The Gravity Probe B mission provided two new quantitative tests of Einstein’s theory of gravity, general relativity (GR), by cryogenic gyroscopes in Earth’s orbit. Data from four gyroscopes gave a geodetic drift-rate of −6601.8 ± 18.3 marc-s yr−1 and a frame-dragging of −37.2 ± 7.2 marc-s yr−1, to be compared with GR predictions of −6606.1 and −39.2 marc-s yr−1 (1 marc-s = 4.848 × 10−9 radians). The present paper introduces the science, engineering, data analysis, and heritage of Gravity Probe B, detailed in the accompanying 20 CQG papers.

We used 8.4 GHz very long baseline interferometry images obtained at up to 35 epochs between 1997 and 2005 to examine the radio structures of the main reference source, 3C 454.3, and two secondary reference sources, B2250+ 194 and B2252+ 172, for the guide star for the NASA/Stanford relativity mission Gravity Probe B ( GP-B). For one epoch in 2004 May, we also obtained images at 5.0 and 15.4 GHz. The 35 8.4 GHz images for quasar 3C 454.3 confirm a complex, evolving, core-jet structure. We identified at each epoch a component, C1, near the easternmost edge of the core region. Simulations of the core region showed that C1 is located, on average, 0.18 +/- 0.06 mas west of the unresolved "core" identified in 43 GHz images. We also identified in 3C 454.3 at 8.4 GHz several additional components that moved away from C1 with proper motions ranging in magnitude between 0.9 c and 5 c. The detailed motions of the components exhibit two distinct bends in the jet axis located similar to 3 and similar to 5.5 mas west of C1. The spectra between 5.0 and 15.4 GHz for the "moving" components are steeper than those for C1. The 8.4 GHz images of B2250+ 194 and B2252+ 172, in contrast to those of 3C 454.3, reveal compact structures. The spectrum between 5.0 and 15.4 GHz for B2250+ 194 is inverted while that for B2252+ 172 is flat. Based on its position near the easternmost edge of the 8.4 GHz radio structure, close spatial association with the 43 GHz core, and relatively flat spectrum, we believe 3C 454.3 component C1 to be the best choice for the ultimate reference point for the GP-B guide star. The compact structures and inverted-to-flat spectra of B2250+ 194 and B2252+ 172 make these objects valuable secondary reference sources.

We describe the NASA/Stanford gyroscope relativity mission, Gravity Probe B (GP-B), and provide an overview of the following series of six astrometric and astrophysical papers that report on our radio observations and analyses made in support of this mission. The main goal of this 8.5 year program of differential very long baseline interferometry astrometry was to determine the proper motion of the guide star of the GP-B mission, the RS CVn binary IM Pegasi (IM Peg; HR 8703). This proper motion is determined with respect to compact, extragalactic reference sources. The results are -20.833 +/- 0.090 mas yr(-1) and -27.267 +/- 0.095 mas yr(-1) for, respectively, the right ascension and declination, in local Cartesian coordinates, of IM Peg's proper motion, and 10.370 +/- 0.074 mas (i. e., 96.43 +/- 0.69 pc) for its parallax (and distance). Each quoted uncertainty is meant to represent an similar to 70% confidence interval that includes the estimated contribution from systematic error. These results are accurate enough not to discernibly degrade the GP-B estimates of its gyroscopes' relativistic precessions: the frame-dragging and geodetic effects.

When very long baseline interferometry (VLBI) observations are used to determine the position or motion of a radio source relative to reference sources nearby on the sky, the astrometric information is usually obtained via (1) phase-referenced maps or (2) parametric model fits to measured fringe phases or multiband delays. In this paper, we describe a "merged" analysis technique which combines some of the most important advantages of these other two approaches. In particular, our merged technique combines the superior model-correction capabilities of parametric model fits with the ability of phase-referenced maps to yield astrometric measurements of sources that are too weak to be used in parametric model fits. We compare the results from this merged technique with the results from phase-referenced maps and from parametric model fits in the analysis of astrometric VLBI observations of the radio-bright star IM Pegasi (HR 8703) and the radio source B2252+ 172 nearby on the sky. In these studies we use central-core components of radio sources 3C 454.3 and B2250+ 194 as our positional references. We obtain astrometric results for IMPeg with our merged technique even when the source is too weak to be used in parametric model fits, and we find that our merged technique yields astrometric results superior to the phase-referenced mapping technique. We used our merged technique to estimate the proper motion and other astrometric parameters of IM Peg in support of the NASA/Stanford Gravity Probe B mission.

We present the principal astrometric results of the very long baseline interferometry (VLBI) program undertaken in support of the Gravity Probe B (GP-B) relativity mission. VLBI observations of the GP-B guide star, the RS CVn binary IM Pegasi (HR 8703), yielded positions at 35 epochs between 1997 and 2005. We discuss the statistical assumptions behind these results and our methods for estimating the systematic errors. We find the proper motion of IM Peg in an extragalactic reference frame closely related to the International Celestial Reference Frame 2 (ICRF2) to be −20.83 ± 0.03 ± 0.09 mas yr−1 in right ascension and −27.27 ± 0.03 ± 0.09 mas yr−1 in declination. For each component, the first uncertainty is the statistical standard error and the second is the total standard error (SE) including plausible systematic errors. We also obtain a parallax of 10.37 ± 0.07 mas (distance: 96.4 ± 0.7 pc), for which there is no evidence of any significant contribution of systematic error. Our parameter estimates for the ∼25 day period orbital motion of the stellar radio emission have SEs corresponding to ∼0.10 mas on the sky in each coordinate. The total SE of our estimate of IM Peg's proper motion is ∼30% smaller than the accuracy goal set by the GP-B project before launch: 0.14 mas yr−1 for each coordinate of IM Peg's proper motion. Our results ensure that the uncertainty in IM Peg's proper motion makes only a very small contribution to the uncertainty of the GP-B relativity tests.

We present a physical interpretation for the locations of the sources of radio emission in IM Pegasi (IM Peg, HR 8703), the guide star for the NASA/ Stanford relativity mission Gravity Probe B. This emission is seen in each of our 35 epochs of 8.4 GHz very long baseline interferometry observations taken from 1997 to 2005. We found that the mean position of the radio emission is at or near the projected center of the primary to within about 27% of its radius, identifying this active star as the radio emitter. The positions of the radio brightness peaks are scattered across the disk of the primary and slightly beyond, preferentially along an axis with position angle, P. A.=-38 degrees +/- 8 degrees, which is closely aligned with the sky projections of the orbit normal (P. A. = -49 degrees.5 +/- 8 degrees.6) and the expected spin axis of the primary. Comparison with simulations suggests that brightness peaks are 3.6+ 0.4-0.7 times more likely to occur (per unit surface area) near the pole regions of the primary (latitude, |lambda| >= 70 degrees) than near the equator (|lambda| <= 20 degrees.), and to also occur close to the surface with similar to 2/3 of them at altitudes not higher than 25% of the radius of the primary.

We present measurements of the total radio flux density as well as very long baseline interferometry images of the star, IM Pegasi, which was used as the guide star for the NASA/ Stanford relativity mission Gravity Probe B. We obtained flux densities and images from 35 sessions of observations at 8.4 GHz (lambda=3.6 cm) between 1997 January and 2005 July. The observations were accurately phase-referenced to several extragalactic reference sources, and we present the images in a star-centered frame, aligned by the position of the star as derived from our fits to its orbital motion, parallax, and proper motion. Both the flux density and the morphology of IM Peg are variable. For most sessions, the emission region has a single-peaked structure, but 25% of the time, we observed a two-peaked (and on one occasion perhaps a three-peaked) structure. On average, the emission region is elongated by 1.4 +/- 0.4 mas (FWHM), with the average direction of elongation being close to that of the sky projection of the orbit normal. The average length of the emission region is approximately equal to the diameter of the primary star. No significant correlation with the orbital phase is found for either the flux density or the direction of elongation, and no preference for any particular longitude on the star is shown by the emission region.

We made very long baseline interferometry observations at 8.4 GHz between 1997 and 2005 to estimate the coordinates of the “core” component of the superluminal quasar, 3C 454.3, the ultimate reference point in the distant universe for the NASA/Stanford Gyroscope Relativity Mission, Gravity Probe B (GP-B). These coordinates are determined relative to those of the brightness peaks of two other compact extragalactic sources, B2250+194 and B2252+172, nearby on the sky, and within a celestial reference frame (CRF), defined by a large suite of compact extragalactic radio sources, and nearly identical to the International Celestial Reference Frame 2 (ICRF2). We find that B2250+194 and B2252+172 are stationary relative to each other, and also in the CRF, to within 1σ upper limits of 15 and 30 μas yr−1 in α and δ, respectively. The core of 3C 454.3 appears to jitter in its position along the jet direction over ∼0.2 mas, likely due to activity close to the putative supermassive black hole nearby, but on average is stationary in the CRF within 1σ upper limits on its proper motion of 39 μas yr−1 (1.0c) and 30 μas yr−1 (0.8c) in α and δ, respectively, for the period 2002–2005. Our corresponding limit over the longer interval, 1998–2005, of more importance to GP-B, is 46 and 56 μas yr−1 in α and δ, respectively. Some of 3C 454.3's jet components show significantly superluminal motion with speeds of up to ∼200 μas yr−1 or 5c in the CRF. The core of 3C 454.3 thus provides for GP-B a sufficiently stable reference in the distant universe.

We used very-long-baseline interferometry (VLBI) radio observations at 8.4~GHz between 1997 and 2005 to determine the coordinates of the ``core'' of the quasar, 3C 454.3, relative to the extragalactic sources, B2250+194, and for the last half of the time also to another extragalactic source, B2252+172, both nearby on the sky. The core of 3C 454.3 is stationary relative to these two sources, with the 1 upper limit on its proper motion being 15 as yr-1 in right ascension and 25 as yr-1 in declination. The corresponding upper limit on the proper motion of this core with respect to the quasi-inertial reference frame determined from separate VLBI observations of many extragalactic radio sources, including B2250+194, is 30 as yr-1 in each of the coordinates. The core of 3C 454.3 provides a sufficiently stable reference with which to measure the proper motion of the Gravity Probe B guide star, IM Pegasi, relative to the distant universe. N. Bartel, R. R. Ransom, M. F. Bietenholz, J. I. Lederman (York University, Toronto, Canada) D. E. Lebach, M. I. Ratner, I. I. Shapiro (Harvard-Smithsonian CfA) L. Petrov (NVI, Inc. NASA / GSFC)

Abstract We used VLBI observations at 8.4 GHz between 1991 and 2005 to determine the motion of the RS CVn binary IM Pegasi (HR 8703), the guide star for the NASA/Stanford gyroscope relativity mission, Gravity Probe B (GP-B). The motion was determined relative to our primary reference, the core of the quasar 3C 454.3. The stability of this core was checked relative to two other extragalactic sources, B2250+194 and B2252+172, the former of which was tied to the ICRF. The core of 3C 454.3 is stationary relative to these two sources to within 30 μas yr−1 in each coordinate. IM Pegasi's radio morphology varies, but appears to be on average centered on the primary. We estimate the proper motion of IM Pegasi with a statistical standard error (sse) of 30 μas yr−1 in each coordinate. We also estimate the parallax with a statistical standard error of 75 μas and parameters of the orbit with sse's corresponding to 110 μas on the sky. Coupled with our upper limit of three times the sse on any systematic errors in each parameter %threefold higher upper limit on the systematic error contributions to each parameter estimate, these results ensure that the uncertainty of IM Pegasi's proper motion makes only a small contribution to the uncertainty of GP-B's tests of general relativity.

We have made multi-epoch VLBI observations at 3.6 cm (8.4 GHz) of the RS CVn binary star HR 8703 (IM Pegasi) in support of the NASA-Stanford relativity gyroscope experiment, Gravity Probe B (GP-B). We present a selection of phase-referenced images of HR 8703 produced from 28 sets of observations made between December 1991 and November 2002. The images show radio source structures that vary in size from ∼0.5 mas to ∼2 mas. Moreover, images from temporal subsets of several observing sessions exhibit both structural evolution in the radio emission and motions of the radio centroid of up to ∼1 mas on hour time scales. Based upon an astrometric analysis of the phase-referenced positions obtained at each epoch, we have (1) made accurate determinations of HR 8703’s parallax and proper motion, and (2) apparently detected the major axis of the orbit of HR 8703’s K2 III primary.

We have regularly observed at 8.4 GHz one to three extragalactic radio sources as references for the astrometric campaign on the guide star HR 8703 (IM Pegasi) in support of the NASA-Stanford gyroscope relativity mission, Gravity Probe B. We present a selection of the images of these sources produced from observations between January 1997 and November 2002. We discuss the observed source structures and examine their possible effects on our astrometric results for HR 8703.

We used very-long-baseline interferometry (VLBI) to measure the deflection by the Sun of radio waves emanating from distant compact radio sources. This bending is characterized in the parametrized post-Newtonian formalism by gamma, which is unity in general relativity. Using a large geodetic VLBI data set, we obtained gamma=0.9998(3)+/-0.0004(5) (estimated standard error). We found no systematic biases from our analysis of subgroups of data.

We present VLBI images of the RS CVn binary star HR 5110 (=BH CVn; HD 118216), obtained from observations made at 8.4 GHz on 1994 May 29/30 in support of the NASA/Stanford Gravity Probe B project. Our images show an emission region with a core-halo morphology. The core was 0.39 +/- 0.09 mas (FWHM) in size, or 66 chromospherically active K subgiant star in the binary system. The halo was 1.95 +/- 0.22 mas (FWHM) in size, or 1.8 +/- 0.2 times the 1.1 +/- 0.1 mas separation of the centers of the K and F stars. The core increased significantly in brightness over the course of the observations and seems to have been the site of flare activity that generated an increase in the total flux density of 200 simultaneously decreased from 10

We present VLBI images of the RS CVn binary star HR 5110 (= BH CVn; HD 118216), obtained from observations made at 8.4 GHz on 1994 May 29/30 in support of the NASA/Stanford Gravity Probe B project. Our images show an emission region with a core-halo morphology. The core was 0.39 ± 0.09 mas (FWHM) in size, or 66% ± 20% of the 0.6 ± 0.1 mas diameter of the chromospherically active K subgiant star in the binary system. The halo was 1.95 ± 0.22 mas (FWHM) in size, or 1.8 ± 0.2 times the 1.1 ± 0.1 mas separation of the centers of the K and F stars. (The uncertainties given for the diameter of the K star and its separation from the F star each reflect the level of agreement of the two most recent published determinations.) The core increased significantly in brightness over the course of the observations and seems to have been the site of flare activity that generated an increase in the total flux density of ~200% in 12 hr. The fractional circular polarization simultaneously decreased from ~10% to 2.5%.

We present the first VLBI images of the RS CVn binary star HR 1099 (=V711 Tauri, HD 22468) obtained from observations at 8.4 GHz in 1996 May and September made in support of the NASA/Stanford Gravity Probe B project. The first set of observations was made during a decay stage of a flare event. The second set of observations was made during a quiescent period. The detected emission region for the active epoch had an estimated major-axis length (FWHM) of 2.7 ± 0.2 mas. This region consisted of a halo and two superimposed compact condensations that were oriented approximately east-west. The centers of the compact condensations were separated by 1.7 ± 0.1 mas. Compared to the ~1.3 mas separation on the sky at this epoch of the centers of the stellar components of the binary, the observed separation of the condensations differs by only 0.4 mas, which is less than the ~0.6 mas angular radius of the larger component. During the observations, the compact western condensation rotated north-northwestward by 24° ± 4°, or by 0.7 ± 0.1 mas, relative to the eastern condensation. We speculate that (1) either both condensations originate from the corona of the larger stellar component or one condensation is close to the surface of each of the two stellar components of the binary and (2) the relative rotation of the two condensations is a consequence of the rotation of the binary system. We speculate further that the halo is a consequence of flare-energized electrons confined by the magnetosphere of the larger stellar component or by the combined magnetospheres of the two stellar components. Our quiescent epoch, in contrast, was characterized by a single emission region with a major axis estimated to be 1.7 ± 0.1 mas (FWHM).