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(assuming [MATH] constant). 3.5.3 The shortest wavelengths dominated by synchrotron emission Is the emission at [MATH] in RQ AGN dominated by synchrotron emission? The FIR emission of RQ AGN is dominated by dust (e.g. Sanders et al. 1989), and one needs to go to long enough wavelengths to make sure that dust contaminat... |
[MATH] . The coldest dust is found at [MATH] (e.g. Hass et al. 2000), and the dust emission drops steeply at [MATH] with a spectral slope for [MATH] of [MATH] , where [MATH] is the characteristic dust absorption opacity index (e.g. Draine & Li 2007). The observed mean SED of RQ AGN indeed shows a sharp break with a [MA... |
3.5.4 Constraints from the brightness temperature An independent constraint on the minimum possible size of a synchrotron emitting region can be obtained using the source brightness temperature [MATH] , given by |
[EQUATION] where [MATH] is the angular diameter of the source. Recasting [MATH] in terms of luminosity and emitting radius, we get |
[EQUATION] To avoid synchrotron self-Compton as the dominant cooling mechanism requires [MATH] K (Kellermann & Pauliny-Toth 1969). In addition, Readhead (1994) finds that equipartition between the electron energy density and the magnetic energy density is obtained for |
[MATH] K. Thus, the lower limits of [MATH] at [MATH] in [MATH] objects imply [MATH] that is just below the Readhead limit of [MATH] |
When the source is optically thick, [MATH] can be expressed in a simple form, independent of [MATH] and [MATH] [EQUATION] which for [MATH] gives |
[EQUATION] Thus, equipartition between the electrons and the [MATH] field is obtained if the electrons emitting at [MATH] are subject to |
[MATH] , and synchrotron self-Compton losses dominate if [MATH] 3.5.5 Observational evidence for extended radio emission in AGN, ULXs, and GBHs |
We conclude that the 5 GHz emission in AGN must be coming from a “radio-sphere” which is [MATH] times larger than the 1 keV emitting region. In cool coronally active stars, interferometric mas scale radio imaging reveal that transient emission originates in compact cores associated with flare regions, but quiescent rad... |
The extended pc scale radio emission seen in nearby RQ Seyferts appears to originate in non-relativistic and relatively poorly collimated plasma flows (e.g. Ulvestad et al. 1999; Middelberg et al. 2004), which may correspond to CMEs from the accretion disk. These outflows can be traced to kpc scale in nearby AGN (Galli... |
It is interesting to note that in ULXs the radio emission also tends to be offset from the X-ray source, and is marginally resolved (Soria et al. 2006), indicating it is coming from a more extended scale compared to the X-ray emission, and may thus also be explained by emission from CMEs. However, the physical scale of... |
[MATH] , and thus if the coronal mechanisms is valid, higher quality observations should reveal that most of the radio flux originates from a compact core which overlaps with the X-ray position. |
Spatially resolved jet-like emission in the radio is seen in Cygnus X-1 (Stirling et al. 2001) and in GRS 1915+105 (Dhawan et al. 2000). However, Heinz (2006) finds that the standard relativistic jet models for Cygnus X-1 appears to be inconsistent with the evidence for interaction with the surrounding ISM (Gallo et al... |
Gallo et al. (2003) suggested that the radio emitting outflows in GBHs in the low hard state are only mildly relativistic (cf. Heinz & Merloni 2004). Clearly, a relatively slow and weakly collimated jet may be just an alternative name for a CME, in particular when taken together with the suggestion that such a jet is f... |
3.6 [MATH] and [MATH] Below we derive limits on the value of [MATH] and [MATH] of the emitting electrons within the radio-sphere based on the observed and predicted variability timescales. We also provide constraints on these properties within the much more compact X-ray emitting corona. |
3.6.1 The radio-sphere Barvainis et al. (2005) and Anderson & Ulvestad (2005) studied the variability timescales at 8.5 GHz in luminous ( [MATH] ) RQ PG quasars, and in very low luminosity ( [MATH] ) AGN, respectively. The shortest variability timescale in luminous AGN was found to be |
[MATH] s, and [MATH] s in the very low luminosity AGN. These timescales provide upper limits on the size of the radio emission region, |
[MATH] , based on the indications that the emission is not relativistically beamed (section 3.1). Interestingly, these upper limits are within a factor of [MATH] of the minimum size predicted for optically thick synchrotron emission (eq.22), suggesting that the synchrotron source is indeed close to being optically thic... |
The time for an electron with an energy [MATH] to loose half its energy through synchrotron emission is [EQUATION] and the peak of the synchrotron emission occurs at |
[EQUATION] (RL). If indeed one observes at the peak frequency, these two simple relations provide a lower limit on [MATH] and an upper limit on |
[MATH] from the observed cooling timescale, [MATH] independently of any other properties of the emitting source, except the assumption that synchrotron cooling dominates other cooling processes. Specifically, assuming [MATH] gives |
[EQUATION] and [EQUATION] (for [MATH] ). Thus, for the luminous PG quasars, where [MATH] at 8.5 GHz, we find that the emission originates in electrons with |
[MATH] , i.e [MATH] MeV, which reside in a [MATH] Gauss field. In very low luminosity AGN [MATH] s, implying [MATH] and [MATH] Gauss. |
The time for a relativistic electron to lose half its energy through Compton scattering is given by [EQUATION] (RL) where [MATH] is the Thomson electron scattering cross section, i.e. |
[EQUATION] The requirement that [MATH] implies that Compton cooling will be fast enough for electrons having [EQUATION] In luminous [MATH] quasars, where the 8.5 GHz radio-sphere occurs at say |
[MATH] (eq.22), Compton cooling will be fast enough for [MATH] , relevant for all synchrotron emitting electrons at 8.5 GHz (eq.30). However, in the lowest luminosity AGN, say where [MATH] and [MATH] Compton cooling will be fast enough only for [MATH] , much higher than the likely [MATH] values of the 8.5 GHz emitting ... |
The relative importance of Compton vs. synchrotron cooling can also be estimated directly by comparing [MATH] and [MATH] In luminous quasars the requirement that [MATH] led to [MATH] (see above), where synchrotron self-absorption implies |
[MATH] (eq.19). For equipartition [MATH] (eq.21) at this radius, and thus Compton cooling can be comparable or faster than the synchrotron cooling if [MATH] This Compton cooling will not be spectrally detectable. Compton scattered photons peak at [MATH] , which for |
[MATH] and [MATH] eV (the UV bump peak) occurs at [MATH] 100-200 keV. This luminosity of the X-ray Compton peak will be only of the order of the radio luminosity (as [MATH] and [MATH] |
are not dramatically different), which is lower by a few orders of magnitude from the observed X-ray emission. In the lowest luminosity AGN ( [MATH] ) the 8.5 GHz radio-sphere, for [MATH] , is located at |
[MATH] , where [MATH] Gauss, and since [MATH] synchrotron cooling likely dominates. Adiabatic cooling occurs on the sound crossing time, [MATH] which must be longer than the light crossing time, [MATH] , and thus likely is too long to explain [MATH] . Introducing clumping will reduce [MATH] |
to [MATH] , where [MATH] is the size of each clump. However, the extent of the emitting region will now have to be much larger than the size of a monolithic emitting region (eq.19), since the observed luminosity density provides a lower limit on the total emitting surface area. If this area is comprised of small clumps... |
The energy loss timescale of relativistic electrons through elastic Coulomb collisions is [EQUATION] where [MATH] is the ambient gas number density (Petrosian 1985). To obtain |
[MATH] requires [MATH] cm -3 in luminous quasars, and [MATH] cm -3 in the lowest luminosity AGN. The implied column in both cases is [MATH] cm -2 , which becomes optically thick to electron scattering, and therefore excluded as it would obscure the AGN. However, we cannot exclude such high densities if the synchrotron ... |
The free-free cooling time [EQUATION] (Petrosian 1985) is [MATH] times longer than [MATH] , and is therefore generally insignificant for cooling mildly relativistic electrons. Blundell & Kuncic (2007) suggested that the radio emission of RQQs is entirely due to thermal free-free emission of hot ( [MATH] K) plasma and n... |
[EQUATION] where [MATH] are the gaunt factors and the weak logarithmic dependence of [MATH] on [MATH] has been neglected. This ratio increases with [MATH] and already overestimates by a few orders of magnitude the observed ratio of |
[EQUATION] where we have used [MATH] (§1) and [MATH] (eq. 1); Not to mention the small contribution free-free emission must have to [MATH] given the observed X-ray spectral slope of AGN, which is consistent with Comptonization. |
To summarize, Compton cooling is effective only in luminous AGN, Coulomb losses are effective only in dense gas, adiabatic losses are likely not fast enough, and free-free cooling of the relativistic electrons is insignificant. Synchrotron cooling is a plausible mechanism, which implies [MATH] Gauss for [MATH] seen in ... |
An additional important conclusion from the fact that [MATH] is that the electrons must be accelerated locally, as the time it would take them to reach the radio-sphere from the nucleus is likely to be much longer than the light crossing time. Such local acceleration is observed in solar CMEs, presumably through the in... |
3.6.2 The X-ray corona As noted above, the [MATH] emission can come directly from the compact coronal region, having [MATH] which produces the rapidly variable soft X-ray ( [MATH] keV) emission. Extrapolating |
[MATH] assuming a flat spectral slope [MATH] ) from 5 GHz to say 200 GHz, implies [MATH] , or a total radio to X-ray cooling ratio of |
[MATH] from the coronal region. What constraints can be obtained from this ratio on the coronal heating mechanisms? In the magnetically heated corona paradigm magnetic energy is converted to kinetic energy of fast electrons through reconnection, the fast electrons dissipate their energy and heat the corona, and the cor... |
What is the required minimum value for [MATH] Assuming a uniform spherical shell with a radius [MATH] , within which reconnection propagates at a velocity [MATH] , leading to complete annihilation of [MATH] , yields a maximal luminosity of |
[EQUATION] The equipartition field ( [MATH] ) at a distance [MATH] obeys [MATH] . Combining both expressions gives [MATH] Since both [MATH] and [MATH] are likely [MATH] , and only a fraction of [MATH] is annihilated, we get that in a magnetically heated corona [MATH] |
Can the power-law X-ray emission be produced directly by the fast electrons through Compton scattering? To produce the [MATH] ratio requires [MATH] , however above we concluded that [MATH] , and thus the observed X-ray emission cannot originate from Compton scattering by the fast electrons which produce the mm radio em... |
How do the fast electrons loose 99.9% of their energy to the background gas? (to maintain [MATH] ). The remaining mechanism is Coulomb collisions. The synchrotron/Coulomb cooling rate ratio is |
[MATH] , and thus if the corona is non-homogeneous, synchrotron losses will be largest for the highest [MATH] electrons, at the regions with the highest [MATH] and lowest [MATH] , and Coulomb losses will dominate for the lower [MATH] electrons, in particular at regions with high [MATH] and low [MATH] . To obtain rough ... |
[EQUATION] which gives [EQUATION] For [MATH] and say [MATH] , we get [EQUATION] which together with the requirement [MATH] gives |
[EQUATION] For example, for plausible values of [MATH] Gauss (e.g. [MATH] extrapolation from the radio-sphere in luminous AGN), [MATH] , we get [MATH] cm -3 , i.e rather high densities which are likely to occur close to the surface of the accretion disk. In the above estimate we assumed that the plasma is optically thi... |
[MATH] Interestingly, the column heated by coulomb collisions is [EQUATION] or [EQUATION] Thus, for plausible [MATH] of a few to a few tens for the fast electrons, the collisionaly heated pathlength along the direction of [MATH] has [MATH] , which would lead to a significant Compton scattering optical depth for the pho... |
[MATH] times larger). This implies that [MATH] , or a coronal covering factor [MATH] for [MATH] . Thus, the corona may be confined to small “active” regions, presumably reconnecting coronal loops, as seen in solar flare activity (see also Haardt et al. 1994; Stern et al. 1995). The scarce covering of the accretion disk... |
Will the corona cool mostly by Compton scattering? Another potentially significant cooling mechanism is thermal emission (essentially pure free-free at this temperature), where the total cooling per unit volume is |
[EQUATION] where [MATH] K (Fig.7.1 in Dopita & Sutherland 2003), implying an electron cooling time of [EQUATION] (note that this is somewhat shorter than [MATH] for relativistic electrons). The Compton cooling time of the thermal electrons is estimated as follows. The mean energy lost by a thermal electron upon scatter... |
[EQUATION] assuming [MATH] (RL). The total Compton cooling per unit volume is then [EQUATION] where [MATH] is the incident (mono directional) flux density, or |
[EQUATION] where [MATH] . The Compton cooling time of the thermal electrons is then [EQUATION] which gives the following simple expression |
[EQUATION] where [MATH] is the underlying flux of the (assumed infinite slab) disk, and [MATH] K. Compton cooling dominates when [MATH] i.e. at |
[EQUATION] which is interestingly close to the lower limit on [MATH] from the requirement that the fast electrons dump 99.9% of their energy as heat in the coronal gas. |
3.6.3 A chromosphere? An additional potential implication, based on solar analogy, is the presence of a transition “chromospheric” layer between the corona and the UV emitting photosphere. Such a layer can be heated by the smaller fraction of faster electrons (say [MATH] ), or ions, which deposit their energy at a larg... |
by the following relation [EQUATION] where the cooling function is [MATH] erg s -1 cm at [MATH] (Sutherland & Dopita 1993), the size of the X-ray coronal region in luminous AGN |
[MATH] cm, the chromospheric column [MATH] cm -2 (for [MATH] ), [MATH] is the coronal covering fraction, and [MATH] erg s -1 , assuming the soft X-ray feature carries |
[MATH] % of the X-ray luminosity, which is [MATH] % of the bolometric luminosity in a luminous [MATH] erg s -1 AGN. These values give |
[MATH] cm -3 , which is comparable to the coronal density inferred above (the apparent lack of a large density gradient between the corona and chromosphere is consistent with a disk which is hydrostatically balanced by radiation pressure, rather than by a gas pressure gradient). The major difference in the microphysics... |
3.6.4 Correlated X-ray and mm variability Additional constraints on the typical [MATH] and [MATH] within the corona can be obtained from measurements of the mm emission variability timescale, as estimated above using the 5 GHz emission variability. In particular, for the 200 GHz emission in luminous AGN to vary on a co... |
to generate the observed [MATH] will be higher, and may reach values of [MATH] Gauss seen in stellar coronally active regions. This is also the expected value of [MATH] if the coronal loops are driven by buoyancy out of the disk (as seen in the Sun) from regions at |
[MATH] K dominated by radiation pressure. The 200 GHz emitting electrons at [MATH] Gauss have [MATH] , implying a cooling time of [MATH] s. Thus, the observed mm emission can vary rapidly, and the observed variability will be dominated by the light crossing time effects over the coronally active regions. |
Current mm arrays are generally not sensitive enough to detect RQ AGN, which are mostly mJy sources. However, more sensitive future mm arrays, in particular ALMA, will be able to detect the predicted rapid (minutes to hours) mm variability at the sub mJy level in RQ AGN. Such studies, in particular with simultaneous X-... |
Conclusions We find that RQ AGN lie on the Güdel-Benz relation, [MATH] found for coronally active stars. Since the X-ray emission in AGN most likely originates from a hot corona, and the corona is likely to be magnetically heated, it is natural to associate the radio emission in RQ AGN with a coronal origin as well. |
The “coronal paradigm” for the radio emission implies a very compact source, which is synchrotron self-absorbed at the GHz range. This implies that a compact flat spectrum source should generally be present in RQ AGN. Self-absorption will become negligible at mm wavelengths, and this emission should originate from the ... |
Despite the factor of [MATH] difference in [MATH] and [MATH] between AGN and coronally active stars, the estimated values of [MATH] in the active regions of the two systems are comparable ( [MATH] Gauss), which may imply similar underlying microphysics in both coronae. The physical mechanism underlying the |
[MATH] ratio in these coronae remains a puzzle. Applying the stellar analogy to the extended radio emission, we suggest that it originates from coronal mass ejections. This emission mechanism differrs from the alternative jet interpretation in that the outflow is relatively slow, and is not well confined, as suggested ... |
There are two additional populations of active radio and X-ray emitting objects, intermediate between stars and AGN. ULXs, where the four objects with radio and X-ray data also fall close to the Güdel-Benz relation, and overlap with the position of NGC 4395, the lowest luminosity type 1 AGN. This is consistent with ULX... |
We thank M. Güdel for providing data in electronic form and A. Merloni for the fundamental-plane relation in his radio-quiet sub-sample. We thank R. Antonucci and S. Jester for valuable comments on the manuscript. We thank the referee for many useful comments that helped us improve the manuscript. This research was sup... |
# Source: arxiv 0808.0652 # Title: Fresnel interferometric arrays for space-based imaging: testbed results # Sections: all # Downloaded: 2026-03-02T07:59:13.721004+00:00 |
\authorinfo Authors e-mails can be built using the following syntax: ”firstname.lastname@ast.obs-mip.fr” Fresnel interferometric arrays for space-based imaging: testbed results |
Abstract This paper presents the results of a Fresnel Interferometric Array testbed. This new concept of imager involves diffraction focussing by a thin foil, in which many thousands of punched subapertures form a pattern related to a Fresnel zone plate. This kind of array is intended for use in space, as a way to real... |
The laboratory test results presented here are obtained with an 8 centimeter side orthogonal array, yielding a 23 meter focal length at 600 nm wavelength. The primary array and the focal optics have been designed and assembled in our lab. This system forms an achromatic image. Test targets of various shapes, sizes, dyn... |
keywords: Orthogonal Fresnel zone plates, interferometric device, achromatism, field-resolution ratio INTRODUCTION Fresnel arrays are interferometric devices involving many hundreds or thousands of ”basic” subapertures: mere holes punched in a large and thin foil. For each of these individual subapertures, diffraction ... |
In our approach, the orthogonal geometry has been preferred to Soret’s concentric rings for two main reasons: its allowance of vacuum rather than a transparent material for transmissive zones, and the higher dynamic range allowed in most of the image field. This optical scheme strongly reduces manufacturing and positio... |
) . An orthogonal Fresnel array of side [MATH] involving [MATH] Fresnel zones results in a focal length [MATH] at its first order of interference, which can be written |
[EQUATION] The unavoidable chromaticity of this kind of focussing element can be corrected using an optical scheme based on Schupmann studies |
, and emerging from the chromatic correction of holograms developed by Faklis & Morris in 1989 . The principle is to place in a pupil plane an optical device whose chromatic dispersion is opposite to that of the Fresnel array. That means in our case to use a diffractive optical device used at the order -1: a diverging ... |
Following [Koechlin et al 2004 ] and [Serre et al 2005 ] , and thanks to a CNES R&T funding, we developed in the past two years at Université Paul Sabatier a Fresnel Interferometric Array breadboard testbed. The main focussing element is an 8 cm side square array and it is associated to optimized focal optics, leading ... |
CONSTITUTIVE ELEMENTS 2.1 Fresnel interferometric array Our Fresnel interferometric array is an 8 cm side orthogonal array, 58 Fresnel zones, i.e. 26680 subapertures, carved by UV laser in an 80 microns thick stainless steal foil. The resulting focal length is 23m at [MATH] nm. In order to allow mechanical resistance o... |
2.2 Focal optics The focal optics are the direct application of the chromatic correction scheme presented in fig. . The elements are (see fig. ): |
- a field lens: in fact a Maksutov telescope associated to a 37mm diameter diaphragm, used off-axis to avoid central obturation; |
- pupil optics: a 116 zones diverging Fresnel lens, carved by ionic engraving using successive masks on a fused silica flat window. The useful diameter is 16 mm, which corresponds to the diagonal of the orthogonal Fresnel array imaged by the field optics. The five central zones of this lens can be seen for illustration... |
] ( submitted ). The individual grooves are 1.37 microns in depth, their different profiles are discretized with 128 depth levels, allowing transmission into order [MATH] better than 90% through a [MATH] spectral bandwidth. |
- an achromatic doublet allows the formation of a real (i.e. non virtual) image on a B&W CCD camera. An eyepiece can also be placed for direct control. |
A narrow cross mask allowing the elimination of order zero of the Fresnel array is placed at the focal plane of the Maksutov telescope. |
2.3 Source simulation As the breadboard testbed is situated in a clean room, we need artificial sources. They are not really constitutive elements of the Fresnel interferometric imager, but are necessary to evaluate it. We disposed different types of sources in the focal plane of a parabolic mirror, collimating them al... |
Measurements 3.1 Angular resolution and chromatic correction The theoretical angular resolution of the whole testbed is [MATH] asec (at [MATH] nm). In order to evaluate the effective resolution, we have used a pinhole (0.5 asec diameter) as a source, illuminated by halogen light and spectral filters centered on 550, 60... |
3.2 Imaging capabilities One can see on fig. an image obtained using the breadbord testbed: the source is a ”galaxy” target carved in a stainless steal foil. The ”galaxy” dimension from limb to limb is 450 microns, that is 72 arc seconds as seen from the Fresnel array. The illuminating source is a halogen lamp, whose s... |
3.3 PSF modeling and rejection rate results We have developed for the Fresnel interferometric array concept a plane-to-plane propagation software based on Fresnel diffraction algorithms, and have applied it to our breadboard testbed. The algorithms take into account the main orthogonal array, achromatic field optics, a... |
In order to evaluate the rejection rate of the PSF, two images are presently necessary: a first one is acquired to measure the unsaturated level of the central peak, and then a second one is acquired with an exposure time multiplied 1000x times. Defining the rejection rate as the mean level of the ”clean” field of the ... |
conclusion We have presented in this paper the first results of an orthogonal Fresnel interferometric array breadboard testbed. We are able to confirm the efficiency of the achromatisation scheme retained, as well as the diffraction-limited performances and the ”wide” field imaging capabilities. The measured rejection ... |
The next steps using this testbed are to evaluate rejection rates with two sources of different luminosity in the same field, to test different manufacturing processes for the blazed diverging Fresnel zone lens, and to assess Fresnel arrays subaperture shapes and layout, allowing higher transmission rates and dynamic r... |
In the next few years, on one hand members of our team (and we hope new people !) aim to evaluate a 2 [MATH] generation of ground-based testbed: its main evolutions will be an increase in dimensions (typically 20 cm side for the Fresnel array), higher number of Fresnel zones, and last but not least: real sky observatio... |
This work was supported by Université Paul Sabatier Toulouse III, CNRS, CNES, Thalès Alenia Space and the Fonds Social Européen. |
# Source: arxiv 0808.0692 # Title: Proper Motions and Brightness Variations of Nonthermal X-ray Filaments in the Cassiopeia A Supernova Remnant # Sections: all # Downloaded: 2026-03-02T07:59:14.889764+00:00 |
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