Spectroscopic and polarimetric study of the microquasar SS433

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Università degli studi di Pisa

Dipartimento di Fisica “E. Fermi”

Corso di Laurea in Astronomia ed Astrofisica

Tesi di Laurea Magistrale

Spectroscopic and polarimetric study

of the microquasar SS 433

Candidato: Paolo Picchi

Relatore: Prof. Steven Neil Shore

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Chapter 1 Introduction

Il tempo è nato insieme al cielo.

Timeo Platone

A

mong cosmic high energy sources there is a class of Galactic objects, the microquasars, that mimic Active Galactic Nuclei (AGN), Quasars to be precise, on scales of stellar radii instead of tens of parsecs. The similarity comes from a range of peculiar properties, standard for the Quasars, which are shown also by these far lower mass objects, i. e., the presence of jets (resolved or unresolved), electromagnetic emission spanning the spectral range from the MHz (neV) to XR (keV), γ (MeV), and sometimes to the TeV energy range, and the strong time variability affecting all the spectral region. This variability is strictly related to the small size of the system. For AGN, for example, the jets extend for hundred of kiloparsecs, while for microquasars they reach 1017−20 cm (0.1 − 10 pc) at most.

Microquasars are massive binary systems whose components are a compact object – a stellar mass Black Hole (BH) – and a massive companion, usually an early-type giant or supergiant of tens of solar masses. The very high luminosity of these systems is powered by mass accretion from the normal star (the loser) by the compact object (the gainer). Depending on the masses and separation of the components, there are two distinct modes of mass loss by the ordinary star. All massive stars have radiatively driven outflows, stellar winds. A companion orbiting within the wind will accrete matter (usually called Bondi-Hoyle-Lyttleton accretion) depending on the velocity of the wind and the gravitational capture radius of the gainer (Frank et al. 2002). Since the periods of wind accretors are long, the orbit of the gainer is usually highly elliptical, leading to alternating cycles of activity and quiescence. The alternate mechanism depends, again, on the period of the binary and the radius of the loser. There is a tidal limit, the Roche surface, at which the photosphere coincides with the inner Lagrangian point of the binary, L1, corresponding to the local three-body saddle point, where the surface gravity locally vanishes. Since the loser is a star, even at L1 there is an outward pressure gradient that forces flow through the point, and the region around it, at the sound speed, resulting in a rarefaction and a convergent stream of matter. This falls, and orbits, toward the gainer, deviated by the Coriolis acceleration and forms a disk around the companion. The process is referred as Roche lobe overflow (RLOF) accretion. It is important to note that if the main accretion mechanism is the RLOF, a radiatively driven wind from the loser are possible, while if the accretion is only through winds, than we can not have the RLOF and the luminosity of the system is lower (because the mass accretion rate is lower).

Gravitational potential energy is released by the infalling matter, while its excess angular momentum leads to the formation of a circum-gainer disk that transfers the material inward

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CHAPTER 1. INTRODUCTION 5

by viscous processes. For a Keplerian disk, the rotation is differential, which leads to different circulation velocities between two neighbouring annuli. Macroscopic chaotic motions inside the gas transfer angular momentum in the radial direction, in a manner resembling viscous coupling (this type of transport is also called shear viscosity ). Although there are continuing debates regarding the origin of the viscosity (necessarily some form of macroscopic turbulent motion, kinetic diffusivity is negligible) there is a broad consensus on the essentials of the physical process: viscous dissipation, related to material shear stresses, transfers angular momentum outward, producing an inward subsonic drift and locally generating heat. This is radiated through the surface of the disk with a temperature that depends only on the distance from the gainer. The local luminosity is just the released potential energy per unit mass times the rate of mass accretion so L ∼ M ˙M /r where M is the mass of the gainer, ˙M is the mass accretion rate (equal to that supplied by the loser), and r is the radial distance.

Either mass loss scenario leads to a disk but the process is far more efficient in the Roche lobe overflow (RLOF) case. There is, however, a limit above which the gainer cannot stably accrete: when the generated luminosity produces a sufficient radiative pressure gradient, matter is driven away from the surface of the gainer and the disk in the form of a wind. This mimics that expected for the loser if the system is well separated but it is not limited by the Roche surface.

The limit on stable accretion is set by the luminosity L ∼ LEdd (LEdd is the Eddington Luminosity) or L > L_Edd; if, instead, the tidal interactions dominate then L < L_Edd. The Eddington Luminosity gives an upper limit for a steady, spherically symmetric accretion for which all the initial kinetic energy is given up to radiation at the neutron star surface or the BH event horizon. This means for the accretion luminosity Lacc:

Lacc= GM ˙M /R∗ (1.1)

where M is the mass of the accreting object and R∗ is the radius of the Neutron Star (NS) (or near the event horizon, if it is a BH). This assumption implies that the limit on the accretion is set by the balance between the radiation and gravitational field, because of the direct conversion between the kinetic energy (due by the direct accretion) in photons’ energy. Then, one obtains the usual expression for the Eddington Limit (Frank et al. 2002):

LEdd= 4πGM mpc/σT (1.2)

where mp is the proton mass, c is the velocity of light and σT is the Thomson cross section (this gives an upper limit on the Luminosity since for bound electrons the cross section can exceed substantially σ_T). Equating the equations 1.1 and 1.2 one can find the limit for the accretion rate. The Eddington limit from equilibrium argument for a self-gravitating mass between the radiation pressure and the gravitational field of a star, in order to study the sta-bility of its hydrostatic structure. It is conceptually different than the Eddington luminosity related to the accretion, but it is linked to it because of the direct conversion between the kinetic and radiative energy. This limit in luminosity can be exceeded in accretion disks since they can violate the assumptions of steadiness and spherical symmetry (the disk, by defini-tion, breaks one of this two assumptions). If the gainer is massive (a BH for example) the gas drifting inward can feel an effective acceleration where the centrifugal force is higher than the local gravity near the gainer. The disk, in order to maintain an equilibrium vertical config-uration, must be supported by its pressure gradient (it is self-regulated), which is not more bonded along the axis of the disk, as for standard thin disks. For a thick disk the mechanical energy can be substantial and overcome the radiative pressure, leading to a super-Eddington accretor. For these systems, the circulation is not uniquely given imposing centrifugal balance (cyclostrophy), so the angular momentum distribution is not unique. Moreover, for a thin

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disk the energy balance is local and governed by the viscosity, while these disks require a global treatment, since the heat generated by dissipative processes can travel in any direction before emerging from the disk.

For thick disks the radiation field may not permit an equilibrium structure, since the luminosity can be very high, matter can escape from the disk through jets. There is still a lot of debate regarding the main mechanisms that could generate and collimate jets to relativistic speeds in microquasars and AGN. Most of microquasars, as SS 433 (also designated V1343 Aql), show extended jets propagating from the central source. In these systems, the binary (and the disk) is extended over a much smaller scale (order of AUs) than the AGN disk (parsecs), thus the time variability is very rapid (order of hours) and is one of the most peculiar properties of these objects. This is manifested in strong time dependence of both brightness and dynamics, in both the accretion and wind processes, leading to a complex environment to study.

SS 433 is the prototype and the first discovered microquasar. It is the first Galactic object that showed extended, mildly relativistic (β = 0.26) jets propagating up to distances of ∼ 1017 cm (Fabrika 2004). These jets are baryonic, since their dynamics are displayed by atomic emission lines. This is very important because in AGN is seen only a leptonic component.

As for all known microquasars SS 433 is a binary system, whose orbital period is 13.08 days. The binary is characterized by an A4-7 supergiant (Gies et al. 2002a, Gies et al. 2002b, Hillwig, Gies, et al. 2004) which is losing mass to a compact object, it is not yet established if this is a NS or a BH. The loser is filling or overfilling its Roche lobe, so the probable accretion mechanism is through RLOF. The binary nature of SS 433 was established through spectroscopic observations (Crampton et al. 1980, Crampton and Hutchings 1981): the measured radial velocities are modulated on the orbital period (see Figure 1.1). Photo-metric observations confirmed this picture by the identification of partial eclipses in the light curves, both in the optical and X-rays, with the same periodic modulation (Cherepashchuk 1988, Kawai and Matsuoka 1989).

The SS 433 jets were discovered by the identification, in the optical, of bright and variables hydrogen and helium lines which were periodically doppler-shifting by tens of thousands of km s−1. This doppler motion was explained by the so called Kinematic Model (Margon et al. 1979a, Margon et al. 1979b, Margon et al. 1979c, Milgrom 1979 and Abell and Margon 1979). The jets emission lines vary on very short time scales, they can appear and then disappear after less than 24 hours and their profiles change a lot even during a single night ( Wagner et al. 1981, Blundell, Bowler, et al. 2007). The jets are observed across the electromagnetic spectrum, from X-rays ( Stewart and Watson 1986, Kawai and Matsuoka 1989 and Marshall et al. 2002) to the low frequency limit (MHz) (Broderick et al. 2018).

The jets precess with a period of 162 days (the precession curve is shown in Figure 1.1). During the precession, precisely at the so called times T1,2, the two jets’ radial velocities coincide, but are not at zero radial velocity, or to the systemic velocity. The residual velocities, ∼ 104 _{km s}−1 _{are due to the transverse Doppler Effect. This effect is observed only in SS} 433. In this thesis, the ephemeris used to calculate the precessional and orbital phases are the most recent in the literature (Goranskij 2011):

J Dprec = 2449998.0 + (162.278) · E (ψ = 0, disk face-on) (1.3) J Dorb= 2450023.746 + (13.08221) · E (φ = 0, primary eclipse) (1.4)

These ephemeris are photometric and set respectively the time of maximum brightness during the precession and the time of center of eclipse. The observed jets precession is related to the disk precession. This peculiarity could be external, i. e., some process linked to the A

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star (or not) forces the disk to be misaligned with the orbital plane of the binary, resulting in the observed precession. Another possible mechanism that could cause the precession is the Lense-Thirring effect. This process induces torques on the inner disk caused by the rotation of the BH. The BH spin, in fact, acts directly on the space-time around it, which starts to rotate differentially as the distance toward the BH changes. This leads to differential rotation effects in the accretion disk and so leads to a precession of it (Armitage and Natarajan 1999, Bardeen and Petterson 1975). However, is not clear what is the driving mechanism of the jets’ precession, so a detailed investigation of the binary structure is needed.

The Kinematic Model provides the fundamental mean precessional parameters, such as the inclination to the line of sight i ∼ 78.08◦, the jets’ axial velocity β ∼ 0.26, the jets’ inclination relative to the orbital plane θ ∼ 20◦ and the precessional period. The determination of these parameters is essential to remove degeneracies of physical quantities caused by geometrical effects. X-ray observations have confirmed the kinematic model with the same parameters as the optical observations: this is an evidence that the jets’ initial propagation is ballistic (Panferov and Fabrika 1997, Marshall et al. 2002): in Figure 1.2 are well seen the various propagating “bullets”.

Interferometric radio imaging confirms the model, and show that the source is embedded in W50, a supernova remnant (SNR) enshrouding SS 433 and interacting with the terminal parts of the jets ( Kirshner and Chevalier 1980, Geldzahler et al. 1980). The remnant is evolutionary tied to SS 433; Figure 1.3 shows the strict connection between the jets and the remnant, especially looking at the two opposite wings (created by the impact of the jets with the boundary of the SNR, whose position angle is aligned with the jets’ axis, i.e. ,∼ 100◦ ). This clear correspondence between a remnant and the object inside it is very important, and the close interaction between the jets and W50 gives a unique scenario to study. The remnant is very extended (∼ 208 pc, Goodall et al. 2011) and must have been born along with the gainer. The shell is centered in SS 433, with a small offset of 5 arcmin, this may be due to a kick given to the system by the originating supernova. This circular region is believed to be the remains of an expanding supernova remnant (SNR) shell.

SS 433 jets have been intensely studied since its discovery. Having access to precise quan-titative information such as the geometrical parameters and most importantly, the velocity and baryonic nature of the jets, render this system a unique bridge for understanding Active Galactic Nuclei (AGN). For the AGN, the jets are leptonic, leading to unresolved questions about generation and energization processes for the electrons. Moreover, the peculiarity of SS

.

Figure 1.1: The two velocity curves regarding the orbital (Crampton and Hutchings 1981) and pre-cessional modulation (Ciatti et al. 1981). Note that in the right panel, the ordinate is the redshift, not in km s−1

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433 relative to other microquasars is the continuous persistence of the jets, that show varia-tions in brightness and (or) structure, but for which the launching mechanism never turns off. Most important, the parameters from the Kinematic Model never change by large amounts, even during outbursts. Other microquasars, e. g., Cyg-X3, have shown strong variations both in the jet velocity (from β ∼ 0.8 to β ∼ 0.6) and propagating direction (a difference of about 60◦) during outburst periods. After the active state, the jets are not visible. It is not clear what would be the conditions to see such a continuous jet emission, as it manifested in SS 433. The presence of a massive gainer is required, but also a high mass accretion rate is needed, in order to sustain the central engine. As the published studies, and this thesis have shown that SS 433 is accreting through RLOF, so the continuous stream of matter pulled off by the loser by the gravitational field of the gainer could maintain the jets launching mechanism and propagation.

The length of AGN jets relative to the central region, is similar for SS 433 and the AGN (∼ 105), so the quantitative study of a microquasar, such as SS 433, informs the modeling of the propagation and generation mechanism of the highly relativistic jets present in AGN, for which the observations are far less comprehensive.

The existence of the jets (with spectroscopy) gives the indication of the presence of an accretion disk: in cases where the accretion is high and the disk itself cannot guarantee the stability of the system the plasma is ejected through the polar directions. Note that the jets do not affect the structure and the dynamics of the disk since are launched very near the BH and are highly collimated , so the disk investigation can be done without take into account the jet contribution. However, no lines in the spectra directly trace a disk structure, indicating instead the presence of multiple, complex outflows and structures which obscure the innermost regions of the binary and vary over the precessional phase. The disk precession produces the strongest variations in the line profiles and makes possible the direct observation of dynamical structures. For example, a strong blueshifted absorption component has been detected in the lines (usually described in the literature as a disk-wind or wind, Fabrika 2004), whose velocity changes with the precessional phase. The disk precession drives a change in

Figure 1.2: The jets’ large scale structure of SS 433 at 1.6 GHz. Note the two opposite plumes at the extreme of the image indicating the bullet nature of the jets. Contour levels are −0.25, 0.25, 0.36, 0.50, 0.71, 1.0, 1.41, 2.0, 2.83, 4.0, 5.66, 8.0, 11.31, 16.0, 22.63, 32.0, 45.25, 64.0, 90.51% of the peak brightness of 248.3 mJy/beam. The restoring beam is 50 mas. (Paragi et al. 1999).

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Figure 1.3: The supernova remnant enshrouding SS 433 taken with LOFAR, at 140 MHZ. (Broderick et al. 2018). Note the two wings indicating the terminal interacting regions of the jets with the remnant.

the line profiles because the forming region is seen thorugh different density and temperature conditions. Many features, like the jets or the wind suggest that the SS 433 disk is thick and characterized by strong outflows that can alter its structure. During flaring events, for example, signatures of the disk revealing itself have been detected in the spectra (Blundell, Schmidtobreick, et al. 2011). This disk-wind flows will be investigated in this thesis, related to the accretion disk structure.

The accretion process in SS 433 leads to the formation of a non-Keplerian, super-Eddington disk (Hut and van den Heuvel 1980): the estimated accretion rate is ˙M ∼ 10−4−10−6_M

yr−1 (the accretion rate is derived from the luminosity, which is obtained through the modeling of the continuum in the optical region). This is really important since is the only source, between X-ray binaries, for which a super-Eddington accretion is certain.

In a non-Keplerian disk the circulatory motion is not given by the simple balance with the gravitational field and that other contributors are affecting the angular momentum of the disk. If tides, or torques of various nature (radiative, advective, gravitational. . . ) are present, or if the disk is thick, then the angular momentum distribution along the disk itself cannot satisfy dynamical equilibrium and stability conditions (see Chapter 5 for discussions related to the SS 433 disk). The disk is not behave as a passive structure that simply redistributes, locally, the incident energy, but it is self-sustained by its pressure gradient, that plays an important role in the dynamics and luminosity of the disk. Since the angular momentum alone cannot maintain equilibrium conditions, and since the high accretion rate can generate a strong radiative pressure, it is possible that this structure is affected by flares or wind ejection events from its surface.

Very little has been said on the spectroscopy information carried by the stationary (to distinguish them for the jets) lines of the system (the few exceptions being Crampton et al. 1980, Gies et al. 2002a, Barnes et al. 2006). That is why my thesis focuses on the inner regions of SS 433 binary, i. e. , a diagnostic study of both the binary nature and the inner structures and accretion flows present between the two components. Although the jets have

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been extensively studied and the general picture is more or less clear, the binary remains an enigma. Not only are the masses of the two components not well determined, but it is not clear if there is a systematic modulation of the line profiles on the precessional and orbital periods. There are no studies in the literature about the forming regions of some lines, like the Na I doublet, the O I 7774 Å for example, which are detected and studied here. Very little has been said about the disk wind (if present), i. e., which lines are coming from it and which regions are mapped. Both polarimetric and spectroscopic measurements were obtained in order to study the dynamical and structural characteristics of the system. Polarization is uniquely able to provide geometric information of unresolved sources (if caused by scattering, as it is for this system, see Chaper 4). This thesis determines for the first time the intrinsic, polarization measurements of SS 433 (for other works regarding polarization in the optical, see Michalsky et al. 1980, McLean and Tapia 1981, Efimov et al. 1984 and Dolan et al. 1997), the physical processes that generates polarized light and their link to the scattering environment. For a super-Eddington accretor this diagnostic method is crucial for constraining the properties of the extended environment around the gainer. Thick disks can have complex shapes (toroidal. . . ) and knowing their geometrical distribution can better hint on the physics governing their equilibrium processes.

The spectroscopic observations, instead, through a multi-line, quantitative analysis trace the dynamics of different structures; this is crucial for understanding the mass transfer and wind ejection mechanisms of a supercritical accretion disk and how the jets ejection mechanism works. The multi-line comparison is a diagnostic procedure for separating different density and line formation processes (from recombination to radiative). A part of the data set also covered a flaring activity of SS 433. For the first time polarization measurements were associated to a flare and help in the understanding the mechanism.

Polarization and spectroscopy are independent methods that lead to different, complemen-tary information. Combined, they have shed light on different aspects and physical processes going on in SS 433. The overall picture remained coherent: the differences in the diagnostics lead to a less biased analysis. A self-consistent picture of the accretion disk and the disk-wind mechanism will be given in the subsequent chapters.

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Chapter 2 Cosmic polarization processes

If light is man’s most useful tool, polarized light is the quintessence of utility.

Polarized light: production and use William Shurcliff This chapter provides a broad overview of polarization in the astrophysical context. Op-tical polarization measurements are not still widely applied in astrophysics, mainly because it is quite difficult to build precise instruments and because of background and calibration issues (see chapter 3).

Usually, statistically significant measurements come from relatively few highly polarized sources, such as Active Galactic Nuclei (AGN), which are strong nonthermal continuum emit-ters. As we will see in this chapter, nonthermal emission from synchrotron radiation by relativistic electrons, is highly polarized (around 40%). Scattering processes, e.g. , Thomson or Compton, yield polarized light that provide information about the geometry of the scat-tering region of an unresolved source. For instance, observing an unresolved binary system in polarized light can help in understanding the structure of the accretion disk (if there is one), or of mass outflows. The microquasar SS 433 has a complex structure in the inner regions, and the polarization can help untangle this. Published spectroscopic analyses had not given unique results for the environment near the accretion region, since the flows are complex and variable and the line profiles are not easily interpreted. The problem is that, in most cases (including SS 433), scattering processes lead to low polarization levels, around 5% and even under 1%, so quantitative measurements require broadband polarimeters with high precisions of a few tenths %. This has been possible after the development of superachromatic wave-plates. Furthermore, the polarization strongly depends on the spectral region, and depending on this interval, a variety of physical processes produce polarized light. For every wavelength region, moreover, one has to take into account important effects that can compromise the analysis (such as Faraday rotation in radio, see A.0.1.1). That is why, although this work deals with optical measurements, I begin with an overview of the transfer of polarized light in all wavelengths. This will help to better understand SS 433 and its multiple, interacting structures.

2.1 Radiative transfer

For a bundle of rays traversing a medium, the monochromatic energy of a ray defined in a solid angle dΩ, coming from an area dσ is defined by

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CHAPTER 2. COSMIC POLARIZATION PROCESSES 12

dEν = I(x, y, z; θ, φ)νdtdσdΩdν (2.1)

where I_ν is the monochromatic intensity of the radiation field (or surface brightness), i.e., the energy at frequency ν crossing a unit area in some amount of time, per unit solid angle emitted in the interva dν. If Iν does not depend on the coordinates the field is homogeneous, if does not depend on the direction (i.e. , θ, φ), isotropic. The emission increases the intensity along some direction (line of sight), the extinction lowers it. In radiative transfer theory, the medium does not change while the radiation is traversing it, i.e. , the response is linear and the fraction of intensity emitted or extincted is proportional to the medium mass density ρ. This is not necessarily always true, but in astrophysics and for this thesis it is. Hence, the extinction coefficient, eν is defined, precisely,

eν = kν + k(s)ν (2.2)

where k_ν is referred to all the processes that lead to absorption, i.e. , the intensity de-creases because of internal energy conversions (from radiative to thermal, for example), while kν(s) defines the losses due to scattering processes, i.e. , the intensity decreases along some direction because scattering changes the photons’ flight direction or frequency, like in Comp-ton scattering, which is explained in Appendix A. The same parametrization applies to the emission coefficient eν; light can be emitted directly from the medium and scattering can lead to more photons along some direction. For simplicity, in the following I will refer to the absorption and scattering coefficient as k_ν and j_ν, and will be explicitly stated when they refer to scattering or thermal processes, or both.

Finally, the transfer of radiation is governed by the following, deceptively simple equation (Chandrasekhar 1960):

ˆ n · ˆkdIν

dτν

= Sν− Iν (2.3)

where ˆn defines the line of sight and ˆk is the direction of the beam, so the equation governs the radiation field’s variations along a one dimenstional path, in function of the optical depth τν, which is a one dimensional function of the path crossed (see equation 2.6). The source function, S_ν, is given by jν

kν, the emissivity coefficient over the opacity coefficient and the

scalar product between ˆn and ˆk derives from the fact that the beam is propagating through a particular direction, or, alternatively, that we are interested in how the intensity changes along our line of sight, moreover, it defines the intensity’s variations respect to the observer, so the reference system is fixed.

If, and only if, a system is in local thermal equilibrium with the radiation, then each point in the atmosphere can be parametrized with the local temperature T , and the source function coincides with the Planck function:

jν kν = Sν = Bν(T ) = 2hν3 c2 1 ehν/kT _{− 1} (2.4)

This source function describes pure thermal absorption and emission processes and is isotropic. In contrast, radiation diffusing inside the medium and only scattering (scattering atmosphere) yields a source function that retains a dependence on angle (see Chandrasekhar 1960), Sν = 1 4π Z π 0 Z 2π 0 p(θ, φ; θ0φ0)Iν(θ0, φ0) sin θ0dθ0dφ0 (2.5)

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where p(θ, φ; θ0φ0), called phase function, describes the specific anisotropy of a scattering process. It is a weighting function that changes the contributions of incident beams from a direction (θ0, φ0) to some line of sight (θ, φ) so it is a redistribution function of photons in solid angle. The plane described by the incident and scattered beams of light is called plane of scattering. Note that in this case the transfer equation is integro-differential, so the intensity variations are strictly related to the scattering process. A constant phase function yields isotropic scattering. If the phase function is normalized to unity, then we have the conservative case of perfect scattering, i.e. , the number of photons does not change; the opposite happens when both scattering and absorption are present, so the phase function is normalized to a number less than one, called albedo.

The optical depth is defined as

dτν = kνρds (2.6)

and defines the fractional path crossed by the radiation through the medium respect to the local mean free path λ, which is defined by λ = _k1

νρ. The infinitesimal pathlength ds is

fixed along a particular direction ˆs, which is the direction of propagation (for the particular case of a plane parallel atmosphere ˆs ≡ ˆz, which is the direction perpendicular to the plane atmosphere, or alternatively, where the radiation escapes from it.). When τ < 1, the medium is optically thin to radiation, if τ ≥ 1, optically thick. This means that radiation from some direction, enters a medium which is optically thin, it proceeds nearly without interaction. If, on the contrary, the medium is optically thick, the intensity changes, since the photons interact many times with the medium and can be absorbed (as in a stellar photosphere), while in the case of a scattering atmosphere, the photon number is unchanged.

To determine univocally the characteristics of the radiation field, however, are needed other two parameters: the phase and the polarization of light. These two are not usually considered in equation 2.3, and must be treated in other ways. Here below the description of the most convenient formulation of polarized light (and its implementation in the radiative transfer equation), introduced by Sir George Stokes in 1852.

2.2 Representation of polarized light

In general, a beam of light is polarized if the electric vector of the electromagnetic wave oscillates in a preferential direction. This is important because if we study the changes (in modulus and direction) of this vector, we can infer important emission and (or) scattering processes of the medium, like synchrotron radiation, Thomson scattering, and even probe the presence (and sometimes the intensity) of the magnetic fields (galactic or stellar).

Consider a monochromatic electromagnetic wave traveling in the z direction, the expres-sion of the electric field, in cartesian coordinates, is given by

E(t, z) = E0cos(ωt − kz − φ) (2.7)

where t is the time, ω is the frequency, k is the wavenumber and φ is the phase of the wave. The x and y components are:

Ex= Ex,0cos(ωt − φ1) (2.8)

Ey = Ey,0cos(ωt − φ2) (2.9)

In a scattering process these two components are parallel and perpendicular to the plane of scattering. In general, the two amplitudes and phases are different, so the electric vector

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traces out an ellipse in the plane xy, i.e. , the plane of the sky if both the amplitudes and the phases are constant and the wave is said to be elliptically polarized. If, instead, φ1 = φ2 (or equals to multiple integers of 2π), the wave is linearly polarized; if the amplitudes are equal and the phases differ by 901 degrees the wave is circularly polarized. Since the complete polarization state is given by the superposition of the two, if one measures both the circular and the linear polarization, then can determine the complete polarization characteristics of the radiation field.

The most convenient, quantitative representation of polarization uses the Stokes parametriza-tion, ( Chandrasekhar (e.g. 1960), van de Hulst (1981)):

I = E_x2+ E_y2 (2.10)

Q = E_x2− E_y2 (2.11)

U = (E_x2− E_y2) tan(2ψ) (2.12)

V = (E_x2− E_y2) sec(2ψ) tan(2χ) (2.13)

The Polarization Angle (PA) ψ is defined in the interval [0◦, 180◦]2. It represents the angle defined by the electric vector and the x axis, counted in the counterclockwise direction. The ellipticity angle, χ, is defined by χ = tan−1 b_a, where a and b are respectively the major and minor axes of the ellipse shown in Figure 2.1. The relations above come from rearranging 2.8 in a convenient way, many different notations exist (see Chandrasekhar (1960) and van de Hulst (1981). The ellipse is represented in the figure below

Figure 2.1: Polarization ellipse drawn by the electric vector. ψ and χ represent respectively the PA and the ellipticity angle.

If we combine equations 2.10, 2.11, 2.12 and 2.13, we obtain

I2= Q2+ U2+ V2 (2.14)

1

Since in the literature the polarization angles are expressed in degrees, I will maintain this convention in this thesis.

2

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Figure 2.2: Examples of the Stokes parameters. The sign dispalys different orientation of Q and U . As already stated, V simply changes its sense of rotation if the sign changes.

The sum of the intensities is the total intensity of the wave: a monochromatic coherent electro-magnetic wave is always 100% polarised. In astrophysics, and in physics in general, however, the signals are a superposition of many monochromatic waves, and the polarization, if present, is macroscopic, i. e., the mean over all the wave oscillations results in a mean polarization state, which can be due to intrinsic (synchrotron radiation) or extrinsic (scattering) processes. This means that the inferred properties represent the mean behavior of the radiation field. If all wave directions are equiprobable, a zero polarization level is expected as in pure thermal emission. If the radiation field is partially polarized, a mean orientation is measured, and

I2 ≥ Q2_{+ U}2_{+ V}2_. _(2.15)

The degree of polarization comes separately from linear and circular polarization,

pL≡ p Q2_{+ U}2 I ∈ [0, 1] (linear) (2.16) pC ≡ V I ∈ [−1, 1] (circular) (2.17)

The sign of V , thus p_C, depends on the orientation of the polarization. By convention, the positive (negative) sign is assigned to light with IRHC − ILHC > 0 (< 0); here, IRHC and ILHC denote the intensities of right-hand circularly and left-hand circularly polarized light, respectively (e.g. , Trippe 2014). The PA and ellipticity angles are given by

ψ =1 2arctan U Q (2.18) χ =1 2 V p Q2_{+ U}2_{+ V}2 (2.19)

The Stokes parameters Q and U represent linear polarization and can be positive or negative. Stokes Q maximises the polarization along the x axis; U , instead, when the electric vector is at +45◦, so it gives information about the inclination of the electric vector. The sign rotates simply the vector by 90◦, see Figure 2.2.

In general, the measured polarization is a global property produced by the mean behavior of many streams of light. However, it is not a linear function of the single streams. The Stokes

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parameters, on the contrary, respect this property. If the polarization state is given by a mix-ture of physical processes, the Stokes parameters for the mixmix-ture is the sum of the respective Stokes parameters of the separate processes. This condition is valid only when there’s no permanent phase relation between the light streams, that is when they are independent (if they come from different, distant regions as when the measured polarization comes from a source and the interposed interstellar medium (ISM)).

In a single scattering process, such as optically thin Thomson or Rayleigh scattering (see 2.3.2.2), the phase function is fixed, so the scattered beams follow a particular, angular pattern. This means that the plane of polarization, that is the plane perpendicular to the plane of scattering, is fixed along some direction. The complete polarization state is specified by the Stokes parameters. By definition, they have the dimensions of the intensity, so the equation of transfer becomes vectorial. Letting

I(θ, φ) = [I(θ, φ), Q(θ, φ), U (θ, φ), V (θ, φ)], (2.20) is possible to write the equation of transfer in the vector form

ˆ n · ˆkdI

dτ(θ, φ) = S(θ, φ) − I(θ, φ), (2.21)

where S(θ, φ) denotes the vector source function. It is possible to generalize equation 2.5 in a vectorial form, where the phase function becomes the 4 × 4 phase matrix P (θ, φ; θ0, φ0), that relates the transformations between the various Stokes parameters. Hence, the description of polarized light requires that whatever interactions the light beam suffers through the source and the telescope must be parametrized as a matrix transformation. For example, when dealing with polarized light measurements, it is the necessity to understand how the telescope and the instrumentation change the characteristics of the beam the observer is going to detect. This can be accomplished using the so called Mueller formalism. This formalism, through the vectorial description of the intensity, I, describes the various transformations the light feels during its path from the source to the telescope: the final, measured quantity is another vector, I’.

I’ = MI (2.22)

Here M is a 4 × 4 matrix and describes the process (or processes, if is obtained by the products of multiple matrices) that changes the vector I. Here some basic examples

Mref =     1 0 0 0 0 1 0 0 0 0 −1 0 0 0 0 −1     (2.23) and Mrot=     1 0 0 0 0 cos(2α) sin(2α) 0 0 − sin(2α) cos(2α) 0 0 0 0 −1     (2.24)

represent the Mueller matrices associated respectively to the reflection through a perfect mirror (i. e. , no dispersion) and to a rotation (respect to the plane of the sky) of an angle α. In Mref, since the mirror is perfect, I sustains only a change of sign in U and V, depending

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on the direction of propagation relative to the observer. Think of a beam with U_I = 1 that goes away from you. If it reflects from a mirror and turns back in the same direction then the sign of U changes since the direction of propagation reverses, see Figure 2.2. The same argument holds for V.

This formalism is very powerful, since it precisely defines the transformations of the po-larized beam. The main difficulty is obtaining the correct Mueller matrix for the entire path, and this is not always possible for two reasons principally: because the matrix associated to a particular process may not be known or because not known all processes that the beam feels before entering the telescope are known. In any case, it is possible to write the correspond-ing Mueller matrix associated to the instrumentation (a careful calibration analysis must be done): the optics, the mirror, the instruments. . .

This permits, through the inverse calculation, to derive the vector I with less contamina-tion, due to the atmosphere for example, and then the final calibration (obtained observing standards, see chapter 3) is better. This formalism is used mainly in radio, since in the other wavelength regions (like optical) one deal with counts of photoelectrons, not with waves, so is better to manipulate directly those to remove systematic effects and then, obtain the Stokes parameters. In the next sections they will be described the main physical processes that lead to polarized light and the main background sources.

2.3 Polarization processes

Here I will review the main processes that produce polarized light, in particular the ones observed, or probably happening, in SS 433. Particular emphasis will be laid on the radio and optical spectral intervals.

2.3.1 Infrared

The infrared usually traces the radiation field in thermal equilibrium with the dust and the grains. This permits to study star forming regions and structures like debris-disk for example (a circumstellar disk of dust and debris around a star or a planet). Debris disks can be studied even in the mm range. Like in the optical, polarization measurements in the infrared give informations of structures through scattering, even if in this case is caused by grains and dust and not by electrons. This require theoretical, numerical models that take into account grains’ characteristics like: the geometry, the emissivity, the dimensions and even how they are distributed. The analysis of infrared polarization is important in particular for the study of the emission coming from the AGNs torus, since is not well known how the radiation is reprocessed and how the dust is distributed. In the infrared, in fact, the resulting polarization is not only related to the geometric properties of the grain, but also on its internal characteristics such as: opacity, emissivity and composition. The composition is related to the cross sections and opacities, and so to the polarization of the light after a scattering process.

2.3.2 Optical and UV

The main polarization processes that happen in these two regions are usually related to scattering, i.e. , Thomson, Rayleigh and dust, since nonthermal emission processes, like Syn-chrotron radiation, require intense magnetic fields or very high energetic particles (so a high γ ). In theory, is possible to detect, through spectropolarimetry, polarization coming from split lines due to the Zeeman effect, but the spectroscopic resolution power needed is too high to detect them in the optical (in the mid, far-infrared and radio is possible).

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Furthermore, there are very few measurements of polarization in the UV region, since it is necessary a space telescope (nowadays only the Hubble Space Telescope can make UV measurements - not polarization -). This is a pity, since it should be possible to map many violent dynamical processes coming from active objects: like novae, microquasars (SS 433), AGNs. . . Polarization, coupled with spectroscopy and photometry, can give key insight of internal, active regions.

2.3.2.1 Thomson scattering

If we have an electron in the non-relativistic limit (so β 1) that interacts with a photon with some frequency ν, then the interaction between the photon and the electric field vector of the electron will produce a scattering process, that is, a change in velocity and direction of the charged particle, that in turn will emit some radiation at the same frequency of the photon. The Thomson cross section is

dσT dΩ = e2 mc2 2 1 + cos2_Θ 2 (2.25)

where e and m are respectively the charge and the mass of the electron and Θ is the angle between the incident and scattered photon. Polarization can give very important properties of a system through this scattering process: if we have a source, say a star, then the light emitted from it is nearly thermal, so not polarized. But, if this star has around it a circumstellar en-velope (due perhaps by an intense wind activity of the star itself) it will scatter the radiation that become partially linearly polarized since the geometry of the envelope is defined and so the scattering plane. If the polarization measured is independent from the frequency then we are in presence of Thomson scattering. The intensity of polarization depends mainly on the geometrical distribution of the electrons and on the number density of them (more electrons, more coherent scattering, more polarized is the light). To understand geometrical structures around a star or a binary system through Thomson scattering are required theoretical models. The first, analytical, models have been developed by Brown and McLean (1977) and Brown, McLean, and Emslie (1978). In these models the sources are considered point-like, the en-velope to be optically thin (so only single-scattering is present) and the enen-velope is assumed to corotate with the binary. These models lead to a Fourier fit of the Stokes parameters as a function of the orbital phase of the binary system (up to the second harmonic). The model gives a unique relation between the Fourier coefficients and the physical parameters, e. g., the orbital inclination i of the binary, the mean optical depth and the electron density ne. However, these methods present some assumptions that can be physically inconsistent: especially in considering the stars as point sources, which give problems for eclipsing binaries. Some numerical models, which are more complete, include obscuration effects, based on the work of Brown and McLean (1977) and Brown, McLean, and Emslie (1978), are derived and exploited in Piirola, Berdyugin, and Mikkola (2005) and Piirola, Berdyugin, Coyne, et al. (2006).

Finally, polarization through Thomson scattering can give very important results about unresolved, internal scattering regions of binary systems, but high level polarization measure-ments are required and many orbital periods have to be covered in order to see a modulation in the light curve and to obtain quantitative results.

2.3.2.2 Rayleigh scattering

Rayleigh scattering happens when the wavelength of the photon is much smaller than the dimension of the particle (grain) involved. The cross section is (Chandrasekhar 1960)

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σR= σT( λ0

λ)

4 _(2.26)

and is valid for λ λ₀, where λ₀ is the wavelength of the atomic species doing the scattering. This type of scattering has the same phase function of Thomson scattering, so, if both processes are present in the same geometrical region, the PA measured will be the same, but the polarization fraction will be higher toward UV because of Rayleigh scattering: infact, contrary to Thomson scattering, this process depends strongly on the wavelength of the incident photon, and is more effective in the UV region (usually is caused by Lyman α in H). In this high-energy region, this process, if present, is clearly caused by atoms3, like hydrogen or helium, and not by particles like electrons, since they’re not bigger than the wavelength of the light emitted.

2.3.2.3 Polarization produced by the ISM

An important polarization mechanism through the UV to the IR is due to the Interstellar Medium (ISM). I discuss this process because SS 433 is located in the Galactic plane, and the extinction of its field is AV ∼ 6 − 7 mag (see section 4.2.1 for details). This fact needs to discuss the ISM polarization contribution, even because it was been an important part of the calibration procedure in this thesis and because there are no intrinsic polarization measurements of SS 433 in the literature, see Chapter 5.

The ISM polarization contribution arises because the dust is aligned by the Galactic magnetic field. What mechanisms cause this alignment are still debated (see Andersson et al. 2015). The reason why the magnetic field directly involved in the ISM polarization and alignment is because the PA measured in the optical is perpendicular to the one measured in the radio region. And since in the ISM the magnetic field is responsible for the radio polarization, due to the synchrotron emission, the PA measured in the optical traces the direction of the projected magnetic field. The optical polarization contribution of the ISM is not large, around 3% at maximum, but if a system has a low instrinsic polarization level and the instrinsic values are needed to infer physical properties then this becomes a strong contamination, which in most cases is difficult to remove.

Even if the theory is not well developed, is possible treat the ISM contribution in the UV-NIR range using a universal empirical law (see Serkowski 1973), shown in Figure 2.3:

p(λ) = pmax· exp[−K ln2( λ λmax

)] (2.27)

Here p(λ) is the linear polarization as a function of the wavelength, pmax is the maximum polarization at wavelength λ_max, and K is a parameter that defines the width of the curve. Originally was kept fixed by Serkowski (K = 1.15), but later works (e. g., Codina-Landaberry and Magalhaes 1976) showed that the best-fit value varies from source to source.

The Serkowski law is valid in a relatively narrow wavelength interval. This is related to the grain size distribution. Detailed modeling (e. g. Mathis (1986), Kim and Martin (1995)) shows that the polarization curve can be reproduced if the total grain size distribution has a small-size cutoff ∼ 0.04 − 0.05µm. Since in the mid and far infrared the temperatures are usually lower, the grains are inferred to be bigger (∼ 0.1 − 0.25µm) and the Serkowski law is not valid. To produce polarization, asymmetric spinning grains must have their angular momentum vectors aligned in space. Random processes (e. g. , mainly gas-grain collisions) that change the grain orientation must be less frequent than the alignment process (Spitzer

3_{In the optical and UV region there is no presence of molecules or grains, since the photons are too energetic}

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Figure 2.3: On the left the Serkowski law for the ISM polarization level and on the right the polar-ization as a function of the extinction (Andersson et al. 2015). The thick straight line represents the upper bound of the correlation plot.

1978). The main process that causes this alignment appears to be radiative: the differential cross sections of the two circularly polarized components of the external radiation field cause a torque on the irregular grain which will spin-up and align along the magnetic field lines (see Andersson et al. 2015).

In the UV, the ISM contribution is lower, and the possible polarization level is due to small grains (less than 0.04µm). In the mid and far infrared, instead, usually is observed a mean polarization decrement up to 350µm, followed by a rise at longer wavelength. However, this trend is not always observed, since depends on the chemical composition (silicates, carbon. . . ) and the relative alignment between the various chemical species.

There is a linear correlation between the ISM polarization and the extinction, and thus, the amount of dust along the line of sight (see 2.3). The thick straight line represents the upper bound,

p AV

≈ 3% mag−1. (2.28)

Clearly this is not a unique relation, and the sparse distribution of points indicate that the contamination due to the ISM strongly depends on the local dust distribution and ag-glomeration, so it is difficult to remove the ISM polarization contribution. In fact, even if the Serkowski law is valid, a better, stable method in order to remove (or at least reduce) the ISM contribution is to directly measure the polarization level of standard unpolarized sources. The polarization obtained through different filters is associated only to the ISM if it follows the Serkowski relation. If, as in this thesis, we are interested in some source and want to obtain intrinsic polarization values, then we must measure the polarization relative to sources that are as near as possible the target in the plane of the sky. In this way, the ISM structure is more likely the same for the various sources. Moreover, a key point is the distance between these unpolarized sources from the Earth, since if their distance is greatly different than the polarized one then the ISM calibration will be inevitably wrong; the dust distribution can change along the line of sight. If the ISM agglomeration changes, or the grain type is different at some distance, then the polarization level and the PA can change substantially. Nowa-days, with the advent of Gaia, this problem is easier to solve, since the distances are better constrained and the ISM contribution can be evaluated through direct measurements of the field stars. Future polarization measurements will be the most intrinsic and accurate. An

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all-sky polarization survey is needed, spanning all Galactic latitudes and covering distances greater than 3 kpc; in this way, apart from the ISM polarization calibration, the astronomical community will have incredible information about the distribution and characteristics of the galactic dust environment.

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Chapter 3 Instrumentation and Data Reduction

We see past time in a telescope and present time in a microscope. Hence the apparent enormities of the present.

Victor Hugo This chapter provides the technical aspects of the work: the telescope, the acquisition methods, the types of instruments used and the data reduction methods.

3.1 The Liverpool telescope

New data for SS 433 were obtained for this thesis with the Liverpool Telescope (LT) : a fully robotic astronomical telescope operated by the Astrophysics Research Institute of Liverpool John Moores University, located in the Canary Islands on the summit of La Palma. The observations for this thesis started the 2018 July 2 and ended the 2018 August 11.

The telescope has the following optical characteristics:

• Ritchey-Chrétien Cassegrain optics;

– f/10 focus at Cassegrain; • Primary mirror; – diameter of 2.0 meters ; – focal ratio f/3; • Secondary mirror; – diameter of 0.62 meters ; – focal ratio f/3;

• Automated Acquisition and Guidance (A&G);

• Field of view: 40 arcmin

The journal of observations of spectra, photometry and polarimetry is provided in Ap-pendix B. Here I describe the instruments, acquisition and reduction methods.

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CHAPTER 3. INSTRUMENTATION AND DATA REDUCTION 23

3.2 Spectra

The spectra analyzed in this work come from the LT and from the ESO science products archives, which can be found at https://archive.eso.org/scienceportal/home. The ESO spectra were acquired from three different spectrographs: XShooter, EMMI and FEROS.

The LT spectra were taken with the spectrograph FRODOSpec (Fibre-fed RObotic Dual-beam Optical Spectrograph). It used the low resolution grating in the red arm configuration. Not all of the nights have spectra because in the period July 2 -11 there was a pointing problem when the LT center was not sited exactly on the central region of the source.

3.2.1 FRODOSpec

FRODOSpec is an Integral-Field Spectrograph (IFS). As the name implies, it is a dual beam design with the beam split before the entrance to individually optimized collimators. The instrument has two resolution options on each arm. Only the red arm was used in this work, see Table 3.1 for specifications of gratings and resolving power of it1. The spectrograph is fed by a fiber bundle from the Cassegrain focus of the telescope.

Resolving Power Wavelength range ( Å )

2200 5800 − 9400

Table 3.1: Red arm specifications of FRODOSpec.

FRODOSpec, as an IFS, receives the light in a fiber matrix (12x12, where 144 is the number of the fibres). This field is reallocated to form a 1D array of fibers, that output a pseudo-slit. The position of each fibre in the matrix corresponds to a particular position along the pseudo-slit and this scheme must be one to one. The optical scheme is represented in Figure 3.1. The pseudo-slit is disposed vertically. After the beam is split, it passes through the grating and then focuses on the CCD chip. Figure 3.2 shows a single acquisition: on the CCD chip there are multiple spectra (each coming from the same field), each of which corresponds to a single fiber. The spectra can cover several pixels (as in Figurefig:frodofits) since the target’s photons fall on the fibers matrix, in which the acquiring fibers are contiguous, but after the 1D mapping they can be reallocated to different rows on the CCD (see the mapping on the top of Figure 3.1). The fibre is wider than a single pixel of the CCD, so the intensity is spread over contiguous pixels. This has to be taken into account when a flat correction is performed.

3.2.2 Spectra reduction

Every spectrum was reduced by an automated pipeline at the LT. The so-called L1 reduction involves routine operations, such as bias and flat corrections of the CCD frame. L2 reduction, instead, is described in detail in Barnsley et al. (2011) and involves procedures such as: fiber identification, fiber extraction flux, wavelength calibration and fiber throughput correction. In fact every fibre can have a different throughput efficiency. To correct for this an additional flat field operation has to be performed.

The archival spectra were pipeline reduced in wavelength and flux (XSHOOTER), or only wavelength (EMMI and FEROS). The FEROS data used in this thesis is a composite

1

For the complete specifications of FRODOSpec see: http://telescope.livjm.ac.uk/TelInst/Inst/ FRODOspec/.

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Figure 3.1: Fibres and optical scheme of FRODOSpec. The image has been partly modified in order to better visualize the scheme, the original can be found in Barnsley et al. (2011).

Figure 3.2: An image of the CCD chip of one of the spectra acquired in this thesis. The horizontal axis is the dispersion axis of the spectrograph and on the vertical axis are located the fibers, note in fact the presence of multiple spectra, each of which comes from a different fibre.

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were filtered and merged to increase the signal to noise ration, which is permissible since they were acquired in a single night. The final high resolution spectrum (see appendix B) has been used in this thesis (see section 4.2.1).

3.3 Polarimetry

In general, dealing with imaging polarimetry involves more issues than standard photometry. These are related to the background and the transmission of the polarized light. During a measurement, the registered signal has not only the intrinsic polarization we want to de-rive but other contributors that must be removed, or at least reduced as more as possible, during the calibration procedure. Background polarization, for instance, is quite difficult to remove, because it can come from completely different sources and from a great variety of physical processes. The most important background contributors are: the atmosphere, for which Rayleigh scattering produces a wavelength dependent, non-isotropic polarization. At-mospheric aerosols (small particles in the atmosphere) add polarization through scattering processes. Atmospheric contaminations are efficiently removed by the Dipol-2 polarimeter, see 3.3.2 for details.

The transmission of polarized light between the source and the detector, besides the atmosphere, alter the polarization. During its path, the light passes through two main media: the interstellar medium (ISM) and the optics of the telescope. The ISM, for weakly polarized sources (like SS 433) is an important contributor (see section 4.1.1 for a detailed discussion, related in particular to this work). The dust grains align with the Galactic magnetic field, this leads to a coherent scattering process of the light coming from some source, and so alter the polarization. The telescope optics introduce a polarization from the telescope’s mirror, because of reflection. In general, the instrumental polarization is corrected looking at unpolarized sources (see section 3.3.3) in the optical, but for other wavelength intervals, e. g., radio, another method is used (see Chapter 2).

In this work, RINGO3 polarization data have been obtained on every observable night. The main methods adopted to measure polarization, useful for discussing the calibration results were the following. Usually, when dealing with linear polarization, there are two main types of instrumental design:

• Discrete rotating analyzer: the beam, after reflecting from the secondary mirror of the telescope, passes through a λ/2 polaroid (which linearly polarizes the light) and then through a Wollaston prism, which separates the two orthogonal components. Then, summing and subtracting the two intensities for various angles of the polaroid, it is pos-sible to derive the Stokes parameters and the polarization parameters (see section 3.3.3 for details).

• The light passes through the polaroid but in this case it rotates continuously, so the single beam measured is modulated by a time dependent angle α:

S(α) = 1

2G(α)[I + Q cos (2α) + U sin (2α)] (3.1)

(see Clarke and Neumayer 2001) where S(α) is the modulated flux and G(α) is the scaling factor related to the pixel response to unit intensity, I is the total intensity of the light and Q and U are the Stokes parameters. RINGO3 follow this prescription in particular.

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If one also needs to measure circular polarization the λ/2 analyzer is replaced by a λ/4 polaroid, but bearing in mind that the λ/4 polaroid converts even linear polarization to circular, one has to first measure the linear polarization and then subtract it from the λ/4 measurements. Circular polarization in the visible is usually very low (around 0.01 − 0.1%), so high precision polarimeters are required. RINGO3 does not have the sufficient precision to measure circular polarization.

After the observing session started we decided, on advice from the LT personnel, to take polarization measures with another polarimeter, Dipol-2, mounted on another LT located in Hawaii. The reason for this decision is related to the possibly inaccurate measurements coming from RINGO3 for SS 433, which has a low polarization: around 2% in the optical, (see Efimov et al. 1984). RINGO3 can introduce important systematic errors, as shown in Table 4.1. Dipol-2, on the contrary, is a high precision polarimeter that gives acceptable results for this peculiar object.

3.3.1 RINGO3

This polarimeter, which uses a continuously roating analyzer, has three cameras:

• Blue : 350 − 640 nm ("e")

• Green : 650 − 760 nm ("f ")

• Red : 770 − 1000 nm ("d")

The instrument design (see Figure 3.3) is such that the light beam is split by a pair of dichroics, providing simultaneous polarization measures in the three bandpasses. For details of the polarimeter design and data reduction see Clarke and Neumayer (2001).

Figure 3.3: On the left, RINGO3 ( http://telescope.livjm.ac.uk/TelInst/Inst/RINGO3/) and on the right, Dipol-2 (Piirola, Berdyugin, and Berdyugina (2014)) technical designs.

For every rotation of the polaroid, eight in 360 degrees, the instrument takes an exposure, obtaining a stacked number of frames (depending on the total exposure times), for every filter, for each of the eight exposures. The frames of a single stack are then summed auto-matically. The polaroid rotates once per second to reduce possible polarization effects due to the atmosphere which has a variability time scale of tens of seconds.

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3.3.2 Dipol-2

Dipol-2, like RINGO3, can make instantaneous measurements in three different bandpasses. These are different than RINGO3: the standards Johnson B, V and R passbands (400 − 800nm). Like RINGO3, the light beam is split by two dichroic lenses and falls on three different CCDs, but unlike RINGO3, Dipol-2 has a calcite block that separates the light in the two orthogonal components (see Figure 3.3). For details of the instrument see Piirola, Berdyugin, and Berdyugina (2014).

The high precision of this instrument is due to the following characteristics:

• Direct sky subtraction is performed by the optics of the polarimeter: this dramatically improves the precision of the measurements. Basically, the extraordinary (ordinary) component from the sky is refracted on the ordinary (extraordinary) component from the sky + star (see Piirola (1973) for details).

• A super-acromatic waveplate: this permits measurements over a wide spectral region without losses due to different modulation efficiencies (that depend on the wavelength of the incident photon if the filter is not acromatic).

• A calcite Wollaston prism: this improves drastically the stability of the instrument with respect to the atmosphere variations.

• A typical polarimetric measurement cycle consists of sixteen exposures at different ori-entations of the retarder with 22.5◦ intervals. This redundancy eliminates the major source of systematic errors, e. g., induced small internal measurement errors arising from dust particles on the retarder (Piirola, Berdyugin, and Berdyugina 2014)).

3.3.3 Data Reduction

For the RINGO3 polarization data reduction, it was necessary to write a dedicated procedure. LT has no automated polarization reduction process. This part of the work required some time, especially because (as predicted by the LT personnel), the polarization data of SS 433 coming from RINGO3 were affected by substantial systematic uncertainties, so the major effort involved improving the software to reduce the systematics. For Dipol-2, instead, the data have been calibrated directly at the telescope, so I will describe only the procedure related to RINGO3 calibration.

3.3.3.1 Calibration of Polarization data

In general, when dealing with polarimetric calibration procedures, one acquires the data for the source, and two standards: one unpolarized (necessary to correct for additional instrumental polarization due to the instrument) and one polarized source (to remove depolarization effects and to correct for the atmosphere). It is, however, not always possible to have many standards per night, because only few of them are known in the sky. The telescope has a fixed list of standards and, if possible, it autonomously observes one or more of them (unpolarized and polarized) per night. Unfortunately, some of the nights have only one or no standard (because the LT only observes them if the night is considered "photometric", so in particularly good conditions). This leads to problems in the calibration procedure.

The calibration procedure was not done for the nights with no standards (both polarized and unpolarized). In cases where there was only one of the possible polarized standards the calibration was performed, and the unpolarized source used was HD14069, in particular the night of 12th of July, because it turns out to be the best option for the calibration. The

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cataloged values of the standards used are published in Schmidt et al. (1992), except for the standard CRL2688, for which I refereed to Shawl and Tarenghi (1975).

As mentioned in section 3.3.1, the data were organized in eight exposures (eight FITS files) per filter per source. The general procedure adopted was:

• Photometry : derive sky subtracted photometric fluxes of every source (both the source and the standards), for each of the eight rotor positions to remove the sky-background contributions;

• Unpolarized standards correction : This procedure is fundamental to correct for the instrumental polarization. For each rotor position, divide the counts from the polarized standards and science targets by those from the zero-polarized standard (like flat-field). Another possible procedure is to subtract the Stokes parameters of the unpolarized source from the polarized targets. After trying both of them, the former procedure was used (as recommended from the LT website). The reason why the first procedure gives better results is related to the fact that this correction involves every rotor position sepa-rately (so it is specific to every frame), and directly uses the counts, so it’s more effective in correcting instrumental errors, acting more upstream than the other procedure. In principle, the two methods are equivalent for a high precision polarimeter.

• Derivation of the polarization parameters : Derive the Stokes parameters, and then the polarization level and polarization angle of the source and the polarized stan-dard. To complete the calibration, use the cataloged values of the standard to derive the effective polarization of the source:

P D = P Dmeas P Df actor

(3.2)

and

P A = P Ameas+ ROT SKY P A + ROT angle + P Ashif t (3.3)

where P D_meas and P D are respectively the measured and derived degree of polariza-tion, and P Df actor is obtained dividing the polarization degree of the standard by its cataloged value. P A is the polarization angle of the source, ROT SKY P A is the sky polarization angle of the image (since the telescopes have an alt-az mount the plane of the image rotates as the telescope moves), ROT angle is the rotation angle of the Cassegrain mount of the telescope and P A_{shif t} is obtained by subtracting the cata-loged polarization angle of the standard from the measured value (analogous to the P Df actor). ROT angle is kept as close to the zero as much as possible (at the telescope the personnel note some systematic deriving from this displacement). SS 433 usually had ROT angle values very different from zero, so I had to correct for it, even if sys-tematic in the polarization angle were evident (in the few cases for which ROT angle was under 25 − 30 degrees the polarization angles derived were much more precise). For polarized standards this problem did not occur.

I now describe the two pipelines PolPhotometry, PolarizationCAL I wrote to obtain the polarization data. These are listed in Appendix C.

Spectroscopic and polarimetric study of the microquasar SS433

Università degli studi di Pisa

Dipartimento di Fisica “E. Fermi”

Spectroscopic and polarimetric study

of the microquasar SS 433

Candidato: Paolo Picchi

Relatore: Prof. Steven Neil Shore

Contents

Chapter 1

Introduction

A

Chapter 2

Cosmic polarization processes

2.1

Radiative transfer

2.2

Representation of polarized light

2.3

Polarization processes

Chapter 3

Instrumentation and Data Reduction

3.1

The Liverpool telescope

3.2

Spectra

3.3

Polarimetry