Using line profiles of the 21 cm line, obtained in September 1982 using the 76 metre Mk 1 telescope at Jodrell Bank, ten galaxies (NGC 891, 1055, 1073, 1232, 2835, 2841, 3511, 5161, 5236 and 6210) were compared.

The total mass contained in each galaxy was found by using the Doppler width of the hydrogen profiles and a simple model of mass distribution within disk galaxies. The mass of neutral hydrogen in each galaxy was calculated from the hydrogen line luminosities of the profiles.

The ratio of the two masses was then calculated and a comparison was made of the two types of galaxies included in the survey, namely types Sb and Sc. The average mass ratio for Sb galaxies is (1.264 G 0.030) % and for Sc galaxies, (2.598 G 0.460) %

1. Introduction

Galaxies

Galaxies are classified according to their structure and, like snowflakes, the shape of each one is unique. There are four general categories, spirals which make up about 83% of the local population, elliptical galaxies which constitute about 13%, roughly 3% are irregular galaxies and the remaining 1% are classified as peculiar as they do not fit into any other category.

Disk galaxies are split up into three main sub categories, lenticulars, spirals and barred spirals. The classification, introduced by Hubble, is shown in figure 1. This is known as the tuning fork diagram and shows the various types of galaxy schematically. Lenticulars are flat ellipses that do not have spiral arms and are classified by the degree of ellipticity. The subject of this study is the composition of spiral galaxies.

Fig 1 [2, 133]

Spirals have a nucleus which consists of population II (older, metal poor) stars, spiral arms which contain population I (younger, metal rich) stars and clouds of interstellar neutral hydrogen (HI), and a halo of population II stars and small globular clusters. In spiral galaxies, the classification progresses from Sa galaxies with prominent central bulges and tightly wound spiral arms, through to Sc galaxies with much smaller bulges and looser arms.

Within galaxies there exists an interstellar medium (the ISM) containing large, low density clouds consisting mainly of HI gas. They are hard to see in the optical but they are visible at radio frequencies due to the spin-flip transition.

Hydrogen also exists in other forms in the ISM. Clouds of molecular hydrogen (H₂) are present in star forming regions but they are not easily observed because H₂ is easily dissociated by the intense ultraviolet radiation from the newly formed stars. In star forming regions, hydrogen ionised by young hot stars (HII) radiates in the infrared (thermal emission) and radio (bremsstrahlung) regions of the spectrum.

HI Emission

Protons and electrons both have an intrinsic spin of ½. In a hydrogen atom the spins of the proton and electron can be aligned parallel or anti-parallel to each other, with the second state having a slightly greater energy then the first. An electron in the slightly higher state will flip to the lower state and the slight change in energy is released as a photon with a characteristic frequency. For HI, this frequency is 1420.405752 Mhz (corresponding to a wavelength of 0.21106 m). This process has a very low probability of occurring and in high density clouds the atoms are more likely to loose energy in collisions before the transition takes place, hence it is only observed in cool, low density clouds.

From observations of external galaxies at this characteristic frequency much useful information can be obtained. The radial velocity of the gas at the edge of the disk can be determined from the Doppler shift in the observed frequency, and these observations can show the motions of the spiral arms. [1, 139] The observations can also be used to calculate a galaxies distance, velocity, total mass and the mass of neutral hydrogen contained within it.

2. Theory

Mass Distribution

The velocity of matter in a galaxy at any radius R is determined only by the total mass contained within the orbit. This can be thought of as being concentrated at a point at the centre of the orbit. The mass outside the orbit has no effect as the forces from masses on opposite sides of the galaxy will cancel each other out since the distribution is symmetrical.

The total mass of stars, dust and gas contained within a galaxy can be determined by finding the velocity of matter at the Holmberg radius, R_max . This is the radius at which the surface brightness is measured to be 25.6 magnitudes per square arcsecond (1 - 2 % of the brightness of the background sky) in blue light [3, 219]. The Holmberg radius is the maximum radius at which the constituents of the galaxy follow an almost circular orbit around the galactic centre.

The total mass, M_T, can be found by equating the gravitational and centrifugal forces acting on a small mass, m, moving at velocity v at a radius of R_max to give

(1)

where G is the gravitational constant.

Finding R_max

The radius R_max is calculated from the distance and observed angular diameter of the galaxy and is given by

(2)

where å is the angular diameter and D is the distance, calculated from Hubble's Law

(3)

where H₀ is Hubble's constant and V_R is the radial velocity determined from a hydrogen line profile and corrected for the observers motion.

Finding v

A hydrogen profile for a galaxy will only provide the line of sight component of the velocity of the gas at R_max . The relationship between the actual velocity (v) required in equation (1) and the apparent velocity (v_i) within the galaxy is

(4)

where i is the angle of inclination of the galaxy to the line of sight of the observer.

Line Luminosities and Hydrogen Mass

The rate of emission from each hydrogen atom is known, and so the total number of hydrogen atoms present in the galaxy, N_H , is found by integrating the flux density of the hydrogen line profile of the galaxy with respect to frequency.

If D is the distance from the observer to the galaxy in parsecs, and is the same as that found by equation (3), and S is the flux density at frequency v in Jansky's, then

(5)

where the coefficient K = 5.91 D 10⁴⁶.

The total mass of HI contained in the galaxy is then given by

(6)

where m_p and m_e are the rest masses of a proton and an electron respectively.

3. Experimental Method

Total mass

Line profiles of the 21 cm line were obtained for each of the ten galaxies included in this study using the Mk 1 radio telescope at Jodrell Bank, UK in September 1982.

There is a centre frequency shift in each of the profiles due to the apparent velocity of the galaxies, see table 1. This shift was used to find the distance from the observer to each galaxy using equation (3). However in this equation,

(7)

where V_A is the apparent radial velocity of the galaxy and V_C is the correction needed for the motion of the observer which also had to be determined.

For galaxies such as these at distances of between 1 and 30 Mpcs, V_A is found from the non-relativistic Doppler equation

(8)

where ÇÛ is the change in wavelength from Û, the rest wavelength and c is the speed of light.

The correction, V_C, to V_A for the solar, and hence the Earth's, velocity, is given by

(9)

where V_M is the velocity of the Sun around the galactic centre and l and b correspond to the position of the galaxy converted from RA+Dec to galactic co-ordinates using the following equations;

(10)

(11)

(12)

where l and b are galactic longitude and latitude, R and D are the right ascension and declination of the object in degrees, R_g =12^h49^m and D_g =+27.4^o are the right ascension and declination of the North Galactic pole, and l_p =123^o is the longitude of the North Celestial pole.

With the distances known, the Holmberg radius, R_max , was found for each galaxy using equation (2) and the angular diameters which are listed in table 1. The gas at R_max has the greatest velocity relative to the observer due to the rotation of the galaxy. Hence the most negative and most positive velocities (the velocities at the edges of the profiles) correspond to the velocity of the gas at R_max .

The apparent velocity, v_i, at the edges of the disk was found by measuring the width of each profile in Mhz and using equation (3) again, with Û now the centre frequency of the profile. However, v_i is not the actual orbital velocity of the gas as the galaxies are not all perfectly side on to our line of sight. The correction to get the actual velocity, v, is given by equation (4) where the angle of inclination of the galaxy, i, is given in table 1. See figure 2. The values for v were then used in equation (1) along with the calculated values for the Holmberg radius to obtain the total mass contained within each galaxy.

Fig 2

Mass of Hydrogen

The mass of hydrogen contained in each galaxy was found by finding the area under each of the line profiles and then applying equations (5) and (6). Once the two masses, M_H and M_T were found, the ratio, M_H / M_T was calculated.

4. Results and Errors

Table 2 shows the average results for the total mass, the mass of hydrogen, and the ratio between the two for each type of galaxy, calculated using the method outlined in section 3. There is a difference between the average ratios but an analysis of the errors is required to see if this difference is significant. The data for each galaxy is shown in figure 3.

Figure 3. The ratio of M_H to M_T for all galaxies in the survey. Darker bars are Sb and lighter bars Sc galaxies.

Table 2.

The significant uncertainty in the final results arises from integrating the profiles. An analysis of the data, using an estimated uncertainty based on the accuracy of the original line profiles, gives uncertainties in the ratio of M_H to M_T of G 0.030 % for Sb and G 0.460 % for Sc galaxies. Systematic uncertainties in the results also arise from the cumulative effect of errors in the systems of distance measurement used in astronomy and an uncertainty in the value of the Hubble constant.

5. Discussion and Conclusion

The data shows that the average mass ratio of M_H to M_T for Sb galaxies is (1.264 G 0.030) % and for Sc galaxies, (2.598 G 0.460) %. Taking the errors into account, it can be seen that there is a definite difference in the proportion of hydrogen between the two types of galaxy.

There is a difference in the percentage of HI between types Sb and Sc galaxies. Going back to the Hubble classification and the tuning fork diagram, type Sa galaxies contain the lowest, and type Sc galaxies the highest, proportion of neutral interstellar hydrogen. [1, 100]

6. References

1. B. F. Burke and F. Graham-Smith, An Introduction to Radio Astronomy. (Cambridge University Press, 1997)

   
   

2. N. Ingham, Astrophysics. (Nelson, 1997) (Images taken from)

   
   

3. I. Ridpath, Dictionary of Astronomy. (Oxford University Press, 1997)

   
   

4. Images from the Digitised Sky Surveys which were produced at the Space Telescope Science Institute under U.S. Government grant NAG W-2166. The images of these surveys are based on photographic data obtained using the Oschin Schmidt Telescope on Palomar Mountain and the UK Schmidt Telescope. The plates were processed into the present compressed digital form with the permission of these institutions.