Requiem for Relativity

Here's the header for the first image.

SIMPLE = T / Written by IDL: Wed Apr 4 03:44:17 2007
BITPIX = -32 / Bits per pixel.
NAXIS = 2 / Number of dimensions
NAXIS1 = 300 / Length of x axis.
NAXIS2 = 300 / Length of y axis.
CTYPE1 = 'RA---TAN' / X-axis type
CTYPE2 = 'DEC--TAN' / Y-axis type
CRVAL1 = 171.6329 / Reference pixel value
CRVAL2 = -9.0335 / Reference pixel value
CRPIX1 = 150.500 / Reference pixel
CRPIX2 = 150.500 / Reference pixel
CDELT1 = -0.00047222222 / Degrees/pixel
CDELT2 = 0.00047222222 / Degrees/pixel
CROTA1 = 0.00000 / Rotation in degrees.
EQUINOX = 2000.00 /Equinox of coordinates
COMMENT
COMMENT This file was produced by the SkyView survey analysis system from
COMMENT available astronomical surveys. The data are formatted
COMMENT as a simple two-dimensional FITS image with the same units as
COMMENT the orginal survey. A single ASCII table extension may be present
COMMENT which describes catalog objects found within the field of view.
COMMENT Copies of relevant copyright notices are included in this file.
COMMENT
COMMENT Questions should be directed to:
COMMENT
COMMENT lmm@skyview.gsfc.nasa.gov
COMMENT or
COMMENT mcglynn@grossc.gsfc.nasa.gov
COMMENT
COMMENT SkyView
COMMENT Code 660.2
COMMENT Goddard Space Flight Center, Greenbelt, MD 20771
COMMENT 301-286-7780
COMMENT
COMMENT SkyView is supported by NASA ADP grant NAS 5-32068.
COMMENT
SURVEY = 'Digitized Sky Survey'
ORIGIN = 'CASB -- STScI' /Origin of FITS image
COMMENT Note these values refer to Southern plates.
TELESCOP= 'UK Schmidt (new optics)' /Telescope where plate taken
SITELONG= '+149:03:42.00' /Longitude of Observatory
SITELAT = '-31:16:24.00' /Latitute of Observatory
SCANIMG = 'CASB -- STScI ' /Name of original scan
COMMENT Properties of original survey:
COMMENT Provenance - Data taken by Royal Observatory of Edinburgh and AAO,
COMMENT Compression and
COMMENT distribution by Space Telescope Science Institute.
COMMENT Copyright - Space Telescope Science Institute and
COMMENT AAO, UK-PPART and ROE, restrictions on data transmissions
COMMENT prior to June, 1995.
COMMENT Frequency- 600 THz (J band image)
COMMENT Pixel Scale - 1.7".
COMMENT Pixel Units - Pixel values are given as scaled densities.
COMMENT Resolution - Depends on plate. Typically 2" or better.
COMMENT Coordinate system - Equatorial
COMMENT Projection - Schmidt
COMMENT Equinox - 2000
COMMENT Epoch - 1973-1994
END
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Dear Stoat:

Above posts noted and appreciated!

- Joe Keller

Apparently a 16" telescope, even with excellent modern digital equipment and technique, is barely enough for this job. I've been studying such photos. A star with USNO-B catalog Red mag +19.6 +/- 0.1 was a "can't miss" in the photo. Yet another star, on the Aladin scan image, with catalog Red mag +18.1 +/- 0.2, in the same field, was absent except for a slight pixel overdensity impossible to recognize unless one knew where to look. Some of this inconsistency seems to be due to inconsistency of the Schmidt sky survey plates and catalog mags, too, but I think much of it is due to the 16" being near its performance limit.

Searching online scans of four overlapping photographic plates from different sky surveys, I've found 21 disappearing dots near Barbarossa's theoretical track, which are plain and starlike on one plate yet absent from multiple others. (The Red plates are compared, inter alia, to at least one other modern Red plate. The Optical Infrared plate is compared, inter alia, to a plate at the wavelength immediately to either side, but not to another of the same wavelength - which I lack.)

The disappearing dots generally are somewhat smaller in diameter and subtly sharper at the edges than stars of similar magnitude. Depending on the response curve of the detector, it is theoretically possible for a dim planet to make a smaller disk than a dim star of the same bolometric magnitude (the planet is brighter than the star far from the center, but the star is brighter than the planet near the center: the star might be able to expose the detector when the planet fails to do so at all).

Thirteen of the disappearing dots are (by comparison to catalog stars) of Red magnitude +19.3 to +20.4; another was about +19 and another +18.8. These 15 dim dots are in position consistent with inner or outer moons of Barbarossa. Each of the three Red plates examined, had at least two dim dots consistent with an inner moon (by the graphing method described below) inside the orbits of Frey & Freya. By magnitude and position, three of them may well be the same inner moon.

Six of the disappearing dots are of magnitude +17.3 through +18.3. So, the distribution of the magnitudes is bimodal. Four of these six bright dots are noticeably oblong, consistent with the 0.7" theoretical one-hour track (the length of the track mainly is due to Earth's motion, not Barbarossa's)(plate exposures were as much as 75 min and maybe as little as 40 min). Three of these oblong ones are sloped roughly 0 degrees and one roughly 45 degrees (SE to NW). The 1.0" pixelization process would tend to introduce luck into the actual apparent direction of the track, but these directions are reassuringly near the theoretical 23 deg.

I converted the plate positions of the six bright dots, to heliocentric celestial coordinates, then graphed them relative to the presumed position of Barbarossa. This revealed that two of the dots are Barbarossa (Red mag +18.0, 18.3), two are Frey (Red mag +17.6, 17.3), and two Freya (Red mag +17.9, 17.9). Sketching the orbital ellipses showed that Frey's orbit is 0.7 AU and Freya's 2.0 AU. Their orbital periods are consistent with Barbarossa having 0.010 solar mass. Both orbits are circular, inclined 5.5deg to our line of sight, and tilted 16.5deg to Barbarossa's track.

Two of these six dots appeared on the 1954 POSS-I Red plate; one of them, presumably Barbarossa, was surrounded by four dimmer disappearing dots ranging from 25" (hence at least ten times the Roche limit even for a moon with only the density of Saturn) to 2' distant. Two of the six dots appeared on the 1997 SERC Optical Infrared plate; I chose as Barbarossa the one which best fit the rest of the theory (the one mentioned in my earlier post, turned out to be Freya). Two appeared on the 1987 SERC Red plate, which, despite its superiority to the 1954 plate, showed no very nearby moons for either; so, I called one of these Frey and the other Freya. Because I found no Barbarossa on the 1987 plate, there I used an interpolated position for Barbarossa, on my graph.

The choices I made, give a period of 2685 yr for Barbarossa, vs. the Saturn:Jupiter 5:2 resonance progression period of 2696 yr. This suggests low eccentricity and an orbital radius of 193 AU (I have used 191 AU in my geocentric-heliocentric corrections). The geocentric coordinates for Barbarossa for 08:01 UT April 5, 2007, would be

RA 11 26 36 Decl -8 58 01

The magnitude of Barbarossa is consistent with 1% visual albedo. Approximately 1% albedo at 5500 Angstroms, in particular, and throughout most of the visual spectrum, is predicted by the main theoretical model of "roaster" ("Class IV") giant planets, which amount to borderline brown dwarfs ( Sudarsky et al, Astrophysical Journal 538(2):885+). At 0.0068 solar mass, Barbarossa would exceed the 0.006 solar mass limit for early lithium burning, so could be just barely a brown dwarf rather than a giant planet. The main theoretical model of brown dwarfs is uncertain in its temperature prediction for Barbarossa, because of Barbarossa's uncertain age, and the strong dependence of log(T) on mass at low masses (A. Burrows et al, RevModPhys 65:301+). One must extrapolate from the corner of Burrows' table to find T=320K for Barbarossa assuming 0.01 solar masses and 4.6 billion yr age. Due to inaccuracy from extrapolation, or in the mass or age of Barbarossa, or in Burrows' model itself, Barbarossa could well in reality be a roaster. The lack of strong infrared sources in the area, on the other hand, suggests that Barbarossa is colder than 100K. Maybe an inaccuracy in Sudarsky et al's albedo model allows Barbarossa to have 1% albedo at cold temperature.

Of twelve expected appearances of Barbarossa+Frey+Freya on four plates, I found at most six. Because a single plate never has more than two bright disappearing dots, maybe Freya is one of the small moons, while Barbarossa and Frey both are giant and orbit each other: this requires only eight appearances of bright dots. The six known dots are roughly consistent with a circular mutual orbit nearly in the plane of the ecliptic. If in 1986 the Barbarossa system were eclipsed by an outer solar system dust cloud causing it to lose one magnitude, then some pair of dim dots from that plate could be Barbarossa & Frey. This would amount to complete detection of Barbarossa & Frey, with detection of a much smaller Freya and miscellaneous minor moons also.

[] sorry about that Joe, I worked out the orbital motion of the dwarf but forgot about the earth moving.

On the imaging of telescopes, what we really need is the application of hdri technology. This is used mainly in the 3d community at the moment but is making its way slowly into the photography realm. It stands for high dynamic range image.

An image set is taken with 20 f stops, then this is merged into one image. let's say we want a picture of the inside of an old church. One f stop will give us detail in the lights but lose detail in the darks. Another f stop will give us dark details but wash out the lights. hdri takes care of that. It will have to be used for imaging any terrestial planets round suns, so i'm sure it's being looked at. The main man for this work is here. Maybe he can be asked to give some thought to the problem. www.debevec.org/

I've stuck up those new coordinates on the Bradford anyway. You never know, we might get lucky.

Still trying to work out that FITS viewer. It seems that one can rotate the fits file but I just haven't managed to do it yet.

[] The Bradford did that job straight away. (not rotated yet)

01:40 on Friday 6 April 2007 (00:40:18 UTC)