Color-brightness diagram

Color-brightness diagram in the BV version
(Ia-V: luminosity classes , B0-M0: spectral classes )

A color-brightness diagram ( FHD for short ) is a two-dimensional diagram in astrophysics in which the absolute brightness of stars is plotted against a color index .

In contrast, in the Hertzsprung-Russell diagram (HRD), the absolute brightnesses are plotted against the spectral class .

BV-color-brightness diagrams

The color-brightness diagram, which is based on the brightnesses of the vision system (see picture), is widely used . The yellow brightness V (for visual , since the human eye is most sensitive at 550 nm ) is plotted against the color index B − V (difference between the blue brightness B at 440 nm and the yellow brightness V ).

This color-brightness diagram has the advantage that its structure is similar to that of the Hertzsprung-Russell diagram; In particular, the main sequence shows a similar course, but is shifted vertically depending on the distance of the group of stars.

In addition, not all star types appear in an FHD of a star group, i. H. certain areas remain empty compared to standard FHD.

application

Branch point of a typical
color-brightness diagram that was superimposed with a standard FHD.

The mentioned comparison with the HRD shows how the FHD can be used:

If a standard HRD is used as a basis, in which the B − V color index is used as the ordinate instead of the spectral types, the main sequence of the resulting FHD, which is usually easy to identify, is shifted vertically depending on the distance. The distance of the star group can be determined from the size of the shift ( distance module ):

{\ displaystyle {\ begin {aligned} V-M_ {V} & = 5 \, \ mathrm {mag} \ cdot \ log _ {10} d-5 \, \ mathrm {mag} \\\ Leftrightarrow d & = 10 ^ {{\ frac {V-M_ {V}} {5 \, \ mathrm {mag}}} + 1} \ end {aligned}}}

With

V : apparent brightness of the stars in the FHD
M _V : absolute brightness of the stars in the standard HRD
likes: Magnitude
d : Distance ( luminosity distance ) of the star group in parsec .

The absence of certain types of stars in an FHD indicates a certain physical stage of development of the group of stars. In particular, one typically sees in an FHD that the main row kinks at a certain color index , i. H. to the left of this branch point (often also called turn-off point ) there are no main sequence stars in the diagram. The obvious reason for this lack of hot main sequence stars is the advanced age of the star group, so that stars to the left of the junction point have already evolved into giant stars .

Using the color index (B − V) _{t of} the branch point, the age a of the star group in years can be estimated from the standard models of stellar evolution :

{\ displaystyle a \ approx 9 \ times 10 ^ {7} \ times 10 ^ {2 {,} 94 \ times (BV) _ {t}}}

Color excess and extinction

The described application of the FHD is based on the fact that the B − V color index is independent of distance. At first glance, this seems plausible, since it is the difference between two apparent brightnesses, which at first glance should actually be independent of the distance.

Due to the interstellar extinction , which in turn is based on Rayleigh scattering , the short-wave light is absorbed more strongly than the longer -wave light , so that the measured color index is greater than the actual one. The difference between the measured B − V color index and the actual one is called color excess : ${\ displaystyle (BV)}$ ${\ displaystyle (BV) _ {0}}$

{\ displaystyle E (BV) = (BV) - (BV) _ {0}> 0}

Since the color excess is quite independent of the wavelength , it essentially causes a horizontal shift in the (B − V) axis of the diagram. Since the main series runs almost linearly in the FHD, this shift cannot be read from the geometry of the diagram, because it remains initially unclear whether the diagram has been shifted to the right due to the excess of color or, depending on the distance, upwards.

The color excess can, however, be determined by additional evaluation of a color-color diagram, in which the UB color index is recorded over the B − V color index. The typical course of the main series in this diagram is a strongly wavy line. The waves are caused by the deviation from the black body radiation , especially by the Balmer jump . Therefore, the color excess can be determined in this diagram, whereby the following applies approximately for the two excesses E (B − V) and E (UB) :

{\ displaystyle {\ frac {E (UB)} {E (BV)}} \ approx 0 {,} 72 + 0 {,} 05 \ cdot E (BV)}

The interstellar extinction A _V , which describes the darkening of the stars by the interstellar dust , can also be written as a function of the excess of color:

{\ displaystyle A_ {V} = R_ {e} \ cdot E (BV)}

with the direction-dependent size and thus eliminate it from the FHD. ${\ displaystyle R_ {e} \ approx 3 {,} 2}$

Individual evidence

^ Joachim Krautter et al .: Meyers Handbuch Weltall , Meyers Lexikonverlag. 7th edition 1994, ISBN 3-411-07757-3 , p. 250 ff
^ Arnold Hanslmeier : Introduction to Astronomy and Astrophysics , spectrum academic publishing house. 2nd edition 2007, ISBN 978-3-8274-1846-3 , p. 273
^ Arnold Hanslmeier, Introduction to Astronomy and Astrophysics , Spektrum Akademischer Verlag, 2nd edition 2007, ISBN 978-3-8274-1846-3 , p. 385ff.
^ Arnold Hanslmeier, Introduction to Astronomy and Astrophysics , Spektrum Akademischer Verlag, 2nd edition 2007, ISBN 978-3-8274-1846-3 , p. 383ff.

[1] Joachim Krautter et al .: Meyers Handbuch Weltall , Meyers Lexikonverlag. 7th edition 1994, ISBN 3-411-07757-3 , p. 250 ff

[2] Arnold Hanslmeier : Introduction to Astronomy and Astrophysics , spectrum academic publishing house. 2nd edition 2007, ISBN 978-3-8274-1846-3 , p. 273

[3] Arnold Hanslmeier, Introduction to Astronomy and Astrophysics , Spektrum Akademischer Verlag, 2nd edition 2007, ISBN 978-3-8274-1846-3 , p. 385ff.

[4] Arnold Hanslmeier, Introduction to Astronomy and Astrophysics , Spektrum Akademischer Verlag, 2nd edition 2007, ISBN 978-3-8274-1846-3 , p. 383ff.