A CUBESAT FOR CALIBRATING GROUND-BASED AND SUB-ORBITAL MILLIMETER-WAVE POLARIMETERS (CALSAT)

In this paper, we describe a low-cost, open-access, CubeSat-based calibration instrument called CalSat that is designed to support ground-based and sub-orbital experiments searching for various polarization signals in the cosmic microwave background (CMB). The CMB is a bath of photons that permeates all of space and carries an image of the Universe as it was 380,000 years after the Big Bang. This image spans the entire sky, but it is not visible to the human eye because the frequency spectrum of the CMB peaks in the millimeter-wave region of the electromagnetic spectrum. Physical processes that operated in the universe when the CMB formed left an imprint that can be detected today. This imprint is observed as angular intensity and linear polarization anisotropies. These primordial CMB anisotropies have proven to be a treasure trove of cosmological information. For example, the precise characterization of the intensity (or temperature) anisotropy of the CMB has helped reveal that spacetime is flat, the universe is 13.8 billion years old, and the energy content of the universe is dominated by cold dark matter and dark energy [see for example, Bennett et al., 2013; Planck Collaboration, 2014]. The density inhomogeneities that produced the detected temperature anisotropies theoretically should generate, through Thomson scattering during the epoch of recombination, a curl-free polarization signal known as “E-mode” polarization. This companion signal has also been observed at the theoretically expected level providing further confidence in the $\Lambda$CDM cosmological model [see for example, Naess et al., 2014; Crites et al., 2015; BICEP2 Collaboration, 2014a; QUIET Collaboration, 2011; Brown et al., 2009].

The inflationary cosmological paradigm posits that a burst of exponential spacetime expansion, called inflation, took place during the first fraction of a second after the Big Bang. Observational evidence to date supports this paradigm and has given it a strong footing, though the precise physical mechanism that caused inflation is unknown. Inflation should have produced a stochastic background of gravitational waves. These gravitational waves would have produced polarization signals separable from E-modes by their divergence-free “B-mode” signature Zaldarriaga & Seljak [1997]; Kamionkowski et al. [1997]. The magnitude of this inflationary gravitational wave (IGW) B-mode signal is proportional to the energy scale at which inflation occurred. See for example, the dashed curves in Figure 1 and note that the IGW signal amplitude is commonly parameterized as $r$, the so-called tensor-to-scalar ratio, which is related to the energy scale of inflation¹¹1The tensor-to-scalar ratio $r$ is related to the energy scale of inflation as $\displaystyle V^{1/4}=1.06\times 10^{16}\left(\frac{r}{0.01}\right)^{1/4}$ [GeV]. Baumann et al. [2009]; Knox & Song [2002]. If the IGW signal ultimately is discovered, then the energy scale of inflation would be experimentally ascertained. This measurement would place a tight constraint on the theoretical models that describe the inflation mechanism, and this constraint would be a breakthrough for both astrophysics and particle physics because there is no way to create inflation-like conditions in a laboratory or particle accelerator. The IGW signal is currently the primary focus of CMB research, and we will discuss the status of current measurements at the end of Section 2.

In addition to the IGW signal, other CMB polarization signals promise to deliver valuable cosmological information. Non-primordial B-modes are generated when E-modes are gravitationally lensed by large-scale structures in the Universe (see the dash-dot curve in Figure 1). This lensing B-mode signal is sensitive to physical parameters such as the sum of the neutrino masses Abazajian et al. [2015a]. B-mode polarization can also be used to probe physics outside the standard cosmological picture. Temperature to B-mode correlations (TB) and E-mode and B-mode correlations (EB) are expected to vanish in the standard model. Therefore, these estimators are sensitive probes for physics outside the standard model if the correlation signals are found to be non-zero. A variety of candidate non-standard-model physical mechanisms that produce cosmological polarization rotation (CPR) already have been identified. Parity violation in the electromagnetic sector via a Chern-Simons coupling can produce TB and EB correlations Kaufman et al. [2014]. A coupling of a pseudo-scalar field to electromagnetism would violate the Einstein Equivalence Principle and would result in TB and EB correlations Ni [1977]; Carroll et al. [1991]. TB and EB correlations can also be used to test chiral gravity models Gluscevic & Kamionkowski [2010] and to search for primordial magnetic fields Pogosian et al. [2009]; Yadav et al. [2012].

The magnitude of the forecasted TB, EB and B-mode signals is faint when compared with unavoidable instrument-induced systematic errors. Therefore, all experiments trying to measure these signals need a robust polarimeter calibration program that will allow the effect of these instrument-induced errors to be mitigated during data analysis. Several performance requirement studies have been published specifically for IGW searches Bock et al. [2006]; O’Dea et al. [2007]; Bock et al. [2009]. These studies indicate the level of systematic error that can be tolerated for a given IGW signal amplitude. For the CalSat design program we chose to use the performance requirements derived by the Task Force on Cosmic Microwave Background Research Bock et al. [2006] as a benchmark. This report proposes a general performance requirement where each systematic error must be suppressed to a factor of ten below an IGW signal corresponding to a tensor-to-scalar ratio of $r=0.01$, which is the level where the gravitational lensing signal starts to dominate the IWG signal at $\ell=100$.

Many of the known systematic errors can be mitigated straightforwardly. However, a robust mitigation strategy for instrument-induced polarization rotation (IPR), which is one of the most critical systematic errors, has not yet been identified. This instrumental effect rotates the apparent orientation of the linearly-polarized pseudo-vectors on the sky, and this rotation converts the brighter E-modes into spurious B-modes. Using the aforementioned performance requirement definition, any IPR must be limited to 0.2 deg for an IGW search targeting $r>0.01$; fainter IGW signals would require a tighter constraint, and even more precision could be needed if delensing techniques ultimately will be used to probe below $r=0.01$ Smith et al. [2012].

To illustrate this effect we performed a simple experiment simulation where a set of Stokes parameter maps ($I$, $Q$, $U$ with $V=0$) containing CMB signals were simulated and then the orientation of the polarization of each pixel was rotated by 2 deg using the Mueller matrix for linear polarization rotation. The input maps were 1000 deg², contained no noise or other beam effects, and all B-mode signals were set to zero. The angular power spectra of the corrupted maps were then estimated, and the estimated power spectra are shown in Figure 1. The open-circle points in this figure (BB, TB and EB) are spurious signals entirely produced by the polarization rotation operation. A rotation of just 2 deg creates a false B-mode signal that is comparable in magnitude to both the lensing signal and the sought-after IGW signal below $\ell\simeq 100$ if the tensor-to-scalar ratio is $r=0.01$. The takeaway message is a very small amount of rotation can produce a false B-mode signal that can obscure the actual sky signal.

To properly characterize the IPR properties of a CMB polarimeter, a linearly polarized source with known polarization properties should be observed with high precision. This required calibration measurement provides the critical relationship between the coordinate system of the polarimeter in the instrument frame and the coordinate system on the sky that defines the astrophysical $Q$ and $U$ Stokes parameters. The ideal source should be point-like in the beam of the telescope and bright enough to generate high signal-to-noise calibration data with a reasonable amount of integration time. But this source should not be too bright, or it will saturate the detector system. Finally, the orientation of the polarization of the observed source on the sky must be known to 0.2 deg or better for $r>0.01$. It is important to note that the magnitude of this systematic error typically varies across the focal plane of the telescope, so the IPR effect must be determined for each detector in any given instrument.

Many current experiments “self-calibrate” their polarization angles by assuming TB and EB correlations are zero Keating et al. [2013]. This self-calibration technique uses the TB and EB spectra on the right in Figure 1 along with the theoretical idea that these spectra should be zero in the absence of CPR to remove the green spurious B-mode points on the left. This approach makes it impossible to use B-mode, TB and EB measurements to constrain the aforementioned isotropic departures from the standard model (see Section 1) because any signal produced by CPR is incorrectly interpreted as an error signal. If this problem is avoided and self-calibration is not used, then the current achieved precision of $\sim$0.5 deg severely limits the ability of experiments to search for any departures from standard cosmology via TB and EB measurements. A more precise calibration procedure is needed to make progress with CPR studies.

Some partially polarized astrophysical sources are available, and at millimeter-wavelengths, the best of these appears to be Tau A. Tau A is a supernova remnant located at Right ascension = 05 34 32 (hms) and Declination = +22 00 52 (dms), and it has an angular extent of $7^{\prime}\times 5^{\prime}$. For calibration, its most relevant properties are (i) the measured polarization angle uncertainty, (ii) the polarized fraction, and (iii) the source brightness. The WMAP satellite measured its polarization properties in spectral bands between 20 and 100 GHz Weiland et al. [2011], the Planck satellite measured its polarization properties in spectral bands between 30 and 353 GHz Planck Collaboration [2015], and Aumont et al. [2010] studied the suitability of Tau A as a calibration source for CMB studies at 90 GHz using the 30 m IRAM telescope. These measurements are summarized in Table 1. ACTpol Naess et al. [2014] and POLARBEAR POLARBEAR Collaboration [2014] recently observed Tau A as part of their respective calibration programs and showed that the polarization intensity morphology at 145 GHz is complicated.

Though Tau A is the best polarized source on the sky at millimeter wavelengths, it does not meet the performance requirements of a calibrator for an IGW-signal search. First and foremost, with a Declination = +22 00 52 (dms), it is not accessible to observatories at the South Pole or on Antarctic balloons. It can be observed from the Atacama Desert in Chile, though it will always be at a zenith angle of 45 deg or more. Second, it is not bright enough to give a high signal-to-noise ratio measurement with a short integration time. Third, the source is extended rather than point-like. And finally, the millimeter-wave spectrum of Tau A is not precisely known, though it is certainly not that of a 2.7 K blackbody. Polarimeters that have frequency-dependent performance, which is common, would need to precisely measure the frequency spectrum of Tau A before using it as a polarization angle calibrator (see Section 4).

Since an ideal celestial calibration source does not exist, some current experiments use ground-based sources for polarimeter calibration BICEP2 Collaboration [2014b]; Crites et al. [2015]. However, these measurements are challenging. For example, the Fraunhofer distance ($2D^{2}/\lambda$) for common telescopes is typically between 0.1 and 100 km, so the calibration source must be placed more than 0.1 to 100 km away, respectively, from the telescope for the desired far-field beam characterization measurement. This kind of measurement is difficult because the detector systems in CMB polarimeters are designed to observe sky backgrounds, which are typically $\sim$10 K or less. To observe a ground-based calibration source more than 0.1 to 100 km away, the zenith angle of the telescope must be set to nearly 90 deg. Background loading from the large airmass and thermal emission from the ground at this zenith angle are high enough to saturate typical detector systems²²2Here we are assuming bolometric detectors are being used. Bolometers are commonly used in CMB observations.. Therefore two-stage bolometers or some kind of signal attenuator must be used for this style of calibration measurement. However, these approaches have their own varieties of systematic error, so awkwardly these calibration measurements could require their own calibration. A near-field measurement of a calibration source observed at smaller zenith angles can be performed instead to mitigate this high background loading problem. Yet, for the near-field measurement to be useful, a model-dependent theoretical correction must be applied to the data to derive the effective far-field calibration. This correction, however, also introduces uncertainty into the calibration, and the quality of the result depends entirely on the accuracy of this difficult theoretical calculation.

Current experiments are beginning to measure B-modes. The BICEP2 Collaboration recently announced a detection of degree-scale B-mode polarization in a 350 deg² patch of sky in the southern hemisphere BICEP2 Collaboration [2014a]. The POLARBEAR and SPTPol Collaborations detected B-mode polarization consistent with the aforementioned gravitational lensing signal on sub-degree scales POLARBEAR Collaboration [2014]; Keisler et al. [2015]. And the Planck Collaboration published a measurement of B-mode polarization from Galactic dust emission at 353 GHz Adam et al. [2014]. This combination of results has added energy to CMB studies because these measurements indicate that faint B-mode signals are there on the sky and that instruments are now sensitive enough to detect them. Currently, BICEP2 and POLARBEAR use the aforementioned self-calibration technique, so it impossible to use these measurements to constrain isotropic departures from the standard model. These results have re-emphasized the need for enhanced foreground discrimination capabilities and robust systematic error control; the latter effect being the major motivation behind CalSat.

For CalSat to be useful, the detected calibration signal needs to be large when compared with the noise level of the calibration measurement. It is difficult to forecast the precise characteristics of every instrument that might observe CalSat. Therefore, to assess the detectability, three primary assumptions were made. First, we assumed the aperture diameter of any instrument observing CalSat is between 0.3 and 10 m, which is the current range for CMB experiments. Second, we assumed A$\Omega=\lambda^{2}$ and $\delta\nu/\nu_{c}=0.3$. Here, $A$ is the aperture area, $\Omega$ is the solid angle of the CMB telescope beam, and $\nu$ is the frequency of the incoming radiation with $\nu_{c}$ being the center frequency of the spectral band of the polarimeter. Third, we assumed the noise in the calibration measurement is dominated by photon noise from the CMB for balloon-borne measurements and the atmosphere for ground-based measurements.

To estimate the photon noise, spectral radiance curves were computed using the publicly available am atmospheric modeling software package¹²¹²12The am software: https://www.cfa.harvard.edu/$\sim$spaine/am/. We used am version 8.0, which implements O₂ line mixing and non-resonant absorption near 60 GHz. Earlier versions of am did not model these effects, so these earlier versions had accuracy issues, which do not affect our calculations. The atmospheric profiles for the following six observatories were used in these simulations: South Pole, Chajnantor, Summit Station in Greenland, Mauna Kea, and balloon-borne observatories near Ft. Sumner, New Mexico, and McMurdo in Antarctica. For all sites, the zenith angle for observations was set to 45 deg. The altitude of the balloon-borne observatories was assumed to be 30 km. For the South Pole, Chajnantor, Greenland, and Mauna Kea observatories, the ambient temperature and PWV was assumed to be 230, 275, 248 and 275 K, and 1, 1, 1 and 4 mm, respectively. Given these conservative assumptions, the background power in the telescope beam and the associated photon noise equivalent power (NEP) were computed. The background power in the telescope beam was computed using

and the photon NEP was computed using

These equations are commonly used and their derivation can be found in the literature Lamarre [1986]; Richards [1994]. For our calculations, ${\cal B}(\nu)$ is the spectral radiance computed by am, ${\cal T}(\nu)$ is the spectral band-pass filter, which is a top-hat with a width equal to $\delta\nu/\nu_{c}=0.3$ and A$\Omega=\lambda^{2}$. We assumed observations are made with detectors that are sensitive to a single-polarization, so $\alpha=0.5$ and $m=1$. The results are shown in Figure 9 and Table 4. The expected millimeter-wave power from CalSat at the telescope aperture was computed using the following equation:

Here, $P_{Gunn}$ is the millimeter-wave power from the source, $g$ is the horn gain in dBi, $D$ is the aperture diameter of the telescope, and $d$ is the distance between CalSat and the telescope; $\Omega$ is the solid angle subtended by the telescope aperture as viewed from CalSat, and it is schematically shown in Figure 6. The power arriving in the telescope aperture from CalSat is plotted versus telescope aperture diameter in Figure 10. For comparison, the power arriving in the telescope aperture from Jupiter, which is a bright and commonly used unpolarized calibrator, was also computed and plotted alongside the CalSat curves in this Figure.

This analysis shows that (i) the brightness of CalSat is similar to the brightness of the background, (ii) the brightness of CalSat is comparable to Jupiter, and (iii) the signal-to-noise ratio for one second of integration is typically between 1,000 and 100,000. These are all characteristics of an ideal calibration source. If CalSat were significantly brighter than the background then the signal would likely saturate the detectors (assuming TES bolometers are being used, which is the current standard at these frequencies).

The CalSat instrument configuration presented in this paper was designed to support the following ongoing experiments and any associated follow-up experiments from these collaborations: ACT Naess et al. [2014], BICEP/KECK Ahmed et al. [2014]; Buder et al. [2014], CLASS Essinger-Hileman et al. [2014], GroundBIRD Tajiman et al. [2012], EBEX Reichborn-Kjennerud et al. [2010], PIPER Lazear et al. [2014], POLARBEAR Arnold et al. [2014]; Tomaru et al. [2012]; Kermish et al. [2012], QUIJOTE Perez-de-Taoro et al. [2014], SPIDER Rahlin et al. [2014], and SPTPol Benson et al. [2014]; Austerman et al. [2012]. Additional experiments that could use CalSat are being designed: GLP Araujo et al. [2014], SKIP Johnson et al. [2014], and QUBIC Ghribi et al. [2014]. And the planned CMB-S4 Abazajian et al. [2015b] program would benefit from CalSat because it could be used to both accurately calibrate deep observations and combine results from different observatories. Though CalSat is designed for CMB polarization experiments, it could also straightforwardly be used to calibrate other observatories such as ALMA and the VLA.

As a narrow-band source, CalSat is not designed to characterize the broad-band spectral properties of CMB polarimeters. Instead it is designed to provide the critical relationship between the coordinate system of the polarimeter in the instrument frame and the coordinate system on the sky that defines the astrophysical $Q$ and $U$ Stokes parameters. The spectral bands in CMB polarimeters are typically broad, and some polarimeter technologies, such as the achromatic half-wave plate and the sinuous antenna multi-chroic pixel, have frequency dependent performance. Therefore polarimeter calibration must be performed over the full spectral bandwidth for experiments using these technologies. CMB experiment teams must characterize the spectral properties of their instruments in the laboratory before deployment and then use the clean and simple CalSat signals together with their lab-based instrument transfer functions during their calibration analyses. For example Figure 11 shows simulated modulation efficiency and polarimeter axis angle curves for an achromatic half-wave plate polarimeter. The 80.0, 140 and 249 GHz CalSat tones could be used to verify that the modulation efficiency is very close to unity at these frequencies and the polarimeter axis varies as expected as a function of frequency.

CalSat is programmed to listen for the ground station each orbit. If the radio uplink from the ground station fails, then the on-board computer turns the CalSat tones off and wait for the link to be restored. This mode of operation guards against out-of-control behavior. If this program malfunctions and the tones stay on, then the batteries will drain and the instrument will shutdown because the power budget can not support continuous operation. Therefore, the most likely failure mode is CalSat would turn off within 24 hours and then de-orbit 16 years later.

The selected tones match the Amateur Satellite Service Bands as stated in the text. We chose to use these bands because there is already an international agreement in place that allows instruments like CalSat to broadcast in these bands. It is possible to request permission to broadcast using other frequencies for a limited time by applying for an “experimental” license from the FCC¹³¹³13FCC Public Notice DA:13-445. We avoided using this approach as a baseline plan because there is some risk involved. Projects using experimental licenses cannot cause interference and they cannot request protection from interference. The aforementioned Table of Frequency Allocations shows that below 300 GHz, all frequencies are already allocated, so interference is possible. Nevertheless, if CalSat moves forward, every effort will be made to maximize the utility of the instrument by adjusting the frequencies so they accommodate all possible users.

All experiments trying to extract cosmological information from the TB, EB and B-mode signals need a robust polarimeter calibration program that will allow the effect of instrument-induced errors to be mitigated during data analysis. A robust mitigation strategy for IPR, which is one of the most critical systematic errors, has not yet been identified because a suitable celestial calibration source does not exist and ground-based solutions are challenging. Moreover, the commonly used self-calibration technique, that uses the TB and EB spectra to remove any spurious B-mode signals, prohibits B-mode measurements from constraining the aforementioned isotropic departures from the standard model. CalSat was designed to be a low-cost, open-access solution to the IPR calibration problem for the CMB community, and its global visibility makes CalSat the only source that can be observed by all terrestrial and sub-orbital experiments. This global visibility makes CalSat a powerful universal standard that permits comparison between experiments from different observatories using appreciably different measurement approaches.

Johnson, Keating and Kaufman acknowledge support from winning a Buchalter Cosmology Prize (Second Prize) in 2014 for their paper entitled “Precision Tests of Parity Violation Over Cosmological Distances” Kaufman et al. [2014]. This paper explores the idea of using TB and EB spectra to study new physics via CPR, and these kinds of measurements rely on precise calibration enhancements; CalSat was used as an example of an enhanced calibration technique in this paper. We would like to thank Ari Buchalter and the Buchalter Cosmology Prize Advisory Board and Judging Panel for acknowledging our work with this prize.