indeed, the information about angle and degree of polarization of the incoming radiation resides in the first part of the photoelectron track so the main effort in the development of this class of polarimetry devices has been devoted to techniques that allow to finely sample the electron path particularly close to the absorption point.

E.g., the track of a 10 keV electron in Silicon is ∼1µm long, which is difficult to be resolved in practice and for this reason semiconductor-based polarimeters have modulation factors below 10%. A longer track (∼ 100µm) can be obtained using a gaseous absorption medium and nowadays two different gas-based po-larimeters exploiting the photoelectric effect are available: the Gas Pixel Detector (GPD) [32], that will be descibed in detail in Chap.3, and the Time Projection Chamber (TPC) [26].

1.5 Historical Remarks

Despite major progress in X-ray imaging, spectroscopy, and timing obtained dur-ing last tens of years, only modest attempts have been done at X-ray polarime-try. The first non-solar dedicated astronomical experiment is due to Bob Novick

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Figure 1.11: Sounding rocket with lithium and crystal polarimeters on board (left) and modulation curves obtained from flight data (right). Images from [69] and [94].

(Columbia University) in 1971. The experiment consisted in a Thomson po-larimeter, using Lithium as absorber, and four Bragg crystal polarimeters, using imperfect crystals of graphite (see Fig.1.11). The experiment was launched in a sounding rocket that observed the Crab Nebula. It measured P = (15.4 ± 5.2)% at a position angle of (156 ± 10)◦ _{[69]. This is the first positive polarization}

measurement of X-ray astronomy. Using the X-ray polarimeter on the Orbiting Solar Observatory (OSO)-8, the result was confirmed [95] with a 19σ detection (P = (19.2±1.0)%) (see Fig.1.8, left panel), conclusively proving the syncrotron origin of the X-ray emission. Due to the short given observing time, only upper limits were obtained for the polarization of the pulsar. In addition, the time res-olution of the polarimeter onboard the OSO-8 allowed to carry out pulse-phased polarimetry of the Crab making it possible to distinguish the pulsar from the neb-ula. Unfortunatly, because of low sensitivity, only 99%-confidence upper limits were found for polarization from other bright X-ray sources (e.g. ≤ 13.5% and ≤ 60% for accreting X-ray pulsars Cen X-3 and Her X-1 [90]). These experi-ments took place over 40 years ago. Since then, even if several missions planned to include an X-ray polarimeter (such as the original Einstein Observatory and Spectrum X-1(v1)), none of these has actually been launched. This is mainly due to the difficulty in building conventional polarimeters (based on Thomson scat-tering and Bragg reflection) with a good sensitivity. The polarization signal from

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CHAPTER 1. X-RAY POLARIMETRY 25 astrophysical sources is in general not expected to be strong (i.e. PL ∼ 10%), so

most of the incoming X-rays carry no polarization information and just increase the noise in the polarization measurement. At the same time, as discussed in Sec.1.4, a large number of photons, with respect to spectroscopy or imaging, is required in order to obtain significant results.

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Chapter 2 The Imaging X-ray Polarimetry

Explorer

The Imaging X-ray Polarimetry Explorer (IXPE) is a partnership mission between NASA and ASI, selected by NASA as part of its Small Explorer program (SMEX) and currently scheduled to be launched in April 2021. This will be the first astron-omy mission completely dedicated to X-ray polarimetry and the first to perform X-ray polarimetric imaging [82]. The goal of IXPE is measuring the polarization of X-rays coming from astrophysical sources. Many targets are being defined, such as the Pulsar Wind Nebulae, which includes both the periodic and the ex-tended source, and the millisecond pulsars, focus of this thesis in Chap.4 and Chap.5. Polarimetric data allows to observationally verify a number of theoreti-cal models and predictions, from geometry to magnetic fields configurations. In order to study these phenomena, given the characteristics of IXPE, it is therefore important to make simulations in order to establish the observational strategies and the analysis for testing specific emission models (see Chap.4). Scientific ob-jectives, followed by the technical overview of the IXPE mission are discussed in this chapter, that is based on [82], [79], [84], [83] and [36].

2.1 Scientific objectives

IXPE will conduct X-ray polarimetry, integrating it with energy, time, and posi-tion, for several categories of cosmic X-ray sources that are likely to be X-ray polarized in order to study their physical nature, magnetic field configuration and geometry. In galactic cosmic ray accelerators, such as pulsar wind nebulae and supernova remnants, polarization signatures from synchrotron emission carry im-portant information about the configuration of the magnetic field. In compact objects, like neutron stars, thermal emission can acquire significant polarization

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CHAPTER 2. THE IMAGING X-RAY POLARIMETRY EXPLORER 27

Figure 2.1: IXPE observation simulation of Cassiopeia A with 1.5 Ms of observa-tion time. Hereafter the HPD circle represents the IXPE angular resoluobserva-tion. by means of scattering. An X-ray polarimetric observation can probe the inner geometry of the system and understand the conformation of local magnetic fields. Finally, the observation of systems with strong gravitational and magnetic fields will be used to probe fundamental physics.

Imaging X-ray polarimetry is crucial to determine a missing key ingredient in the acceleration mechanism of cosmic rays: the structure and level of order of the magnetic field at the acceleration sites. Indeed, while polarimetry at longer wave-lengths probes the magnetic field at different spatial scales, X-ray polarimetry has access to the acceleration conditions directly at the injection sites. In addi-tion, X-ray polarimetry together with timing observations will help understand the physical processes involved in periodic systems, with a tool directly linked to its magnetic field lines.

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2.1.1 Supernova Remnants

One of the most important acceleration site is the supernova remnant (SNR). When a star explodes in a supernova, a nebula that expands at up to 104_km/s,

bounded by a shock wave, is formed, generating the SNR. These are considered the sources of Galactic cosmic rays, that are accelerated up to 1015 _{eV through}

diffusive shock interaction, consisting of repeated crossings of the surface of the shock [29].

Several SNRs have got some regions near the shock fronts that emit X-ray synchrotron radiation, proving that electrons are accelerated there up to 10-100 TeV in a magnetic field of a few hundred µG [88]. An imaging X-ray polarimeter like IXPE can measure the magnetic field direction and uniformity of the spec-troscopic located region. SNRs have a crucial role even in the distribution of the heavy elements, formed with the explosion, via neutron capture processes.

A simulation of an observation of the supernova remnant Cas-A (made with ixpeobssim, see Chap.4) is shown in Fig.2.1. SNR spectra show high energies ex-cesses, clearly marking the presence of non-thermal mechanisms in the emission, that, in some cases, can even be the dominant component [37]. The synchrotron radiation is the natural explanation of this phenomenon. In a supernova shock wave, charged particles can be confined by the turbulence induced near the shock front and be forced to cross it many times [20]. Such a mechanism can accelerate electrons to energies over the TeV, with a power-law distribution. Synchrotron radiation (see Sec.1.3.2 for details) describes well the observed spectra and, by measuring the degree of polarization, a direct check of this model can be per-formed.

2.1.2 Pulsar Wind Nebulae

A Pulsar Wind Nebula (PWN) is a kind of nebula created when the wind from a central pulsar interacts with the surrounding SNR or with the interstellar medium. This is another important site for particle accelerations and is considered the most efficient one. PWNe are characterized by a non-thermal continuum emission from the radio up to soft gamma-ray band, principally due to synchrotron and inverse Compton emission [89]. Optical and radio polarimetry made on these objects shows that the magnetic fields in PWNe are rather well ordered, with a PL≈ 60%

in the innermost regions. In the X-rays, the Crab Nebula (simulation shown in Fig.2.2) is the only astronomical source with a high confidence X-ray polarization measurement of PL = (19.2 ± 1.0)% (see Sec.1.5 for details). Moreover,

obser-vations in the X-rays with the Chandra satellite reveal a complex morphology of PWNe. E.g. the Crab and Vela nebulae show a torus plus jet geometry, which is really peculiar considering the morphology observed at longer wavelengths.

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Figure 2.2: IXPE observation simulation of the Crab Nebula with 30 ks of obser-vation time.

Spatial resolved polarimetry with IXPE will allow to determine the magnetic field orientation and level of turbulence in the torus, in the jet and at various dis-tances from the pulsar, providing important information to test recent magneto-hydrodynamics models. In addition, IXPE will permit to isolate the central pulsar and to study the phase-resolved polarization pattern, thus testing various rotation-powered pulsar magnetosphere models.

2.1.3 Black Hole Systems

Black hole systems, such as micro-quasars and AGNs, contain accretion disks, coronae and, in some cases, relativistic jets. In this systems, the disk emits ther-mal (thus unpolarized) primary emission and acquires polarization by means of scattering processes. The spatially averaged polarization depends on the geom-etry of the system, that is as high as the system is asymmetric. Thus, the X-ray polarimetry will provide a powerful tool to investigate the spatially unresolved internal structure of these systems. In addition, polarization signatures in

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non-CHAPTER 2. THE IMAGING X-RAY POLARIMETRY EXPLORER 30

Figure 2.3: Spherical (right panel) and slab (left panel) configuration of micro-quasar hot corona[1].

thermal emission from jets provide other important information, like its shock interactions with the external medium.

Micro-quasars

Micro-quasars are X-ray binaries (compact objects accreting from a donor star) containing a black hole that exhibit strong X-ray outbursts and relativistic jets. Here black holes are typically of 10 ÷ 20 M. Usually the falling matter forms

an accretion disk around the black hole which emits X-rays. Micro-quasars can be found in two different X-ray spectral states: the soft and the hard state. In the soft state the thermal emission of the accretion disk is dominant up to several keV. At higher energies the spectrum presents a steep power law component, usually interpreted as due to Inverse Compton scattering of low-energy photons from the accretion disk in the hot corona surrounding the black hole. No jet is present in this state. In the hard state a jet is present and the spectrum is dominated by a flat powerlaw componet [63][60]. It is still unclear if the spectrum in the hard state is due to Comptonization in the corona or to synchrotron emission from the jet. The expected polarization degree from corona emission is less than 5%, that is much lower than the polarization degree expected from jet emission (more than 10%). Any measurement at such polarization level by IXPE would then prove that the X-rays come from the jet rather than from the corona, finally resolving the puzzle about the nature of micro-quasars X-ray emission.

In the case of corona emission the polarization degree of the X-rays depends on the geometry of the corona, which is still unknown. Polarization measurements with IXPE will thus permit to put constraints on the geometry of the corona and to distinguish between the two main models of a spherical and a slab geometry (see Fig. 2.3). This represents an important information, since the geometry of the corona is related to its evolution.

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Figure 2.4: Picture of the unified emission model for AGNs [13], underlining the regions where primary and reflected X-ray photons are emitted along the line of sight. Image from [1].

Active Galactic Nuclei

An Active Galactic Nucleus (AGN) is a compact region at the center of a galaxy which has a luminosity that can even exceed the remaining luminosity of the host galaxy. The standard picture of AGN is given in Fig. 2.4. In the nucleus, a super-massive (106_{÷ 10}9_M

) black hole accretes matter thanks to an accretion disk.

According to AGN unification models [13], the nucleus is surrounded by a toroidal magnetic field that holds matter. Outside this region, a ionized material is present. If the line of sight intercepts the torus, the nucleous is not visible and the AGN is classified as type-2, otherwise, if the nucleous is visible, it is classified as type-1 [62]. AGNs can be classified even as radio-quiet or radio-loud, depending on the level of the observed radio emission. Radio-loud AGNs present a high-collimated relativistic jet, while the innermost region of radio-quiet AGNs can be considered an up-scaled version of a micro-quasar. The main difference with this is that in the innermost region there is a super-massive black hole, so AGNs emit photons at optical/UV energies, while in microquasars (∼10M) the mean emission is in the X-ray band. It follows that X-ray emission

from radio-quiet AGNs comes from the hot corona and, if this is even a type-1 AGN, it is expected to be polarized, so IXPE can constrain the geometry of the corona also for these sources. Observations of type-2 radio-quiet AGN can instead provide information about the actual morphology of the torus which, despite the name, is still largely unknown. Indeed, primary X-ray photons can be scattered

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CHAPTER 2. THE IMAGING X-RAY POLARIMETRY EXPLORER 32 by the torus and the reflected emission should be highly polarized, with the polar-ization angle related to the orientation of the torus.

In radio-laud AGNs, on the other hand, an highly collimated relativistic jet is present and when the jet is pointing toward Earth the AGN is classified as "Blazar". One of the challenges in high energy astrophysics is to understand how matter is accelerated in jets and how they form and evolve. In Blazars the jet dom-inates emission at all frequencies and the spectral energy distribution is character-ized by two peaks: the first one is due to synchrotron emission, while the second one is due to inverse Compton scattering. In some blazars synchrotron emission dominates in rays. In this sources, multi-wavelength polarimetry, including X-rays, allows to determine the emission regions at the different energies and their relative size, allowing to study its magnetic field properties. In other blazars, X-ray emission is dominated by inverse Compton scattering. In this case, IXPE can disentangle the origin of photons undergoing inverse Compton scattering, which can be either synchrotron self-comptonized photons or external comptonized pho-tons from the accretion disk.

Finally, in non-blazar radio-loud AGN the jet is not pointing toward Earth and can be directly imaged by IXPE for close and bright sources such as Centaurus A (see Fig.2.5), allowing to determine the structure of the magnetic field along the jet and the emission process at the origin of its X-ray emission.

Galactic Center

Sagittarius A* (hereafter Sgr A*) is the super-massive black hole in our Galactic Center. It has a mass of about4×106_M

and it is remarkably a X-ray weak source.

However, some molecular clouds close to it, such as Sgr B and Sgr C, are hard X-ray sources with a pure reflection spectrum due to illumination by an external source X-ray reflection nebulae. Since there are no sufficiently bright irradiating sources in the surroundings, the observed X-ray emission is likely what is left from the past activity of Sgr A*, happened about three hundred years ago. If true, this would mean that our Galaxy was a low luminosity AGN in the recent past. This can be verified by IXPE, since the reflected emission from the nebulae must be highly polarized, with a direction of polarization orthogonal to the direction of the illuminating source.

2.1.4 Pulsars and Magnetars

Compact objects like neutron stars exibit intense time-varying magnetic fields, that causes polarized emission because of syncrotron and curvature radiation [59]. If these are in a binary system, polarized radiation can be also caused because of matter channeled along the field lines, creating largely asymmetric X-ray emission

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Figure 2.5: IXPE observation simulation of Centaurus A with 1.5 Ms of obser-vation time. An ultra-luminous X-ray source (ULX) is identified, along with the core of Cen A and some knots (bright spots that may identify some particle accel-eration sites).

on its surface, because of scattering geometries. These effects can be observed by IXPE, providing information about the geometry of these sources and the configu-ration of the magnetic field lines. These phenomenons are known as pulsars (both isolated and accreting) and magnetars, depending on the magnetic field value, and they are summarized in this section. A peculiar class of accreting pulsars are the transitional millisecond pulsar, focus of this thesis, that will be described in depth in Chap.5.

Accreting Millisecond Pulsar

Accreting Millisecond X-ray Pulsars (AMXPs) are rapidly spinning pulsars, with a rotational period in the range 1-10 ms [59] and a relatively weak magnetic field (B ∼ 108 _{÷ 10}9 _{G). They are spun-up in binary systems, through the transfer of}

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Figure 2.6: Schematic of the accretion process in AMPs, where that channeling matter, that interacts with neutron star surface, generates polarized emission from hot-spots. Image from [5].

the accreting matter follows the pulsar’s magnetic field lines and hits the surface close to the magnetic poles, resulting in a pair of hot-spots on the surface (see Fig.2.6). The AMXPs spectra has two components: a blackbody component at soft energies and a hard power-law component at higher energies. The blackbody emission is due to thermal emission from the hot-spots on the neutron star surface. This thermal radiation likely undergoes comptonization in the accretion shock at the bottom of the magnetic field lines, giving rise to the power-law component of the spectra [73].

Scattered radiation should be linearly polarized, up to 20% with the polariza-tion degree and angle depending on the pulse phase, the photon energy and the geometry of the system. Phase-resolved X-ray polarimetry with IXPE will allow to test the comptonization model and to determine the magnetosphere configu-ration. Parameters like orbital and magnetic axis inclinations are important to recover the neutron star mass and radius and therefore to constrain the neutron star equation of state.

Today, tens of AMXPs (like SAXJ1808) are known and all of them are tran-sients going into outburst for 2 weeks every few years, thus is plausible that they will be observed by IXPE during the first two years. Spectral measurements dur-ing X-ray burst, combined with phase-resolved polarimetric measurements, can give additional constraints on the mass and the radius of the neutron star and clar-ifications on the type of emission involved.

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Figure 2.7: Possible geometries of the emission region in XRPs: fan beam (left) and pencil beam (right) patterns. Image from [82].

Accreting X-ray Pulsar

Accreting X-ray Pulsars (XRPs) are among the brightest X-ray sources. They are highly (B ∼1012_÷1013_{G) magnetized neutron stars belonging to a binary system}

in which they accrete matter from a companion star via an accretion disk. As for AMXPs, in XRPs the accreting matter follows the neutron star’s magnetic field lines and hits the surface close to the magnetic poles, resulting in a pair of hot-spots on the surface. The pulsed X-ray emission from XRPs originates primarily in these hotspots as the pulsar rotates [31]. However, the structure of the emission region is complicate and still uncertain. It is generally believed that in low lumi-nosity objects (LX <1037erg/s), the accretion flow stops close to the neutron star

surface by Coulomb interaction and nuclear collisions with atmospheric particles. In this case, the atmosphere is a plane parallel section of the polar cap and emits radiation upwards, parallel to the magnetic field, in a pencil beam pattern (see Fig.2.7, right panel). At higher luminosities, the accretion flow is stopped by ra-diative pressure and an accretion column sticking out above the surface is formed. Radiation is mainly emitted from the sides orthogonal to the magnetic field lines, in a fan beam pattern (see Fig.2.7, left panel) [65].

The linear polarization depends on the geometry of the emission region, thus on the pulse phase, and allows to distinguish between the fan and the pencil beam scenarios. The flux and polarization degree are in-phase for fan beams, and out-of-phase for pencil beams.

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Figure 2.8: Illustration of the globally twisted dipolar field model for magnetars. Image from [86].

Magnetars

Magnetars are isolated neutron stars with an ultra-high magnetic field (B ∼ 1014_÷

1015 _{G) and a spin period in the range 1-10 s. Magnetars are characterized by}

a relatively high persistent X-ray luminosity (LX ∼ 1033 ÷ 1036 erg/s) and by

bursting activity. The persistent luminosity of these sources is higher than the rotational energy loss rate, suggesting that they are powered by their own large magnetic field. Their spectrum has a thermal component and a power-law tail. The thermal component is likely due to photons emitted from the star surface, while the power-law component arises from the thermal photons that are scattered in the magnetosphere. This magnetosphere is supposed to be twisted, i.e. the star’s external magnetic field is not simply dipolar but (as a consequence of the crustal deformations induced by internal magnetic stresses) it comprises a toroidal component (see Fig.2.8) [86].

The thermal photons coming from the star’s surface acquire a strong polar-ization as they propagate through the magnetized plasma that characterizes the neutron star atmosphere. Their polarization state may change depending on scat-tering. Polarimetric measurements with IXPE will allow to asses the geometry

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CHAPTER 2. THE IMAGING X-RAY POLARIMETRY EXPLORER 37 of the emitting region, which cannot be recovered from spectral measurements alone, determining important geometrical parameters such as the inclination of the line of sight and of the magnetic axis with respect to the spin axis. IXPE will also probe the magnetic field strength and geometry, testing the twisted magnetic field model.

2.1.5 Fundamental Physics

Cosmic sources provide a natural laboratory to study effects of Fundamental Physics which are not accessible on Earth. Indeed the test of different physical theories requires strong gravitational and magnetic fields as well as distances that cannot be achieved in laboratory. In many of these theories specific X-ray polarization signatures are expected, making X-ray polarimetry again a powerful tool.

Quantum Electrodynamics

X-ray polarized photons from magnetars provide the opportunity to test the Quan-tum Electrodynamics (QED) effect of the vacuum birefringence induced by a strong magnetic field, predicted more than 80 years ago [46]. According to QED, a strong magnetic field polarizes the vacuum and the dielectric and magnetic per-meability tensors are consequently perturbed [44]. This means that the refraction index in vacuum is different for photons polarized parallel (O-mode) or perpen-dicular (X-mode) to the magnetic field, namely:

n// = 1 + 7α 90πsin 2 θ B Bc 2 n⊥= 1 + 4α 90πsin 2_θ B Bc 2

where Bc = m2ec3/e~ ≈ 4.4 × 1013 G is the critical field, i.e. the value of the

magnetic field at which the vacuum polarization becomes not negligible, θ is the angle between the direction of propagation of the photon and the magnetic field and α is the fine structure constant [30]. This effect is hard to measure on Earth as it scales in this way with B:

n//− n⊥≈ 4 × 10−24

B 1T

2

Even in the case of magnetars the difference between the refraction indexes is only a few percent, but the vacuum birefringence has an important effect also on the X-ray radiation coming from magnetized sorces [48].

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Figure 2.9: Simulated 500-ks IXPE of a bright showing (from left) unabsorbed 2–6 keV flux, polarization degree and angle as functions of the pulse phase. Green lines denote the model (including vacuum polarization) used to generate the data; red/blue lines, best-fit vacuum-polarization on (“QED-on”)/(“QED-off”) models. Image from [82].

As discussed in Sec.2.1.4, the radiation emitted from the neutron star’s surface is expected to be strongly polarized (because of the reduced opacity for X-mode photons) and its polarization state may change upon scattering in the magneto-sphere. As radiation propagates outwards, the strong magnetic field, combined with a sufficiently large length scale, causes vacuum birefringence to decouple the polarizaton states, increasing the expected X-ray polarization degree by even a factor of ten. This is shown in Fig.2.9 for a magnetar similar to 1RXS J170849.0-400910, where the difference in the polarization pattern when birefringence is taken or not into account is remarkable. IXPE will allow to discriminate between models with and without vacuum polarization, finally testing this QED effect. Strong Gravity

The observation of micro-quasars with IXPE permits to probe strong gravity ef-fects and to measure the black hole spin. As discussed in Sec.2.1.3, for micro-quasars in the soft state the dominant spectral component (up to several keV) is the thermal emission from the accretion disk, which acquires polarization up to 12% by means of scattering. The polarization angle rotates due to strong gravity effects as radiation progresses along a geodesic towards the observer and a net ro-tation remains also after integrating the emission over the disk atzimuthal angle. Since the angle rotation is grater for emission closer to the black hole (where the disk is hotter and the energy of the emitted X-ray is higher) a dependence of the polarization angle on energy is expected [63]. The measurement of this energy dependence with IXPE will be a probe of the General Relativity effects in the strong field regime. In order to measure the black hole spin, since the inner disk

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Figure 2.10: Polarization degree (left) and angle (right) at different energy values of the spin parameter (a) for the micro-quasar GRS1915+105. Dotted lines are based on model calculations, while solid lines are fits to the data obtained from a 200 ks observation simulation with IXPE. Image from [94].

radius decreases as the spin increases, the rotation of the polarization angle, that increases with the spin, can be measured as well by IXPE. This measurement of the black hole spin should be compared with the results obtained with the other techniques employed so far in X-rays (not in agreement with each other). A sim-ulated observation of the micro-quasar GRS1915+105 in the soft state with IXPE is shown in Fig.2.10.

As for micro-quasars, the observation of AGN with IXPE will permit to probe strong gravity effects and to measure the spin of the black hole. In this case (see Sec.2.1.3) the disk thermal emission is outside the working band of IXPE, but strong gravity effects may still manifest in soft X-ray band. Indeed, a fraction of the X-ray corona emission illuminates the accretion disk, where it is scattered and reflected. This coming radiation is expected to be polarized and, since the corona height varies with time, the polarization degree and angle should vary with time as well. This time variation depends on the spin of the black hole [62], thus X-ray polarimetry can provide the effect of strong gravity to the radiative transfer, estimating again the black hole spin.

Axion-like Particles

Axion-like particles (ALPs) are ultra light spin zero bosons predicted by many extensions of the Standard Model (SM) Theory. They are excellent candidates for cold dark matter, responsible for the formation of structures like Galaxies in the Universe. In the presence of an external magnetic field, ALPs mix with photons

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Figure 2.11: IXPE observatory showing key elements. The Mirror Module As-semblies, on the right, and the Detector Units, on the left, are connected with the deployed boom.

giving rise to ALP-photon or photon-ALP conversions for those photons which are polarized parallel to the magnetic field [34]. The existence of ALPs would then lead to polarization signatures from sources that emit X-ray photons that propagate through large magnetized regions. E.g. the radiation coming from po-larized sources (such as blazars) can be depopo-larized, while radiation coming from unpolarized sources (such as Galaxy Clusters) can become polarized. IXPE can search for these effects, leading to the evidence of the ALPs existence.

2.2 Technical Overview

The IXPE payload consists of a set of three identical telescope systems, co-aligned with the pointing axis of the spacecraft. Each system, operating independently, comprises a Mirror Module Assembly with a 4m focal length that focuses X-rays onto a polarization-sensitive imaging detector (the Gas Pixel Detector), inside a Detector Unit. The section of the spacecraft with the three Mirror Module As-semblies and the one with the three Detector Units are connected together with a deployable boom. An image of how IXPE will looks like in orbit is shown in Fig.2.11. More details about this are in [2].

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Figure 2.12: Pegasus XL rocket, that will carry IXPE to its orbit from ∼12 km to 540 km of altitude.

2.2.1 Launch and Operation

IXPE is scheduled for a launch in mid-2021 on a Pegasus XL launch vehicle from the Reagan Test Site (RTS) at Kwajalein Atoll. The Pegasus XL (Fig.2.12) is released by a carrier aircraft at an altitude of ∼ 12 km and will take IXPE to its orbit, which is a circular orbit at 540 km of altitude and at 0◦ inclination. The altitude has been selected to set the timescale for the spacecraft natural reentry well beyond the planned two-years lifespan of the mission, with the option of a one-year extension. The orbital decay is mainly due to air drag, solar activity and actual initial height. Since IXPE has no propulsion system, the natural orbit reentry will occur at least 4 years after launch, with a 99% probability.

To accommodate the IXPE focal length in Pegasus XL, a deployable boom is needed to provide a compact stowed package for the launch and to create the nec-essary separation between the mirror module assemblies (described in Sec.2.2.2) and their respective detector units (details in Sec.2.2.4) in orbit. IXPE in a com-pact form is shown in Fig.2.13.

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Figure 2.13: IXPE payload in the stowed configuration, compact enough to fit inside the Pegasus XL rocket.

During this period IXPE will have a simple operation mode: it will typically perform point-and-stare observations of known targets. Malindi ground station (Kenya) will represent the primary contact for communications with the IXPE Observatory via an S-band link.

2.2.2 Mirror Module Assemblies

The Mirror Module Assemblies (MMAs) focus X-ray source photons onto the polarization-sensitive detectors. These mirrors enable imaging, key for IXPE sci-ence, and also provide a large amount of background reduction by concentrating the source flux into a small detector area. Each 300 mm-diameter optics module features 24 concentrically nested X-ray-mirror shells.

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Figure 2.14: Mirror Module Assemblies of IXPE. On the left there is the section of the spacecraft with the Mirror Module Assemblies. The shields are deployed. On the right a detail of the enclosure of a single Mirror Module Assembly. The spider structure is highlighted.

[43]. The angle below which they can be efficiently scattered (called critical angle θc) scales with energy:

θc∝

√ Z E

where Z is the atomic number of the mirror material and E is the X-ray energy. The shells are built with the Wolter type I telescope configuration (details in Sec.2.2.3). Each module holds an effective area of 230 cm2 at 2.3 keV and 249 cm2 _{at 4.5 keV (Fig.2.15). The packing of the mirrors allows to greatly reduce}

the amount of stray X-rays impinging on the detector from sources outside the field of view. The shells, made of a nickel-cobalt alloy, are held in position only at one end by a spider fabricated from a type of stainless steel having a thermal expansion coefficient matched closely to that of the shells. A spider structure is visible in Fig.2.14, made of a ring attached to one end of the outer cylindrical shell with a number of "legs".

The three IXPE MMAs are mounted on a composite support that also con-tains deployable shields which, in combination with the collimators at the top of each DU, block virtually all X-rays that have not passed through the MMAs from entering the detectors. The shields are 97% opaque at 8 keV and 99.96% at 6 keV.

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Figure 2.15: IXPE effective area for a single MMA and for the combination of three MMAs as function of the energy.

2.2.3 Wolter Telescopes

The optics of IXPE are modeled as Wolter type I telescopes. These optics are specifically developed for X-ray astronomy [96]. Fig.2.16 shows a representation of the mirrors used.

The basic concept is that X-rays are transmitted or absorbed by mirrors, rather than reflected, for almost any incidence angle, except for when they are almost parallel to the reflecting surface (that is, when the reflection angle is very small). That is why Wolter telescopes use only grazing incidence optics.

Wolter I and II type telescopes focus photons with two consecutive reflections, first on a paraboloidal mirror and then on a hyperboloidal one. Type II telescopes use these king of mirrors with the second reflection that takes place on the outer surface of the hyperboloid. The II type allows for a more compact designs, but the I type, that reflects X-ray light as shown in Fig.2.16, is the one used for IXPE be-cause it is the most widely focusing and has the enormous mechanical advantage of allowing each couple of mirror to be made of a single shell.

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Figure 2.16: Schematic view of an array of Wolter type I optics, made of a set of paraboloid and hyperboloid mirrors that focus X-ray onto the detector. Image from [3].

2.2.4 Detector Units

At the focal plane of each telescope system there is the Detector Unit (DU) which houses the polarization-sensitive Gas Pixel Detector (GPD), that will be exten-sively discussed in Chap.3. Each DU is mounted on the top of the spacecraft aligned with the corresponding MMA (Fig.2.17, left panel). Thermal stability is guaranteed by means of heaters and a shared radiator at the aft end of the obser-vatory.

Along the path from the optics to the focal plane, and atop each GPD, there is the Gold-coated Aluminum collimator (250 mm high) and a Filter-Wheel (FW) assembly. The FW features three different apertures (one fully open, one fully closed and a third with a Beryllium filter that attenuates the flux from bright ob-jects) and a set of calibration sources, including [82]:

• unpolarized, broad-beam 55_{Fe and} 109_{Cd sources;}

• an unpolarized, collimated 55_{Fe source;}

• a polarized source, obtained with a 55_{Fe source and 45}◦_{Bragg diffraction on}

lithium flouride and graphite crystals that provide almost 100% polarized X-rays at 2.6 keV and 88% polarized at 5.9 keV (Bragg diffraction is described in Sec.1.4.1).

The instrument electronics complete the equipment of each DU. These include three different boards: one, interfacing with the GPD, responsible for the event data and payload housekeeping acquisition (DAQ board), and two for the detector

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Figure 2.17: Representation of the IXPE focal plane with the DUs (left) and opened view of DU components (right).

power supply (low and high voltages boards). The right image of Fig.2.17 is an overview of one DU, showing the principal elements. Finally, the DUs interface with a single payload computer, located in the Detector Service Unit (DSU) on the aft side of the top deck. The DSU controls all three DUs and is responsi-ble for their power supply, thermal control, time and operation management, and transmits science and housekeeping telemetry data to the integrated avionics unit (IAU) of the spacecraft. The DSU receives ground commands through the IAU.

Study of Periodic Polarized X-ray Emission with IXPE

Universit`

a di Pisa

Study of Periodic Polarized X-ray Emission with IXPE

Introduction

Contents

Chapter 1

X-ray Polarimetry

1.1

Polarimetry of Electro-Magnetic Waves

1.2

Polarization Statistics

1.2.1

Stokes Parameters

1.3

Polarized Photons Creation

1.3.1

Scattered Photons

1.3.2

Syncrotron Radiation

1.4

Polarized Photons Detection

1.4.1

Bragg Crystal Polarimeters

1.4.2

Scattering Polarimeters

1.4.3

Photoelectric Polarimeters

1.5

Historical Remarks

Chapter 2

The Imaging X-ray Polarimetry

Explorer

2.1

Scientific objectives

2.1.1

Supernova Remnants

2.1.2

Pulsar Wind Nebulae

2.1.3

Black Hole Systems

2.1.4

Pulsars and Magnetars

2.1.5

Fundamental Physics

2.2

Technical Overview

2.2.1

Launch and Operation

2.2.2

Mirror Module Assemblies

2.2.3

Wolter Telescopes

2.2.4

Detector Units