High-fidelity radio interferometric data calibration that minimizes spurious spectral structure in the calibrated data is essential in astrophysical applications, such as 21 cm cosmology, which rely on knowledge of the relative spectral smoothness of distinct astrophysical emission components to extract the signal of interest. Existing approaches to radio interferometric calibration have been shown to impart spurious spectral structure to the calibrated data if the sky model used to calibrate the data is incomplete. In this paper, we introduce BayesCal: a novel solution to the sky-model incompleteness problem in interferometric calibration, designed to enable high-fidelity data calibration. The BayesCal data model supplements the a priori known component of the forward model of the sky with a statistical model for the missing and uncertain flux contribution to the data, constrained by a prior on the power in the model. We demonstrate how the parameters of this model can be marginalized out analytically, reducing the dimensionality of the parameter space to be sampled from and allowing one to sample directly from the posterior probability distribution of the calibration parameters. Additionally, we show how physically motivated priors derived from theoretical and measurement-based constraints on the spectral smoothness of the instrumental gains can be used to constrain the calibration solutions. In a companion paper, we apply this algorithm to simulated observations with a HERA-like array and demonstrate that it enables up to four orders of magnitude suppression of power in spurious spectral fluctuations relative to standard calibration approaches.
In a companion paper, we presented bayescal, a mathematical formalism for mitigating sky-model incompleteness in interferometric calibration. In this paper, we demonstrate the use of bayescal to calibrate the degenerate gain parameters of full-Stokes simulated observations with a HERA-like hexagonal close-packed redundant array, for three assumed levels of completeness of the a priori known component of the calibration sky model. We compare the bayescal calibration solutions to those recovered by calibrating the degenerate gain parameters with only the a priori known component of the calibration sky model both with and without imposing physically motivated priors on the gain amplitude solutions and for two choices of baseline length range over which to calibrate. We find that bayescal provides calibration solutions with up to 4 orders of magnitude lower power in spurious gain amplitude fluctuations than the calibration solutions derived for the same data set with the alternate approaches, and between ∼107 and ∼1010 times smaller than in the mean degenerate gain amplitude, on the full range of spectral scales accessible in the data. Additionally, we find that in the scenarios modelled only bayescal has sufficiently high fidelity calibration solutions for unbiased recovery of the 21-cm power spectrum on large spectral scales (k∥ ≲ 0.15 hMpc−1). In all other cases, in the completeness regimes studied, those scales are contaminated.
more » « less- Award ID(s):
- 1907777
- NSF-PAR ID:
- 10373248
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 517
- Issue:
- 1
- ISSN:
- 0035-8711
- Page Range / eLocation ID:
- p. 935-961
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
more » « less
ABSTRACT -
null (Ed.)ABSTRACT Precision calibration poses challenges to experiments probing the redshifted 21-cm signal of neutral hydrogen from the Cosmic Dawn and Epoch of Reionization (z ∼ 30–6). In both interferometric and global signal experiments, systematic calibration is the leading source of error. Though many aspects of calibration have been studied, the overlap between the two types of instruments has received less attention. We investigate the sky based calibration of total power measurements with a HERA dish and an EDGES-style antenna to understand the role of autocorrelations in the calibration of an interferometer and the role of sky in calibrating a total power instrument. Using simulations we study various scenarios such as time variable gain, incomplete sky calibration model, and primary beam model. We find that temporal gain drifts, sky model incompleteness, and beam inaccuracies cause biases in the receiver gain amplitude and the receiver temperature estimates. In some cases, these biases mix spectral structure between beam and sky resulting in spectrally variable gain errors. Applying the calibration method to the HERA and EDGES data, we find good agreement with calibration via the more standard methods. Although instrumental gains are consistent with beam and sky errors similar in scale to those simulated, the receiver temperatures show significant deviations from expected values. While we show that it is possible to partially mitigate biases due to model inaccuracies by incorporating a time-dependent gain model in calibration, the resulting errors on calibration products are larger and more correlated. Completely addressing these biases will require more accurate sky and primary beam models.more » « less
-
more » « less
SUMMARY Accurate synthetic seismic wavefields can now be computed in 3-D earth models using the spectral element method (SEM), which helps improve resolution in full waveform global tomography. However, computational costs are still a challenge. These costs can be reduced by implementing a source stacking method, in which multiple earthquake sources are simultaneously triggered in only one teleseismic SEM simulation. One drawback of this approach is the perceived loss of resolution at depth, in particular because high-amplitude fundamental mode surface waves dominate the summed waveforms, without the possibility of windowing and weighting as in conventional waveform tomography.
This can be addressed by redefining the cost-function and computing the cross-correlation wavefield between pairs of stations before each inversion iteration. While the Green’s function between the two stations is not reconstructed as well as in the case of ambient noise tomography, where sources are distributed more uniformly around the globe, this is not a drawback, since the same processing is applied to the 3-D synthetics and to the data, and the source parameters are known to a good approximation. By doing so, we can separate time windows with large energy arrivals corresponding to fundamental mode surface waves. This opens the possibility of designing a weighting scheme to bring out the contribution of overtones and body waves. It also makes it possible to balance the contributions of frequently sampled paths versus rarely sampled ones, as in more conventional tomography.
Here we present the results of proof of concept testing of such an approach for a synthetic 3-component long period waveform data set (periods longer than 60 s), computed for 273 globally distributed events in a simple toy 3-D radially anisotropic upper mantle model which contains shear wave anomalies at different scales. We compare the results of inversion of 10 000 s long stacked time-series, starting from a 1-D model, using source stacked waveforms and station-pair cross-correlations of these stacked waveforms in the definition of the cost function. We compute the gradient and the Hessian using normal mode perturbation theory, which avoids the problem of cross-talk encountered when forming the gradient using an adjoint approach. We perform inversions with and without realistic noise added and show that the model can be recovered equally well using one or the other cost function.
The proposed approach is computationally very efficient. While application to more realistic synthetic data sets is beyond the scope of this paper, as well as to real data, since that requires additional steps to account for such issues as missing data, we illustrate how this methodology can help inform first order questions such as model resolution in the presence of noise, and trade-offs between different physical parameters (anisotropy, attenuation, crustal structure, etc.) that would be computationally very costly to address adequately, when using conventional full waveform tomography based on single-event wavefield computations.
-
During the survey phase of the Kepler mission, several thousand stars were observed in short cadence, allowing for the detection of solar-like oscillations in more than 500 main-sequence and subgiant stars. These detections showed the power of asteroseismology in determining fundamental stellar parameters. However, the Kepler Science Office discovered an issue in the calibration that affected half of the store of short-cadence data, leading to a new data release (DR25) with corrections on the light curves. In this work, we re-analyzed the one-month time series of the Kepler survey phase to search for solar-like oscillations that might have been missed when using the previous data release. We studied the seismic parameters of 99 stars, among which there are 46 targets with new reported solar-like oscillations, increasing, by around 8%, the known sample of solar-like stars with an asteroseismic analysis of the short-cadence data from this mission. The majority of these stars have mid- to high-resolution spectroscopy publicly available with the LAMOST and APOGEE surveys, respectively, as well as precise Gaia parallaxes. We computed the masses and radii using seismic scaling relations and we find that this new sample features massive stars (above 1.2 M ⊙ and up to 2 M ⊙ ) and subgiants. We determined the granulation parameters and amplitude of the modes, which agree with the scaling relations derived for dwarfs and subgiants. The stars studied here are slightly fainter than the previously known sample of main-sequence and subgiants with asteroseismic detections. We also studied the surface rotation and magnetic activity levels of those stars. Our sample of 99 stars has similar levels of activity compared to the previously known sample and is in the same range as the Sun between the minimum and maximum of its activity cycle. We find that for seven stars, a possible blend could be the reason for the non-detection with the early data release. Finally, we compared the radii obtained from the scaling relations with the Gaia ones and we find that the Gaia radii are overestimated by 4.4%, on average, compared to the seismic radii, with a scatter of 12.3% and a decreasing trend according to the evolutionary stage. In addition, for homogeneity purposes, we re-analyzed the DR25 of the main-sequence and subgiant stars with solar-like oscillations that were previously detected and, as a result, we provide the global seismic parameters for a total of 525 stars.more » « less
-
null (Ed.)The Sun has a well-known periodicity in sunspot number and magnetic field variation. The underlying cause of this 11-year cycle is not fully understood and has yet to be connected with those processes in other stellar objects. The Full-sun Ultraviolet Rocket SpecTrograph (FURST) is a sounding rocket payload being developed by Montana State University (MSU) alongside the Marshall Space Flight Center (MSFC) solar physics group. Scheduled to launch from White Sands Missile Range (WSMR) in 2022, this instrument is unique in that it will provide the connection between stellar observatories with measurements of our Sun. It will achieve this through measuring high-resolution full-disk spectral irradiance. We aim to obtain a wavelength resolution R > 10,000 in the 120 - 181 nm UltraViolet (UV) range, on par with that of the Hubble (HST) Space Telescope Imaging Spectrograph (STIS). This resolution goal will allow us to study the relatively low-temperature plasma in the chromosphere and lower corona with spectral accuracy down to 0.1 Å (a Doppler-shift of about ± 30 km/s). In addition, the Lyman Alpha (121 nm) line is known to saturate most CCD electronics. These factors illustrate the particular challenge of precise wavelength calibration for this spectral range. We are building a collimator in order to calibrate the FURST instrument under these strict spectral requirements. This paper will present the results of our simulation of the diagnostic lamp signal to be used for wavelength calibration. The simulation allows us to begin to account for photon noise, electronic readout noise, and statistical error. These in turn lead to the development of our pre- and post-launch calibration plans. Future work includes absolute radiometric and wavelength calibration with this new collimator. In addition, the ability of FURST to measure small Doppler-shifts will provide capabilities for planetary atmospheric scientists. This impact is coupled with the diverse international partnership created by the closely-knit Sounding Rocket teams around the globe. Sounding Rockets like FURST have an even broader impact, as they encourage future satellite missions under the prospect of long-term observations.more » « less
