Extremely long baseline interferometry with Origins Space Telescope
Dominic W. Pesce, Kari Haworth, Gary J. Melnick, Lindy Blackburn, Maciek Wielgus, Michael D. Johnson, Alexander Raymond, Jonathan Weintroub, Daniel C. M. Palumbo, Sheperd S. Doeleman, David J. James
AAstro2020 APC White Paper
Extremely long baseline interferometrywith Origins Space Telescope
Dominic W. Pesce † , , Kari Haworth , Gary J. Melnick , Lindy Blackburn , , Maciek Wielgus , , Michael D. Johnson , , Alexander Raymond , , JonathanWeintroub , Daniel C. M. Palumbo , , Sheperd S. Doeleman , , David J. James , Abstract:
Operating . × km from Earth at the Sun-Earth L2 Lagrange point, the Ori-gins Space Telescope equipped with a slightly modified version of its HERO heterodyne in-strument could function as a uniquely valuable node in a VLBI network. The unprecedentedangular resolution resulting from the combination of Origins with existing ground-basedmillimeter/submillimeter telescope arrays would increase the number of spatially resolvableblack holes by a factor of , permit the study of these black holes across all of cosmichistory, and enable new tests of general relativity by unveiling the photon ring substructurein the nearest black holes. Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA † Corresponding author: [email protected] a r X i v : . [ a s t r o - ph . I M ] S e p Introduction
A leap forward in our understanding of black holes came earlier this year, when the EventHorizon Telescope (EHT) collaboration revealed the first horizon-scale image of the activegalactic nucleus of M87 [3]. This feat was accomplished using a ground-based very long base-line interferometry (VLBI) network with baselines extending across the planet, reaching thehighest angular resolution currently achievable from the surface of the Earth. We could soonhave an opportunity to make another leap by utilizing the extremely long baselines betweenEarth and the Origins Space Telescope (OST). The corresponding ∼ × improvement inangular resolution would increase the expected number of spatially resolvable black holeshadows from ∼ to (cid:38) , enabling new studies of black hole demographics across cosmichistory. For the closest supermassive black holes – such as the one in M87 – the unprece-dented angular resolution would yield access to photon ring substructure, providing a newtool for making precise black hole spin measurements and testing the validity of generalrelativity (GR).OST is one of four NASA-funded Flagship mission concepts prepared for the 2020 DecadalReview. OST would incorporate a 5.9-meter diameter on-axis telescope operating between2.8 and 588 microns, and it would observe from the Sun-Earth L2 Lagrange point 1.5 millionkilometers from Earth. The primary mirror has a total wavefront error of less than 2.5microns, making it a superb antenna at (sub)millimeter wavelengths.As proposed to the Decadal Review, OST is designed with sufficient mass, power, andvolume margins to accommodate two additional instruments beyond the baseline complementshould the Decadal Review decide their inclusion is desired. One of these instruments,the HEterodyne Receiver for OST (HERO, [12]), has been studied extensively by many ofthe same people that built the Heterodyne Instrument for the Far-Infrared (HIFI) flownsuccessfully aboard the Herschel Space Observatory. HERO is presently designed to operatein four bands that span the range between 486 GHz and 2700 GHz, and it would permitboth dual-polarization and dual-frequency observations.Expanding the HERO instrument to be an interferometric station will require severalmodest technology enhancements. Top-level discussions have not revealed any fundamentalobstacles to these added requirements, which are presented here. Dramatically improving the angular resolution of (sub)mm VLBI is an exciting but daunt-ing prospect that requires either increasing the observing frequency, extending the baselinelengths, or both. Not many sites on Earth offer atmospheric conditions that are goodenough for observations at (sub)mm wavelengths to be routinely viable, and the currentlongest baselines are already nearly equal to one Earth diameter. Sizable angular resolutionimprovements will thus inevitably require stations in space. The L2 orbit planned for OSTprovides a unique opportunity for extending VLBI to extremely long baselines by observingin tandem with sensitive ground-based stations (such as ALMA, LMT, NOEMA, GBT, orngVLA). Such observations would achieve an unprecedented angular resolution. The EHTis currently the highest-frequency ground-based VLBI network, operating at a frequency of230 GHz and attaining a resolution of ∼ µ as; by comparison, an Earth-L2 baseline wouldhave typical fringe spacings well under a microarcsecond at observing frequencies of 86, 230,345, and 690 GHz. For a black hole viewed by an observer at infinity, the locus of event horizon-grazing photontrajectories forms a nearly circular closed curve on the sky [1]. This boundary defines theinner edge of the “photon ring,” and for astrophysical black holes emission from the blackhole “shadow” region interior to the photon ring is expected to be substantially depressed(see [3] and references therein).Given a uniform distribution of supermassive black holes (SMBHs) in flat space, weexpect the number of sources N with spatially resolved black hole shadows to increase asthe cube of the maximum baseline length. Current Earth-based arrays, such as the EHT,are able to spatially resolve black hole shadows for N ≈ source [3, 4, 5]. Extending abaseline from Earth to L2, at a distance of ∼
120 Earth diameters, would increasethe expected number of spatially resolvable black hole shadows from N ≈ to N ≈ > . Each black hole with a resolved shadow would have a corresponding blackhole mass estimate (or, more specifically, an estimate of the mass-to-distance ratio
M/D ),enabling studies of SMBH mass demographics with access to an unprecedented statisticalsample.In our Universe, the angular diameter distance reaches a maximum value at a redshift of z ≈ ; sources of a given physical size thus have a minimum possible angular size, and if asource can be spatially resolved at z ≈ then it can be spatially resolved at any redshift.The left panel of Figure 1 shows that on the extremely long baselines between Earth andL2, with fringe spacings θ (cid:46) . µ as, this minimum angular size ensures that SMBHs withmasses M (cid:38) M (cid:12) have shadow diameters that can be spatially resolved across cosmichistory. Measurements of the SMBH mass distribution as a function of redshift would shedlight on SMBH-galaxy coevolution and inform cosmological models of structure formation,helping to understand how supermassive black holes formed in the early Universe (see, e.g.,[10]). For the nearest SMBHs, such as M87, a baseline between Earth and L2 opens up the possibil-ity of spatially resolving the substructure of the photon ring itself, enabling new, stringenttests of GR . As detailed by Johnson et al. [7], the self-similar nature of the photon ring isnaturally decomposed by interferometers, with successive “windings” of photon orbits dom-inating the signal in discrete baseline intervals (see right panel of Figure 1). The period of For a non-spinning black hole the locus is perfectly circular with a radius equal to √ times theSchwarzschild radius. For spinning black holes that aren’t observed pole-on, the locus appears flattened onone side and the radius changes by ±∼ %. More precisely, we are considering a subset of SMBHs for which the shadow could be seen through thesurrounding material, which in general depends on the details of the particular accretion flow.
All extremely long baseline observations will face sensitivity challenges related to the phys-ical brightness temperature limits of synchrotron radiation imposed by self-absorption andinverse-Compton scattering ([9]; see left panel of Figure 2). On a maximal Earth–L2 base-line, no source is expected to have a flux density exceeding ∼ mJy. This strict sensitivityrequirement drives the technology considerations.The sensitivity of an interferometric baseline depends on: (1) the geometric mean of thesystem equivalent flux densities of the individual telescopes; (2) the averaged bandwidth;and (3) the coherent integration time. The first property allows telescopes such as OST(at 5.9-meter diameter) to form sensitive baselines when paired with a large ground-basedtelescope (e.g., ALMA or ngVLA). The second allows digital enhancements (e.g., widerrecorded bandwidths) to offset limitations in telescope sensitivity. The third ties sensitivityto phase stability, which is limited by the atmosphere and reference frequency.The following component recommendations are based on first-pass analyses and discus-sions, and are meant to give a general idea of the technology enhancements OST would needto perform as an interferometric VLBI station. Atmospheric conditions above ground based stations limit the data collection frequenciesto windows around 86 GHz, 230 GHz, 345 GHz, and 690 GHz. Band 1 of the HEROinstrument already includes 690 GHz. The remaining frequencies could be covered usingtwo additional bands, one that spans the 86 GHz and 230 GHz windows, and another thatcovers 230 GHz through 345 GHz. Simultaneous multifrequency observations will be usefulas the ground-based array expands its capabilities to include multifrequency phase transfer.
To achieve the sensitivities required for an Earth–L2 baseline, a combination of wide band-widths and long integration times are needed. Though an improvement of one relaxes therequirement of the other, a first-pass operational configuration suggests that a total band-width of 64 GHz (16 GHz per sideband) for an integration time of two hours could achieve By “maximal” here, we mean the baseline length with no projection; only sources located at the eclipticpole see exclusively maximal baselines, but every source in the sky sees a maximal baseline at some point inthe orbit.
Onboard data processing requires high-speed analog-to-digital converters (ADCs) and a high-performance Field Programmable Gate Array (FPGA). The FPGA quantizes and packetizesthe digitized data for storage. Each of the four 8 GHz channels sampled at Nyquist requiresa 16 Gbps ADC. The FPGA receives multiple streams and quantizes the data from the 4-bitsample to 2 bits, giving a total data rate of 256 Gbps. Current FPGA transceiver technologymeets the speeds required, and both Xilinx (Ultrascale Kintex) and Microsemi (RTG-4) arecurrently working to make these high-speed interfaces available in space-qualified compo-nents.
With an observation time of 6 hours, a 1/3 duty cycle and a rate of 256 Gbps, a total ofapproximately 230 TB of data will be captured. A tradeoff between onboard storage anddownlink speed will need to be conducted to determine the most optimal design. Storagecontinues to increase in both capacity and speed, with 1TB currently available in a small (22mm ×
80 mm) package. Downlink capabilities, pushed by the telecommunications industry,are also getting faster with laser communication speeds currently at 200 Gbps from LEO tosmall ground-based receivers [11].
To achieve phase stability on a single baseline for integration times of ∼ hours requires eitherthat both stations are individually equipped with extremely stable timing references or thatthey share a common reference. Individual clocks would need to have Allan deviationsbetter than ∼ × − over the integration time, which is roughly three orders of magnitudemore stable than current ground-based technology and likely unachievable on a 1–2 decadetimescale. Instead, a shared reference would relax the more stringent stability requirementalmost entirely and will likely prove to be the more feasible option. A shared ground-spacetiming reference has been demonstrated at lower observing frequencies by RadioAstron [8],though additional work would be required to extend such capabilities to higher observingfrequencies and to a station at L2. Antenna position and velocity (and possibly higher order derivatives) must be known in or-der to coherently average the correlated signal across finite bandwidth and over time. Initialsearches can be conducted with wide search windows in the associated delay, delay-rate, andacceleration parameters, with residual values being used to refine the orbit determination, as5s currently done for RadioAstron [13]. To create a baseline of position, velocity, and accel-eration requirements, we take the RadioAstron specifications and increase the requirementby a factor of 10 for velocity and acceleration: • Position error less than 600 m • Velocity error less than 2 mm s − • Acceleration error less than − m s − These requirements can be potentially relaxed with improvements in computational delayand rate searching routines at the correlation stage.
Extremely long baseline interferometry with OST would create new and exciting possibili-ties for the study of black holes and general relativity under the most extreme conditions.Moreover, the technology required to enable this possibility appears either feasible today, orwithin reach during the time OST would be built. Given the immense scientific potential,it is our hope that the Decadal Review will seize this opportunity and recommend that thiscapability be considered for inclusion in OST.6 eferences [1] J. M. Bardeen. “Timelike and Null Geodesics in the Kerr Metric”. In:Black Holes (Les Astres Occlus). Ed. by C. Dewitt and B. S. Dewitt. Gordon andBreach Scientific Publishers, 1973, p. 215.[2] A. E. Broderick et al. “Testing the No-hair Theorem with Event Horizon TelescopeObservations of Sagittarius A*”. In: ApJ 784, 7 (Mar. 2014), p. 7. doi : . arXiv: .[3] Event Horizon Telescope Collaboration et al. “First M87 Event Horizon TelescopeResults. I. The Shadow of the Supermassive Black Hole”. In: ApJ 875.1, L1 (Apr.2019), p. L1. doi : .[4] Event Horizon Telescope Collaboration et al. “First M87 Event Horizon TelescopeResults. III. Data Processing and Calibration”. In: ApJ 875.1, L3 (Apr. 2019), p. L3. doi : .[5] Event Horizon Telescope Collaboration et al. “First M87 Event Horizon TelescopeResults. IV. Imaging the Central Supermassive Black Hole”. In: ApJ 875.1, L4 (Apr.2019), p. L4. doi : .[6] T. Johannsen and D. Psaltis. “Testing the No-hair Theorem with Observations in theElectromagnetic Spectrum. II. Black Hole Images”. In: ApJ 718 (July 2010),pp. 446–454. doi : . arXiv: .[7] Michael D. Johnson et al. “Universal Interferometric Signatures of a Black Hole’sPhoton Ring”. In: arXiv e-prints, arXiv:1907.04329 (July 2019), arXiv:1907.04329.arXiv: .[8] N. S. Kardashev et al. ““RadioAstron”-A telescope with a size of 300 000 km: Mainparameters and first observational results”. In: Astronomy Reports 57 (Mar. 2013),pp. 153–194. doi : . arXiv: .[9] K. I. Kellermann and I. I. K. Pauliny-Toth. “The Spectra of Opaque Radio Sources”.In: ApJ 155 (Feb. 1969), p. L71. doi : .[10] M. A. Latif et al. “Black hole formation in the early Universe”. In: MNRAS 433.2(Aug. 2013), pp. 1607–1618. doi : . arXiv: .[11] B. S Robinson et al. “TeraByte InfraRed Delivery (TBIRD): a demonstration oflarge-volume direct-to-Earth data transfer from low-Earth orbit”. eng. In: vol. 10524.SPIE, 2018, pp. 105240V–105240V-6. isbn : 9781510615335.[12] Martina C. Wiedner et al. “A Proposed Heterodyne Receiver for the Origins SpaceTelescope”. In: IEEE Transactions on Terahertz Science and Technology 8.6 (Nov.2018), pp. 558–571. doi : .[13] M. V. Zakhvatkin et al. “RadioAstron orbit determination and evaluation of itsresults using correlation of space-VLBI observations”. In: arXiv e-prints,arXiv:1812.01623 (Dec. 2018), arXiv:1812.01623. arXiv: .7 × M (cid:12) × M (cid:12) × M (cid:12) × M (cid:12) Redshift ( z )10 − − S h a d o w d i a m e t e r ( µ a s ) On an Earth-L2 baseline, black holes withlarge enough masses can be spatiallyresolved at any redshift Baseline length (G λ )10 − − − − F l u x d e n s i t y ( m J y ) Earth L2
Figure 1:
Left : Black hole shadow diameter vs. redshift for SMBHs of varying mass; therange of sizes accessible with a maximal Earth–L2 baseline operating at frequencies of 86–690 GHz is shaded in purple. We can see that as shadows reach a minimum size at z ≈ ,SMBHs with masses greater than ∼ M (cid:12) are resolvable at all redshifts. Right : Fluxdensity as a function of baseline length is plotted in gray for a simple model of the M87photon ring structure [7], with the envelope shown as a dashed black line; note that theperiodic structure evident at short baselines continues at longer baselines with the sameperiod. The purple shaded region shows the range of baselines accessible over the course of ayear on an Earth–L2 baseline operating at frequencies of 86–690 GHz; the long-baseline endof this range corresponds to a maximal baseline at 690 GHz, while the short-baseline endof the range corresponds to a minimal projected baseline (for M87, the minimal projectedbaseline is a factor of ∼ Baseline length (G λ ) − − − − F l u x d e n s i t y ( m J y ) G H z G H z G H z G H z L2Earth
86 230 345 690
Observing frequency (GHz)0.11101001000 I n t e g r a t i o n t i m e ( m i nu t e s ) Integration times for baselines between OSTand potential ground-based anchor stations atdifferent observing frequencies ngVLA (full)ngVLA (compact)ALMANOEMALMTGBT
Figure 2:
Left : For baselines to L2, synchrotron self-absorption and inverse-Compton scat-tering limit the brightness temperature to T b (cid:46) K [9]; the black lines mark this limitfor each of the labeled observing frequencies. Below each of these lines, the region shadedpurple indicates physically allowed flux densities observable on Earth-L2 baselines rangingbetween 10–100% of the maximum projected baseline length; overlapping regions indicatewhere sources could be observed with matched resolution at two or more frequencies (al-beit at different times). The red shaded regions are analogous to the purple ones, but forEarth-Earth baselines at 86 and 230 GHz only.
Right : Estimated integration times requiredto achieve a σ detection of a source with brightness temperature T b = 1012