«c 2009 Frans Snik Alle rechten voorbehouden ISBN 978-90-393-5184-0 Geprint door W¨hrmann Print Service te Zutphen o Cover images credit: ...»
c 2009 Frans Snik
Alle rechten voorbehouden
Geprint door W¨hrmann Print Service te Zutphen
Cover images credit: astroshed.com, SOHO, HST, Apollo 17
new concepts, new instruments, new measurements & observations
nieuwe concepten, nieuwe instrumenten, nieuwe metingen & waarnemingen
(met een samenvatting in het Nederlands)
ter verkrijging van de graad van doctor aan de
Universiteit Utrecht op gezag van de rector magniﬁcus, prof. dr. J. C. Stoof, ingevolge het besluit van het college voor promoties in het openbaar te verdedigen op maandag 26 oktober 2009 des middags te 2.30 uur door Frans Snik geboren op 14 december 1979 te Groningen Promotor: Prof. dr. C. U. Keller Contents Glossary vii 1 Introduction 1
1.1 Why polarimetry?...................................................... 2
1.2 Polarization formalisms................................................... 2
1.3 The creation of polarization................................................ 5
1.4 The measurement of polarization.............................................. 10
1.5 Thesis outline........................................................ 12
1.6 Outlook for astronomical polarimetry............................................ 15 I New polarimetric concepts
1.1 Why polarimetry?
Every astronomical object is polarized to some degree. Astronomical polarimetry, by nature, therefore yields more information than imaging and/or spectroscopy alone. Polarization, i.e. the vector properties of (scattered) starlight is particularly dependent on the physical circumstances of the location where the light originated. For instance, many properties of scattering dust clouds or (exo-)planetary atmospheres can be determined through polarimetry: the sizes, shapes and chemical composition of scatterers. Even the content, structure and stratiﬁcation of the atmosphere of an exoplanet can, in principle, be characterized, without optically resolving the planet.
Therefore, astronomical polarimetry has a unique capability to detect traces of extraterrestrial life. Another important and unique capability of polarimetry is the measurement of magnetic ﬁelds. Magnetic ﬁelds are ubiquitous in astronomical contexts of all scales, but their exact inﬂuence on many physical processes is often poorly understood. The physical understanding of stars and galaxies is incomplete without taking into account the eﬀect of magnetic ﬁelds, which have been frequently swept under the rug in the past.
Signiﬁcant progress on the understanding of magnetic ﬁelds is currently being enabled by advanced magnetohydrodynamic (MHD) computer models and, indeed, astronomical polarimetry. In many cases the models precede the observations. An example is the prediction of the presence of local dynamo action in the solar photosphere. The observational veriﬁcation (or falsiﬁcation) thereof requires very precise polarimetry, which even in the case of the Sun is challenging. There are also cases where polarimetric observations challenge the current models. For example, the unexpected discovery of magnetic ﬁelds on hot (i.e. non-convective) stars proves that crucial knowledge about the generation and sustenance of magnetic ﬁelds is lacking. Only the measurement of magnetic ﬁelds through polarimetry allows for the understanding of stars through all stages of their lives, from their formation out of magnetized molecular clouds, to stellar activity during their time on the main sequence, and to their ﬁnal breaths and their after-life as pulsars or magnetars.
In several ways, astronomical polarimetry is “orthogonal” to imaging and spectroscopy. Most importantly, polarimetry yields astronomical information that is very complementary. But also, the technical implementation of polarimetry in the optical regime in conjunction with imaging or spectroscopy (“spectropolarimetry”) and also interferometry (“polarimetric interferometry”) almost always requires trade-oﬀs on either side. For instance, a well-performing adaptive optics (AO) system may deliver a good image quality, but its many mirrors may have modiﬁed the source polarization and added polarization of its own (instrumental polarization) in the process. On the other side, polarization optics add signiﬁcantly to wave-front errors (aberrations) and reduce the transmission of the optical system. A polarizer even reduces the amount of light (in one beam) by a factor of a half. High spatial or spectral resolution therefore appears to be mutually exclusive with polarimetric precision. Moreover, polarimetry, being a diﬀerential technique, is usually fraught with all kinds of systematic errors. Spurious polarization signals can be created by e.g. varying atmospheric properties or by imperfect knowledge of the optics or the detector properties. Also, polarimetry is a photon-hungry technique requiring large-aperture telescopes and eﬃcient optics. The implementation of polarimetry in an astronomical instrument therefore always requires a careful instrument design. The reason that polarimetry is currently an under-exploited technique and considered very specialistic is not due to a lack of appealing science cases, but due to technical impediments compared to more classical astronomical techniques. Astronomical polarimetry in the optical regime is therefore still a developing ﬁeld and the work in this thesis aims to contribute to the advancement of it.
For a more extensive overview of astronomical polarimetry, see the book by Tinbergen (1996) and the review by Keller (2002).
1.2 Polarization formalisms In short, polarization is the evolution of the electric ﬁeld vector of light. Several formalisms exist to describe polarization, the application of which depending on the polarimetric principle. The Jones formalism describes single electro-magnetic (EM) waves, which, by deﬁnition, are 100% polarized and contain phase information. In the context of astronomical polarimetry, this formalism applies to the radio regime, where the detectors are antennae which output scales with the E-vector. The Stokes formalism applies to intensity measurements of photon ﬂuxes in the optical regime. It can describe partial polarization, which is particularly useful for astronomical polarimetry because most sources have a degree of polarization of at most a few per cent. Interference phenomena cannot be described with the Stokes formalism. Considerable fundamental work still has to be performed to theoretically describe polarimetric interferometry Introduction 3 or to calculate a partially polarized point spread function (PSF).
The [1,1] element merely describes the transmission of the polarization-modifying element(s), and becomes 1 when using normalized
Stokes vectors. Mueller matrices of a train of optical elements are multiplicative, but non-commutative:
With these three elements (polarizer, retarder, and rotation), most manipulations of the Stokes parameters Q, U and V can be achieved: the creation of all (fully polarized) polarization states and the measurement of all polarization states. Also the creation of partially polarized light can be described with Mueller matrices, e.g. with the use of a partial (imperfect) polarizer, or a depolarizer.
The latter has no very practical counterpart as an optical component, but in real physical environments or instruments depolarization does occur, for instance due to scattering.
1.3 The creation of polarization In general, polarization is created (or modiﬁed) anywhere where the cylindrical symmetry of the propagating light is broken. This breaking of the symmetry can be due to the change of direction of the light itself or due to the presence of unidirectional magnetic (or
electric) ﬁelds. The following physical processes are all known to produce and/or modify polarization:
• Anisotropic scattering or reﬂection of continuum radiation. For instance Rayleigh scattering in the Earth’s (or another planet’s) atmosphere, Mie scattering by large particles, or Thomson scattering by free electrons.
• Anisotropic scattering of line radiation. Here, the emergent polarization depends largely on the quantum numbers of the transition.
• Diﬀerential absorption or scattering by magnetically aligned non-spherical dust grains. This creates continuum polarization particularly in the infrared (IR) range and beyond.
• Synchrotron radiation from charged particles in a magnetic ﬁeld exhibits continuum polarization.
• Magnetic ﬁelds also produce line polarization through the Zeeman eﬀect (and the Paschen-Back eﬀect). This line polarization may be modiﬁed by magneto-optical eﬀects (i.e. birefringence of the medium due to the magnetic ﬁeld; the Faraday eﬀect and the Voigt eﬀect).
• Electric ﬁelds can produce a similar line polarization (the Stark eﬀect).
• Magnetic ﬁelds also modify and depolarize line polarization due to scattering through the Hanle eﬀect.
The prime work-horses of polarimetric diagnostics in the visible are scattering polarization (Rayleigh and Mie scattering), the Zeeman eﬀect, and –more recently and only in solar physics– line polarization and the Hanle eﬀect. The instruments and observations described in this thesis rely mostly on these eﬀects, which will be discussed in more detail below.
Note that polarization optics also relies on anisotropic eﬀects. For instance, a polarizer polarizes the light by diﬀerential absorption of orthogonal polarization states or by diﬀerential refraction (“birefringence”) in an anisotropic crystal. Retarders can modify the polarization owing to their anisotropic material or design. Non-polarimetric optics like mirrors or lenses unfortunately do also aﬀect the polarization if they are used at non-normal incidence. That is why only a completely rotationally symmetric system can be assumed to be “polarization-free”. One folding mirror already changes the source polarization.
1.3.1 Scattering Scattering is the most well-known mechanism for creating polarization, because it is the reason that the blue sky is polarized and that Polaroid sunglasses are so eﬀective at blocking scattered sunlight. The (continuum) scattering polarization is maximum for a scattering angle of 90◦ and the degree of polarization can exceed 50%. Polarimetry of scattering media is a particularly useful diagnostic for imaging and characterization of circumstellar material, such as (protoplanetary and debris) disks and exoplanetary atmospheres. Usually, these disks and exoplanets cannot be imaged directly because they are drowned in the light of the central star that is diﬀracted and scattered in the instrument itself. But, because the light of the circumstellar material is heavily polarized and the direct starlight is to a very large extent unpolarized, polarimetry constitutes a powerful technique to reduce the contrast and enable the direct imaging of these disks and exoplanets. The orientation of linear polarization due to single scattering is always azimuthal with respect to the central star.
Moreover, the polarization spectrum contains a lot of information on the scattering medium, e.g. due to the 1/λ4 behavior of Rayleigh scattering, the speciﬁc scattering phase behavior of diﬀerent particles, and the depolarization patterns of spectral bands and the albedo. In fact, it is known that the intensity spectrum alone is very insensitive to the microphysical parameters of the scatterers (size, shape, chemical composition) and that spectropolarimetry is required to unambiguously determine these parameters. Therefore, polarimetry of scattered sun- or starlight is a very powerful tool for characterizing an (exo-)planetary atmosphere.
1.3.2 The Zeeman eﬀect The Zeeman eﬀect (Zeeman 1897, Stenﬂo 1994) is the most famous eﬀect that involves modiﬁcation of line polarization by a magnetic ﬁeld. It involves the splitting in energy of the magnetic sublevels of the atom, which makes the spectral lines appear to be split into diﬀerent components. These components have a diﬀerent polarization, depending on the quantum numbers of the corresponding sublevels.
The impact of a magnetic ﬁeld on the emergent line polarization through the Zeeman eﬀect is explained with the cartoon model of Figure 1.1. Here, the transition is represented by a 3D oscillator. The magnetic ﬁeld couples the oscillators perpendicular to it to two circular oscillators and makes them precess around it. Because the right-handed precession around the magnetic ﬁeld is energetically favored, it is blue-shifted, whereas the other is red-shifted. The splitting in energy is proportional with the magnetic ﬁeld strength.
The third oscillator component parallel to the magnetic ﬁeld stays at the same energy and therefore the same wavelength.
In quantummechanical terms, the circular oscillators correspond to the σ components of the transition, i.e. the ones with ∆mJ = ±1, and therefore carry angular momentum. The linear oscillator corresponds to the π component (∆mJ = 0).
The connection to polarization is obvious: the σ components are circularly polarized with opposite handedness when looking along the magnetic ﬁeld direction. The π component then disappears. When observing the magnetic ﬁeld at an angle of 90◦, the σ component appears linearly polarized, and perpendicular to the π component.