Pie Town Research Articles

The importance of co-located VLBI Intensive stations and GNSS receivers

Frequent, low-latency measurements of the Earth’s rotation phase, expressed as UT1-UTC critically support the current estimate and short-term prediction of this highly variable Earth orientation parameter (EOP). Very long baseline interferometry (VLBI) Intensive sessions provide the required data. However, the Intensive UT1-UTC measurement accuracy depends on the accuracy of numerous models, including the VLBI station position. Intensives observed with the Maunakea (Mk) and Pie Town (Pt) stations of the Very Long Baseline Array (VLBA) illustrate how a geologic event (i.e., the M_w 6.9 Hawai‘i Earthquake of May 4th, 2018) can cause a station displacement and an associated offset in the values of UT1-UTC measured by that baseline, rendering the data from the series useless until it is corrected. Using the nonparametric Nadaraya–Watson estimator to smooth the measured UT1-UTC values before and after the earthquake, we calculate the offset in the measurement to be 75.7 ± 4.6 upmu s. Analysis of the sensitivity of the Mk-Pt baseline’s UT1-UTC measurement to station position changes shows that the measured offset is consistent with the 67.2 ± 5.9 upmu s expected offset based on the 12.4 ± 0.6 mm total coseismic displacement of the Maunakea VLBA station determined from the displacement of the co-located global navigation satellite system (GNSS) station. GNSS station position information is known with a latency on the order of tens of hours and thus can be used to correct the a priori position model of a co-located VLBI station such that it can continue to provide accurate measurements of the critical EOP UT1-UTC as part of Intensive sessions. In the absence of a co-located GNSS receiver, the VLBI station position model would likely not be updated for several months, and a near real-time correction would not be possible. This contrast highlights the benefit of co-located GNSS and VLBI stations in support of the monitoring of UT1-UTC with single-baseline Intensives.

Picturing Migrants: The Grapes of Wrath and New Deal Documentary Photography

Picturing Migrants: The Grapes of Wrath and New Deal Documentary Photography

Temporal evolution of the size and temperature of Betelgeuse’s extended atmosphere

We use the Very Large Array (VLA) in the A configuration with the Pie Town (PT) Very Long Baseline Array (VLBA) antenna to spatially resolve the extended atmosphere of Betelgeuse over multiple epochs at 0.7, 1.3, 2.0, 3.5, and 6.1 cm. The extended atmosphere deviates from circular symmetry at all wavelengths while at some epochs we find possible evidence for small pockets of gas significantly cooler than the mean global temperature. We find no evidence for the recently reported e-MERLIN radio hotspots in any of our multi-epoch VLA/PT data, despite having sufficient spatial resolution and sensitivity at short wavelengths, and conclude that these radio hotspots are most likely interferometric artefacts. The mean gas temperature of the extended atmosphere has a typical value of 3000 K at 2 $R_{\star}$ and decreases to 1800 K at 6 $R_{\star}$, in broad agreement with the findings of the single epoch study from Lim et al. (1998). The overall temperature profile of the extended atmosphere between $2 R_{\star} \lesssim r \lesssim 6 R_{\star}$ can be described by a power law of the form $T_{\mathrm{gas}}(r) \propto r^{-0.6}$, with temporal variability of a few 100 K evident at some epochs. Finally, we present over 12 years of V band photometry, part of which overlaps our multi-epoch radio data. We find a correlation between the fractional flux density variability at V band with most radio wavelengths. This correlation is likely due to shock waves induced by stellar pulsations, which heat the inner atmosphere and ionize the more extended atmosphere through radiative means. Stellar pulsations may play an important role in exciting Betelgeuse's extended atmosphere.

THE DENSITY AND MASS OF UNSHOCKED EJECTA IN CASSIOPEIA A THROUGH LOW FREQUENCY RADIO ABSORPTION

Characterizing the ejecta in young supernova remnants is a requisite step towards a better understanding of stellar evolution. In Cassiopeia A the density and total mass remaining in the unshocked ejecta are important parameters for modeling its explosion and subsequent evolution. Low frequency (<100 MHz) radio observations of sufficient angular resolution offer a unique probe of unshocked ejecta revealed via free-free absorption against the synchrotron emitting shell. We have used the Very Large Array plus Pie Town Link extension to probe this cool, ionized absorber at 9 arcseconds and 18.5 arcseconds resolution at 74 MHz. Together with higher frequency data we estimate an electron density of 4.2 electrons per cubic centimeters and a total mass of 0.39 Solar masses with uncertainties of a factor of about 2. This is a significant improvement over the 100 electrons per cubic centimeter upper limit offered by infrared [S III] line ratios from the Spitzer Space Telescope. Our estimates are sensitive to a number of factors including temperature and geometry. However using reasonable values for each, our unshocked mass estimate agrees with predictions from dynamical models. We also consider the presence, or absence, of cold iron- and carbon-rich ejecta and how these affect our calculations. Finally we reconcile the intrinsic absorption from unshocked ejecta with the turnover in Cas A's integrated spectrum documented decades ago at much lower frequencies. These and other recent observations below 100 MHz confirm that spatially resolved thermal absorption, when extended to lower frequencies and higher resolution, will offer a powerful new tool for low frequency astrophysics.

Determining asteroid spin states using radar speckles

Knowing the shapes and spin states of near-Earth asteroids is essential to understanding their dynamical evolution because of the Yarkovsky and YORP effects. Delay-Doppler radar imaging is the most powerful ground-based technique for imaging near-Earth asteroids and can obtain spatial resolution of <10 m, but frequently produces ambiguous pole direction solutions. A radar echo from an asteroid consists of a pattern of speckles caused by the interference of reflections from different parts of the surface. It is possible to determine an asteroid’s pole direction by tracking the motion of the radar speckle pattern. Speckle tracking can potentially measure the poles of at least several radar targets each year, rapidly increasing the available sample of NEA pole directions. We observed the near-Earth asteroid 2008 EV5 with the Arecibo planetary radar and the Very Long Baseline Array in December 2008. By tracking the speckles moving from the Pie Town to Los Alamos VLBA stations, we have shown that EV5 rotates retrograde. This is the first speckle detection of a near-Earth asteroid.

The 74 MHz System on the Very Large Array

The Naval Research Laboratory and the National Radio Astronomy Observatory completed implementation of a low-frequency capability on the Very Large Array at 73.8 MHz in 1998. This frequency band offers unprecedented sensitivity (~25 mJy beam-1) and resolution for low-frequency observations. The longest baselines in the VLA itself provide 25'' resolution; the system has recently been extended to the nearby Pie Town antenna of the Very Long Baseline Array, which provides resolutions as high as 12''. This paper reviews the hardware, the calibration, and imaging strategies of this relatively new system. Ionospheric phase fluctuations pose the major difficulty in calibrating the array, and they influence the choice of calibration strategy. Over restricted fields of view (e.g., when imaging a strong source) or at times of extremely quiescent ionospheric (when the ionospheric isoplanatic patch size is larger than the field of view), an angle-invariant calibration strategy can be used. In this approach a single phase correction is devised for each antenna, typically via self-calibration; this approach is similar to that used at higher frequencies. Over larger fields of view or at times of more normal ionospheric weather when the ionospheric isoplanatic patch size is smaller than the field of view, we adopt a field-based strategy in which the phase correction depends on location within the field of view. In practice, we have implemented this second calibration strategy by modeling the ionosphere above the array using Zernike polynomials. Images of 3C sources of moderate strength are provided as examples of routine, angle-invariant calibration and imaging. Flux density measurements of a subsample of these sources with previously well-determined low-frequency spectra indicate that the 74 MHz flux scale at the Very Large Array is stable to a few percent and that flux densities tied to the Baars et al. value of Cygnus A are reliable to at least 5%. We also present an example of a wide-field image, devoid of bright objects and containing hundreds of weaker sources, constructed from the field-based calibration. The paper also reviews other practical aspects of low-frequency observations, in so far as they differ from those encountered at higher frequencies, including aspects of interference excision and wide-field imaging. We close with a summary of lessons that the 74 MHz system offers as a model for new and developing low-frequency telescopes.

The hyperyoung H ii region in G24.78+0.08 A1

Context. G24.78+0.08 A1 is a 20 $M_\odot$ star surrounded by a hypercompact (HC) Hii region, driving a CO bipolar outflow, and located at the center of a massive rotating toroid undergoing infall towards the HC Hii region. Recent water maser observations suggest that the HC Hii region is expanding and accretion onto the star is halted. Aims. To confirm the expansion scenario proposed for the HC Hii region on the basis of recent H 2 O maser observations. Methods. We carried out continuum VLA observations at 1.3 cm and 7 mm with the A array plus Pie Town configuration to map the HC Hii region towards G24.78+0.08 A1. Results. The emission of the HC Hii region has been resolved and shows a ring-shape structure. The profiles of the emission obtained by taking slices at different angles passing through the barycenter of the HC Hii region confirm the shell structure of the emission. The ratio between the inner and the outer radius of the shell, $R_{\rm i}/R_{\rm o}$, derived by fitting the normalized brightness temperature profile passing through the peak of the 7 mm emission, is 0.9, which indicates that the shell is thin. The deconvolved outer radius estimated from the fit is 590 AU. These results imply that the HC Hii region in G24 A1 cannot be described in terms of a classical, homogeneous Hii region but is instead an ionized shell. This gives support to the model of an expanding wind-driven, ionized shell suggested by the kinematics and distribution of the H 2 O masers associated with the HC Hii region. According to this model, the HC Hii region is expanding on very short times scales, 21–66 yr.

Very Large Array Plus Pie Town Astrometry of 46 Radio Stars

We have used the Very Large Array, linked with the Pie Town Very Long Baseline Array antenna, to determine astrometric positions of 46 radio stars in the International Celestial Reference Frame (ICRF). Positions were obtained in the ICRF directly through phase referencing of the stars to nearby ICRF quasars whose positions are accurate at the 0.25 mas level. Radio star positions are estimated to be accurate at the 10 mas level, with position errors approaching a few milliarcseconds for some of the stars observed. Our measured positions were combined with previous measurements taken from as early as 1978 to obtain proper-motion estimates for all 46 stars with average uncertainties of ≈1.7 mas yr-1. We compared our radio star positions and proper motions with the Hipparcos Catalogue data and found consistency in the reference frames produced by each data set on the 1 σ level, with errors of ~2.7 mas per axis for the reference frame orientation angles at our mean epoch of 2003.78. No significant spin is found between our radio data frame and the Hipparcos Celestial Reference Frame, with the largest rotation rates of +0.55 and -0.41 mas yr-1 around the x- and z-axes, respectively, with 1 σ errors of 0.36 mas yr-1. Thus, our results are consistent with a nonrotating Hipparcos frame with respect to the ICRF.

The Intrinsic Size of Sagittarius A* from 0.35 to 6 cm

We present new high-resolution observations of Sagittarius A* at wavelengths of 17.4 to 23.8 cm with the Very Large Array in A configuration with the Pie Town Very Long Baseline Array antenna. We use the measured sizes to calibrate the interstellar scattering law and find that the major axis size of the scattering law is smaller by ~6% than previous estimates. Using the new scattering law, we are able to determine the intrinsic size of Sgr A* at wavelengths from 0.35 cm to 6 cm using existing results from the VLBA. The new law increases the intrinsic size at 0.7 cm by ~20% and <5% at 0.35 cm. The intrinsic size is 13^{+7}_{-3} Schwarzschild radii at 0.35 cm and is proportional to lambda^gamma, where gamma is in the range 1.3 to 1.7.

First results of the 74-MHz Very Large Array-Pie Town link. Hercules A at low frequencies

We present the results of the first successful observations of the Pie Town link with the Very Large Array at 74 MHz on Hercules A. The improvement in resolution from 25 to 10 arcsec resolves the helical- and ring-like features seen at higher frequencies. We also present new high dynamic range images of this powerful radio galaxy at 325 MHz. Our low-frequency observations confirm the multiple outburst interpretation of the spectral index differences at high frequencies. A comparison between our radio and ROSAT X-ray data does not reveal any association between the X-ray emission from the cluster and the radio lobes. There are no extra regions of radio emission at 74 MHz.

Silko: Writing Storyteller and Medicine Woman (review)

Reviewed by: Silko: Writing Storyteller and Medicine Woman Ellen L. Arnold Brewster E. Fitz. Silko: Writing Storyteller and Medicine Woman. Norman: U of Oklahoma P, 2004. xii + 288 pp. Brewster Fitz's collection of eight interconnected essays on textual or secondary orality in Leslie Marmon Silko's narrative prose offers exciting new perspectives on Silko's work. Fitz states that he discovered Storyteller in 1992, and given his interests in literary theory, he was particularly attracted by the "aesthetic, ethical, linguistic, and formal problems posed by the interaction between literacy and orality" in Silko's work (ix). Framing his study within poststructuralist, postmodern approaches to American Indian literature, Fitz presents fresh readings of old favorites like Ceremony and "Lullaby," as well as groundbreaking interpretations of such underappreciated, undertheorized texts as "From Humaweepi, the Warrior Priest," "Coyote Holds a Full House in His Hand," and Silko's newest novel, Gardens in the Dunes. Drawing on passages from Storyteller and Silko's essay "Books: Notes on Mixtec and Maya Screenfolds, Picture Books of Preconquest Mexico," Fitz makes the case in his Introduction, "The Writing Storyteller," that Silko interiorized writing at an early age from the Marmon family tradition of the writing storyteller epitomized by Silko's Carlisle-educated great-aunt, Aunt Susie. Fitz argues that the tension in Silko's work between this interiorized literacy and her desire to write from within a primarily oral culture that is threatened by literacy reflects Silko's yearning for a culturally syncretic textual orality, a "writerly dream of grounding the oral tradition and her texts in an ontologically privileged kind of universal language in which writing and orality are organically one, life-affirming, all-embracing, and motherly" (7). In chapter 1, "Bears: Writing and Madness," Fitz examines bear stories in "From Humaweepi, the Warrior Priest," the short story [End Page 194] "Storyteller" and other selections from Storyteller, and Ceremony, to explore interrelationships of writing, orality, and madness, and to describe a narrative point of view he finds characteristic of Silko's writing. Comparable to magic realism or Victor Turner's notion of "total perspective," this point of view erases boundaries between the imaginary and real, natural and supernatural, creating a realm "where language has ontological efficacy, . . . creating the things to which the words refer" (35). In this syncretic and liminal space, Silko ceremonially "rebirths" herself, becoming, Fitz suggests, a "writing medicine woman" who heals cultural wounds through written orality (50). Chapter 2, "Back to the Text: 'Lullaby,'" examines writing as both an instrument of destruction of Navajo culture (figured in the unraveling Army blanket that belonged to Ayah's dead son), and the healing remedy administered by the writing storyteller to restore the oral world it has wounded (represented by the beautiful woven traditional blankets that now exist for Ayah only in memory). Thus, says Fitz, Silko "stand[s] in for the Navajo medicine man" and the story itself becomes "the maternal blanket in which the vitality of Navajo ceremony is warmly wrapped" (81, 90). Chapter 3, "'The Battle of Pie Town,' or Littlecock's Last Stand," compares Silko's "A Geronimo Story" to Austin N. Leiby's historical account of the service of Laguna scouts in the 1885 Apache campaign (based in part on records kept by Silko's great-grandfather Robert G. Marmon and his brother Walter). Using the tradutorre (translator)/traditore (traitor) aphorism, Fitz examines the rhetorical and linguistic battle at the heart of the story. Here Fitz finds most clearly articulated the cultural wound—the loss of the Keresan language—that he assumes to be the origin of Silko's yearning for a "perfect tongue" (237). Chapter 4, "Dialogic Witchery in 'Tony's Story,'" compares journalistic accounts of the historical murder behind "Tony's Story" to Silko's fictional version, arguing that Silko rewrites the "journalistic and legal story that is a classic example of the narrative of assimilation" as "a narrative of ethnic resurgence" (119). By changing the date of the events from Good Friday to San Lorenzo Day, the day in 1680 on which the Pueblo Revolt began, Fitz observes, Silko continues the Revolt textually, "seek[ing] justice in written orality" (128). The final three chapters of the book...

The Birth of a Super-Star Cluster: NGC 5253

We present images of the 7 mm free-free emission from the radio supernebula in NGC 5253 made with the Very Large Array and the Pie Town link. The images reveal structure in the nebula, which has a ≤1 pc (~50 mas radius) core requiring the excitation of 1200 O7 stars. The nebula is elongated, with an arc of emission curving to the northeast and to the south. The total ionizing flux within the central 12 (~20 pc) is 7 × 1052 s-1, corresponding to 7000 O7 stars. We propose that the radio source is coincident with a small very red near-IR cluster and apparently linked to a larger optical source some 10 pc away on the sky. We speculate on the causes of this structure and what it might tell us about the birth of the embedded young super-star cluster.

Astrometric Positions and Proper Motions of 19 Radio Stars

We have used the Very Large Array, linked with the Pie Town Very Long Baseline Array antenna, to determine the astrometric positions of 19 radio stars in the International Celestial Reference Frame (ICRF). The positions of these stars were directly linked to the positions of distant quasars through phase-referencing observations. The positions of the ICRF quasars are known to 0.25 mas, thus providing an absolute reference at the angular resolution of our radio observations. Average values for the errors in our derived positions for all sources were 13 and 16 mas in α cos δ and δ, respectively, with accuracies approaching 1–2 mas for some of the stars observed. Differences between the ICRF positions of the 38 quasars and those measured from our observations showed no systematic offsets, with mean values of -0.3 mas in α cos δ and -1.0 mas in δ. Standard deviations of the quasar position differences of 17 and 11 mas in α cos δ and δ, respectively, are consistent with the mean position errors determined for the stars. Our measured positions were combined with previous Very Large Array measurements taken from 1978 to 1995 to determine the proper motions of 15 of the stars in our list. With mean errors of ≈1.6 mas yr-1, the accuracies of our proper motions approach those derived from Hipparcos and, for a few of the stars in our program, are better than the Hipparcos values. Comparing the positions of our radio stars with the Hipparcos Catalogue, we find that at the epoch of our observations, the two frames are aligned to within formal errors of approximately 3 mas. This result confirms that the Hipparcos frame is inertial at the expected level.

The Binary Jet in L1551 IRS 5

We have used the Very Large Array with the Pie Town antenna of the Very Long Baseline Array to image for the first time L1551 IRS 5 at 3.5 cm with an angular resolution of ~01. These observations clearly reveal the presence of a binary jet, with each component approximately centered on the 7 mm compact protoplanetary disks previously reported. As anticipated from results at various wavelengths, L1551 IRS 5 is a binary system where each star is surrounded by a disk and drives a collimated jet. The curved morphology of the northern jet, showing reflection symmetry, is suggestive of that expected for a source in a binary orbit. A region of radio emission located between the two jets could be a zone of shock interaction between the two outflows.

The Size of the Extragalactic Source J1801−231 and the Association of Pulsar PSR B1758−23 with the Supernova Remnant W28

We have used the NRAO Very Large Array (VLA) in conjunction with the Very Long Baseline Array (VLBA) Pie Town antenna as a real-time interferometer system to measure the size of the extragalactic source J1801-231 as a function of frequency from 1285 to 4885 MHz. These observations were made in an attempt to determine the effect interstellar scattering has on the observed sizes of OH (1720 MHz) masers in the nearby (d=2.5 kpc) supernova remnant W28. The observations clearly show that J1801-231 displays angular broadening due to turbulence in the Galaxy's interstellar medium. The minimum distance of the nearby (two arcminutes from J1801-231) pulsar PSR B1758-23 is constrained to be 9.4 +/- 2.4 kpc. This value is based on both the measured size of 220 mas for J1801-231 at 1715 MHz and the temporal broadening of the pulsar. A single thin scattering screen along the line of sight to the W28 OH(1720 MHz) masers must be at 4.7 +/- 1.2 kpc for this minimum pulsar distance. The screen may be placed closer to the Earth, but for reasonable values of the pulsar distance (i.e., the pulsar is within the Galaxy), this choice leads to a negligible scattering contribution to the sizes of the masers. Thus the OH(1720 MHz) masers, at a distance of 2.5 +/- 0.7 kpc, are unaffected by interstellar scattering, and the measured maser sizes must be intrinsic. Our measured upper limits to the size of the pulsar itself are consistent with the distance estimates to the pulsar and the scattering screen.

A parsec-scale study of the 5/15-GHz spectral indices of the compact radio sources in M82

Observations of the starburst galaxy, M82, have been made with the Very Large Array (VLA) in its A configuration at 15 GHz and the Multi-Element Radio-Linked Interferometer Network (MERLIN) at 5 GHz, enabling a spectral analysis of the compact radio structure on a scale of <0.1 arcsec (1.6 pc). Crucial to these observations was the inclusion of the Pie Town Very Long Baseline Array (VLBA) antenna, which increased the resolution of the VLA observations by a factor of ∼2. A number of the weaker sources are shown to have thermal spectra and are identified as H II regions with emission measures ∼10 7 cm - 6 pc. Some of the sources appear to be optically thick at 5 GHz, implying even higher emission measures of ∼10 8 cm - 6 pc. The number of compact radio sources in M82 whose origin has been determined is now 46, of which 30 are supernova-related and the remaining 16 are HII regions. An additional 15 sources are noted, but have yet to be identified, meaning that the total number of compact sources in M82 is at least 61. Also, it is shown that the distribution of HII regions is correlated with the large-scale ionized gas distribution, but is different from the distribution of supernova remnants. In addition, the brightest HII region at (B1950) 09 h 51 m 42 s .21 + 69°54'59.2 shows a spectral index gradient across its resolved structure which we attribute to the source becoming optically thick towards its centre.

Proper-Motion Measurements of Pulsar B1951+32 in the Supernova Remnant CTB 80

Using the Very Large Array and the Pie Town antenna, we have measured the position of the radio pulsar B1951+32 relative to nearby background radio sources at four epochs between 1989 and 2000. These data show a clear motion for the pulsar of 25 ± 4 mas yr-1 at a position angle 252° ± 7° (north through east), corresponding to a transverse velocity 240 ± 40 km s-1 for a distance to the source of 2 kpc. The measured direction of motion confirms that the pulsar is moving away from the center of its associated supernova remnant, the first time that such a result has been demonstrated. Independent of assumptions made about the pulsar birthplace, we show that the measured proper motion implies an age for the pulsar of 64 ± 18 kyr, somewhat less than its characteristic age of 107 kyr. This discrepancy can be explained if the initial spin period of the pulsar was P0 = 27 ± 6 ms.

Pie Town Woman: The Hard Life and Good Times of a New Mexico Homesteader

Pie Town, New Mexico, was immortalised in 1940 in the photographs of Russell Lee, who documented life in the high, dry farming community as part of the Farm Security Administration's New Deal survey of American life. This book tells the story of one of the women photographed by Lee. Doris Caudill lived on a homestead with her husband and daughter, who was six years old when Lee made his famous photographs, many of which show Doris planting her garden, canning vegetables, and milking cows. Now, more than sixty years later, Joan Myers, herself a distinguished photographer, introduces us to the woman behind the pictures.

Evidence for a solar system-size accretion disk around the massive protostar G192.16-3.82.

Seven-millimeter continuum observations of a massive bipolar outflow source, G192.16-3.82, were made at a milli-arc-second resolution with a capability that links the National Radio Astronomy Observatory's Very Large Array radio interferometer with the Very Long Baseline Array antenna, located in Pie Town, New Mexico. The observations provide evidence for a true accretion disk that is about the size of our solar system and located around a massive star. A model of the radio emission suggests the presence of a binary protostellar system. The primary protostar, G192 S1, at the center of the outflow, with a protostar mass of about 8 to 10 times the solar mass, is surrounded by an accretion disk with a diameter of 130 astronomical units (AU). The mass of the disk is on the order of the protostar mass. The outflow is poorly collimated with a full opening angle of about 40 degrees; there is no indication of a more highly collimated jetlike component. The companion source, G192 S2, is located 80 AU north of the primary source.

Structure of Sagittarius A* at 86 GH[CLC]z[/CLC] using VLBI Closure Quantities

At radio wavelengths, images of the compact radio source Sagittarius A* (Sgr A*) in the Galactic center are scatter broadened with a j2 dependence due to an intervening ionized medium. We present VLBI observations of Sgr A* at 86 GHz using a six station array, including the VLBA antennas at Pie Town, Fort Davis, and Los Alamos, the 12 m antenna at Kitt Peak, and the millimeter arrays at Hat Creek and Owens Valley. To avoid systematic errors due to imperfect antenna calibration, the data were modeled using interferometric closure information. The data are best modeled by a circular Gaussian brightness distribution of FWHM 0.18 ^ 0.02 mas. The data are also shown to be consistent with an elliptical model corresponding to the scattering of a point source. The source structure in the northsouth direction, which is less well determined than in the east-west direction because of the limited north-south u-v coverage of the array, is constrained to be less than 0.27 mas by these measurements. These results are consistent with extrapolations of intrinsic structure estimates obtained with VLBI at a 7 mm wavelength, assuming the intrinsic size of Sgr A* has a greater dependence than j0.9 with wavelength.