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Students determined the age of the universe using an 11 inch telescope and they discover the necessary physical laws experimentally. As a second step they developed a progressive series of mathematical models for the dynamics of the universe and calculated that the usual matter amounts only 5 % of all matter and energy in the universe. Easy to use learning material is included for schools as well as for the interested public. More detailed learning material may be requested. The material has been tested successively for three age groups: With the conceptual material, students of classes 4 or higher can comprehend the topic. With more advanced material, students of class 7 or higher can evaluate the measurements mathematically. With fully advanced material, students of class 9 or higher can develop mathematical models for the dynamics of the universe and calculate the statistical significance of the measurements.

•1 gostou•973 visualizações

Denunciar

Compartilhar

Students determined the age of the universe using an 11 inch telescope and they discover the necessary physical laws experimentally. As a second step they developed a progressive series of mathematical models for the dynamics of the universe and calculated that the usual matter amounts only 5 % of all matter and energy in the universe. Easy to use learning material is included for schools as well as for the interested public. More detailed learning material may be requested. The material has been tested successively for three age groups: With the conceptual material, students of classes 4 or higher can comprehend the topic. With more advanced material, students of class 7 or higher can evaluate the measurements mathematically. With fully advanced material, students of class 9 or higher can develop mathematical models for the dynamics of the universe and calculate the statistical significance of the measurements.

- 1. How Students Can Observe the Bing Bang with an 11 Inch Telescope Hans-Otto Carmesin*, Fabian Heimann, Jan-Oliver Kahl *Gymnasium Athenaeum Stade, Harsefelder Straße 40, 21680 Stade Studienseminar für das Lehramt an Gymnasien, Stade, Bahnhofstraße 5, 21682 Stade Fachbereich 1, Institut für Physik, Universität Bremen, 28334 Bremen Hans-Otto.Carmesin@t-online.de URL: http://hans-otto.carmesin.org Abstract Students at the age of 12 to 18 observed the Bing Bang on their own with a telescope of the type C11. Additionally, they evaluated their own observations, interpreted them and deduced the underlying theories. Furthermore, they analyzed other observations of galaxies with a red shift of Δλ/λ greater than 0.2, these observations were awarded with the Nobel Prize in Physics 2011. From these observations they deduced quantitative conclusions about the cosmological curvature of the universe as well as the density of the universe and of dark matter. These results were also presented in public. In addition, students at the age of 10 evaluated these observations in a simplified form. In this article we report on the experiences we gained from this project, which can be transferred to other classes. 1.Introduction Many students would like to see on their own what it means, when adults assert that there was the Big Bang 14 Billion years ago (Muckenfuß. 1999). Until now, this is only possible with quite large telescopes. The Orange Lutheran High-School from Orange in California used a reasonably small telescope, when they observed cosmological redshifts with a 14 inch telescope (La Pointe, 2008). However they not determined the distance of those galaxies. Here we present a project, in which students at the age of 12 to 18 observed the Big Bang at the observatory of the Gymnasium Athenaeum in Stade with an 11 inch telescope. They achieved measuring significant and highly significant red shifts and distances of several galaxies. Additionally, they interpreted them cosmologically, calculated the age of the universe and presented their results in public. 2.Aims of the project The Big Bang is in some way notional from the point of view of students, because they know that no human was an eye witness. They also know that the Big Bang is often questioned in public. Even professors cause a stir with the argument the Big Bang is basically marketing (Gast, 2012). One goal of this project is therefore to enable as many students as possible to conduct an independent observation and analysis of the Big Bang. For this, a small telescope is beneficial. This means we do not favor a huge telescope that produces as accurate data as possible. We rather prefer a small telescope that creates repeatable, clear and significant data. The observation of the Big Bang was developed and conducted by students. Thus, we pursue the goals to develop competences, spark interest, motivate independent work including evaluation and stimulate talents. Fig. 1: Spectrum of the galaxy NGC 3516 (Beare, 2007, Kennicutt, 1992). The thick emission line above 6563 Ȧ is the H-Alpha-line. This line was often used to determine the red shift. 3. Composition of the teams Two students at the age of 17 and 18 took part in the required extension of our observatory and developed gradually an effective technique for observing galaxies (Heimann, 2011). About 15 students from our working group for astronomy took part in the observations, developed model experiments, visualizations and explanations. They presented them in public at several suitable occasions. Meanwhile a third team was formed with the aim to simplify the observations and to improve the signal-to-noise ratio. 4. Used instruments Our telescope is a C11 from Celestron. It is mounted on a Gemini G40 in a dome with a diameter of 2 m. For obtaining spectra we use the Deep Space Spectrograph DSS-7 from SBIG. It is attached on a SBIG ST-402
- 2. camera. For the navigation we use a finder scope with a focal length of 300 mm in combination with an EOS camera by Canon plus the telescope drive unit FS2 by Michael Koch. More convenient would be an automatic mount as it was used by the Orange Lutheran High School (La Pointe, 2008). Moreover, a camera with less dead pixels would improve the signal-to-noise ratio. Fig. 2: Recording of the spectrum of the galaxy NGC 3516: Slit widths from top to bottom: 400 µm, 100 µm, 50 µm, 200 µm und 400 µm. The horizontal bright line represents the light of the galaxy. The other vertical lines mainly represent the light pollution in Stade. The bright pixels are caused by malfunctions of the camera. 5. Selection of the galaxies Since our telescope is relatively small, it is difficult to create significant spectra (s. Fig. 1) (University Strasbourg, 2012) of distant galaxies at all. This is also hindered by the fact, that light pollution can't be neglected in Stade. Therefore, we choose galaxies with as strong spectral lines as possible. These are galaxies, in which many young stars emerging (Beare, 2007, Unsöld, 1999). An example is the galaxy NGC 3516 (s. Fig. 1) (University Strasbourg, 2012). 6.Observations Altogether, the students conducted observations on five galaxies (s. e.g. Fig. 2). These observations contained substantial statistical dispersion. Here, we present observations of three galaxies in this paper, in which the dispersion seems to be acceptable based on visual considerations and a statistical analysis. Recording a single spectrum took 300 s in general, 222s in one case. We also recorded and subtracted dark frames to compensate for dead pixels. The camera was cooled to a temperature of -9° C to decrease thermal noise. In the spectrograph, we used a slit with a width of 100 µm. At several observation nights, different groups of students took part so that most members of the astronomy working group were able to experience an observation of the Big Bang. Fig. 3: Recording of the spectrum of the galaxy NGC 3516: The part with the light of the galaxy was extracted. However it still contains light pollution. The dark line at the right presents the absorption of the oxygen in the earth’s atmosphere. 7. Extracting the spectrum of the galaxies To separate the light of the galaxy as accurate as possible from the light pollution, an interval of the raw spectrum (see Fig. 2) is taken (see Fig. 3). 8. Calibrating the spectrograph The spectrograph was calibrated with a common Neon lamp at the start of each observation. For this purpose, we placed the Neon lamp in front of the telescope and recorded a spectrum. For the calibration, we used the absolute maximum at a wavelength of 7032 Ȧ and the left maximum at a wavelength of 5852Ȧ (s. Fig. 4). In this manner, we identified a clear allocation of the wavelength which is independent of atmospheric, stellar and galactic features. Fig. 4: Calibration with a Neon lamp: Lateral axis: Channels of the spectrograph. Vertical axis: Recorded intensities of the Neon lamp. The specifications of the wavelengths were taken from literature. 9. Verifying the recorded spectra Comparing the spectrum of the Neon lamp with the one of the galaxy, there is a significantly lower noise in the recording of the Neon lamp. This confirms that the instrument works properly. In contrast, light from distant galaxies is overlaid by the light pollution and the statistical noise. To evaluate our results we developed the following procedure: (a) Initially, a clear horizontal line should set apart from the light pollution, as shown in Fig. 2. (b) To ensure that the spectrum was taken correctly, we determine the wavelengths of two known strong lines and compare them with literature. So the lines of mercury at 4358 Ȧ and oxygen at 7594 Ȧ were confirmed (s. Fig. 5). This verification is necessary due to the used Celestron telescope. Because it is possible, that small shifts of the mirror might occur (La Pointe,
- 3. 2008). For instance, averaging two spectra could increase the signal-to-noise ratio in principle. However, if the maxima are shifted apart, the mean signal value is halved. As a consequence, the observed signal-to-noise ratio of 3 (highly significant) would decrease to 1.5 (not significant at all). Thus not verifying the spectra might cause a severe problem. Fig. 5: Spectrum of the galaxy NGC 3516. The light smog is relatively bright, especially the three lines of mercury lamps. The letter A marks the Fraunhofer – A - line of oxygen. The hydrogen of the galaxy NGC3516 is marked by the H-Alpha- line. 10. Analyzing the components of the spectrum (a) 5300 Ȧ < λ < 6300 Ȧ: Even if no galaxy and no star in shown in the raw data, a spectrum can be analyzed. (s. Fig. 6) This spectrum is interpreted as the sky background and mainly contains light pollution of near street lamps. Because this light pollution is quite strong between 5300 Ȧ and 6300 Ȧ, this interval of λ will not be used any more. Fig. 6: Background: From the spectrum (see Fig. 2), a horizontal stripe was extracted below the stripe with the light of the galaxy (see Fig. 3). The light pollution is clearly visible. There is no H-Alpha-Line. (b) 6300 Ȧ < λ: At these wavelengths the intensity reduces approximately linear. We interpret this as a systematic error for the analysis of individual lines. Therefore we use a linear regression (see Fig. 7) which offers the following expression for the intensity: 6837.4 – λ∙0.5991/Ȧ. This linear term was subtracted from the raw spectrum. (see Fig. 8). (c) λ < 5300 Ȧ: At these wavelengths we proceed appropriate to the wavelengths greater than 6300 Ȧ (s. Fig. 9). Fig. 7: Linear Regression: For analyzing single spectral lines, there is a systematic error which was identified by linear regression and eliminated by subtraction. 11. Determining significant spectral lines The observed data are a good example for an analysis of statistical spread. Since empirical data is collected and evaluated in several fields of activities (examples are natural sciences, engineering sciences, election analysis, psychology, medicine or sociology), the ability of determining statistical parameters has a high importance for the future lives of the students. Therefore, we conduct such analyses in our working group for astronomy. Fig. 8: Spectral lines and statistical errors: Vertical axis: Signal overlaid by statistical dispersion. The absolute maximum is the H-Alpha-Line and has a signal-to-noise ratio of 3.24. It is therefore highly significant. To find significant spectral lines in the linear corrected spectra, we first calculate the experimental standard deviation σ. For this purpose, we first calculate the empirical variance as mean value of the squared intensity values. Then, the standard deviation is obtained as the square of the variance. For wavelengths greater than 6300 Ȧ we get σ> = 96 and for wavelengths below 5300 Ȧ σ< = 115. From the standard deviations we calculate the signal-to-noise ratio as the quotient of the used signal and the standard deviation as it is usual e.g. in image
- 4. processing. According to evaluating statistics the result is significant if the signal-to-noise ratio is greater than 1.96 σ. Appropriate to this interval is a probability of error of 5%. A result is highly significant if the signal- to-noise ratio is at least 2.58 σ. This interval corresponds to a probability of error of 1%. Here the signal is the intensity of the H-alpha line. This has a signal-to-noise ratio of 3.2. Therefore, we have a probability of error of 0.14 %. In the appendix, one can find all significant spectral lines of the observations shown in figures 7 and 8 as well as their analysis and interpretation. The observations of the students are thus highly significant according to the methods of evaluating statistics. Nevertheless, there are many improvement opportunities, which should not be discussed here. Our data shows that we have achieved our main aim to provide the significant observation of the Big Bang to many students. Fig. 9: Spectral lines and statistical errors: Vertical axis: Signal overlaid by statistical dispersion. The absolute maximum is the Hg-line with 4358 Ȧ. It has a signal-to-noise ratio of 2.18 and is therefore significant. 12. Interpretation of the observed emission line The students realized that the only observable significant line caused by the galaxy is the emission line at approximately 6590 Ȧ. (See also the appendix about significant spectral lines.) The spectrum of NGC 3516, which is known from the literature, suggests that this is the H-alpha line of the galaxy (s. Fig. 1). But it is also possible, that the line is caused by the oxygen (O-III) of the galaxy at approximately 5050 Ȧ (s. Fig. 1). To find a clear decision, we calculated the raw counts of both lines. (See appendix about intensities of the lines.) We determined an intensity of the H-alpha-line of 19.81, while the oxygen line has only an intensity of 5.52. The ratio is 3.6. Therefore, we consider the interpretation as highly significant. 13. Observed redshift We showed above, that students measured the H-alpha- line in a highly significant way. The wavelength of the maximum is 6590 Ȧ. As one can see in Fig. 1, the H- alpha-line is relatively thick. Accordingly, we found a second significant line at 6601 Ȧ with a signal-to-noise ratio of 2.34 (s. Fig. 8). Since there are no strong atomic lines in the surrounding, we calculated the mean value and used the resulting 6595.5 Ȧ as the wavelength for H-alpha. The mean value between both images is 6614 Ȧ. From this we get a redshift of z = Δλ/λ = (6614 Ȧ - 6563 Ȧ)/6563 Ȧ = 0.0077, literature: 0.0087 (University Strasbourg, 2012). Next we compared our wavelengths 6590 Ȧ and 6601 Ȧ obtained for the H-alpha line with the corresponding wavelength 6614 Ȧ contained in the data of Fig. 1. For this purpose we determined the half width of the data of Fig. 1 and obtained 25 Ȧ. So our result seems reasonable. But can we expect our results with our conditions of observation? In order to investigate this question, we modeled the spectrum that we should obtain based on the data of Fig. 1, the light pollution at our observatory, the size of our telescope and the electronic noise of our camera. As a result we obtain maxima of the intensity typically ranging from 6580 Ȧ to 6640 Ȧ. Thus we can explain our measurements also by computer simulations. The wavelength of the H-alpha line is λ = 6563 Ȧ when it is not shifted. We conducted similar observations for the galaxy M66 and got a wavelength for H-alpha of 6583 Ȧ. The corresponding redshift is z = 0,003; literature 0.0024 (University Strasbourg, 2012). These results were included in our distance-velocity-diagram for evaluation. Fig. 10: Determination of energy flux density: At the star GSC 4391 701, top left, the software displays 20 counts (background subtracted). At the galaxy, top right, the software displays 32 counts (background subtracted). 14. Determination of the distance To get a rough value of the distance of the galaxy, we introduce the approximation that the Milky Way consists of 100 Billion stars that all have the same intensity as the sun. This gives a power of P = 3.85∙1037 W. Furthermore, we assume that all observed galaxies have the same power. With our camera we observed the energy flux density of the galaxy with (s. Fig. 10). According to the star map Guide 8 this star has an apparent magnitude of m = 11.15. From this, we calculate the energy flux density S = 1367 W/m2 *10- 0.4*(m+26.83) = 0,879pW/m2 (Unsöld, 1999). Therefore, the galaxy has an energy flux density of S = 0.879pW/m2 ∙ 32/20 = 1.41 pW/m2 . Because of that the distance of the galaxy, is d = [P/(4πS)]0,5 = 0.156 Billion light years (literature: 0,12 Billion light years (La Pointe, 2008); discrepancy 30%). Using a survey, we investigated the error of the distance that one should expect in general
- 5. and we obtained an error of 33.8 %, see worksheet in the appendix. In the same way, we estimated the distance for the galaxy NGC 3227: d = 0.06 Billion light years. We also included these in our Hubble diagram (Unsöld, 1999) (s. Fig. 11). Fig. 11: Velocity-Distance-Diagram: Milky Way (bottom left), M66 (center left), NGC3227 (center right, SNR =1,55) and NGC3516 (top right). The graph is nearly linear. The slope is 20 Gy (Gigayears) and corresponds to the so-called age of the universe (Literature: 13Gy to 20Gy (Unsöld, 1999)). 15. Creating a distance-velocity-diagram The redshift z = Δλ/λ is equal to the velocity v of the galaxy in light years per year or in the units of c. This was derived by students, see below. We plot the velocity v against the distance d. The graph is almost a line through the origin (s. Fig. 11). The proportionality between the distance d and the velocity v is called Hubble’s Law (Unsöld, 1999). The gradient d/v gives the age of the universe. It is approximately 20 Billion years (literature: 13Gy to 20Gy (Unsöld, 1999) or rather 13.72 Gy (Freedman, 2009)). As a comparison, students determined the age of the universe with distances from the literature and with self-measured redshifts, like it was done by the students of the Orange Lutheran High School (La Pointe, 2008). The result was 15.8 Gy. As expected our distance determination is less accurate than the determination of the redshift. 16. Conception of the astronomy evenings Our public astronomy evenings address a broad audience and a variety of themes. We held one astronomy evening concerning the Big Bang only. The students of the working group hold several lectures. In a first section, a general understanding of the Big Bang was established, whereas in a second section we develop a mathematical and theoretical understanding. 17. Model experiment: Distance measurement A model experiment for distance measurement starts with a luxmeter. Attendant children were asked whether it is brighter in front of a beamer or at the wall. Even 10 years old students supposed that the intensity of the light is high in front of the beamer and decreases at larger distances. The children also measured this with a luxmeter and with the light sensor of a smartphone. From this, one can see that you can calculate the distance to the source of light after measuring the intensity at an arbitrary point. For the older students, we showed in the break at an experimental station that the intensity is proportional to the inverse square of the distance. Fig. 12: Water waves spread behind a hole (TU Clausthal 2013). 18. Model experiment: Wave nature of light In order to illustrate the wave nature of light, we presented water waves behind a hole (s. Fig. 12) and laser light behind a hole (s. Fig. 13). Both spread behind a hole and this similarity suggests the wave nature of light. Moreover Fig. 13 suggests that the wavelength can be determined from the color of the light. Fig. 13: Light spreads behind a hole. 19. Model experiment: Discrete atomic spectra Next students investigated the spectra of several gas lamps with a hand spectroscope. In particular they investigated spectra of a neon lamp, an energy saving lamp using mercury and a hydrogen lamp. So they developed the competence to identify a material using
- 6. spectra. Conversely they predicted the spectrum knowing the material emitting the light. Students of class 7 or higher additionally took a spectrum of the star Vega. They concluded by comparison with the other spectra that in a star there is rarely mercury but much hydrogen. In particular, they asserted that the light of hydrogen contains the distinctive H-alpha line and that it has a wavelength of 6563 Ȧ. Fig. 14: Increase of the wavelength behind a swimming duck (Carmesin, 2013). 20. Model experiment: Doppler shift Next the students discovered the increase of the wavelength behind a moving source from a photo of a swimming duck (s. Fig. 14) or alternatively from a swimming toy duck propelled by a motor. Fig. 15: Worksheet for the development of the Doppler shift formula v = c∙z. 21. Model experiment: Doppler shift formula Next the students of class 7 or higher developed the Doppler shift formula v = c∙z using a work sheet (s. Fig. 15). 22. Cosmology without forces To get a simple general interpretation of the observed data1 , we roughly approximated the results for the galaxy NGC 3516 to get simple numbers and units. The galaxy departs from earth with a velocity 100 Zm/Gy. That means the galaxy increases its distance by 100 Zetameter every Gigayear. The current distance is: Distance today: d = 1400 Zm At this step the 10 year old students calculated the distance of the galaxy one Gigayear ago: Distance one Gy ago: d = 1300 Zm Thereupon the students calculated the distance of the galaxy two Gigayears ago: Distance 2 Gy ago: d = 1200 Zm Afterwards they calculated the distance three Gigayears ago: Distance 3 Gy ago: d = 1100 Zm Subsequent they calculated the distance of the galaxy 4 Gigayears ago: Distance 4 Gy ago: d = 1000 Zm This was continued in the same way. In the penultimate step they calculated the distance of the galaxy 13 Gigayears ago: Distance 13 Gy ago: d = 100 Zm Finally they determined the distance of the galaxy 14 Gy ago: Distance 14 Gy ago: d = 0 Zm In this way the 10 year old students discovered that the galaxy was here 14 Gigayears ago. At this step already 10 year old students asked, what the students of the astronomy working group found out about the other galaxies. We regarded the galaxy NGC 3227 as another example and also used similar simplified data. For this galaxy, we got a velocity of 50 Zm/Gy and a distance of 700 Zm. In the same way as above, the 10 year old students quickly found out that the galaxy was here 14 Gigayears ago. In this way the 10 year old students discovered that all galaxies moved away from here at the same time, they discovered the equality of start times. 1 See Carmesin 2012a for more details.
- 7. The 10 year old students liked most the model of a glass that falls down on the floor and all cullets move away in different directions with different velocities. The cullets correspond to the galaxies. They also start at the same time and the pieces with a higher velocity will have a larger distance (s. Fig. 11). Students from age 11 to 14 recognized without difficulty that the distance is proportional to the velocity. This proportionality is also very useful for Math lessons (Carmesin 2002). For the beginning of the expansion we introduced the term Big Bang. Since we only have observations for the time after the Big Bang, we call the time elapsed after the Big Bang the age of the universe τ. Fig. 14: Glass model fort the Big Bang: The picture sequence presents a glass falling to bottom and brakes into pieces. Top: the glass is far above the bottom. Second picture: the glass approaches the bottom. Third picture: the glass just arrives at the bottom. Bottom: the glass brakes into pieces. 23. Cosmology with gravitational forces Initially, we considered a spherical volume with the radius R, the mass M and an expansion velocity of the universe of v=ΔR/Δt (Harrison 1990). For this, we used the energy term for a sample mass m (s. Fig. 15). The students recognized that a football shot from the earth vertically has an energy term with an identical structure. Here we have the mass of the ball m, the mass of the earth M, the distance between the ball and center of earth R and the velocity v of the ball. The students concluded that there are generally three possibilities: 1) If the initial velocity is lower than the escape velocity, the ball will return. This correlates to a universe that first expands and then collapses. 2) If the initial velocity is higher than the escape velocity, the ball will not return. This correlates to a universe that expands continuously. 3) The third possibility is the borderline case that the initial velocity equals exactly the expansion velocity and the ball will not return. Fig. 15: Text on blackboard: Cosmology with gravity. 24. Cosmology with curvature of space The students analyzed the curvature of space using the example of the earth. Here they examined the consequences for the GPS. This is presented in another article in detail (Carmesin, 2012b). The students were able to transfer the results to cosmology: They knew from the Schwarzschild Metric that mass or energy curves the space hyperbolically. Therefore, the space should be curved hyperbolically if the energy is positive. If the energy is zero, the space should be flat. If the energy is negative and therefore the expansion restricted, the space should be curved elliptically. This means a sphere like curvature. A derivation for students is shown in the appendix. Fig. 16: Text on blackboard: Cosmology with density of vacuum. 25. Cosmology with a vacuum mass In Mathematics, the properties of space are described axiomatically. But the example of a curved space shows that the properties of space must be measured. This suggests that we also cannot assume the density of space ρV, but have to measure it. Accordingly, we extended the above cosmology with gravitational forces in such a way that the mass of the vacuum MV is added to the mass of the galaxies MG (Carmesin, 2002). We deduced a term for the potential energy (s. Fig. 16). The students also plotted this term. They conducted a functional analysis discovering the local maximum and calculated that at the maximum the density of matter ρM = MG/(4/3πR3 ) is twice as large as the density ρV of the vacuum. From this, they concluded that in the special case of a vanishing velocity there is an unstable balance in which the universe neither expands nor contracts. Furthermore they concluded that the universe will expand in an accelerated manner, if the density of matter is less than twice the density of the vacuum. In contrast the universe will contract in an accelerated manner, if the density of matter is higher than twice the density of the vacuum. They deduced that one can estimate the
- 8. density of vacuum by measuring the acceleration of the galaxies relative to the earth. 26. Cosmology with a vacuum mass: Friedmann- Lemaitre Equations To get any demanded acceleration, the students determined the force F = m∙R‘‘ that affects a sample mass m as the negative derivative of the potential energy that was calculated above: m∙M∙G/R2 + 8πG/3 ∙ m∙ρV∙R = m∙R‘‘ Rewriting this equation gives one of the two Friedmann- Lemaitre Equations (Unsöld, 1999): R‘‘/R = 4πG/3 ∙ (2ρV – ρM) The students instantly recognized at this step the above conditions for the non-accelerated universe. Additionally, they recognized from the algebraic sign that the vacuum density accelerates the expansion, while the density of matter decelerates it. From the above cosmology with gravitational forces the students know that they need the term for the energy of a sample mass m for the curvature of space of the universe and establish the energy term: E = m∙(R‘)2 /2 - m∙M∙G/R - 4πG/3 ∙ m∙ρV∙R2 Rewriting this equation gives: (R‘/R)2 = 8πG/3 ∙ (ρV + ρM) – k∙c2 /R2 Here we substituted the normalized energy k = - 2E/(mc2 ). This is the second Friedmann-Lemaitre Equation. Since the students knew that energy/mass leads to a curvature of space, they interpreted it as a quantity that describes the curvature of the universe. They explained the 3 general cases shown above. Fig. 17: Velocity-Distance-Diagram: Horizontal axis: Velocity v in lightyears per year or v in c or redshift z of a galaxy. Vertical axis: Distance d of a galaxy in Gly. The galaxies with z below 0.01 have been observed by the students. The galaxies with 0.01 < z < 0.3 have been investigated with infrared radiation (Freedman, 2009). This includes the galaxy at z=0.2 with d = 2,8 GLy. The galaxy at the top right has a redshift of 0.46 and a distance of 11.15GLy (Riess, 2000). 27. Cosmology with a vacuum mass: evaluation To get easier data we introduced the scaled density: Ω = ρ/ρk with 4πG/3∙ρk = 0.0028/Gy2 This is equal to ρk = 10-26 kg/m3 because Gy means 1 Gigayear. So the Friedmann-Lemaitre Equations take the following form: R‘‘/R = 0.0028 ∙ (2ΩV – ΩM)/Gy2 (R‘/R)2 = 0.0056 ∙ (ΩV + ΩM)/Gy2 – k∙c2 /R2 The students wanted to estimate the three unknown parameters: density of the vacuum ΩV, density of matter ΩM and curvature parameter k. For this, they used recent data of galaxies with high redshifts, which were awarded with the Nobel Prize in Physics 2011 (s. Fig. 11). Initially, the students recognized that the Hubble’s Law is valid for redshifts less than 0.2. They highlighted these as a straight line (s. Fig. 17). The galaxy at z=0.2 meaning v=0.2c has a distance of d=2.8 GLy. Therefore, the slope of the line is: d/v = 2.8/0.2 Gy = 14Gy = τ The students set up an equation for the accelerated motion: R(t) = R0 + v∙t + 0,5∙v‘∙t2 Afterwards, they got the terms for R‘ and R‘‘ by taking the derivative: R‘ = v + v‘∙t and R‘‘ = v‘ To estimate R‘‘ = v‘ = Δv/Δt, the students accounted the galaxy at z=0.46 (s. Fig. 17). According to Hubble’s Law the redshift should have the following value: v = d/τ = 0.80 c or z = 0.80 The deviation is: Δz = -0.34 or Δv = -0.34c Since the galaxy has a distance of 11.15 Gly and the light came from the galaxy to the earth with the speed of light, it was emitted at the following time: Δt = -11.15Gy Therefore the demanded parameter R‘‘ is: R‘‘ = 0.34c/11.15Gy = 0.030c/Gy Thus the quotient in the Friedmann-Lemaitre Equation is R‘‘/R = 0.03c/Gy/11.15GLy, thus R‘‘/R = 0.0027/Gy2 The students divided the above term for R’ by R: R‘/R = v/R+v‘/R∙t Here they inserted the observed redshift for v. Further they inserted the above estimated value 0.0027/Gy2 for R‘‘/R = v’/R. Moreover they inserted t=d/c for the time. For the galaxy at z = 0.2 they obtained the term: R‘/R = 0.2c/2.8GLy+0.0027/Gy2 ∙2.8Gy thus R’/R = 0.079/Gy For the galaxy at z=0.46 they calculated accordingly: R‘/R = 0.46c/11.15GLy+0.0027/Gy2 ∙11.15Gy thus R’/R = 0.071/Gy Since only the galaxy at z=0.46 shows a difference from Hubble’s Law, the students set up the first Friedmann- Lemaitre Equation only for this galaxy: 0.0027/Gy2 = 0.0028 ∙ (2ΩV – ΩM)/Gy2 Simplifying gives the first equation for the determination of the parameters: 0.96 = 2ΩV – ΩM For the second Friedmann-Lemaitre Equation the students inserted the data of the galaxy at z=0.2: (0.079/Gy)2 = 0.0056 ∙ (ΩV + ΩM)/Gy2 – k/(2.8Gy)2 Simplifying gives the second equation for the determination of the parameters: 1.1 = ΩV + ΩM – 23k
- 9. For the other galaxy (for z = 0.46) they get accordingly the third equation for the determination of the parameters: 0.89 = ΩV + ΩM – 1.4k The students solved the linear system of three equations and got the curvature parameter (literature value -0.0179 < k < 0.0081 (Riess, 2000, Freedman, 2009)): k = -0.009 They got the density of the vacuum: ΩV = 0.61 They also got the density of matter: ΩM = 0.26 The students recognized that the curvature parameter is relatively small and therefore the space as a whole can be considered as not curved. Furthermore, the students determined the relative ratio of the density of vacuum (literature value 72.6 % (Riess, 2000, Freedman, 2009)) 0.61/(0.61+0.26) = 70% ρV as well as the relative ratio of the density of matter: 0.26/(0.61+0.26) = 30%. ρM Knowing from dark matter lectures that 5/6 from the 30% of the density of matter is dark matter (literature 22.8 % (Hinshaw, 2009)) they calculated ρ Dark Matter 25 % The common matter described by the periodic table has only the remaining part of (literature 4.56 % (Riess, 2000, Freedman, 2009)): ρ Common Matter 5 % They recognized that one does barely know anything about 95 % of the energy or matter. Consequently there remains much more to be discovered. Fig. 18: Telescope with equipment. 28. Students evaluate cosmological models The students evaluate the common cosmological models by means of their interpretation of distant galaxies: (a) In 1917, Einstein proposed a static universe, which is characterized by the unstable equilibrium (Unsöld, 1999). The students disproved this with their own observations. (b) Between 1922 and 1924, Carl Wirtz discovered the relation between distance and the redshift. In this way he derived and interpreted a model of an expanding universe (Wirtz, 1922, Wirtz, 1924, Appenzeller, 2009, Unsöld 1999). The students confirmed this by observation. (c) In 1917 de Sitter introduced a model with a vanishing density of matter (Unsöld, 1999). The students disproved this with their own observation. (d) In 1922 using the densities of matter and vacuum, Friedmann introduced his well-known cosmological equations. In 1927, Lemaitre proposed a corresponding equation independently (Unsöld, 1999). This model was confirmed by the students. (e) From approximately 1930 to 1998, the so-called standard model has been popular (Unsöld, 1999). This assumed vanishing density of vacuum. The students disproved this with their evaluations of observations (Riess, 2000). 29. Experiences The students from age 11 to 18 were able to observe the Big Bang on their own with a telescope of the type C11 (s. Fig. 18). Both the measured distances and the measured red shifts are sufficiently accurate for the discovery of the increasing distances of distant galaxies. Moreover, the observations are highly significant. For comparison, the signal-to-noise ratio of 3.2 achieved by the students is comparable to the SNR of nearly 4 announced by the CERN in July 2012 for its discovery of the Higgs particle (Gast, 2012) (hereby the ‘look elsewhere effect’ is included). So the students obtained the principle of the Big Bang on their own. Also, 10 year-old students were able to comprehend the basic principles and students of age 11 to 18 can explain the observations with model experiments. For the 10 year old students it was important to use units of the metric system rather than light years, to use simple numbers rather than the scientific notation of numbers and to use the equality of start times rather than the equivalent Hubble law. The students obtained theoretical explanations at four levels of complexity: (a) A cosmology without forces can already be understood by 10 year-old students. They can evaluate the results with rounded data. Additionally, students from the age 11 to 15 discovered and analyzed the proportionality between distance and velocity. (b) A cosmology with gravitational forces can be understood by students from age 16 or above. (c) A cosmology with curvature of space can be qualitatively understood on the basis of the Schwarzschild Solution. The Schwarzschild Solution can be deduced by students of age 16 or above on their own with linear regression (Carmesin, 2012b). (d) Students of the age 16 or older can deduce a cosmology with a vacuum mass on their own on the basis of Newtonian Mechanics. All students can present their results to the public. The subject of the Big Bang is of interest for many people. For this reason the students of the astronomy working group were dedicatedly concerned with
- 10. relatively difficult observations, model experiments and theories. This is also the main reason why many people came to our Astronomy-Evening and discussed questions and ideas thoroughly with us in the break. This immense interest was shown by a variety of audiences at different events. Additionally, we noticed that the participants learned many sophisticated skills concerning Mathematics, Physics and science in general. 30. Prospect Currently, students conduct observations to decrease the signal-to-noise ratio. Other students optimize our equipment in order to enable as many people as possible to observe the Big Bang on their own. Meanwhile, Hans-Otto2 prepared an alternative approach in which students discover the necessary physical laws with model experiments and simulate the measurements using Stellarium as well as the self-made software Spectrarium for the simulation of astronomic spectroscopy. Based on either of the two alternatives, the students can independently establish their own opinion on the origin of the universe. 31. Summary In the project presented above, students from age 12 to 18 observed the Big Bang leading to highly significant results. They interpreted their self-obtained results on various levels of complexity. Even 10 year-old students were able to analyze selected data both qualitatively and quantitatively in the context of a cosmology without forces. Students at the age of 16 or above were able to develop a cosmology with gravitational forces, a cosmology with curvature of space and one with a density of vacuum. They were also able to review the common cosmological models and evaluate up-to-date observational data appropriately and quantitatively. In particular, they discovered that matter which can be described by the table of elements only amounts 5% of the total matter and energy. They concluded that there remains a lot to be discovered by future generations. A largely independent work of the students was possible because they deduced cosmological models on various levels of complexity: These ranged from Geometry over Newtonian Theory to results of the more complicated Theory of General Relativity. So, each student could pick his individually adequate level of complexity. This focus to individually discover the essential content progressively is favored due to reasons of learning theory, cognition theory and epistemology (Rosenstock-Huessy, 1968). Literature Appenzeller, I. (2009): Carl Wirtz und die Hubble- Beziehung. Sterne und Weltraum, 44-52. 2 Lessons many worksheets and the software Spectrarium have been prepared by Hans-Otto and can be requested. Beare, R. (2007): Specimen Spectra for Bright Galaxies. Retrieved from http://www.docstoc.com/docs/14258744/Template- spectra-for-galaxies-as-used-by-SDSS Carmesin, H.-O. (2002): Urknallmechanik im Unterricht. In: Nordmeier, V. (Ed.): Conference-CD Fachdidaktik Physik. ISBN 3-936427-11-9. Carmesin, H.-O. (2003): Einführung der Wellenlehre mit Hilfe eines Kontrabasses. In: Nordmeier, V. (Ed.): Conference-CD Fachdidaktik Physik. ISBN 3-936427- 71-2. Carmesin, H.-O. (2012a): Schüler beobachten den Urknall mit einem C11-Teleskop. Internetzeitschrift: PhyDid B - Didaktik der Physik - Beiträge zur DPG-Frühjahrstagung (ISSN 2191-379- DD21p03). Carmesin, H.-O. (2012b): Schüler entdecken die Einstein-Geometrie mit dem Beschleunigungssensor. Internetzeitschrift: PhyDid B - Didaktik der Physik - Beiträge zur DPG-Frühjahrstagung (ISSN 2191-379- DD15p06). Carmesin, H.-O. (2013): Jugendliche beobachten den Urknall in der Schulsternwarte. MINT Zirkel, September/October 2013, p. 18. Freedman, W. et al. (2009): The Carnegie Supernova Project: The first Near-Infrared Hubble-Diagram to z~0,7. Astrophys.J.704:1036-1058. Retrieved from http://arxiv.org/abs/0907.4524v1 Gast, R. (2012). Hässliches wird passieren. ZEIT, 16, 38. Gast, R. (2012): Das Gespenst von Genf wird greifbar. Spektrum der Wissenschaft, Sonderausgabe Higgs Juli 2012, 1-4. Harrison, E. (1990): Kosmologie. 3rd Ed. Darmstadt, Verlag Darmstätter Blätter. Heimann, F & Kahl, J. O. (2011). Beobachtung der Urknalldynamik mit einem 11-Zoll-Teleskop. Jugend forscht Thesis. Hinshaw, G.. et al. (2009): Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, & Basic Results. Astrophys.J.Suppl.180:225-245. Retrieved from http://lanl.arxiv.org/abs/0803.0732v2 Kennicutt, R. (1992): A Spectrophotometric Atlas of Galaxies. The Astrophysical Journal Supplement Series, 79, 255-284. La Pointe, R. et al. (2008). Measuring the Hubble Constant Using SBIG’s DSS-7. Society for Astronomical Sciences, 137-141. Retrieved from http://adsabs.harvard.edu/full/2008SASS...27..137L Muckenfuß, H. (1995). Lernen im sinnstiftenden Kontext. Berlin, Germany, Cornelsen. Riess, Adam G. et al. (2000): Tests of the Accelerating Universe with Near-Infrared Observations of a High- Redshift Type Ia Supernova. Astrophys. J. 536, 62, Retrieved from http://lanl.arxiv.org/abs/astro- ph/0001384v1.
- 11. Rosenstock-Huessy, E. (1968): William Ockham. In: Grolier (Ed.): The American Peoples Encyclopedia Vol. 19. New York: Grolier. TU Clausthal: URL: http://www2.pe.tu- clausthal.de/agbalck/biosensor/wellen-le-g-005.jpg. Retrieved 2013. University Strasbourg (2012). Astronomical Database SIMBAD. Retrieved from http://simbad.u- strasbg.fr/simbad/ Unsöld, A. & Baschek, B. (1999). Der neue Kosmos. 6th Edition, Berlin, Springer. Wirtz, C. (1922): Die Radialbewegungen der Gasnebel. Astronomische Nachrichten 215, 19. Wirtz, C. (1924): De Sitters Kosmologie und die Radialbewegungen der Spiralnebel, Astronomische Nachrichten 222, 21. Retrieved from http://articles.adsabs.harvard.edu/cgi-bin/nph- iarticle_query?1924AN....222...21W& data_type=PDF_HIGH&whole_paper=YES& type=PRINTER&filetype=.pdf Acknowledgements We are grateful to the EWE-foundation and its von Klitzing-award. The money of the award was used to buy the equipment necessary for our observation of the Big Bang. We are grateful to the pupil Marvin Ruder who took part in observations and investigated noise sources of out equipement.
- 12. with P = 13 quadrillion YW Dmeasured Dtheoretical Error Nr. F in fW/m^2 in Zm in Zm in % 1 180,07 3113 2397 23,0 2 5,82 32805 13327 59,4 3 4,50 11882 15170 27,7 4 3,79 19490 16511 15,3 5 2,95 34900 18724 46,3 6 2,61 31037 19915 35,8 7 2,20 37701 21670 42,5 8 1,96 46868 22973 51,0 9 1,85 35459 23625 33,4 10 1,64 32756 25099 23,4 11 1,45 40048 26722 33,3 12 1,46 66121 26616 59,7 13 1,21 31105 29281 5,9 14 1,17 49863 29722 40,4 15 1,11 44772 30500 31,9 16 1,02 35010 31912 8,8 17 0,95 51606 32973 36,1 18 0,91 46852 33756 28,0 19 0,89 26715 34049 27,5 20 0,81 25132 35641 41,8 21 0,76 53544 36844 31,2 22 0,73 45672 37542 17,8 23 0,69 61605 38709 37,2 24 0,70 61490 38348 37,6 25 0,67 74472 39360 47,1 26 0,65 47206 39852 15,6 27 0,65 56496 40037 29,1 28 0,63 39849 40389 1,4 29 0,58 28565 42149 47,6 30 0,60 50445 41396 17,9 31 0,58 50306 42376 15,8 32 0,53 50468 44082 12,7 33 0,47 58323 46985 19,4 34 0,44 53009 48349 8,8 35 0,42 55370 49369 10,8 36 0,46 58114 47258 18,7 37 0,43 65951 48909 25,8 38 0,45 39508 47754 20,9 39 0,39 80315 51529 35,8 40 0,41 53429 50261 5,9 41 0,41 50468 50522 0,1 42 0,34 52125 55346 6,2 43 0,34 47300 55506 17,3 44 0,34 46925 55063 17,3 45 0,33 68811 56013 18,6 46 0,32 76774 56650 26,2 47 0,29 55686 59994 7,7 48 0,27 46368 61882 33,5 49 0,28 24517 61320 150,1 50 0,28 58332 60432 3,6 51 0,28 62698 60997 2,7 52 0,22 50182 68567 36,6 53 0,21 61555 70319 14,2 54 0,24 84931 65429 23,0 55 0,19 27170 74355 173,7 56 0,21 80281 70423 12,3 57 0,17 76787 77525 1,0 58 0,16 85419 79911 6,4 59 0,15 55612 83896 50,9 60 0,13 66369 90245 36,0 61 0,10 39021 102068 161,6 62 0,07 46723 124751 167,0 Means 49217 46827 33,8 Appendix Worksheet, Astronomy Group, Dr. Carmesin, 2013 Table: Columns 1-3: Galaxy Survey [1]. Column 4: Dtheoretical = (P/(4πF))0,5 with: P = 13 quadrillion YW or P = 13∙1036 W Column 5: |Dmeasured – Dtheoretical|∙100% Exercise: Control Dtheoretical for Nr. 1. [1](Yee, H. K. C. u. a.: The CNOC2 Field Galaxy Redshift Survey. I. The Survey and the catalog for the Patch CNOC 0223+00. The Astrophysical Journal Supplement Series, 129, 475-492, 2000.