Module 09

Colour Index

TABLE OF CONTENTS

1. Learning Outcomes 2. Introduction 3. Dependence of magnitudes on wavelength 3.1. UBV System of Johnson and Morgan 3.2. Colour Index 3.3. Colour-Colour Diagrams 3.4. Colour Excess 3.5. Reddening and Redshift 4. Summary

1. Learning Outcomes After studying this module, you should be able to

 Appreciate that the depends on the wavelength at which it is measured  Understand the need of UBV  Realize that the UBV system at present measures magnitudes at various wavelength bands other than the visual region  Understand why magnitudes of at various wavelength bands of their spectra are not equal  Grasp the concept of colour index  Understand that the colour index follows the surface temperature of the  Realize the importance of colour-colour diagrams in describing stars

2. Introduction

In the last module we introduced the concept of magnitudes. is a number assigned to a star (or any other celestial object) to indicate its brightness. Brighter stars are

assigned lower magnitudes and fainter stars are characterized by higher magnitudes. Only stars brighter than 6th magnitude are visible to the unaided eye. Since brightness is a function of distance and the intrinsic brightness of a star, apparent magnitude does not allow us to compare stars with respect to their intrinsic brightness. Therefore, to compare brightness all stars are thought to be at a standard distance of 10 pc. The apparent magnitude at this distance is called the of the star. It turns out that the difference between the absolute magnitudes of two stars is proportional to the ratio of their . So, in absolute magnitude, we have now a handle to estimate the of as star. We also found that the difference between the apparent and absolute magnitudes of a star, the distance modulus, allows us to determine the distance of the star.

It was pointed out that overwhelming majority of stars in the sky are faint stars; there is real paucity of bright stars. The number of stars brighter than 6th magnitude, those visible to the naked eye, is only about 5000. Also most stars are less luminous than the ; very few stars have luminosity greater than the Sun.

We know that stars radiate in many wavelengths. Therefore, we now turn to the dependence of magnitudes on wavelength and introduce an important quantity: colour index.

3. Dependence of magnitudes on wavelength

If the radiation of stars were monochromatic, magnitude differences would be entirely independent of the instruments used to determine them. But stellar radiation is not monochromatic. Moreover, the measuring instruments select a band of wavelengths rather than a single wavelength (Fig. 9.1). Therefore, magnitude becomes instrument dependent. However, this is not the case with the instruments which are nonselective, such as radiometers, bolometers and thermocouples. These instruments measure the true luminosities of stars once they have been corrected for absorption of radiation in the atmosphere of the earth. Unfortunately, these instruments are rather insensitive and, therefore, are not used for determining stellar luminosities. Instead one uses an indirect method which employs the idea of bolometric correction, as we shall see later.

3.1. UBV System of Johnson and Morgan

Magnitudes are measured these days with special filters attached to the telescopes. The filters belong to what is called the UBV Johnson Morgan photometric system. The V band was provided to approximate to the visual magnitude system. The B band approximated to the . The peak sensitivity of the filter in the visual region (denoted by V), for example, centres around a wavelength to which the eye is most sensitive, 훌545 nm in the yellow-green region of the spectrum. Similarly, filters for blue (B) and (U) have their peak sensitivities centred around 훌435 nm and 훌350 nm, respectively (Fig. 9.1). A filter in the red region (푹) has its peak sensitivity around 훌640 nm, and the one in the infrared region has peak around 훌800 nm (Fig. 9.2).

)

훌

Sensitivity S( Sensitivity

Fig. 9.1. Sensitivity functions of the U, B and V filters (Johnson and Morgan, 1953).

The magnitudes determined with these filters are denoted as 푚푉, 푚퐵, and 푚푈, or simply as 푉, 퐵, and 푈. Notice that these are all apparent magnitudes. The corresponding absolute magnitudes are denoted by 푀푉, 푀퐵, and 푀푈.

Fig. 9.2. Modern system of filters. (Source: Bessell, Annu. Rev. Astron. Astrophys., 2005).

All the magnitudes of a star in various wavelength bands are not equal, because each filter samples a different region of the blackbody spectrum corresponding to the surface temperature

Blue Filter Yellow Green Filter

Black Body Curve at Star’s Temperature

Higher Intensity Temperature

Lower Temperature

Wavelength

Fig. 9.3. Blue band and yellow-green band filters sample different regions of the spectrum. The blue magnitude of the star at higher temperature is lower than the yellow-green magnitude. Opposite is the case with the star at lower temperature.

of the star. Referring to Fig. 9.3, the blue filter samples higher intensity region of the spectrum at higher temperature while yellow-green filter samples region of lower intensity of the same curve. At lower temperature the blue filter samples the lower intensity and the yellow-green filter samples the higher intensity. Since higher brightness is associated with a lower

magnitude, and vice versa, the blue magnitude of the star at higher temperature in Fig. 9.3 is lower than its visual magnitude. On the other hand, for the star at lower temperature in the same figure, the blue magnitude will be slightly higher than the yellow-green magnitude.

3.2. Colour Index

The difference between the magnitudes of a star at different wavelengths is called its colour index (C.I.), or just the colour, of the star. It is obvious that the colour index is a measure of the surface temperature of the star. That is why instead of the temperature of the star, many times its colour index is stated. We shall state the precise relationship between the temperature and the colour index a little later. One kind of colour index is defined as

C. I. = 푚퐵 − 푚푉 = 퐵 − 푉. (9.1)

The colour index is stated in units of magnitude. Another colour index is 푈 − 퐵:

푚푈 − 푚퐵 = 푈 − 퐵. (9.2)

The reference star for measuring colour indices is star (Surface temperature, 9602 K;

Apparent magnitude, 0.03; Luminosity, 50 푳ʘ; Distance, 7.68 pc). For this star, by definition, all the three indices are equal, that is, 푼 = 푩 = 푽, which implies that 푩 − 푽 = ퟎ. ퟎ and 푼 − 푩 = ퟎ. ퟎ. So, star Vega is a white star. A star with 푩 − 푽 < ퟎ has higher intensity in the blue region than Vega. We usually say that the star is bluer than Vega; a star with 푩 − 푽 > ퟎ is redder than Vega.

Table 9.1 shows the sample calibration of various colour indices for stars of various surface temperatures, 푻풆풇풇. The first column in the Table shows the spectral class of the star. We shall study spectral classification of stars later. For the present, you can ignore the first column.

Table 9.1. Sample Calibration Colour Indices of Stars of various Surface Temperatures

Class 푩– 푽 푼– 푩 푽– 푹 푹– 푰 푻풆풇풇 (K)

O5V –0.33 –1.19 –0.15 –0.32 42,000

B0V –0.30 –1.08 –0.13 –0.29 30,000

A0V –0.02 –0.02 0.02 –0.02 9,790

F0V 0.30 0.03 0.30 0.17 7,300

G0V 0.58 0.06 0.50 0.31 5,940

K0V 0.81 0.45 0.64 0.42 5,150

M0V 1.40 1.22 1.28 0.91 3,840

Source of data: Zombeck, Martin V. (1990). "Calibration of MK spectral types". Handbook of Space Astronomy and Astrophysics (2nd ed.). Cambridge University Press. p. 105. ISBN 0-521-34787-4.

Look at the 퐵 − 푉 colour index of stars of temperatures 42000 K and 30000 K. They have very high intensity in the blue colour of their spectra. These are called blue stars. Stars of temperature ~ 1000, of the type of star Vega, are white. Stars of lower temperatures are redder than Vega, redness increasing as the temperature decreases. Sun, with a surface temperature ~ 6000 K is yellowish in colour, while stars with temperatures ~ 4000 K are red stars. Colour index (푩 − 푽) for the Sun has been estimated as 0.656.

A category of dwarf stars are stars. These stars actually outnumber all other categories of stars. Their surface temperatures are low and their masses are a fraction of solar mass while -4 their luminosities are typically 10 L⨀. There are also stars which are many times larger in size

than the Sun. These, the so-called red giants and red supergiants are also red because of their low surface temperatures.

Another collection of red stars is a . Globular clusters are very old clusters, 10 billion years or older. They contain very old, therefore, red stars. There are about 150 of such clusters in the Milky way .

The new-born stars are blue because of their high surface temperatures. in which there is a burst of new stars, star burst galaxies, appear blue, because of preponderance of blue stars in them. An example of a blue star is the star Rigel, the brightest star in Orion . Just like red giants, there exist also stars, stars of huge sizes and high surface temperatures.

Fig. 9.4. Plot of temperature against colour index (퐵 − 푉) based on the data from

Hipparcos satellite. (Source: http://spiff.rit.edu/classes/phys440/lectures/color/color.html )

The colour indices (퐵 − 푉) and (푈 − 퐵) follow quite faithfully the surface temperature of stars as shown in Figs. 9.4 and 9.5.

Fig. 9.5. Plot of (푈 − 퐵) against the temperature of stars. (Source: http://astro.unl.edu/naap/blackbody/colorindex.html )

3.3. Colour-Colour Diagrams

The plot of 푈 − 퐵 against 퐵 − 푉, known as colour-colour diagram, is an important tool for the . For example, the stars lie along a typical curve (Fig. 9.6). Any object not lying along this curve is most likely not a main sequence star.

This is more clearly seen in Fig. 9.7. Here supergiant stars are also shown (supergiant and main sequence stars are types of stars about which we shall learn in details later). More importantly, we find that a star emits less ultraviolet light than a black body of the same colour B-V.

퐵 −

푈

퐵 − 푉 Fig. 9.6. A colour-colour diagram for the main sequence stars.

Fig. 9.7. of a black body compared with the B-V and U-B colour index of main sequence and super giant stars in what is called a color-color diagram [after E. Böhm-Vitense (1989)]. Stars emit less ultraviolet radiation than a black body with the same B-V index. (Source: Wikipedia)

Another category of objects which can be recognized easily by a colour-colour plot are quasi- stellar radio sources, or quasars. As the name suggests, these objects look like stars, though they are not stars. They are at huge distances from us and are more like galaxies (they belong to the type of galaxies called active galaxies). Early samples of these objects were very powerful sources of radio emission. It turns out now that most of these objects do not have detectable radio emission: they are radio – quiet. In the U-B Vs B-V diagram they are found to congregate in a region around 0 – 1 in B-V and 0 – -1 in U-B (Fig. 9.8). This circumstance makes it easy to set them apart from stars.

Fig. 9.8. The location of 788 quasars on a colour-colour diagram. (Source:

ned.ipac.caltech.edu)

Colour index is now a basic parameter to describe stars. It is convenient, too, because measuring magnitudes is much easier than obtaining detailed spectra of stars and garner the necessary information about them.

3.4. Colour Excess When stars are observed through an absorbing interstellar medium, they appear redder than similar stars closer to us. The reason for reddening of is that the interstellar medium absorbs blue colour much more strongly than the red colour. That is why the absorption caused by the interstellar medium is called reddening or .

Fig. 9.9. On passing through a strong absorbing cloud of gas and dust in the interstellar space, the starlight appears reddish.

The extinction of a star is measured by the colour excess which is the difference between the observed colour index of the star and its intrinsic colour index (the theoretical colour index it would have if not affected by absorption). It is denoted by 퐸(퐵 − 푉):

퐸(퐵 − 푉) = (퐵 − 푉)푂푏푠푒푟푏푒푑 − (퐵 − 푉)퐼푛푡푟푖푛푠푖푐. (9.3)

Information on colour excess of an object helps us in mapping the chemical composition of the absorbing region between the object and the observer. Within a few kpc of the earth the extinction in the visual band is ~ 1.8 magnitude/kpc.

3.5. Reddening and Redshift

It is important not to confuse between redshift and reddening. Redshift is caused by the motion of an object towards or away from us. In redshift, each line of the spectrum of the object shifts to the red (blue) as the object moves away from (towards) us. In reddening, the higher frequency part of the spectrum suffers greater attenuation than the lower frequency part on passing through the interstellar absorbing medium; there is no shift in the lines of the spectrum.

Fig. 9.10 shows an historical redshifted spectrum of an object which led to the identification of the object as the first quasar, 3C 273.

Fig. 9.10. The red shift in the spectrum of 3C 273 led to its identification as the first quasar. (Source:

http://www.parkes.atnf.csiro.au/people/sar049/3C273/ )

4. Summary

 Magnitudes of stars are these days measured through filters centred on wavelengths corresponding to 푈, 퐵, 푉 wavelengths and other regions of . This system is called UBV .  푈, 퐵 and 푉 magnitudes of a star are generally unequal.  The difference between any two of these magnitudes is called colour index.  Star Vega has been chosen as standard for measuring colour index.  By definition for star Vega 푈 = 퐵 = 푉. This implies Vega is white.  A star with (퐵 − 푉) < 0, is bluer than Vega; (퐵 − 푉) > 0 implies redder than Vega.  Colour index gives a clue to the surface temperature of a star.  Colour-colour diagram is a tool to describe the characteristics of stars.  Main sequence stars fall along a typical curve in the colour-colour diagram.  Quasars occupy a certain region of the colour-colour diagram which distinguishes them from other objects.  The absorption of the light of a star in the interstellar medium is the cause of its extinction or reddening.  Extinction is measured by colour excess.  Colour excess is the difference between the observed colour index of a star and its theoretically calculated colour index.  Colour excess gives a clue to nature of absorbing medium between the star and the observer.  Reddening should not be confused with redshift. The latter is caused by the motion of the object away (or towards) us. Each line of the spectrum undergoes redshift. In reddening there is differential absorption of light, but no shift in the lines of the spectrum.