Technical Annex PHY00045 (Max 10 pages)

“Development of a photon counting high time resolution Stokes' polarimeter for astronomical observation on future large telescopes and for optical science”

What is the question that this proposal addresses?

The question has two parts, both of them significant – a technological/scientific and an astronomical/scientific part. We ask, ultimately, what is the short-term variability (with time resolution ~100 μs, over a broad bandwidth of 500-900 nm) of the Stokes' vector in compact astronomical sources such as pulsars, catalclysmic variable stars (CVs), gamma-ray bursts, (GRBs), etc, because a knowledge of these variations will inform and constrain modelling of the electrodynamic properties in these compact, and extreme, source regions.

However, as no suitable instrument exists, in the first part of the question, we must first ask how to design and construct the Galway Stokes’ Polarimeter (GaSP) a high-speed broad-band Stokes' polarimeter for astronomy. The design and construction of GaSP, which will have unique capabilities for High Time Resolution Astrophysics represents a significant scientific challenge in its own right, and will form the substantive part of the work for the first two years of the project.

As a specific example to be answered in the second part we wish to investigate the single pulse photo-polarimetric properties of the crab pulsar. This is, actually, a most challenging example, requiring very high performance from GaSP, because random variations – evidence for an underlying stochastic process - exist down to 100 μs. This is a very short interval in which to measure polarisation, ruling out many conventional polarimeter designs.

Why is this problem significant?

The long term goal of this project is to enable measurements of random variability, at high speed, of the full Stokes’ vector for a number of astrophysical sources – the significance of these measurements is explained in this section. Within the three year limits of the project the goals are (a) the development of GaSP, and (b) measurement of the random variability of the crab pulsar down to 100 μs.

Development Of A High-Speed Stokes’ Photo-Polarimeter (GaSP)

Astronomical polarimetry has been a somewhat neglected area of astronomical observation - mainly because it is rather difficult. Javier Trujillo-Bueno & Fernando Moreno-Insertis (eds) in the Preface to “Astrophysical Spectropolarimetry, CUP, 2002, state “…The polarisation of light is the key to unlocking many new discoveries and obtaining the information we need to understand the physics of many phenomena occurring in the Universe….” A full description of the polarisation state of a light beam requires a knowledge of 4 numbers (the components of the Stokes’ vector, I,Q,U,V), namely, total intensity (I), intensity of linear polarisation in a certain direction (Q), intensity of linear polarisation in a direction at 450 to that (U), and intensity of the right or left handed circularly polarised component (V). Linear polarisation gives us information on the degree of asymmetry present in the emission zone and/or subsequent passage between source and observer. The prime causes of linear polarisation include scattering and reflection as well as magnetic field structure in the source region in the case of non-thermal radiation – such as synchrotron emission. The degree of polarisation and the angle of polarisation constrains the geometry of the local magnetic field – knowledge of which is crucial to increasing our understanding of GRBs, AGNs, CVs and isolated neutron stars, including pulsars. Circular polarisation gives us information about magnetic fields.

Stokes' polarimetry is a powerful technique, used in the laboratory to measure the properties of scattering surfaces and birefringent materials, and in astronomy to map out magnetic fields (see, for example, "Stokes Imaging of the Acretion Region in Magnetic Cataclysmic Variables - II V347 Pav", S.B.Potter, P.J.Hakala, Mark Cropper, MNRAS, 315, 423-430, 2000). Up to now Stokes’ photo-polarimetry has been limited to cases where there is adequate light, and slow variation. In learning how to build GaSP we will be breaking new ground because (a) the high speed requirement rules out rotating components, (b) the high speed requirement (and consequent lack of photons) necessitates a high throughput and an extremely wide bandwidth – ruling out modulated components (which are very chromatic), and linear dichroic filters, etc., and (c) the high speed necessitates the use of a photon-counting detector.

The term high speed, describing the proposed instrument, is, of course, a relative one and depends upon the context. A bandwidth of 10 kHz would not be described as high speed for some tasks in instrumentation, but to measure the Stokes’ vector with this bandwidth is very challenging indeed, particularly for faint sources and might justifiably be described as “high speed”. An instrument capable of doing this will find many applications as the next generations of 10-20m diameter and 30-100m diameter telescopes will provide the photon fluxes needed to investigate many more objects, and for applications in other areas of science.

Investigation of Short Time Variability of the Stokes’ Vector in Pulsars, CVs, and GRBs

Pulsars

Most neutron stars are formed as one of the end points in the evolution of a massive star. When a large star (one with a mass > 10 solar masses) exhausts its nuclear fuel it undergoes core collapse that leads to a supernova explosion. During this explosion the central core is compressed until its density approaches that of the atomic nucleus at this point it can be said to be a neutron star. If at this stage it is of sufficient mass it should collapse further and form a low mass black hole. Isolated neutron stars are normally observed as radio pulsars. The preferred theory to describe their emission assumes that the radio pulses originate from coherent interactions between the high-energy plasma and the strong magnetic field that surrounds the pulsar and that the high energy emission from the infra-red to gamma-rays results from processes such incoherent synchrotron. From the asymmetries in the production process we expect this radiation to be polarised. Furthermore as the pulsars rotate with periods ranging from a few milliseconds to a few seconds we require detectors that are sensitive at short time scales and to polarisation levels of <1%. In the radio this is a relatively straightforward process, but in the higher energy regime it is really only in the optical where significant observations can be made with currently available technology. One of the problems with pulsars studies has been our inability to determine the location of the emission zone. The polarisation gives a good estimate of the relative orientation of the observer and the local magnetic field. A possible solution to the problem can come from a mix of polarisation studies of individual and coherently summed optical pulses and detailed geometric models (see O’ Connor, PhD thesis, NUI, Galway 2004 and O’ Connor et al (2005) submitted to MNRAS).

To extend this work we need the following

i)good average polarisation measurements throughout the pulsar profile at a level better than 0.5% based upon summed profiles

ii)observations of the polarisation of individual optical pulses during giant radio pulse events (see for example Shearer et al, Science, 301, 493(2003))

iii)detailed geometrical models to combine the magnetic field structure and plasma density with

For studies of pulsars we require a polarimeter that instantaneously measures all of the Stokes parameters and not the time-averaged polarisation, which most systems determine. The same can be said for observations of stochastic variability – e.g. CVs where the fluctuations in the local plasma during flares and flickering events will generate short-lived local magnetic fields that can cause variations in the polarisation. Here the polarisation observations are measuring both the field strength and indirectly the density of the plasma.

Gamma-Ray Bursts

There are a number of possible explanations to the phenomena of gamma-ray bursts. To explain initial fluctuations on time scales of milliseconds to seconds requires compact objects, and neutron stars, either through coalescence or as part of their formation are normally part of the model. In both of these scenarios the emission is likely to be in the form of an ultra-relativistic jet. The association of a supernova with GRB 030329 (Hjorth et al, 423, 847 (2003)) for example indicates that at least some GRBs are associated with a supernova event. Studies of the polarisation of the early light curve of a GRB will give information about the evolution of the jet as it ploughs into the local ISM. The polarisation comes in part from inhomogeneities in the magnetic field as the strong magnetic field around the neutron star breaks up or from dynamically created fields within the fireball (Lyutikov, astro-ph/0409489). (Greiner et al (astro-ph/0312089) showed that polarisation was measurable in the range 1-3% and consistent with turbulent behaviour at timescales of hours. Of interest will be what is the minimum timescale observable with our proposed instrument. We will be sensitive to polarisation variations of <1% using a 10m telescope (say SALT) at time scales of 10 second for a 19th magnitude optical afterglow. From this we would be able to follow the evolution of the polarisation and hence the evolution of the fireball or jet within a turbulent magnetic field.

Cataclysmic Variables

Cataclysmic Variables are a class of binary system where a main sequence star accretes matter onto an evolved companion. The companion is normally a white dwarf. The orbital period of the system ranges from several tens of minutes to hours. The rotational period of the white dwarf will of the order of 100 seconds. The systems are characterised by turbulent flow within the accretion disk that are modified by the reasonably strong magnetic fields (>104 G) around the white dwarf to a few hundred Gauss within the disk. Our proposed system will be sensitive to both studies of the white dwarf surface at time resolutions of 100s milliseconds to short-time (<1µs) stochastic variability with the accretion disk. As with other studies polarisation gives information related to the magnetic field – its variable geometry, lifetime and strength. When this is combined with Doppler tomography to measure the physical structure of the accretion disk and the associated magnetic field strength and orientation.

The Stokes’ Vector of the Crab Pulsar

We propose to measure the Stokes' vector for the Crab pulsar for individual pulses to ~100μs.

A small number of pulsars exhibit a giant radio pulse phenomena where theluminosity of the pulsar dramatically increase for one pulse. This happens at random but is a significant event with radio brightness temperatures in approaching of 1040K (Soglasnov et al, ApJ, 616, 439 (2004)).The origin of these pulses, which have widths down to a few nanoseconds, is unknown but is likely to reflect some form of plasma instability or magnetic field pinching – but the radiation must be coming from some coherent source. The physical size of the emission region is of the order of metres. The Galway Group observed a slight optical enhancement during GRP events from the Crab Pulsar (Shearer, Redfern, et al, Science, 301, 493, (2003)). These observations provided the first correlation between the strength of pulsar radio emission and the optical flux – indicating at some level the processes or emissions zones are linked. We need more observations to establish this correlation. We are interested in studying the polarization of the optical flux during GRP events as an indicator of the local magnetic field geometry. As this requires that the optical pulses are selected off-line for comparison with radio GRP times we require the ability to measure instantaneously all Stokes’ parameters so that we can measure the polarization sweep through an individual pulse. No currently available instrument is capable of these measurements.

How will the question be answered? [Describe the experimental or theoretical methodology, plus a brief project management plan, milestones and expected output.]

We will use an investigation of the polarisation in individual pulses in the Crab Pulsar as a demonstrator of GaSP. In order to address one half of the question - what is the magnetic field distribution in the Crab pulsar during giant radio pulses? - it will be necessary to design and build a verify a unique optical Stokes' polarimeter. This forms the complementary part of the question - how does one do this?

Development of GaSP

The required properties of GaSP are defined by the demonstration problem.

The Crab pulse period is ~33 ms, having pulses ~1 ms wide. The source is bright – figure (below) shows a train of 10 individual pulses obtained by our TRIFFID camera using the Russian 6m Bolshoi Telescope in 2003, using a photon-counting photodiode detector. The polarimetric accuracy (assuming <=100% efficiency) to be achieved may be extrapolated (from Hofman et. al. 2002, Design Study for the PEPSI Polarimeter for the LBT) - 10% in 1ms at 6m diameter and 4% at 11m diameter, and hence 1% at 6m diameter by the co-addition of >100 optical pulses selected by coincidence with giant radio pulses.

  • High DQE detectors must be used
  • Linear dichroic filters, and other absorbing filters cannot be used
  • An extremely broad bandwidth is necessitated – essentially as broad as is possible within the constraints of detector cutoffs and the achromatism of optical components - to maximise the signal from a flat spectrum source. Modulated components (such as ferroelectric liquid crystal retarders) are intrinsically chromatic and cannot be used.

The optical pulses which we wish to investigate are those which coincide with the "giant radio pulses", which occur randomly. The usual form of polarimeter simply will not work - see, for example, "Optical Pulse Phased Polarimetry of PSR 0656+14", B.Kern et. al., Ap.J., 597, 1049-1058, 2003, in which a linear dichroic filter was slowly rotated, (so that there was actually no measurement of Stokes' V at all) and in any case different phases of the repetitive waveform were constructed by sampling. Individual random pulses must be observed so the polarimeter needs an intrinsic high-speed time response. This means:

  • Rotating components cannot be used within the required timescale (100 μs).
  • A photon counting detector, and a time resolution of at least 100 μs must be used. This rules out conventional CCDs.

We have identified in the literature, an unusual, but rather suitable polarimeter design. ("Broadband Division of Amplitude Polarimeter Based On Uncoated Prisms", E.Compain, B.Drevillon, Appl.Opt., 37#25, 5938, 1998) Figure 1 shows a diagram of the arrangement. They describe a laboratory instrument with excellent precision (<1%) over the spectral range 400-2000nm. The division of amplitude is due to reflection at an uncoated dielectric surface. Intrinsically, this can be achromatic over a broad spectral range - limited only by dispersion within the dielectric. Incoming light is divided into 2 beams by reflection from the top surface of the prism. The internal beam experiences 2 internal reflections before being partially reflected and partly absorbed on the bottom surface. The 2 external beams are further beamsplit by polarising beamsplitters to produce the required 4 beams. The 2 internal reflections act as a Fresnel rhomb-type retarder to allow the Stokes' vector to be obtained by inversion of the output vector. In the original design the input beam S(t) is a single accurately collimated beam.

Starting in September 2004, we have been conducting an intensive theoretical study, modellisation and laboratory investigation of this Stokes’ polarimeter design in collaboration with the original authors (from the Ecole Polytechnique, Paliseau, France). This will be completed before the start of this project.

We have shown (Golden et al, A&A, 363, p617, 2000) that aperture photometry of faint sources in the presence of background and variable atmospheric properties (seeing) is best achieved, in fact, by using an imaging detector capable of resolving a small region encompassing both the source (an aperture defined in software), and a comparison background region, under all conditions of seeing, telescope wobble, etc., rather than a physical aperture The reasons for this are as follows:

  • One is able, post-exposure, to determine the, variable, optimum aperture size to maximise the signal-to-noise adaptively during the observation.
  • One is able, post-exposure, to track movements of the aperture centroid (due to seeing and also wobble) and to select from the data stream only photons falling within this aperture.
  • A physical (rather than software) aperture cannot be optimised and must be sufficiently large to ensure that the target is easily acquired, and that 100% of the target photons are intercepted - otherwise, seeing-induced variations in brightness will occur, which are damaging to high precision time series analysis. A software-defined, adaptive aperture can therefore be smaller than a fixed, physical aperture, and can consistently give optimum signal to noise.
  • One is able to select, post-exposure, background photons from a comparable region close to the adaptive aperture. This is always essential in order to achieve accurate photometry, but is even more important when background polarisation may be variable across the field.

Our (optimised) DOAP has the required properties for GaSP, namely,

  • Wide bandwidth, at least as wide as available detector bandwidths (500-900 nm for a GaAs photocathode).
  • Static components, and division of almost 100% of the light into four, equal intensity, individually detected, external beams.
  • Minimisation of the effects of photon noise on the inversion of the output vector.
  • The ability to invert the output vector with precision for a small range of input angles for S(t) corresponding to collimated beams from an image region of 10”-15” on the sky – 2-30 in the collimated beam - depending upon the telescope used. This will enable the polarisation vector across a small image field to be determined.
  • The ability to re-image the four output beams into small sub-images on a single imaging photon-counting detector.

The choice of detector is crucial for this project. We have, for two years, been in collaboration with the Experimental Astrophysics Group in the Space Sciences Laboratory of the University of California, Berkeley (Professor Oswald Siegmund, and Dr Barry Walsh). This has resulted in a successful collaborative proposal to NSF, namely, “The Development of A Novel Photon Counting GaAs Detector for Sub-millisecond Astronomy”, in which we have the responsibility to test the new detector using our current high time resolution photometer – called NGTriffid, developed under the Enterprise Ireland Basic Research Scheme. As a consequence, we propose to utilise the detector type being developed under this grant, which will become available during the second year of this proposal. The tube and electronic units will be purchased under the supervision of SSL, Berkeley, and they will supply all software free of charge.