31 replies to this topic

[DGK]

Thanks for taking a look at the photon flux values and confirming I am good. Just a minor correction regarding my B-V's - those you quote are the CALSPEC values which I put in front of the names, my calculated values are very close to yours (HZ44 -0.28 and Sun +0.65). The difference likely is because we are using slightly different V-band response. Curious why we are not getting the same as the CALSPEC values. One day I will load the half million point resolution of the spectra's and see if that is why, but not today.

 

The BCv's have beaten me as well, but due to my inexperience it took me substantially longer than a few hours to arrive at that point! I just can't get sensible numbers out of what Bessel 1998 describes (see citation post #16). I plugged the real spectra for Vega (V-band not much different to a BB by the way, just sayin') and I just can't get any where near the 0.03 mag using his V (p242). I triple checked all my unit conversions to the weird non-SI ones astronomers' use. Very frustrating. 

[FredDawes]

Not to hijack this thread but I just happened to be working through a problem related to bolometric correction in Carroll and Ostlie's textbook "An Introduction to Modern Astrophysics" (2017 edition) and was wondering if someone who knows this topic or has the book could help me with a beginner-level question.

 

My question is:

 

How are bolometric corrections calculated in practice?

 

The formula given in the book for bolometric correction (page 76, equation 3.30) is:

 

BC = m_bol - V = M_bol - M_V

 

where "_" denotes subscript, m_bol is the star's bolometric magnitude, V is the star's visual magnitude, M_bol is the star's absolute bolometric magnitude, and M_V is the star's absolute visible magnitude.

 

In Example 3.6.1 on page 76, the bolometric correction for Sirius is given as BC = -0.09 without derivation or comment.  How did the authors arrive at this value for Sirius?

 

My hypothesis is that if a star's distance is known (say, for example, from parallax) you can calculate M_bol (absolute bolometric magnitude); and furthermore that if a star's distance is known, you can calculate M_V and subtract the two values to get BC.  Is this method how values for BC are generated in practice?

Edited by FredDawes, 18 February 2025 - 08:02 PM.

[robin_astro]

 

 

My question is:

 

How are bolometric corrections calculated in practice?

 

 

They are calculated from the spectrum of stars of the specific spectral type. Since it is difficult/impossible to measure the full spectral energy distribution of a star, these days the bolometric flux is mainly derived from modelling of stellar spectra. The total (ie bolometric) flux relative to the flux in the band you are measuring in (eg Johnson V) gives the bolometric correction, taking into  account the fact that (by somewhat arbitrary definition) the zero points used for the two magnitude systems will be different.  The introduction of this paper for example has an overview with references

https://ui.adsabs.ha...A.105C/abstract

 

Cheers

Robin

Edited by robin_astro, 18 February 2025 - 08:16 PM.

[StupendousMan]

It's easy to measure a star's apparent magnitude in the V-band, m_V.  If we know the distance to the star, then we can compute the absolute magnitude in the V-band, M_V.  So far, so good.

 

It's impossible to measure a star's bolometric apparent magnitude, because we can't measure its light at all wavelengths.  The best we can do is to measure its radiation at a number of wavelengths -- say, in several optical and IR bands -- and then apply some sort of model to estimate its emission across the entire electromagnetic spectrum.   That would give us a guess at the apparent bolometric magnitude, m_bol.  If we know the distance, then we can again convert apparent to absolute magnitude, M_bol.

 

Subtract to find the bolometric correction: BC = M_bol - M_V.

 

The real question here is: what sort of model can one apply to estimate the sum of all energy radiated by a star at all wavelengths?  That's where all the magic happens.

[DGK]

... apply some sort of model to estimate its emission across the entire electromagnetic spectrum.   That would give us a guess at the apparent bolometric magnitude, m_bol.  If we know the distance, then we can again convert apparent to absolute magnitude, M_bol.

 

Subtract to find the bolometric correction: BC = M_bol - M_V.

 

Which is what I was trying to do before I gave up - I had the naive thought that I could compare BCv's derived from a pure black body model and compare them with published BCv's. When I get over the bruising I'll take a look at that paper Robin cited and see if that helps me understand where all my required fiddles are arising. Like see attached this graph which I was too worn out to share earlier! The spectra are those I selected from CALSPEC above.

Attached Thumbnails

• 

[DGK]

I decided to take a different approach to answering my question - ".... how close the black body assumption is on average to reported main sequence BC's". I decided to treat BCv values as whatever are required to achieve best model fit to the spectra - so as arbitrary as the model. I went ahead and estimated Tbb and BCv's using a +/-30nm maximum least squares minimization fit to the CALSPEC spectra I have been using. The objective being to have the BB curve sit on top of the spectra in the band 400-700nm under the assumption that the peaks are where there's minimal attenuation.

 

The resulting Tbb and BCv's are shown in the two graphs attached. Not surprisingly the Tbb's are a lot higher at the blue and red ends, and the larger BCv's reflect that. Proper stellar models that include gravity, abundances and goodness knows what else are obviously where the more sensible published values are coming from. Maybe one day I'll look into those but not this day.

 

I've managed to answer my question with the the help given on this thread - thanks! And I will go and read a bit more on BCv's eventually, probably when I take a look at stellar models....

Attached Thumbnails

• 
• 

[DGK]

The CALSPEC spectra BB fits as described in previous post are in the attached pdf.

Attached Files

•  CALSPEC Spectra.pdf   461.48KB   3 downloads