Resolving Auriga Theta

[N3ptune]

Hi,

I have this interrogation today about the resolution of a double star.

Yesterday I watched the double ϴ (Theta) and I just want to be able to identify the right companion related to the primary star. For exemple, on Wikipedia I can see the following information about this double.

There is a +7.2 magnitude companion, 4.5[3] magnitudes fainter than the primary, located at an angular separation of 3.91 arcseconds

They are separated by 3.91", they are quite close to each others.

Now I am trying to measure the distances in the AFOV of all my eyepieces to be able to evaluate what  represents 3.91 arc seconds.

--> Ultimately to identify the right companion of the primary star.. or just to be able to tell if it's even possible for me to see this companion with my instrument. it's now always easy to tell which one is the right one actually.

(Maybe I won't be able to resolve 3.91 with bad seeing so I have to evaluate distances, I guess)

==============

My next step was to figure out the TFOV of my eyepieces (My telescope is 203mm x 1000mm) so for my 18 mm eyepiece I would have this:

18mm
AFOV = 60°/(1000/18=55.555) = TFOV = 1.08° (degrees)

1.08° = 64.8 Arc minutes (1.08 x 60' = 64.8')
1.08° = 3888 Arc secondes (64.8'x 60" = 3888")

--> When I watch in my 18mm piece, the AFOV of 60°, all I can see is a total 3888"

So if I do a proportion to evaluate what 3.91" is towards 3888, well, it's so small I am not sure ill be able to resolve this double star with my 18mm eyepiece.

Like the following image for example that would represent approximately my actual idea of distances.



===============
NOTE:
The resolving limit of my instrument 203mm (8 inches) x 1000mm is 5.5/8 = 0.6875 " <-- The instrument is capable of resolving 0.68 seconds so theoretically it can resolve 3.91"

===============
If i put on my 4.7mm eyepiece:
4.7mm
AFOV = 82/212.7659 = .03854° (Which is better)

.03854°= 23.12'
.03854°= 1378.44"

--> I am not sure the companion will be visible with this eyepiece either, 1378" still seems to be a lot mixed with bad seeing and scintillation, the primary star might cover the companion because of that.

Do i get it right here with this reasoning

Thanks

[YKSE]

Your calculations look right to me.

I usually do the thinking in much simplified way, based on two practical extreme cases:

1. The double double in Lyra. about 2.3" and 2.5" seperations of about equal brightness, many times it's quite easy split in 60x-70x with scopes of 80mm upwards. When seeing was bad, it may need 100x or more. that is, we can split it with magnifcation to 2' - 3'. as EDZ discussed here

2. Sirius B(mag 8), the seperation is about 13", but the huge magnitude difference between the primary and secondary makes it much more difficult to split than the double double. Only under excellent seeing have observers managed to see the pup(secondary), with magnication 100x to 200x, corresponding to 20'-40'.

My simplified approach is starting with an eyepiece with magnification somewhere between the above mentioned extremes, based on the double's seperation and magnitude differences, then going upwards, since I like to find the minimum mag needed. A zoom is a very handy tool.

As already mentioned, the most important thing is the seeing for splitting difficult doubles.

Chris Lord has a paper on uneven doubles if you're interested(look like you need to use hard copy to have an easy read).

[N3ptune]

Thanks for the link on cloudy nights it's an interesting discussion, there, a few thing to learn.

I know I can resolve 2.3 arc seconds doubles now, obviously the magnitude difference and seeing will influence a lot. Yesterday I could not split Theta Auriga even at 200x..  there was another star visible close but I don't think it was the companion, too far away, more then 3 arc seconds I am sure of that. 

I felt the companion was not visible because of the magnitude difference...  and maybe the coma effect  coming out of the primary star.

 

[N3ptune]

The second document, is quite complicated.. I don't know if I have the will (or the qualifications) to handle it yet.

[John]

16 minutes ago, N3ptune said:

The second document, is quite complicated.. I don't know if I have the will (or the qualifications) to handle it yet.

The theory is interesting but getting out there and seeing what can be done is even better I reckon !

[N3ptune]

hehehe it's interesting if you can understand it Although doing the effort to understand can be interesting too. I just have some difficulties loving maths... big problem, I have to focus on the artistic side of astronomy exclusively.

I can wait to get out and look at more double stars with beautiful contrasting colors (: So simple and I can't see the time pass.. strange. 

 

 

[YKSE]

200x on 3.9" seperation gives an image of seperation of 13' on retina, just about the middle of the mentioned extreme cases

You can't help to pounding the findings: the Moon is 30', so 30' on retina when observing naked eyes, and these difficult doubles need to be magnified to half/full moon size seperations to be seen. Our vision in dark is so much more limited than under day lights.

Going out and do observing is no doubt the best way to gain experience and train your eyes, while reading during cloudy nights and understaning the logic with help of theories will  shorten the learning curve, possibly save your valuable observing time and money.

[N3ptune]

Quote

200x on 3.9" seperation gives an image of seperation of 13' on retina

Can I learn how to figure that one out inside Chris lord's paper?  I am scared of these papers a little bit.

[YKSE]

That 13' is the same as your calculations, 200x3.9"=780"=13'.

Chris Lord's paper is an improved Rayleigh/Dawes' limit by taking into account of impact of magnitude differences.

Info in this page is somewhat easier than that paper

[N3ptune]

I began reading the second document, thanks for that link YKSE.

 

[F15Rules]

I have to confess that all that theory means nothing to me and interests me even less.

But it did prompt me to have a good look at Theta Aur the other night..it was an easy split in the Vixen ED103s at x120 and also cleanly split in my 80mm F15 at x150. I haven't looked at this star for a long time, and I was surprised at the magnitude difference between the primary and the companion. A very nice double:-).

Thanks for reminding me about this one!

Dave

[N3ptune]

F15

Great great (;

-->this thread was useful to generate happiness (: I am glad you had a good time looking at Thetra Auriga! (: Perhaps I also resolved it and saw the companion, I need to look again to validate that.

 

 

 

[N3ptune]

Obviously there is something wrong with my understanding, I still don't figure how to identify which star is the companion on a specific case. So I tried to program my telescope and eyepieces into Stellarium to do a simulation for the Auriga Theta Double star and see if my understanding make sense --> but it don't.

This below is a screen shot from Stellarium imported in AutoCAD to take some measurements, it's a work of proportions.

On this example, my eyepiece is 111x so the TFOV is:

AFOV = 60°/111x = TFOV = 0.54° / 32.4'  (I guess at 111x?) Stellarium seems to agree with me.

The double star separation is 4.1" so 111x4.1 = 455.1" / 60 = 7.58' 

-->I think I can see 0.54° / 32.4' total in this eyepiece at 111x and the companion star is 7.58' apart from the primary star. (But this can't be true apparently)

On this proportional drawing I did, there is no companion star at 7.58' so how can I know which one is the right companion ? (I suppose is the closer star, but it's just a supposition)

What am I doing wrong? is there a simple way to explain it to me?



Thanks again.

 

 

[Riemann]

9 hours ago, N3ptune said:

AFOV = 60°/111x = TFOV = 0.54° / 32.4'  (I guess at 111x?) Stellarium seems to agree with me.

The double star separation is 4.1" so 111x4.1 = 455.1" / 60 = 7.58' 

What am I doing wrong? is there a simple way to explain it to me?
 

 

The first line above is fine and gives you the true amount of angular separation in the sky you will see through your eyepiece (assuming f=1000, 18mm 60 AFOV eyepiece and 2x barlow)

The second line is not right.    You should not be magnifying up the angular separation of the binary.   The true separation is the true separation.    So to mark the binary split on your diagram you need to mark 4" i.e about 0.067' in proportion.

[EDIT: perhaps "not right" is unfair, but the result of your second calculation is the apparent separation through the eyepiece, and if you are going to use this then you need to mark it on a diagram where the scale is 60 degrees for the whole field of view.   You'll end up with the same result in terms of position on the diagram.]
 

This will lie in the fuzzy blob in the middle of your diagram.    I.e if the primary really does appear with a big fuzzy halo around it you will not be able to split it, especially as the secondary is so much fainter than the primary.   I have never tried this double but it may be a double for very good seeing conditions only.

Incidentally I am not sure where you get 4.1" as the separation on this double from.   Wiki gives 3.9" and a list of doubles I looked at gave 3.6"

My advice would be to start with an easier double (not such a big difference in magnitude between the two stars and/or slightly bigger separation) and just try it.   When you are actually observing and manage to split a double, you will know which the secondary star is because through the eyepiece it will be really really close to the primary.   The problem is separating tough doubles at all, not knowing which the two stars are.

 

[Stu]

I would agree with Riemann, have a try at some other easier doubles so you begin to get an idea of what the image scale is with different eyepieces. I also agree that the problem is normally splitting the double rather than identifying the secondary ie it is usually obvious which the closest star is.

Have a look at Polaris which has a primary of 2,  a secondary of 9.1 and a separation of 18.2"

Rigel has a primary of 0.28, secondary is 6.8 and the separation is 9.3"

How about Castor which has a primary of 1.58 a secondary of 2.97 and a separation of 5.1", slightly more than Theta Aur. (Note I've just corrected the magnitudes because they were totally wrong!!)

Izar is a good challenge, a more even double but quite tight; 2.5, 4.81 and a separation of 3.0"

Algieba might be an interesting reference too at 2.23, 3.64 and a separation of 4.6"

As said, these should give you some more experience in the separations and brightness differences to help with further understanding?

[Riemann]

2 hours ago, Stu said:

Have a look at Polaris which has a primary of 2,  a secondary of 9.1 and a separation of 18.2"

Rigel has a primary of 0.28, secondary is 6.8 and the separation is 9.3"

How about Castor which has a primary of 2.88, a secondary of 9.83 and a separation of 5.1", slightly more than Theta Aur.

Izar is a good challenge, a more even double but quite tight; 2.5, 4.81 and a separation of 3.0"

Algieba might be an interesting reference too at 2.23, 3.64 and a separation of 4.6"

This is nice list of doubles from Stu.    A few comments that might help you N3ptune....

Rigel I find quite a tough split, dependent on good conditions, the challenge being to get a really clean split with black between the primary and secondary.   

Castor is relatively easy probably helped by it being high in the sky.

Izar is tight as Stu says, and you will may need more magnification than 111 to get a clean split.

Algieba is an easy split.

 

I generally like 150x or 200x for splitting doubles.

You might also like to try the trapezium in Orion and try to split two extra stars.

[N3ptune]

Riemann

Ok now it's clear, i should have thought that the true separation is the true separation... Now I know double stars are really close from one another, no doubt about it. (Took time but now I understand)

The 4.1" came from the cambridge double star atlas second edition, I also saw 3.9 on wikipedia. The number is moving from one place to another it seems.

The primary is 2.6 magnitude and the secondairy is 7.2, for a distance of 4.1"

For me this one is hard apparently, the primary is quite bright in the eyepiece too.

STU

I tried Castor, really interesting system. I can see 2 stars touching, the book says it's a sextuple system. Hope to see more stars on a better day.

Thanks for the suggestion also, i wrote the names on a post it for next time.

(: soon the great sky will come back.

[Don Pensack]

When looking to see double stars as separate, people with excellent vision will tolerate an apparent separation of 4' of arc.

Good, but not excellent vision tends to prefer separations of 6' to 8' (8' is easy for everyone).

Let's figure the magnifications needed, and bear in mind this calculation can be used on any double star:

4' is 240"

6' is 360"

8' is 480"

Divide any of those by the separation of the double star, and you'll have the magnification needed to easily see the stars as separate.

3.91" separation means 61.4x, 92.1x, and 122.8x, or fairly low magnifications.

But, seeing is all-important.  On a superb seeing night, I can resolve the 4 stars of epsilon Lyrae at 59x.  On a "wooly" night, it takes 120-140x to do it.

So it would be in your 8", too.

So let's be conservative and take the apparent separation of 8' to be the easier magnification, i.e. 122.8x

Are there circumstances where this wouldn't be enough?  Yes.  If the separation of the magnitudes exceeds, say, 6 magnitudes, then higher magnifications will be needed to guarantee you can see a tiny pin-prick in the vicinity of a really bright companion.

For instance, take Sirius.  The separation is wide enough now that the 8' apparent separation should only require 45-50x.  But the secondary is so faint compared to the primary (close to ten magnitudes!) and even the slightest seeing anomalies

will cause the primary to bloat up with all kinds of spikes, that a magnification of 100x or more is really preferable to spot the companion, an apparent separation of over 16' (!).

 

Someone mentioned Castor in Gemini: the individual components are magnitude 1.93, 2.97, and 9.83 (aka YY Geminorum).  All 3 stars are spectroscopic binaries (i.e. only a spectrum reveals the companions--they are too close to resolve optically).

And that 3rd star is far enough away and faint enough it pretty much doesn't really turn Castor into a triple star.  So, to all intents and purposes, Castor is a double star with a separation of about 7.4", a test object in a 0.61" telescope (i.e. resolvable by all telescopes), and only needs 65x to be comfortably split.

[N3ptune]

DON

Thanks for these explanations on double stars, really simple and understandable, it helped me even more. The rule of thumbs 4' is 240", 6' is 360" , 8' is 480"  great idea to choose in relation with the information inside my atlas like difference of magnitude for unequal inside my book and seeing (Sirius). I am getting better at this (:

I was not even aware yet that the spectroscopic binaries were too close to resolve optically.. It's good to know to waste less time...

==============

Then I tried Auriga Theta again, (This beautiful constellation is going away, slowly )

I did a sketch a few days ago, 2016-04-16 of Theta, the angle is not good on my drawing, should be like the Stellarium illustration. I think I could see the companion has pointed, I am not 100% sure but lt looks like it, really close, really faint.

 

 

[N3ptune]

Deleted double

[N3ptune]

if someone indulges in watching this star, Auriga Theta, I would be fun to know if my latest drawing is accurate just to compare and see.