Measuring Visual Binary Starswith an 8-inch Telescope

N.Y.A.A, R.A.S.C. (Belleville), R.A.S.D.Dave Cotterell

Why measure binary stars?A brief history.

First double star discoveries:Mizar, 1650, RiccioliGamma Arietis, 1664, Hooke Alpha Crucis, 1685, Fontenay All early discoveries were thought to bechance alignments The brighter the star, the nearerit was thought to be.

Astronomers in the 17th century and early 18th century..had mostly accepted the work ofCopernicus and Kepler,as applied to the Solar System .still assumed all Stars were intrinsicallythe same brightness. Apparent Brightness showed Distance..BUT

Double Stars were closely observedto use parallax to determine the distance to stars

JuneDec.Therefore.

They expected to see the brighter, nearerstar to wobble back and forth relativeto the further, fainter star.

June 1675Dec. 1675June 1676Dec. 1676June 1677

But, to their surprise..

They saw a constant, very slow curved path.

The universe was Copernican and Keplerian!!!The masses of stars could be found!Along with spectral studies and an accurate magnitude scale.

Modern Astrophysics was born

What do we measure?SSeparation(Rho)180

How do we measurebinary stars?Pre-digital Era:Filar micrometer.Reticle eyepieceDigital Era:Speckle InterferometryLucky video ImagingPlate Solving from Images

Filar Micrometer

1700s to the present day..

Problems with the Filar MicrometerPlacing the stars on the filaments. Illuminated filaments drown out faint companionsSlow, painstaking work. Up to 10 measures / hour of ONE pair which are averaged to constitutea single measure for publication .Seeing makes the stars dance at the long focal lengthsnecessary for 0.1 accuracy.Difficulty getting filaments to be perpendicular to sub-arcsecond accuracyDifficulty ensuring moving filamentmaintains perfect perpendicularity.

Despite these issues, the Filar Micrometerwas the ONLY methodology availablefrom the 17th century until the 1960s.Skilled observers like F.G.W. Struve, J. HerschelBurnham, van den Bos, Aitken and many othersachieved consistent, sub-arc second accuracyin their measures...using LARGE refractors of 10 to 40 inchesaperture.

Reticle Eyepiece

1980s to present dayRestricted to quite wide and bright pairsdue to limitations of the engraved grids.

Speckle Interferometry

Single starBinary Star1960s to the present daysingle frameapply fourier transform (computer wizardry)ResultRequires large apertures to get specklesSome amateurs are using this method successfully

Plate SolvingSoftware can derive the Pixel (x , y)coordinates of all stars in a particular field of view.The rotational angle of the camerarelative to celestial north canalso be foundUnfortunately my set-up has a field of view of only 2 x 3 and does not containenough stars for Plate Solving tobe useful.

A closer look at my methodology.

Lucky Imaging.Begin with a short video.

Lucky Imaging

Gamma Leonis.

After Aligning and StackingReady for measurement.This imagerepresents the position of each componentaveraged over 200 frames.It is the equivalent of measuring each of 200 frames independently and findingthe means of the P.A. and Separation

My Equipment

8-inch Maksutov Cassegrainf/15.5, 3100mm f.l.

Canon 60Da in crop video mode640 x 480 pixels

My Laptop

Aligning and Stacking software:For PC:Deepsky Stacker RegimIRISautostakkertRegistaxNebulosity $AIP $Images Plus $$AstroArt $$Pixinsight $$Maxim $$$

For MAC:Keiths Image Stacker $LynkeosAstrostack$Nebulosity $Pixinsight $$

Analysis/Measurement Software:For PC: REDUCREDUC is all-in-one, double star specificsoftware. Just drag in your .avi or .bmpvideo files and it does EVERYTHING!And it is free!!!!!!But my Canon DSLR doesnt produce .avi files.Converting them might corrupt data at the pixel level which will ruin my accuracy.So

AstroimageJ

AstroimageJ was originally developedto analyze microscope imageryfor bacterial, viral and tissue research.It finds Centroids of stellar images to sub-sub-pixel accuracyIt will also calculate stellar magnitudescompared to a calibration star.Is available for both PC and MAC platforms And it is FREE!!!!

The Importance of CalibrationThe angle of the camera relative to the telescope, and the sky, must be knownto as much precision as possible to produce accurate Position Anglemeasurements.The plate scale of the telescope/cameracombination must be known to as much precision as possible to produce accurateSeparation measurements.

Calibration for Position AngleSimple question: at what angle to celestialnorth is my DSLR inserted into my telescope?

Position Angle CalibrationPutting the camera into the telescopeso that north is exactly at the top of the frameis neither accurate nor repeatable.I acquire a drift image of a 3 rd mag star across the full frameby taking an exposure while the scope drive is off.It is then measured for PA trigonometrically.

Frame Edge (e-w)Actual (E-W) line

Frame Edge (e-w)Actual (E-W) lineThe position angle of the line will exceed 270 degrees relative to the frame in the above case. Say, 285degrees for example.So, all P.A.s measured with the camera in this position will overestimate the P.A. by 15 degrees.A correction factor of -15 degrees is enteredin the calculating spreadsheet to yieldthe actual P.A. of each measured pair.

If the line is tilted the other way the correctionwill be positive.

Calibration for Plate Scale:Simple Question: At what focal lengthis my image acquisition system operatingand how is that related to the size of the pixels in my camera?

Calibrating Plate Scale.Plate Scale=206 265Pixel size in microns1000xfocal length (mm)x

For my telescope, 202mm f/15.5 the focal lengthis 3131 mm.

My pixels are 4.29 microns.Crunching the numbers we get a plate scale of:

0.2826 per pixel.

Simple, right?!?!

Not so fast.

The plate scale hinges entirely upon knowingthe precise focal length of the telescope.Do you really know this important number?For scopes such as SCTs and, Maksutovs which move the main mirror to achieve focusit is well known that the focal length changes with the separation betweenthe primary and secondary mirrors.As much as 10 or more percent!!!Refractors change their focal lengthby as much as 1% overthe -30C to +30C range as well

Two main ways to calibrate the plate scale.1. Image and measure a pair of stars of known separation.

Three Calibration pairsrecommended by the Washington Double Star Catalog

STF 2032inCorona Bor.5.53, 6.497.2238 d

STF 2199in Draco7.87, 8.601.952.7 d

70 Ophiuchi

4.19, 6.176.3126 d

Not reliable.

Human errorUsing an erroneous measure todetermine plate scale or Position angle correctionreduces my accuracy greatlyMeasuring the calibration pair involvessome error. This error compounds thesame error in the measured stars data

using measurements of double stars to calibrate the measurements of other double stars is certainly circular (or, if you will, Keplerian). We strongly advocate the use of other absolute calibration techniques. (6th Catalog of Orbits, WDS).As the Washington Double Star Catalog itselftells us:

A method independent of human error.depending only on the grid spacing and the wavelength of light.Enter, the Diffraction Grating

White light entering a multiple slitdiffraction grating.

I need to get ridof the rainbows.Hydrogen alpha filter with7nm bandpass @656.281 nm

Here is my diffraction grating..The mean centre-to-centre spacingof the slits in my grating is 6.015625 mm

should give me a pattern like the bottom one..The more slits, the more stellar are the points.

The angular separation of the central point and the first pointon either sideI have called z

So, since Z=206 265 x lambdaSlit Spacingthen Z=206 265 x 656.2816.015625 x 1000Z=22.5027 Z is the angular separation of the0th and 1st order images

First Order ImageFirst Order Image

22.502745.0054

Actual image of Vega with my diffraction mask0th or central image

The two first-order imagesseem to be rounder and morestellar so I measure this 2z spacing

If my analysis software shows thatthese two first order centroids are 180 pixels apart (for example)then the plate scale for that image is

45.0054180

= 0.25003 arc seconds per pixelNote that this figure is found withoutneeding to know the exact pixel size of my camera or the focal lengthof the scope/camera system!!Any pixel-size error or approximationgiven by my cameras manufacturercan be ignored!

Step by Step.

Acquire the video of the target binaries.Take a drift image, 1.5 - 2 minutes,full frame, to establish E-W line.Take a diffraction mask video of a first magnitude star. (H-alpha filter)-remove mask and filter.Field ProtocolFocus on 1st mag star carefullyusing Bahtinov Mask - remove when done

Lock focus and camera rotationTake a final drift image to checkthat camera has not rotated.

Home Protocol (1)

Analyze drift image to establishPosition Angle correction.Align and Stack and analyzeDiffraction Grating videoto determine plate scale.

Enter these calibration values in the spreadsheet

Home Protocol (2)Align and stack the videosfor each measurement pair Find the centroids of the stellar images,record (X, Y) valuesEnter (X, Y) values of the measured pairs in the calculating spreadsheet

Assemble results, write a paper,get published in the JDSO, win Nobel Prize..

The Spreadsheet AB(x,y)(x,y)dxdyD(pix)(/pix)

MeasuredSeparation

MeasuredP.A. DegreesEnter calibrated plate scale here

Enter P.A. correction value here

Typical Results. I often measure Iota Cancri (STF 1268)since its Separation, 30.1 and Position Angle, 308 degreesare virtually unchanged since its discovery in 1777I use this pair as a calibration checkon my own calibration methods. I have done seven measures of this pair.

Date:2014.122014.332014.402015.132015.132015.272015.35Theta:307.1308.4308.4307.5307.9308.0307.2Rho:30.1229.9830.1530.1829.9930.1930.06Iota Cancri Measures, 2014-2015Each measure is a stack of around 200 frames.In effect we have about 1400 individualframes measured here (if done by micrometer)Means: 307.8 degrees, 30.096

The Journal of Double Star Observations:where the Pros and the Amateurs meet on equal ground..

What can Amateurs do??

Other Amateur Double Star Contributions:Discovering new pairsDeveloping novel techniquesInvolving High School and Collegeundergrads.Contributing measures to the WDSPhotometry Data Mining - Common Proper Motion StudiesAdapting amateur-sized equipment to professional quality work

There is plenty of work to be done!

Nowan actual Align, Stack and AnalysisDemonstration.Align and Stacking software:Lynkeos.(PC folks use Registax or any other Stacking software).Centroid-finding software:AstroimageJ(available for Mac or PC)