Atlas of Nearby Stars: Projects in Virtual Astronomy

INTRODUCTION

Astronomy software like Starry Night Deluxe and The Sky are excellent commercial products that can be used in the classroom to visualise a wide range of astronomical concepts. These include the following:

While many important astronomical phenomenon can be simulated with available commercial products, the stellar parallax of nearby stars can not be simulated with most commercial astronomy programs. Interactive software running on home computers often imposes computational constraints that require simulated stars to be fixed on the celestial sphere at an infinite distance from the sun. As such, star positions are usually not plotted in 3D, so radial motion and parallax cannot be visualised with these tools.

Professional astronomers determine the distance to nearby stars using highly accurate instruments, taking parallax measurements from images produced over six months (Ducourant , 1998). In an educational environment, waiting six months to make these measurements is not realistic and the required equipment is often not available.

The technique used by professional astronomers to measure the distance to nearby stars is difficult for some students to visualise. In part, this is due to the lack of adequate educational software and because taking real measurements in the field is impractical. This paper describes the development of a Java applet written to overcome these difficulties.

The applet supports virtual astronomy experiments that enable the distance to nearby stars to be calculated using simulated parallax measurements. Distances may also be estimated using the inverse square law, knowing the apparent magnitude for a star and utilising the absolute magnitude as recorded on the Hertzsprung-Russell (H-R) Diagram that is included in the applet.

Several virtual astronomy experiments suitable for classroom use or in distance education are suggested. These virtual experiments are compared to an alternative experiment suggested by de Jong (1972), used prior to the introduction of computer technology into the classroom.

 

BACKGROUND

Professional astronomers use parallax measurements to determine the distance to nearby stars. Once the distance to the star is known, the luminosity and absolute magnitude of a star can be determined from the apparent magnitude using the Inverse Square Law.

 

FIGURE 1. Parallax geometry

PARALLAX AND DISTANCE ESTIMATES

If a human being alternates between closing the right and left eye, objects appear to jump back and forth since each eye is seeing the same scene from a slightly different position. This effect is known as parallax. The human brain takes both simultaneous views and merges them to allow an individual to perceive depth.

Surveyors can exploit parallax in determining the distance to a nearby structure. The length of a baseline is accurately measured. From both ends of the baseline , the angle to the nearby object is determined and basic trigonometry is applied to determine the distance to the object.

In the same way, astronomers can measure the distance to nearby stars by taking two images of the night sky taken six months apart, and applying basic trigonometry given the geometry shown in Figure 1.

Nearby stars will appear to move against the background of more distant stars, whose position will appear fixed due to their great distance.

In Figure 1, the geometry used to measure the parallax of a nearby star is shown. The earth is shown in light blue on opposite sides of the sun at two points in its orbit, separated in time by six months.

The angleis measured from multiple images taken six months apart.

By measuring the observed angular parallax theta as shown in Figure 1, then the distance to the nearby star can be calculated according to:

[EQU 1]

d=r/tan(theta)

where:

d

=

distance to nearby star

f

=

radius of earth's orbit, usually taken as 1 Astronomical Unit (AU)

=

observed parallax angle

 

The distance from the earth to the sun is one Astronomical Unit (AU) by definition.theta is usually measured in units of arc seconds. One arc second is one sixtieth of an arc minute. One arc minute is one sixtieth of a degree.

Whentheta is very small:

[EQU 2]

tan(theta) is around theta

Consequently, equation 1 may be rewritten in as:

[EQU 3]

d=1/theta

where d is expressed in units of parsecs by definition.

Prior to the introduction of computers into traditional education environments, de Jong (1972) suggested a laboratory exercise to acquaint undergraduate astronomy students with the parallax technique used by professional astronomers to calculate the distance to nearby stars.

In de Jong's exercise, students were directed to use a Polaroid camera to take photographs of a lamp in the physics laboratory from two positions on a circle of known radius. Students measured parallax from the two photographs, and calculated the distance to the lamp based on these measurements.

 

THE INVERSE SQUARE LAW, BRIGHTNESS, AND MAGNITUDE

The luminosity of a star is defined as the energy radiated by the star per second. Luminosity is usually given in units of Watts or Joules per second. As this energy radiates into space, it is distributed over an increasing area. The apparent brightness is therefore a function of the luminosity and the surface area of a hypothetical shell over which this energy is distributed at a given distance (Kaufmann and Freedman, 1999, p.p460-461). This results in the well-known Inverse Square Law, which may be written as:

[EQU 4]

b= L  / (4pd^

where:

b

=

apparent brightness (watts per metre squared)

L

=

luminosity (watts)

d

=

distance (metres)

 

The apparent brightness can be measured using a CCD camera or photometer. A direct consequence of the Inverse Square law is that if an astronomer on earth can measure both the distance to a star and its apparent brightness, then the luminosity of the star can be calculated.

Apparent brightness, however, is often presented in the more familiar magnitude scale. This is a logarithmic scale invented by the ancient Greeks and refined by 19th century astronomers. On this scale, brighter stars have smaller magnitude. An increase in magnitude of 1 corresponds to a decrease in brightness by a factor of 2.5. Comparing the brightness and magnitude of two stars can therefore be expressed as (Kaufmann and Freedman. 1999, page464):

[EQU5]

m2 - m1 = 2.5 log (b1/b2)

mi

=

apparent magnitude of star i

bi

=

brightness of star i

 

Apparent magnitude can be normalised to provide a relative measure of luminosity irrespective of distance. The Absolute Magnitude is defined as the apparent magnitude if the star were viewed from a distance of 10 parsecs. Apparent Magnitude can be converted to Absolute Magnitude using (Kaufmann and Freedman, 1999, page 465):

[EQU 6]

m-M = 5 log 3 - 5

where:

m

=

apparent magnitude

M

=

absolute magnitude

d

=

distance to star in parsecs

Distance and apparent brightness are used to calculate luminosity, given the Inverse Square Law expressed in Equation 4. Using Equation 5, brightness can be converted to apparent magnitude by using another star as a reference. Apparent magnitude can be converted to absolute magnitude using Equation 6.

The parallax technique is limited to computing the distances to nearby stars only. The distance to other more distant stars can sometimes be computed by other means. For example, Cepheid variable stars are known to exhibit a direct relationship between the average luminosity and period. Once the distance to a single Cepheid was found, astronomers were able to invoke the Inverse Square Law to determine the distance to other Cepheids as a function of their period and apparent magnitude. Since Cepheid variables are very luminous, Cepheids in other galaxies can be used to determine the distance to the galaxy in which they reside.

 

H-R Diagram for stars in the solar neighbourhood

THE HERTZSPRUNG-RUSSEL DIAGRAM

Using the Inverse Square Law, astronomers can compute the absolute magnitude and luminosity of a star given its distance and apparent magnitude.

Through spectral analysis, astronomers can determine the surface temperature of a star. The surface temperature, in conjunction with other spectral features, is used to classify stars. Spectral types in the standard classification system range from hot blue-violet "O" stars to cooler red "M" stars.

In the early twentieth century, Enjar Hertzsprung and Henry Russell independently realised that luminosity and surface temperature are related stellar properties. A plot of luminosity or absolute magnitude on the vertical scale, and surface temperature or spectral type on the horizontal scale is known as a Hertzsprung-Russell Diagram, and demonstrates the relationship of these properties.

Hertzsprung-Russell Diagrams are particularly useful for evaluating the evolutionary status of a group of stars. Figure 2 shows a Hertzsprung-Russell Diagram for stars in the neighbourhood of the sun. Stars in the figure are less than 13 light years away, with the exception that stars in the constellation Crux are also included. Stars in Crux are included since they are part of the virtual astronomy environment to be discussed later. However, the Crux stars are not considered to be in the solar neighbourhood since their distances range from 58 light years in the case of Epsilon Crux, to 424 light years in the case of Beta Crux.

A normal star is said to be on the main sequence during the relatively long and stable period that it converts hydrogen to helium through nuclear fusion in its core. A main sequence star of high mass is hot and very luminous. Such a star remains on the main sequence for a shorter period of time than a low mass star because hydrogen is consumed at a more rapid rate. A low mass star remains on the main sequence for a longer period of time, since the rate at which hydrogen is converted to helium is significantly less.

In Figure 2, stars on the main sequence fall along the purple line.

Two stars in Figure 2 are seen to exist above and to the right of the main sequence. These are the red giant stars Epsilon and Gamma Crux. Red giant stars have consumed all of the hydrogen in their core, and have left the main sequence. The core of a red giant is compressed under the force of gravity once hydrogen burning ceases in the core. This is balanced by an increase in outward pressure, causing the star to swell to up to 200 times its main sequence size. As a result, red giant stars exhibit a substantial increase in luminosity due to an increase in surface area.

Also in Figure 2, two stars are shown below and to the left of the main sequence. These represent the white dwarf stars Procyon B and Sirius B. White dwarf stars are what remains after an average mass star dies when nuclear fusion ceases and the star's outer layers have been blown into deep space. White dwarf luminance is due to residual thermal energy only, since all nuclear fusion has ceased.

It is interesting to note that the investigation into the evolutionary status of a group of stars begins with distance calculations since these measurements are required to determine stellar luminosities and absolute magnitudes. Consequently, accurately measuring stellar distances is a necessary first step towards understanding stellar evolution and the properties of stars (Perryman et al., 1995).

 

METHODOLOGY

The Nearby Star Atlas: Experiments in Virtual Reality is a computer simulation tool, designed to enable astronomy students to make virtual measurement similar to those made by professional astronomers when calculating the distance to nearby stars.

The simulation tool is an applet written in the Java programming language and is available on the Internet at http://www.cs.curtin.edu.au/~bvk/astronomy/HET603/atlas/.

To generate the database used by the applet, known stellar distances and absolute and apparent magnitude were taken from Appendix 4 of Kaufmann and Freedman (1999). This was supplemented with Right Ascension (RA) and Declination (Dec) data from other sources (Manly, 1994; Tirion, 1998; Starry Night). The applet uses this data to calculate a Cartesian coordinate for each star, with the Sun at the origin. Stars of the constellation Crux were also added to provide a more realistic experience when viewing the region of the southern sky near the "pointer stars", Alpha and Beta Centauri.

The applet constructs a viewing frustum using a field of view supplied by the user. The viewing frustum is translated into the proper position to simulate the earth's position as it moves in its orbit. This frustum is then rotated so that the RA and Dec coordinates for the target star selected by the user lie along a vector in the ZX plane and parallel to the Z axis.

Well-known graphics transformations are applied to plot the position of the star within this frustum against a fixed grid in a variety of display modes (Foley et al., 1990). This is augmented with an H-R diagram plotting the absolute magnitude versus spectral type for each star included in the database.

A updated version of de Jong's classroom exercise was also conducted to facilitate a subjective comparison with the effectiveness of the Java applet in educational environments.

 

USING THE APPLET

When using the applet, users can select the Field of View and a target star in a Graphical User Interface (GUI). In the display window, the target star is shown in green. Other stars are shown in white. The operation mode can also be selected from the GUI. These are defined below.

Parallel Projection Mode- The user is presented with a parallel view of the stars in the neighbourhood of the sun from a point in deep space. By clicking and dragging on the window, users are able to move around the neighbourhood of the sun and view it from different positions in space. The displayed size of the star is directly related to the absolute magnitude of the star. The target star is selected in the GUI, and is rendered in green in the display window. The target star is circled with a green bullseye since dim stars can be difficult to spot. Changing the field of view has no effect in parallel mode since all 3-D points are projected into the viewing plane in parallel by definition. This means that parallax and perspective effects are not apparent when in parallel mode. This mode is provided to familiarise users with the stars in the neighbourhood of the sun, and with the position of stars relative to others in the local neighbourhood. It gives the user an idea of the distances to the various stars relative to the sun without introducing the effects of perspective foreshortening. This serves as a warm-up exercise before proceeding to more advanced topics. Note that stars in the constellation Crux are not visible in Parallel or Perspective Modes as these modes are restricted to stars in the local neighbourhood of the sun.

Perspective Projection Mode- The user is presented with a perspective view of the stars in the neighbourhood of the sun from a point in deep space. The distance from the sun is determined by the field of view. That is, the user travels to the point in deep space required to fit the entire solar neighbourhood into the specified field of view. Smaller fields of view result in a viewing distance that is farther away in space. The displayed size of the star is directly related to the apparent magnitude of that star as seen from the viewing position. Stars are always rendered using at least one pixel, however, to avoid dim stars from disappearing from view. By clicking and dragging on the display window, users are able to move around the neighbourhood of the sun at the distance determined by the field of view.

Parallax Measurement Mode- The position of the target star is plotted at one month intervals for one year using the field of view selected by the user. The target star is shown in green. All other stars are shown in white. The displayed size of the star is directly related to the apparent magnitude as seen from the earth. The user can measure the target star's parallax using two mouse clicks to determine the distance from the centre of the parallax path ellipse to the end of the major axis. The reciprocal of the measured parallax calculates the distance to the star in parsecs, as given in Equation 3.

Parallax With Timer Mode- This mode is similar to Parallax Measurement Mode, except that the user advances time by clicking on a dynamic clock icon in the upper left hand corner of the display. The position of the target star for the current month is shown in a brighter shade of green than for previous months. Months of the year are shown on the clock to emphasise the passage of time, however the display shown is for no particular month, day, or year. Users may measure parallax in the same manner as Parallax Measurement Mode. Note that the parallax path ellipse advances in either a clockwise or counter clockwise depending on the celestial hemisphere in which the star is found.

Hertzsprung-Russel Diagram Mode- This mode gives the user a standard Hertzsprung-Russell Diagram for stars included in the applet database. Prior to entering this mode, users can calculate the distance to a target star using parallax measurement or parallax with timer mode. Apparent Magnitude from the earth can be read in the data window. Distance and apparent magnitude can be used in Equation 6 to calculate the absolute magnitude of the target star on the vertical axis of the HR Diagram. The horizontal axis can be determined from the spectral type, listed in the data window. The field of view cannot be changed in H-R Diagram mode. On Microsoft Internet Explorer, the Field of View menu is grey and cannot be selected. In Netscape Navigator, it is not grey, but cannot be selected.

 

FIGURE 3. Applet layout

FIGURE 3. Applet layout

Figure 3 shows the layout of the Applet. Although it may look slightly different on your browser, the layout will be the same. Pulldown menus in the upper left hand corner of the applet enable the user to select the target star, field of view, and operation mode. Mouse hints are provided for most operation modes in the upper left hand corner of the display window. A text area is provided in the lower left hand corner to display data about the selected target star. The target star is always shown in green in the display window. Note that green was selected to avoid visibility issues against the range of star colours in the H-R Diagram operation mode.

RESULTS

Original links containing results for several suggested virtual experiments and for the experiment modelled after de Jong's (1972) classroom exercise and are found below. Note that many of the links describing the virtual experiments contain animated GIF images showing results that were collected using screen grabs. They are not instances of the applet running. To try the experiment for yourself, select the Atlas icon.

 

 

DISCUSSION

The de Jong experiment is a hands-on tactile experience. Because a camera is used, the student is reminded that parallax measurements require the analysis of actual images taken in the field. It also acquaints students with the rudimentary mechanics of the measurement technique.

However, because of practical issues related to distance and scale, the de Jong experiment conducted here used Equation 1 instead of Equation 3, the latter of which invokes the small angle theorem and the definition of the parsec. In this regard, the virtual parallax experiment better reflects the actual technique utilised by professional astronomers.

The virtual technique also allows the student to experience other concepts well understood by professional astronomers. These include:

This latter point is particularly significant, especially if one considers the deleterious effects of the earth's atmosphere in making accurate ground-based measurements at the required resolution. For this reason, recent Hipparcos satellite data, unhampered by the earth's atmosphere, has helped professional astronomers refine accurate distance estimates for nearby stars (Perryman, et al., 1995). This issue is not apparent to students conducting the de Jong version of the parallax experiment. Accuracy and resolution issues are readily obvious, however, when attempting to take virtual measurements at different Fields of View in the Atlas of Nearby Stars. To this end, a future version of the Atlas of Nearby Stars could introduce random variation to the rendered position of stars in an attempt to simulate images produced during times of poor seeing.

Given the complementary nature of the de Jong exercise and the virtual experiments, it is recommended that astronomy students conduct both experiments when feasible.

If the Atlas of Nearby Stars: Experiments in Virtual Astronomy were extended to include spectroscopy simulation, students would be able to construct an entire HR Diagram using virtual tools similar to those used by real astronomers. This would have a significant educational impact on virtual experiment 7.

Given the educational benefit of this type of experience, many universities are expanding the virtual tool-kits they offer students in a wide range of disciplines. Disciplines utilising the new technology include physics (Caley, HREF 1999) and computer science (Marriott et al., 1997).

Additionally, it should be noted that there has been increased interest in nearby star systems, given the possibility that earth-like extrasolar planets might soon be detected in one of them (Space Views, HREF 1999). As such, it is likely that there will be an increased need for Java-based tools for analysing, distributing, and presenting astrometry and other data associated with nearby star-systems.

The Atlas of Nearby Stars: Experiments in Virtual Astronomy is an education application written entirely in the Java programming language. Although Java3D will be available soon, it not currently available for all platforms and graphics environments, and assumes special graphics hardware in most cases. Consequently, the Atlas of Nearby Stars uses a custom class library to implement necessary 3D functions.

Others have used the Virtual Reality Modelling Language (VRML) to visualise three-dimensional space-science data (Mathews, 1996), including the 3D sky in the neighbourhood of the sun (HoneyLocust Media Systems , HREF 1999). Three-dimensional rendering and shading capabilities included in VRML is computationally expensive, limits bandwidth, and is unnecessary for simulating the tools used to measure stellar parallax. Furthermore, VRML requires a plug-in that is not a standard feature on many browsers. For these reasons, it was not selected for use in the Atlas of Nearby Stars, given the wide range of computer platforms potentially used by distance education students.

The Atlas of Nearby Stars and related web pages were tested on both Macintosh and PC platforms.

Images presented in the results from the de Jong experiment were produced using a digital camera and processed for display on a Macintosh computer. Consequently, the colour gamut is somewhat dark when displayed on some PC monitors, although increasing monitor brightness is a reasonable solution to this problem for most PC users. This issue does not effect use of the applet, however.

At the low end, The Atlas of Nearby Stars was tested on a 75 MHz Power Macintosh 7200/75 and was seen to perform adequately. It was tested on both Netscape Communicator 4.51 using the Symantec Java Virtual Machine (JVM) and Microsoft Internet Explorer 4.5 using the Microsoft JVM. The applet was also tested using Metrowerks JVM and Apple MRJ JVM. In all cases, including the 75 MHz Power Macintosh, applet performance was seen to be adequate. From the standpoint of performance and compatibility, indications are that it is well suited for use in a distance education environment on a diverse mix of computing platforms.

 

CONCLUSIONS

The Atlas of Nearby Stars: Experiments in Virtual Astronomy enables astronomy students to perform virtual parallax measurements for stars in the neighbourhood of the sun. Astronomy students are able to use this tool to make virtual parallax measurements, such that the distance to nearby stars can be calculated. This can be used to calculate stellar absolute magnitudes for use in constructing HR-Diagrams.

An additional applet for virtual spectroscopy would further complement the existing tool-set and provide all the virtual tools necessary for students to build an HR diagram based on first principals using elementary data. A virtual spectroscopy applet would be of similar scope to the project presented here, and should be considered for the next round of projects in HET 603: Exploring the Stars and the Milky Way, or HET 606: The Tools of Modern Astronomy.

The Atlas of Nearby Stars: Experiments in Virtual Astronomy has been created for use on the internet in a Java capable web browser. It provides astronomy students with an on-line resource that can be used in both distance education and traditional classroom settings. It is indicated that the new tool will enable students to develop an appreciation for fundamental tools used by professional astronomers. The new virtual tools have the advantage that students are not required to wait six months to make exhaustive measurements, or have access to expensive and scarce resources like telescopes, photometers, and CCD cameras. This is particularly relevant in distance education settings, where students can only be assumed to have access to a home computer.

The Atlas of Nearby Stars applet can be used in conjunction with traditional laboratory experiments such as those suggested by de Jong (1972), providing a complementary set of educational experiences.

The educational efficacy of the new approach has not been rigorously tested. However, it is indicated that it will provide students with an active learning environment that will ultimately lead to a hands-on understanding of the tools of modern astronomy; the tools professionals use to investigate the nature and evolution of the stars.

 

ACKNOWLEDGEMENTS

This applet was a student project for HET 603: Exploring the Stars and the Milky Way. Thank you to Dr Margaret Mazzollini and Dr Matthew Bailes for their insightful comments and suggestions early in the semester, which helped improve the Atlas of Nearby Stars! See you next semester for HET 604!

 

REFERENCES

Caley, D (HREF 1999) Physics Applets, University of Oregon, Department of Physics, http://jersey.uoregon.edu/vlab

De Jong, M.L. (1972) A Stellar Parallax Exercise for the Introductory Astronomy Course, American Journal of Physics, 40(5):762-763.

Ducourant, C., Daupoles, B., Rapaport, M., and Colin, J. (1998) CCD Parallaxes of Nearby Faint Stars, Astronomical Society of the Pacific Conference Series, 134:109-111.

Foley, J.D., van Dam, A. Feiner, S.K., and Hughes, J.F. (1990) Computer Graphics: Principles and Practice. Addison-Wesley Publishing Company, New York.

HoneyLocust Media Systems (HREF 1999) The 3D Sky, http://www.honeylocust.com/Stars/.

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Space Views (HREF 1999) Nearby Stars Come Under Greater Scrutiny, http://www.spaceviews.com/1999/01/10b.html.

Talbot, J. (HREF 1999) Spectra of Gas Discharges, http://www.achilles.net/~jtalbot/data/elements/index.html.

Tiron, W. (1998) The Cambridge Star Atlas, 2nd ed., Cambridge University Press, Cambridge.