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Using B-V indexes to "find" absorption nebulae?

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#1 Enkidu

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Posted 13 September 2019 - 01:30 PM

–Is there a formula that gives an intrinsic B-V index by stellar temperature?
–Is there also a constant for the ISM that can be multiplied by distance to determine reddening?

 

If so, couldn't you combine the two and compare the results with actual B-V values?
–Stars whose B-V values match the calculation could be considered a "clear view" through the ISM.
–Single star anomalies might indicate an atmosphere or nearby shell that obscures the light.
–Groups of stars in the same area with a similar B-V shift could indicate nebulosity and provide a rough distance.

 

With a list of stellar temperatures and distances (down to mag ~6) in excel, it wouldn't take long to find the outliers; maybe a little more complicated to plot them.

 

Perhaps it would be interesting for areas away from the galactic equator? I’ve oversimplified things, but crudely tracing nebulae based on data seems like a nice preparation for contemplative observing.



#2 Feidb

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Posted 14 September 2019 - 10:38 PM

Geez, I don't even know what that is.


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#3 Enkidu

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Posted 15 September 2019 - 04:13 AM

B-V is a star color index, obtained by subtracting apparent visual magnitude from the blue-only magnitude: Vega is 0, hotter stars are negative numbers and bluer, while positive numbers are increasingly red.

 

ISM is the interstellar medium. Starlight passing through it gradually becomes more red, since blue light scatters more easily. This is known as interstellar extinction. The ISM is not uniform in temperature or density, but it causes much less extinction than absorption/dark nebulae.

 

Matter in a star's atmosphere can also absorb blue light (such as carbon stars) or by a surrounding gas cloud like Mu Cep's, however I thought it would be interesting to comb the data and collect evidence for dark nebulae. They're relatively easy to spot visually against the Milky Way, but I'd like to observe other parts of the sky and imagine them out there.


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#4 Tony Flanders

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Posted 15 September 2019 - 02:36 PM

–Is there a formula that gives an intrinsic B-V index by stellar temperature?


Sure, this is the black-body radiation curve for that temperature. Stars aren't quite black bodies -- and for that matter, they don't have uniform temperatures, because the poles of a spinning star are quite a bit closer to the core than the equator is. But in most cases, the black-body radiation curve is close enough.

Sadly, it's not so easy to measure a star's temperature accurately. You get a pretty good indication based on absorption lines, the method that classifies stars as OBAFGKM. But it's rather crude.
 

–Is there also a constant for the ISM that can be multiplied by distance to determine reddening?


No, the interstellar medium is inhomogeneous at every scale. To a first approximation, it's high near the galactic plane and thins out rapidly as you move out of the plane of the galaxy. But the details are complex.

 

Moreover, the only way to measure a star's distance that doesn't in itself make assumptions about the star's age, chemical composition, and rotation, as well as the interstellar medium, is parallax. And prior to GAIA, parallax was only reliable out to about 1,00 0 light-years, including just a tiny slice of the Milky Way's Local Arm. Even now, parallax isn't well known for many important stars.

So you're correct that this is possible in principle, and it is certainly something that astronomers work on. But the uncertainties are huge every step of the way.


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#5 catalogman

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Posted 15 September 2019 - 08:00 PM

–Is there a formula that gives an intrinsic B-V index by stellar temperature?
–Is there also a constant for the ISM that can be multiplied by distance to determine reddening?

 

<snip>

The formula that the OP is looking for is the color temperature:

 

  Tc = 7300 / [(B - V) + 0.73]

 

Interstellar reddening can be determined by either the cluster method or the reddening-curve method

(see Galactic Astronomy, by Mihalas and Routly, 1968; pp. 70-76).

 

-- catalogman


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#6 Enkidu

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Posted 17 September 2019 - 02:42 AM

Rock stars! Thank you both very much for taking the time to respond in detail.

 

catalogman, that is the formula I was looking for. I've had my eye on a more recent version of that book.

 

Even "getting to know the neighborhood" within a kiloparsec, I could possibly trace the Taurus dark cloud. A primitive experiment, but useful (for me).

 

I wasn't aware of the crudeness of spectroscopic temperature readings. Very interesting!

 

ISM.JPG



#7 happylimpet

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Posted 17 September 2019 - 03:45 AM

–Is there a formula that gives an intrinsic B-V index by stellar temperature?
–Is there also a constant for the ISM that can be multiplied by distance to determine reddening?

 

If so, couldn't you combine the two and compare the results with actual B-V values?
–Stars whose B-V values match the calculation could be considered a "clear view" through the ISM.
–Single star anomalies might indicate an atmosphere or nearby shell that obscures the light.
–Groups of stars in the same area with a similar B-V shift could indicate nebulosity and provide a rough distance.

 

With a list of stellar temperatures and distances (down to mag ~6) in excel, it wouldn't take long to find the outliers; maybe a little more complicated to plot them.

 

Perhaps it would be interesting for areas away from the galactic equator? I’ve oversimplified things, but crudely tracing nebulae based on data seems like a nice preparation for contemplative observing.

 

The thing is it would be a slightly circular argument, as most stellar temperatures are determined photometrically in the first place. Only the brightest stars (by which i mean maybe the brightest 100,000 stars) will have spectroscopic classifications which can be cross-checked with colour temp.

 

However, as there are so many stars in even small patches of sky, I dont see why you couldnt plot the mean (B-V) colour for, say, all stars within 10x10' patches of sky to find places where excess reddening occurred suggestive of dust. There would be a lot of scatter, and places where star clusters skewed the result, but it would all be interesting. I'd be fascinated to see the result.

 

I'd also be surprised if no-one has done this!

 

Good idea though.


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#8 catalogman

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Posted 17 September 2019 - 06:29 PM

If you don't want to buy or borrow the book, then here's my summary:

 

Reddening is measured by color excess, which is the difference of the observed color index and the intrinsic

color index. To see it graphically, plot U - B vs. B - V.  The slope of the reddening line is nearly 0.72 for all

spectral types but the y-intercepts differ. For spectrum types O and B only, this slope is related to the parameter Q:

 

Q = (U - B) - 0.72(B - V)

 

From Q, the precise O/B spectral subtype and absolute mag M are determined, so no spectra are needed and the

reasoning is not circular.

 

In the cluster method, the slope of V - M vs. E(B - V) gives R, the ratio of absorption in magnitudes to the observed

color excess. This is 3.0 in the Double Cluster, 4.8 in Orion's Belt, 5.7 in Orion's Sword, and 6.0 in the Rosette Nebula.

So, to answer the second part of the OP, there is no uniform interstellar reddening law like Hubble's Law; this has

been confirmed by more recent studies:

 

http://adsabs.harvar...ASPC..482..275S

 

For more details, here are the early studies which are summarized in the book:

 

http://adsabs.harvar...ApJ...117..313J

http://adsabs.harvar...ApJ...124..367H

http://adsabs.harvar...ApJ...141..923J

 

-- catalogman


Edited by catalogman, 17 September 2019 - 06:30 PM.

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#9 happylimpet

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Posted 18 September 2019 - 04:58 AM

If you don't want to buy or borrow the book, then here's my summary:

 

Reddening is measured by color excess, which is the difference of the observed color index and the intrinsic

color index. To see it graphically, plot U - B vs. B - V.  The slope of the reddening line is nearly 0.72 for all

spectral types but the y-intercepts differ. For spectrum types O and B only, this slope is related to the parameter Q:

 

Q = (U - B) - 0.72(B - V)

 

From Q, the precise O/B spectral subtype and absolute mag M are determined, so no spectra are needed and the

reasoning is not circular.

 

In the cluster method, the slope of V - M vs. E(B - V) gives R, the ratio of absorption in magnitudes to the observed

color excess. This is 3.0 in the Double Cluster, 4.8 in Orion's Belt, 5.7 in Orion's Sword, and 6.0 in the Rosette Nebula.

So, to answer the second part of the OP, there is no uniform interstellar reddening law like Hubble's Law; this has

been confirmed by more recent studies:

 

http://adsabs.harvar...ASPC..482..275S

 

For more details, here are the early studies which are summarized in the book:

 

http://adsabs.harvar...ApJ...117..313J

http://adsabs.harvar...ApJ...124..367H

http://adsabs.harvar...ApJ...141..923J

 

-- catalogman

Nice summary, thanks for that - and I really should have known that too......

 

I always used (probably quite sloppily) a generic R of Av=3.1 x E(B-V), or was the constant 2.7? I didnt realise it was so variable.

 

Blimey its been too long.....



#10 catalogman

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Posted 19 September 2019 - 01:37 PM

Professional astronomers originally accepted a value of Rvis = 3.0 +/ 0.2. Sharpless (1952) found the

first deviation of Rvis = 6 near the Orion Nebula; the last paper by Johnson (cf. Post #8) gives others.

 

For more info, I will pm a scan of some pages from the book Galactic Astronomy. This should also

answer both of the original questions by the OP.

 

-- catalogman


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