CATCH A STAR! 2005
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|The Fireworks Galaxy - NGC6946|
NGC6946 is an extraordinary galaxy - it offers the stargazers a unique, face-on view and nobody stays indifferent watching the frequent supernovae exciting different generations of astronomers. In this project, we discuss the importance of the observations and investigation of galaxies and supernovae for astronomy and cosmology, and, in particular, what makes The Fireworks Galaxy - NGC 6946 - so different and exceptional for us. Also, we discuss possible future observations, that can be carried out using the world's largest telescopes, focusing on VLT, OWL and ALMA.In addition, we have prepared two practical exercises: in the first, the mass of the galaxy is calculated by two different ways (giving the same result!); in the second, we discussed the importance of the spirals in astronomy, and studied the spiral structures of NGC 6946.
“…I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.”
Isaac Newton, Memoirs of the Life, Writings, and Discoveries of Sir Isaac Newton (1855) by Sir David Brewster (Volume II. Ch. 27)
It is incredible how insignificant we are in comparison with the Universe but how eagerly we explore its secrets trying to understand its unfathomable laws and to find our part in this awesome puzzle. One of the most important ways of collecting information about the Universe and our place in it is investigation of galaxies. Often, this investigation gives us unexcepted information, which makes the observations even more interesting. Undoubtedly the most fascinating and formidable phenomenon observed in galaxies, which has attracted the attention of astronomers from ancient times up to now, is a supernova burst. In a single galaxy, supernovae occur very rarely - the last one in the Milky Way appeared 400 years ago. But, observing all the galaxies, we could obtain much more information – 340 supernovae were recorded in the last year, 2005. .
The Fireworks Galaxy has a profilic recent history of supernovae explosions - since 1900, 8 bursts occured in that galaxy, and the last one in 2004.For this reason NGC 6946 is a preferred object by the professional astronomers who are faced with a great number of unresolved problems, as well as by the stargazers who wait for the next celestial show.
2. GALAXY CLASSIFICATION
For a long time astronomers didn't know whether the nebulae they were observing belong to our galaxy or not. It was not until 1924 that Edwin Hubble realized that some of these nebulae are in fact other galaxies. Galaxies are gravitationally bound systems of stars and interstellar matter, orbiting a common gravitational centre. They contain up to hundreds of billions of stars. Moreover, galaxies were found to be of different types depending on their form and orientation in space relative to us.Three main morphological types are distinguished today:
• Elliptical galaxies are called so because of their form.They are denoted by the letter "E".They look like an ellipse which can be more or less compressed. On this bases elliptical galaxies are classified in subtypes from E0 to E7 with E7 being the most compressed one.
• Spiral galaxies possess more or less pronounced spiral arms.They are denoted by "S".In addition,according to how pronounced the spirals are, the letters a,b,c and d (or two at a time) can be added.Thus a galaxy of type Sb has less pronounced spiral structures than a galaxy of type Sc. Sab means that the type is between Sa and Sb.Type S0 means that the galaxy is a spiral one,but the spiral armes are not pronounced at all.
• Irregular galaxies are galaxies that cannot be classified in either of the previous types.
Sometimes additional structures are observed in spiral galaxies such as the bar across the centre.If it is present,the galaxy is called a barred galaxy and the letter B is added to its type.The Milky way is a galaxy of type SBc. Hubble has classified galaxies in his famous "Tuning fork diagram". Originally he thought that it had an evolutionary meaning-that first galaxies are elliptical, then they evolve into spiral and finally they become irregular.Now it is clear that galaxies do not evolve and their type remains the same since their birth.
3. MAIN CHARACTERISTICS OF NGC6946
The type of the galaxy is Scd, which mean that it is a spiral galaxy, but more precisely, it has poorly developed bar across the middle (this characteristic results in the 'AB' abbreviation), and also has a an inner confused ring (resulting in the '(rs)' abbreviation). Nowadays, NGC 6946 has a moderate star formation rate, similar with that of the Milky Way.
The most fascinating characteristic of this galaxy are the frequent supernova explosions, facing the astrophysists to a great number of scientific problems.
4. HOW THE SCIENTISTS OBSERVE THE FIREWORKS GALAXY
The telescope of Sir William Herschel, Leisure Hour,1867, page 729
4.1. Historical notes
NGC6946 was discovered by William Herschel on September 9, 1798. For the greatest part of his discoveries, and probably for the discovery of NGC 6946, Herschel used his largest, 126 cm reflector, with a field of view of 15'4".
4.2. Why the Supernovae are important to the science?
The pioneer of supernovae observations is the Swiss-American astronomer Fritz Zwicky (born in Varna, Bulgaria), who was the first to distinguish the novae and the supernovae explosions. Since then, the supernovae science has become a very important part of the modern astronomy and cosmology.
Type Ia supernovae are used for standard candles - astronomers believe that their absolute magnitude is a constant value. So, they have to observe their visual magnitude, which gives us directly the distance to the supernova. Because of the great luminousity of the supernovae, they are visible even from distant galaxies, so we can directly determine the distance to these galaxies, which is crucial for the modern cosmological models.
The light coming from the supernovae travels some time before reaching us. So, when we observe supernovae, we observe their past. Determining precisely the distance to different supernovae, cosmologist calculate the expansion rate of the Universe at different moments in the past. Comparing these moments, they have concluded that the expansion of the Universe is accelerating. That suggests the Universe has a mysterious property described by the so-called “cosmological constant” first introduced by Albert Einstein.
4.3. The Supernovae Hunters
Because of their importance, the localisation and the follow-up observation of a recent supernovae bursts is crucial for the astronomers, especially the cosmologists, who want to observe the explosion over its entire cycle, and to learn as much as possible about it.
But every minute on the world-class telescopes is precious (and expensive!), which gives the amateurs (who have all the time on their telescopes) the incredible opportunity to be on the front line of this science.
4.4. The Supernovae in NGC 6946
Image credit: James R. Foster
In the XXth and the XXIst century 8 supernovae were observed in NGC6946: 2004et, 2002hh, 1980K, 1969P, 1968P, 1948B, 1939C, 1917A, more than any other galaxy. SN2004et is the latest supernova appeared in the Fireworks galaxy.It was discovered by Stefano Moretti during an almost full moon on 22nd September 2004.It is a type II supernova.Its peak was 12.7 mag. The picture shows its position in the galaxy.
4.5. Remnants collision
Lower left: Ground based image, obtained with the 4-m KPNO telescope.
In 1997 astronomers, using the Hubble Space Telescope, observed a bright point-like source in the bright northern spiral arm of The Fireworks Galaxy. Before the observation, this object was believed to be a bright supernova remnant, but there was a problem: the great brightness of this remnant suggested that it is a young one, but at the same time, its expansion velocity was very small, suggesting that the explosion happened a long time ago. By analyzing the observations, carried out with the Hubble Space Telescope, the astronomers learned that in fact, the expanding shell of a relatively recent supernova is colliding with an older, larger shell of a previous explosion. This was the first observation of this phenomenon, which is very difficult, because it lasts only few hundred years - a cosmological eye-blink.
4.6. Calculation of the distance to NGC 6946
Estimating the distance to the galaxies has always been an important, but difficult task for the astronomers. They used the period-luminosity relation of the cepheids, diameters of the HII regions, diameters of the galaxies, absolute magnitude of supernovae type Ia. To find the distance to NGC 6946 astronomers used the Karachentsev and Tikhonov's method.Observing a set of galaxies, the distances to which were determined using the cepheid method they derived the following connection between the mean magnitude of the three brightest blue stars (), the total magnitude of the galaxy in B band () and the distance modulus :
Where AB is the interstellar absobtion, that can be calculated using the Massey's method.
According to Pogson's law for the distance:
Then, by using (1):
The estimations vary between 5.1 and 6Mpc.
4.7. FURTHER OBSERVATIONS
"The important thing is not to stop questioning. Curiosity has its own reason for existing."
NGC 6946 is a unique galaxy.It has revealed a great amount of interesting facts about itself such as unusual rate of supernovae explosions,supernovae remnants and broad H II regions as well as phenomena never observed before,like a collision of two supernovae remnants.However,there are still many unanswered questions and undisclosed secrets waiting for us. The only way to cast new light upon this incredible galaxy and its secrets is to observe it with modern instruments such as VLT(Very Large Telescope)and the prospective submm ALMA(Atacama Large Millimeter Array) and OWL(OverWhelmingly Large).
The future OWL telescope. Image credit: ESO
One aspect, in which these telescopes can help,is identifying supernova remnants.
Briefly,a supernova remnant (SNR) is the remain of a supernova explosion.It is a rapidly expanding cloud mixing with the interstellar medium.Examples are the Crab nebula in the constellation of Taurus and the Veil nebula in Cygnus. Scientists have detected 37 supernova remnant candidates in the Fireworks galaxy.However,they are not sure whether some of these objects should be classified as supernovae remnants or regions with ionised hydrogen(H II regions).With its theorethical capability of reaching 38 magnitude,the OWL telescope can provide extremely much information about these objects. It was not until the Hubble telescope photographed the object MF16 until it was clear that it were two colliding remnants.Therefore,more observations are needed in order to find out what in fact these sources are.The future observations can be in visible light, X-rays and radio waves since classifying an object as a SNR involves studying its entire electromagnetic spectrum.
The Crab Nebula.Credits: ESO PR Photo 40f/99, image taken with the VLT
In addition to high-resolution images,spectra of these remnant candidates should also be obtained.Typical for SNR-s are emission lines of [OI] or [SII], i.e. forbidden lines of neutral oxygen and ionised sodium.However,it is difficult to obtain spectra of dim objects since light has to be dispersed on wider area in comparison to simply photographing it.That is why spectra of faint light sources should be obtained with telescopes having large diameter because the larger the diameter,the more light the telescope gathers.In this aspect huge telescopes such as VLT and the future 100-m OWL are unsurpassed. Not only identifying supernova remnants is a challenge of these instruments. Large telescopes can also provide images of heretofore unknown supernova remnants in the Fireworks galaxy.
Another realm in which present and future generation telescopes can help,is investigation of the dwarf galaxies in the NGC 6946-system.These companions are very dim objects and this fact obstructs their observation.Besides,they have been found quite recently which indicates the possibility of more existing irregular galaxies in the system.Their discovery is another task of VLT,ALMA and especially OWL. Nearby objects which are true or possible companions of NGC 6946 are the following: kkr46; kkh90; kkr48; kkh92; kkr51; kk250; kk251; kk252; kk254; kkr55; kkr57; kkr58; Ceph1; kh93; kkr59; kkr60; kkr62
A number of these objects needs future observations.
•kkr57 seems to be a blue irregular galaxy but it is unclear why it is undetected in the HI line. Therefore, spectral observations are needed.
•kkr56 seems to be a true companion of the Fireworks galaxy but in order for this supposition to be confirmed, H alpha observations should be carried out.
•hhr59 should also be observed in the H alpha line.
•kkr62 is another interesting case. Due to the extremely high extinction that obscures it, scientists are not sure whther it is a galaxy(and if so,does it belong to the group?) or it is simply a planetary or a reflection nebula.
•kkr55 and kkr56 also need optical spectra and radio observations.
A detailed study on the position, orbital parameters, radial velocities of all these companions is needed, in order to increase the precision for the mass, caclculated as is shown in the first practical exercise.
5. COMPARAISON TO THE MILKY WAY AND TO M83
Comparing different objects astronomers obtain extra information about them. For example comparing the nebulae, Hubble found that the "spiral nebulae" are star formations like our Milky way. Also, after dividing supernovae in two classes astronomers understood that the mechanism of their explosions is quite different.
Compared to the other galaxies NGC6946 is a usual galaxy and at the same time very different. It is a spiral galaxy like 78% of the known galaxies.And now it is thought that all galaxies are formed at the same time.But the high star formation, frequent supernovae,the huge amount of supernovae remnants and numerous star clusters in NGC6946 makes it unusual and interesting.
Now let us compare it to two concrete galaxies. Let one of them be the Milky Way, because it is the most studied galaxy. It is interesting to compare it also to M83 because of the latter's great number of supernovae. The three galaxies are spiral.NGC6946 is type SABcd, similar to ours(SBc) and M83 is SABc.The diameter of NGC 6946 is 70 000ly and M83 is a bit smaller(30 000 ly). The Milky way is larger - 100 000ly.Luminosities of the three galaxies are similar, too - respectively 109 , 1010 and 1010 solar luminousities.But their speed of star formation is different. In NGC6946 and M83 there are more nebulae and young stars (resulting in their blue colour).And the frequency of supernova explosions in them differs very much - in the Fireworks galaxy there have been observed eight supernovae for 88 years, in M83 - seven for 82 years and in the Milky Way - 2 for a 100 years.Their group members are also different. In the group of NGC 6946 there are at least eight members - one spiral and the other are supposed to be dwarf irregulars. In M83 group there are fourteen galaxies which are spiral and irregular and one is peculiar. In our local group there are forty six galaxies of all types.
In short, the Fireworks galaxy is quite more similar to M83 than to the Milky way, although the three galaxies appear similar at first sight. Our comparison does not give us directly the reason for the unusual phenomena in NGC6946 but it is clear that these phenomena do exist and they are worth investigating.
6. OUR OBSERVATIONS
6.1. How to find NGC 6946 in the sky
Generated with Guide 7 software
Since NGC 6946 is a dim galaxy, it is almost impossible to find it without a star map.The best way to direct your telescope to its position is to find the constellation of Cepheus first. Once this is done, find the brightest star in it(alpha Cephei) or "Alderamin".A little west of it(some 5 degrees or so) there are two fainter stars - η and θ Cephei (look at the picture on the right). The Fireworks galaxy forms an almost equilateral triangle with them - its position is marked with a red dot. In addition to it you may see a star cluster which by coincidence is projected near NGC 6946.Its name is NGC 6939. However, it belongs to our own galaxy and does not have anything in common with the object we are considering. Anyway, nowhere in the sky there can be seen such a spectacular show - a galaxy and a star cluster in the same telescopic field.
The Fireworks galaxy can be seen from the whole Northern hemisphere and down to 30° southern latitude.
6.2. CCD observations
The image on the left was obtained by Alexandra Georgieva and Filip Fratev during the "Belite Brezi" national observational camp in Bulgaria, August 2005. It was additionaly treated by Rumen Stamatov. It is a mosaic of 60, 20sec exposures of NGC6946. For the observation was used a 25.4cm f/4.7 newtonian telescope with Starlight Xpress MX716 CCD camera, kindly granted by Mr Filip Fratev.
7. PRACTICAL ACTIVITIES
7.1. Estimating the mass of NGC 6946
Along with diameter, luminosity and apparent dimension, mass is also an important characteristic of galaxies. There are several methods of determining the mass of a galaxy. One of them is by using the so-called mass-to-luminosity ratio. If we take the ratio of the mass of all stars to the luminosity of all stars located in a certain volume around the Sun,we can notice that this ratio is about 2,meaning that the total mass of the stars, measured in solar masses, is twice their total luminosity ,measured in solar luminosities.
However, investigations have shown that this ratio is much greater in the outermost parts of galaxies. There the luminosity is poor but the mass is formidable. This can be explained by the supposition that there is some unknown, undetectable matter which gives off no light. It is eventually called “dark matter”. Due to the dark matter, the mass-to-luminosity ratio in galaxies is found to be about 100 – 300. Thus, the visible matter accounts for only about 5% of the total mass.
In estimating the mass of the Fireworks galaxy, let us assume the mass-to-luminosity ratio to be 102.
Let be the mass of the galaxy; – its luminosity in solar luminosities(); and – the absolute magnitudes of the NGC 6946 and the Sun, respectively; – the visual magnitude of NGC 6946; – the distance to the Fireworks galaxy in parsecs(pc).
To find the mass we proceed as follows:
By using the Pogson’s law and the definition about absolute magnitude, we have:
According to the Pogson’s law:
Then, by using (1)
we calculate the mass of NGC 6946:
As we have considered only the magnitude of the mass-to-luminosity ratio, we can conclude that the mass of NGC 6946 is solar masses. By comparison, the mass of the Milky way galaxy is determined to be at least solar masses. Therefore, since masses of spiral galaxies rarely differ by more than one magnitude, the above is a good estimation.
There is another way of determining the mass of a galaxy, which, despite its disadvantages, can cope with the previously discussed problem of the “hidden mass”. By using this procedure scientists estimate not only masses of galaxies, but also those of star clusters, stars, planets, and, surprisingly as it might be, planets and asteroids. It is the Newton’s law of gravitation.
Let us consider a material particle following a circular orbit around a much heavier body of mass . The law of gravitation states that the acceleration exercised on the particle a distance apart from the central body is given by the following expression:
where G is the so-called “gravitational constant”.
Setting (1) equal to (2) yields for the mass
Now we find the lower bound of the desired mass. Let the Fireworks galaxy be the central body in the above equations. Relatively recent investigations have shown that it has several irregular dwarf-galaxies companions. Let us take one of them: [kk98a] 251. The parameters we need are presented in the table.
First we find the apparent distance between the two galaxies on the sky. Since the observed portion of the sky sphere is comparatively small, we can neglect its spherical form. Using the Pythagorean theorem, the apparent distance is
y = 65.6 arc min = 0.0191 rad.
We cannot tell how greater than this the mass really is, but what we can do is to repeat these calculations for several other companions. The results are similar in order: K × 1011 solar masses, where K is a one-digit number less than 5. So, we conclude again that the mass of NGC 6946 is similar to 1011.
7.2.Studying the spiral structures in NGC 6946
Spriral arms in general
Spiral arms are the most significant morphological features of galaxies. But these structures are common not only in spiral galaxies. They appear everywhere in nature. If we take a look at a cyclone, a whirlpool, a snail and even at the DNA molecules in our body, we will see that all they are alike in having spiral structure. Hawks approach their prey in a spiral. Insects approach light sources in a spiral, too.
Studying the spiral arms of galaxies is important because their structure reveals the way of rotation, the evolution, and the gravitational interaction with other galaxies.
Several hypotheses exist as to how spiral structures originate. It is believed that gravitational interactions sometimes produce radial fluctuations which cause the matter in galaxies to compress and expand. As these waves move from the center outwards, they wind up because of the differential rotation, i.e. rotation predicted by the Newton’s law of gravitation. The greater the distance to the centre is, the less the gravitational force and the less the velocity is.
This is how logarithmic spirals are supposed to be formed. In other words, if the spiral arms of a galaxy represent logarithmic spirals, it is true that its rotational velocity is inversely proportional to the root of the distance to the centre.
Like stars, spirals participate in the orbital rotation, too. But the velocity of a given spiral arm is usually lower than that of the adjacent stars. This curious fact is the reason for the observed active star formation in these areas: since the stars travel faster, they create dense regions in which eventually young stars are formed.
Here arises a problem: if the spiral structure were due to differential rotation only, the range of the observed spiral structures must be much more than 360º because these structures should exist during several complete revolutions. In fact such spirals are not observed. In NGC 6946 the range is about 310º. The reason for this paradox has not yet been clearly understood. It is suggested that there should be a stabilizing factor which prevents spirals from further winding. A very common conjecture is the so-called “Density wave theory”.
There are several types of spirals. In most spiral galaxies we observe logarithmic spirals.
A little mathematics
Let O be the centre, or the “origin”, of a spiral (see the figure 1); A and B – random points on it. Let us denote OA by r1 and OB by r2.Mathematicians call a spiral logarithmic if it satisfies the following law:
where is the angle between OA and OB, and μ is the characteristic angle called “pitch”-the angle between the spiral and a circle centered at the origin. This is equivalent to:
Therefore, there is a linear dependency between lg r and , called polar coordinates (that is why this type of spiral is named “logarithmic”).
Determination of the pitch angle
If we measure the polar coordinates of several points on each structure, we can say whether it is a logarithmic spiral or not as well as to measure its pitch. Using a photo of the Fireworks galaxy (fig. 2a), let us first trace the spiral arms on a piece of transparent paper (fig.2b).
Next we measure the polar coordinates of several points of the four spiral structures (a, b, c, and d on fig.2b).We build the four graphs showing the dependency between lg r and . the following graph is for the spiral arm (b). The other 3 look in a similar way.
Indeed, the linear dependency exists which means that the spirals can be considered logarithmic. Therefore, the rotation is differential and equation can be applied for NGC 6946.
In general for a linear graph the ratio of the change in quantity on the y-axis (the “rise”) and that on the x-axis (the “run”) is a constant value called “slope”. Thus, the slope of a versus lg r graph is:
If we substitute with m in equation (1), we get:
The pitch angles range from 22 to 37 degrees as in most spiral galaxies of the same type. In comparison, the pitch of the Milky way galaxy has been determined to be 12°.Therefore,the spiral arms of our galaxy are quite more wound than those of NGC 6946.
The Fireworks galaxy (NGC 6946) offers not only a spectacular show with its magnificent spirals and formidable supernovae explosions, but it is also of great interest for the science nowadays. Throughout our work on this incredible galaxy we have found that it is a unique one in having 8 recorded supernovae explosions, numerous supernovae remnants and interesting dwarf galaxies-companions. However, there is still much room for increasing our knowledge about this sky treasure. Observations with modern telescopes such as VLT,OWL and ALMA may and will provide those missing parts of the puzzle we are looking for-namely, new supernovae remnants and dim irregular galaxies in the system. It is possible that even at the moment there is a new supernova there waiting for us to discover. All in all, the Fireworks galaxy is the most exceptional and interesting object in the Northern sky. If you agree, immediately begin observing and investigating it. If you don't, just take a look at it and you will change your mind.
9. OUR TEAM
We express our thankfulness to our team leader, Mr Petar Todorov(firstname.lastname@example.org), for his help and support during our work.
We acknowledge the help of the following people: Dr. Petar Pessev, for his advices and for the idea to work on NGC 6946;
Mr. Filip Fratev, who gave up to us access to his telescope and CCD camera, and for his help during the observations;
The sources for the images are mentioned for every image with its appereance
The mathematical formulae are typed in