RADIOASTRON OBSERVATIONS OF THE QUASAR 3C273: A CHALLENGE TO THE BRIGHTNESS TEMPERATURE LIMIT

The discovery, half a century ago, of quasar radio flux density variability on timescales as short as months (Sholomitsky 1965a, 1965b; Dent 1965) indicated linear sizes as small as light months, corresponding to angular dimensions of the order of one mas or less and suggesting extraordinarily high apparent brightness temperatures (Pauliny-Toth & Kellermann 1966). The subsequent discovery, using with very long baseline interferometry (VLBI), of superluminal motion and relativistic beaming with Doppler factors of δ ∼ 10 (e.g., Lister et al. 2013) appeared to explain the extreme values of the apparent size and brightness temperature inferred from intrinsic variability (Kellermann & Pauliny-Toth 1981). For incoherent synchrotron emission of relativistic electrons, in the absence of relativistic boosting, the maximum brightness temperature is limited by inverse Compton cooling to about 10^11.5 K (Kellermann & Pauliny-Toth 1969; Readhead 1994) or 5 × 10¹⁰ K if there is equilibrium between the energy in particles and magnetic fields (Readhead 1994). Relativistic boosting can increase the observed brightness temperature, T_obs = δ × T_int by the Doppler factor $\delta ={(1-{\beta }^{2})}^{1/2}{(1-\beta \mathrm{cos}\varphi )}^{-1},$ where T_int is the intrinsic brightness temperature, $\beta =v/c$ is the jet speed in units of the speed of light, and φ is the angle between the jet velocity vector and the line of sight. The apparent jet speed ${\beta }_{\mathrm{app}}=\beta \mathrm{sin}\varphi {(1-\beta \mathrm{cos}\varphi )}^{-1}$.

However, observations of interstellar scintillation in many flat-spectrum sources (e.g., Lovell et al. 2008), reflecting very small angular sizes and very high brightness temperatures, as well as rapidly varying TeV emission from some quasars (Hinton & Hofmann 2009), suggested either much higher Doppler factors than those estimated from VLBI observations of quasar kinematics (Lister et al. 2013), or possibly a different emission mechanism than incoherent synchrotron radiation from relativistic electrons (e.g., Blandford & Königl 1979). Previous ground-based (Kovalev et al. 2005; Lee et al. 2008) and space-based (Frey et al. 2000; Tingay et al. 2001; Dodson et al. 2008) VLBI (SVLBI) observations are consistent with the expected small sizes and high observed brightness temperatures of quasars deduced from their intrinsic variability as well as with the limits discussed above. However, previous VLBI measurements could not attain the baseline length or angular resolution needed to address the question of high brightness temperature conclusively.

With the launch by the Russian Federal Space Agency of the RadioAstron Space Radio Telescope (SRT) on 2011 July 18, it is now possible to directly test the regime of extremely high apparent brightness temperatures. The "Spektr-R" satellite is in a nine-day highly elliptical orbit around the Earth with a variable apogee of up to 350,000 km. It carries a 10 m parabolic radio telescope and operates at 330 MHz (92 cm), 1.7 GHz (18 cm), 4.8 GHz (6.2 cm), and 22 GHz (1.3 cm) (Kardashev et al. 2013).

The quasar 3C 273 has a redshift of z = 0.158, is at a luminosity distance of 750 Mpc, and has been regularly imaged over the past four decades, including observations at 15 GHz with the Very Long Baseline Array (VLBA) as part of the MOJAVE survey (Lister et al. 2013). As seen in Figure 1, the jet rapidly becomes well resolved. However, the fringe amplitude remains near several jansky out to maximum ground baselines. This corresponds to the bright feature at the apparent base of the jet where the optical depth approaches unity. Previous brightness temperature estimates for the core of 3C 273 include 5 × 10¹¹ K from space-based (Dodson et al. 2008) and up to 6 × 10¹² K from ground-based (Kovalev et al. 2005) VLBI experiments.

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Here we report the results of space VLBI observations of 3C 273 at 1.3, 6.2, and 18 cm wavelengths on interferometer baselines from RadioAstron to the NRAO 100 m Robert C. Byrd Green Bank Telescope (GBT), the phased Karl G. Jansky Very Large Array (VLA), the 100 m Effelsberg radio telescope, and the 305 m Arecibo Observatory William E. Gordon Radio Telescope in the 2012 December–2013 February period. The projected interferometer baselines ranged up to 171,000 km and $7.6\times {10}^{9}\lambda$ (see Table 1 for details). We note that later RadioAstron observations of 3C 273 at 18, 6.2, and 1.3 cm up until the middle of 2015 have not delivered any detections for projected baselines longer than 1.1 Gλ. We adopt a cosmology with Ω_m = 0.27, Ω_Λ = 0.73, and ${H}_{o}=71\;\mathrm{km}\;{{\rm{s}}}^{-1}\;{\mathrm{Mpc}}^{-1}$ (Komatsu et al. 2009).

Table 1.  RadioAstron Ground-to-space Radio Interferometer Measurements of the Quasar 3C 273

λ	Epoch	GRT	ruv	P.A.	S/N	St	Sc	θ	Tb	${T}_{{\rm{b}},\mathrm{min}}$	${T}_{{\rm{b}},\mathrm{char}}$
(cm)			(103 km; Gλ)	(deg)		(Jy)	(mJy)	(μas)	(1012 K)	(1012 K)	(1012 K)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
1.3	2013 Feb 02	Gb, Y27	103; 7.6	−7	9.8	3.4	125 ± 22	26	14	5.3	12
6.2	2012 Dec 30	Ar, Ef	90; 1.45	10	18.6	4.3	125 ± 17	142	13	4.5	18
6.2	2013 Feb 02	Ar	103; 1.69	−8	11.6	4.3	123 ± 19	122	17	5.2	15
18	2013 Jan 08	Gb	157; 0.87	−32	8.9	5.0	42 ± 7	275	34	4.0	10
18	2013 Jan 25	Ar, Gb	171; 0.95	−38	12.0	5.0	52 ± 9	246	42	6.3	18

Note. (1) The wavelength of observation; (2) the date of observation shown as year-month-day; (3) the ground radio telescopes with which significant SVLBI fringes were detected (Ef: Effelsberg, Gb: the GBT, Y27: phased VLA, Ar: Arecibo); (4) the average projected interferometer baseline in the plane of the sky and in units of wavelength; (5) the position angle of the projected baseline; (6) the highest signal-to-noise ratio of fringe detection observed in a 9.5 minute integration; (7) estimated flux density of the core component (see the text for details); (8) the highest measured interferometric (fringe) amplitude with its rms error for the given observing segment, the error estimate includes the amplitude calibration uncertainty following Kovalev et al. (2014); (9) the estimated angular size of the observed structure, full width at half maximum for the assumed circular Gaussian brightness distribution; (10) brightness temperature in the source frame corresponding to the size given in column (8); (11 and 12) minimum and characteristic brightness temperature in the source frame obtained following the approach suggested by Lobanov (2015).

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Observations were made either in two 16 MHz wide IF channels for the orthogonal circular polarizations in a given frequency band, or simultaneously in two frequency bands with a single polarization in each band. The central frequencies of observations were: 1668.0 MHz (L-band), 4836.0 MHz (C-band), and 22236.0 MHz (K-band). For the SRT, after conversion to baseband, the four 16 MHz IF bands were sampled at the Nyquist rate with 1 bit sampling. Samplers and local oscillators were controlled by highly stable hydrogen clocks located at every antenna, including the SRT. The 128 Mbps data stream was transmitted to Earth over a 15 GHz downlink to the 22 m antenna located at the Pushchino Radio Astronomy Observatory near Moscow. After decoding, the data were stored and then sent over the network link to the Astro Space Center (ASC) in Moscow where they were cross-correlated with the data recorded with 2 bit sampling at Arecibo, Effelsberg, the GBT, or the VLA using both ASC-developed (Kardashev et al. 2013) and DiFX (Deller et al. 2011; Bruni et al. 2014) software correlators.

In a space VLBI system, where the accuracy of the orbit determination is limited and the uncertainty of the baseline vector and its time derivatives is large, the interferometric response needs to be searched over a wide range of trial delays, delay rates, and delay accelerations. Post-correlation data analysis was performed using the PIMA software package (Petrov et al. 2011) including fringe fitting with compensation for all three terms. Figure 2 shows a plot of fringe amplitude as a function of phase delay and fringe frequency for the SRT–GBT observations of 3C 273 at 22 GHz on 2013 February 2. After applying the initial residual delay of 17.7 μs, fringe rate offset of 2.45 Hz, and residual acceleration of less than 3 × 10⁻¹⁶ s/s⁻², the data were re-correlated so that the interferometric response appears close to the origin in Figure 2.

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The interferometer response shown in Figure 2, as well as the signal-to-noise ratio (S/N) values presented in Table 1, were integrated over 9.5 minutes. The probability of false detection for every measurement shown is estimated to be less than 10⁻¹². Extensive checks have shown that none of the maser-based local oscillator systems, either on the ground or on the spacecraft, limit the coherence over the 9.5-minute scan intervals. Interferometers with ground–ground baselines have coherence losses associated with random phase variations along the path through the atmosphere to both stations. Space-to-ground interferometers have coherence losses associated with propagation through the atmosphere to only one station, so the resulting coherence time using baselines to the SRT is longer than that typically achieved with ground–ground systems. Our analysis of many RadioAstron observations has shown that after applying a residual orbit acceleration term to the data, there are no significant coherence losses within a 9.5-minute integration at 6 and 18 cm in most experiments. A partial coherence loss occurs at 1.3 cm; it affects the fringe amplitudes and, consequently, S/N measured by the baseline-based fringe fitting (Table 1, column 6). The residual ground-based phase variations are risky to compensate in cases of degenerate ground-to-space telescope triangles with low S/N SVLBI baselines due to the possible overestimation of the RadioAstron fringe amplitude (see Martí-Vidal & Marcaide 2008 for details). Because of that, we have used 200 s integrations to estimate correlated flux densities shown in column (8) of Table 1 since coherence analysis of ground-based data has shown no significant losses over this time interval.

3.1. Brightness Temperature Estimates from Single-component Gaussian Models

3.2. Visibility-based Estimates of Brightness Temperature Limits

The highest brightness temperatures implied by our measurements are at 18 cm, where we estimate ${T}_{{\rm{b}}}\gt 4\times {10}^{13}\;{\rm{K}}$. At this wavelength, scatter broadening may be non-negligible, and estimates that account for the scatter broadening would be even higher. However, the recent discovery of refractive substructure in SgrA* (Gwinn et al. 2014) suggests that scattering in the turbulent interstellar medium can result in an overestimate of the correlated flux density on long Earth-space baselines with a corresponding overestimate of the apparent brightness temperature (Johnson & Gwinn 2015) at 18 cm. Even if this effect is present in our data, we underline that values up to 2 × 10¹³ K are revealed at shorter wavelengths, where scattering is weak and the effects of substructure are negligible. A detailed analysis of this effect is presented in an accompanying paper by Johnson et al. (2016), who estimate that T_b = 7 × 10¹² K at 18 cm. Thus, the inferred brightness temperatures are likely to be close to 10¹³ K at each of our observing wavelengths.

The apparent extreme brightness temperature in 3C 273 reported here is difficult to explain. VLBA monitoring of 3C 273 at 15 GHz indicates a maximum observed jet speed ${\beta }_{\mathrm{app}}\approx 15$c (Lister et al. 2013), implying an amplification $\delta \lesssim 13$, as estimated by Jorstad et al. (2005) and Savolainen et al. (2010). Considering the Compton limit of 10^11.5 K or the equipartition brightness temperature value of 5 × 10¹⁰ K, this amplification is at least 10–60 times too small to produce the observed brightness temperature at 18 cm, and it is 3–20 times too small to explain the 1.3 cm results. This suggests that the radio emission from 3C 273 may not be well described by incoherent synchrotron radiation from relativistic electrons (Kardashev 2000).

We have considered the possibility that the jet velocities observed with the VLBA (Lister et al. 2013) are much lower than the bulk flow velocity relevant to Doppler boosting. However, the observed relationship between apparent brightness temperature and apparent speed of quasars follows that expected if the flow velocity and pattern velocity are related (Kovalev et al. 2005; Homan et al. 2006). Another possibility is that there is sufficient injection or acceleration of relativistic electrons to balance losses due to inverse Compton cooling. However, this requires that the acceleration occurs in the region, which must be several parsecs away from the central nucleus due to synchrotron self-absorption closer to the central engine (Blandford & Königl 1979; Pushkarev et al. 2012). Moreover, Readhead (1994) has noted that sustained γ-ray luminosities would likely be required at a level that is not observed (see the low level of γ-ray flux around 2013.0 in Ramakrishnan et al. 2015). Quantitative calculations are strongly model dependent. Petropoulou et al. (2015) determined observational signatures of the Compton catastrophe and noted that they were not realized in 3C 273. Alternatively, some or all of the observed radio emission from 3C 273 might be due to synchrotron radiation from relativistic protons, rather than electrons, which would raise the theoretical brightness temperature limit by a factor of ${({m}_{{\rm{p}}}/{m}_{{\rm{e}}})}^{9/7}\approx 1.5\times {10}^{4}$ (Jukes 1967). However, this would increase the required magnetic field by a factor of ${({m}_{{\rm{p}}}/{m}_{{\rm{e}}})}^{2}\approx 4\times {10}^{6}$, which makes a proton synchrotron model problematic. Moreover, Rees (1968) has pointed out that unless the observing frequency is below the electron gyro frequency, absorption by electrons would still limit the observed brightness temperatures to the canonical values. This would imply magnetic field values of an order of 10³ G, far in excess of that thought to exist in quasar jets. Models considering synchrotron emission from particle-dominated electron–positron flows with a monoenergetic particle distribution (Tsang & Kirk 2007) can accommodate brightness temperatures of 0.5–2 × 10¹⁴ K, for the physical conditions measured in the jet of 3C 273 (Savolainen et al. 2010), but due to synchrotron radiation losses, an initially monochromatic spectrum would be broadened. Coherent or collective processes such as plasma waves or stimulated synchrotron (Melrose 1999) or cyclotron (Begelman et al. 2005) emission may also lead to brightness temperatures well in excess of 10¹² K.

Because our observations only detect these extreme brightness temperatures in the wide frequency range over a period of about two months—less than the light crossing time—they may also indicate the existence of a short-lived phenomenon that drives the emitting plasma far from equipartition. However, identifying such a variable region with the jet core may still be challenging due to synchrotron opacity and expected time delays between the frequencies. Nevertheless, the core location is still more likely for this emission, as the optically thin jet of 3C 273 has not shown very bright unresolved knots in any observations obtained from previous ground-based monitoring programs. We note that the inverse Compton loss timescale should be about one day or less at these frequencies, as estimated by Slysh (1992) and Readhead (1994).

Multi-frequency 1.7, 4.8, and 22 GHz Space VLBI observations of the RadioAstron mission have revealed extremely compact structure in the jet of the archetypical quasar 3C 273 with interferometer detections up to 13.5 Earth diameters, most likely its apparent core. The core brightness temperature is estimated to reach values in excess of 10¹³ K. Sub-structure introduced by interstellar scattering (Johnson et al. 2016) can significantly affect estimates at 1.7 GHz. At the same time, our brightness temperature values at 4.8 or 22 GHz remain unaffected. We conclude that it is difficult to interpret the data in terms of conventional incoherent synchrotron radiation. An ongoing analysis of a large sample of AGNs at the long RadioAstron baselines will help to resolve this mystery.

The RadioAstron project is led by the Astro Space Center of the Lebedev Physical Institute of the Russian Academy of Sciences and the Lavochkin Association of the Russian Federal Space Agency, and is a collaboration with partner institutions in Russia and other countries. The Arecibo Observatory is operated by SRI International under a cooperative agreement with the National Science Foundation (AST-1100968), and in alliance with Ana G. Mendez-Universidad Metropolitana, and the Universities Space Research Association. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. This research is partly based on observations with the 100 m telescope of the MPIfR (Max-Planck-Institute for Radio Astronomy) at Effelsberg. This research has made use of data from the MOJAVE database, which is maintained by the MOJAVE team (Lister et al. 2009). We have processed and used archival VLBA observations at 18 cm (code BG196I). We would like to extend thanks to the NRAO group responsible for developing and deploying phased-array VLBI capabilities at the newly upgraded VLA. We thank Tuomas Savolainen, Alexander Pushkarev, Richard Schilizzi, Phil Edwards, Sergio Colafrancesco, and Martin Rees for helpful discussions. We thank the referee for constructive comments. This project was supported by the Russian Foundation for Basic Research grant 13-02-12103.

Facilities: RadioAstron Space Radio Telescope (Spektr-R) - , Arecibo, GBT, VLA, Effelsberg.